Mgchanica! Design of Process Systems Volumel Piping and Pressure Vessels
A.Keith Escoe
Gulf Publishing Company Book Division Houston, London, Paris, Tokyo
Mechanical Dsign
of hocess Sy$erns Volume
I
Piping ard
hesun \bsels
O 1986 by Gulf Publishing Compann Houston,'Ibxas. rights reserved. Printed in the United States of America. This book, or parts thereof, may not be reproduc€d in any form without permission of the publisher. Copyright
All
Library of Congrcss Cataloging-in-Publication Data Escoe, A. Keith. Mechanical design of process systems. Bibliography: p. Includes index. 1. Chemical plants-Design and consbuction.
L Title. TP155.5.E83
1986
[email protected]' 8l
85-22005
ISBN G87201-562-9 (Vol. 1) ISBN G 87201-565-3 (Vol. 2)
IY
Contents
Foreword
...,....vii
Fluid Forces Exerted on Piping Systems,
by John J. McKetta
.. , .... ...
Preface Chapter 1 Piping Fluid
Mechanics
...........
ix
1
Basic Equations, I Non-Newtonian Fluids, 5 Velocity Heads, 8 Pipe Flow Geometries, 22 Comoressible Flow. 25 Piping Fluid Mechanics Problem Formulation, 25 Example 1-1: Friction Pressure Drop for a Hydrocarbon Gas-Steam Mixture in a Pipe, 27
Example 1-2: Frictional Ptessure Drop for a Hot Oil System of a Process Thnk, 33 Example 1-3: Friction Pressure Drop for a Waste Heat Recovery System, 42 Example 1-4: Pressure Drop in Relief Valve Piping System, 43 Notation, 45 References, 45
81
Extraneous Piping Loads, 83 Example 2-l: Applying the Stiffness Method to a Modular Skid-Mounted Gas Liquefaction
Facility,88 Example 2-2: Applying the Flexibility Method to a Steam Turbine Exhaust Line, 95 Example 2-3: Flexibility Analysis for Hot Oil Piping,96 Example 2-42 Lug Design, 98 Example 2-5: Relief Valve Piping System, 99 Example 2-61 Wind-Induced Vibrations of Piping, 100 Notation, 101 References, 101
Chapter 3 Heat Transfer in Piping and Equipment
...
Jacketed Pipe versus Traced Pipe, 103
Tracing Piping Systems, 106 Traced Piping without Heat Tmnsfer Cement. Traced Piping with Heat Transfer Cement. Condensate Return. Jacketed Pipe. Vessel and Equipment Traced Systems.
Heat Transfer in Residual Systems, 132
Chapter 2 The Engineering Mechanics of Piping
.,...47
Piping Criteria, 47
Primary and Secondary Stresses, 49 Allowable stress Range for Secondary Stresses.
Flexibility and Stiffness of Piping Systems, 52 Stiffness Method Advantages. Flexibility Method Advantages.
Stiffness Method and Large Piping, 58 Flexibility Method of Piping Mechanics. Pipe Loops.
PiDe - Restraints and Anchors. 68
Pipe Lug Supports. Spfing Supports. Expansion Joints. Pre-stressed Piping.
Heat Transfer through Cylindrical Shells. Residual Heat Transfer through Pipe Shoes.
Example 3-1: Example 3-2: Example 3-3: Example 3-4: Thnk, 140 Example 3-5: Tank, 142
Steam Tracing Design, 136
Hot Oil Tracing Design, 137 Jacketed Pipe Design, 139
Thermal Evaluation of a Process Thermal Design of a Process
Internal Baffle Plates Film Coefficient. Film Coefficient External to Baffles-Forced Convection. Heat Duty of Internal Vessel Plates. Outside Heat Transfer Jacket Plates. Heat Duty of Jacket Plates Clamped to Bottom Vessel Head. Total Heat Duty of Tank.
103
Example 3-6: Transient and Static Heat Transfer Design, 148
Example 4-3: Seismic Analysis of a Vertical Tower, 237 Example 44: Vibration Analysis for Tower with Large Vortex-Induced Displacements, 241
Static Heat Transfer Analysis. Total Heat Removal. Water Required for Cooling. Transient Hear Transfer Analysis.
Moments of Inertia. Wind Deflections.
Example 3-7: Heat Transfer through Vessel Skirts, 152 Example 3-E: Residual Heat Transfer, 154 Example 3-9: Heat Transfer through Pipe Shoe,
Example 4-5: Saddle Plate Analysis of Horizontal Vessel, 249
Saddle Plate Buckling Analysis. Horizontal Reaction Force on Saddle.
156
Notation,252 References,254
Notation, 156 References, 157
Appendix A Partial Volumes and Pressure Vessel
Chapter 4 The Engineering Mechanics of Pressure
Vessels
... . .....
Cafcufations
159
Longitudinal Bending Stresses. Location of Saddle Supports. Wear Plate Design. Zick Stiffening Rings.
Steel Saddle Plate Design, 174 Saddle Bearing Plate Thickness, 180 Design of Self-Supported Vertical Vessels, 180
Minimum Shell Thickness Reouired for Combined Loads, 181 Support Skirt Design, 183 Anchor Bolts, 184 Base Plate Thickness Design, 186 Compression Ring and Gusset Plate Design, 189 Anchor Bolt Torque, 189 Whd Aralysis of Towers, 190
Appendix B National Wind Design Standards
Appendix C Properties of
Pipe.
,.....271
Insulation Weight Factors, 278
Appendix D Conversion Factors
1t i
Wear Plate Requirement Analysis,
.....
. 303
Alphabetical Conversion Factors, 304
215
Example 12: Mechanical Design of Process Column. 215
Synchronous Speeds, 31 1 Temperature Conversion. 3l 2 Altitude and Atmospheric Pressures, 313 Pressure Conversion Chart, 314
Sectron lt{omenls of Inertial lbwer Section Stress Calcularions. Skirt and Base Plate Design- Section Centroids. Vortex-Induced
vibrarion. Equivalent Diameter Approach
-{\S[
265
Weights of Piping Materials, 279
Seismic Design of Tall Towers, 209 \anical Distribution of Shear Forces. Tower Shell Discontinuities and Conical Sections,
versus
.........
Criteria for Determining Wind Speed, 265 Wind Speed Relationships, 266 ANSI A58.1-1982 Wind Cateeories. 267
r'\'ind Design Speeds. Wind-Induced Moments. $ ind-Induced Deflections of Towers. l ind-Induced Vibrations on Tall Towers. O\aling. Criteda for Vibration Analysis.
{-l:
.....25s
Partial Volumes of Spherically Dished Heads, 256 Partial Volumes of Elliptical Heads, 257 Partial Volumes of Torispherical Heads, 259 Internal Pressure ASME Formulations with Outside Dimensions, 261 Internal Pressure ASME Formulations with Inside Dimensions,262
Designing for Internal Pressure, 159 Designing for External Pressure, 160 Design of Horizontal Pressure Vessels, 166
Exanple
a
Index
A58.1- 1982.
vl
..
.
.... . ...
315
Foreword
proper respect in two excellent chapters on fluid mechanics and the engineering mechanics of piping. The chapter on heat transfer in vessels and piping illustrates lucidly the interrelationship between process and mechanical design. Every engineer working with industrial process systems will benefit from reading this
The engineer who understands the impact of process design decisions on mechanical design details is in a position to save his client or his company a lot of money. That is because the test of any process design is in how cost-effectively it yields the desired product, and how "cost" generally translates to "equipment": How much will the process require? How long will it last? How much energy will it consume per unit of product?
chaDter.
Although the author has made a herculean effort in covering the mechanical design of pressure vessels, heat exchangers, rotating equipment, and bins, silos and stacks, it is true that there are omissions. It is hoped that, as the author hints in his preface, a future volume might be added covering multiphase flow, specific cogeneration processes, turbines, and detailed piping dynamics. Still, at this writing these two volumes comprise an outstanding practical reference for chemical and mechanical engineers and a detailed instructional manual for students. I recommend these volumes highly for each design engineer's professional library.
In this two-volume work on Mechanical Design of A. K. Escoe has performed a monumental service for mechanical design engineers and
Process Systems,
chemical process engineers alike. It is presented in such a manner that even the neophyte engineer can grasp its full value. He has produced an in-depth review of the way in which process design specifications are interpreted into precise equipment designs. Perhaps most valuable of all are the extensive worked examples throughout the text, of actual designs that have been successfully executed in the field. The piping system is the central nervous system of a fluid flow orocess. and the author has treated this with
John J. McKexa. Ph.D., P.E. Joe C. Waher Professor of Chemical Engineering UniversitY of Texas ' Austin
vii
Dedication
To the memory of my beloved parents, Aubrey H. Escoe and Odessa Davies Escoe; and to. the dedicated engineer, Dr. Judith Arlene Resnik, U.S. astronaut aboard
the ill-fated space shuttle Chnllenger (Flight
v|ll
5l-L).
d{ ry,'
heface to Volume I
This book's purpose is to show how to apply mechanical engineering concepts to process system design. Process systems are common to a wide variety of industries including petrochemical processing, food and pharmaceutical manufacturing, power generation (including co-
felt that this book is a valuable supplement to any standard or code used. The book is slanted toward the practices of the ASME vessel and piping codes. In one area of vessel design the British Standard is favored because it nrovides excellent technical information on Zick rings. The book is written to be useful regardless of which code or standard is used. The intent is not to be heavily prejudiced toward any standard, but to discuss the issue-engineering. If one feels that a certain standard or code should be mentione.d, please keep in mind that there are others who may be using different standards and it is impossible to
generation), ship building, and even the aerospace industry. The book is based on years of proven, successful practice, and almost all of the examples described are from process systems now in operation. While practicality is probably its key asset, this first volume contains a unique collection ofvaluable information, such as velocity head data; comparison ofthe flexibility and stiffness methods of pipe stress analyses; anal-
discuss all of them. The reader's academic level is assumed to be a bachelor of science degree in mechanical engineering, but engineers with bachelor of science degrees in civil, chemical, electrical, or other engineering disciplines should have little difficulty with the book, provided, of course, that they have received adequate academic training or experience.
ysis of heat transfer through pipe supports and vessel skirts; a comprehensive method on the design of horizontal vessel saddles as well as a method to determine when wear plates are required; detailed static and dynamic methods of tower design considering wind gusts, vortex-induced vibration and seismic analysis of towers; and a comparative synopsis of the various national wind
Junior or senior undergraduate engineering students
cooes.
Topics include.d in the text are considered to be those
should find the book a useful introduction to the application of mechanical engineering to process systems. Professors should find the book a helpful reference (and a source for potential exam problems), as well as a practi-
typically encountered in engineering practice. Therefore, because most mechanical systems involve singlephase flow, two-phase flow is not covered. Because of its ubiquitous coverage in the literature, flange design is also excluded in this presentation. Since all of the major pressure vessel codes thoroughly discuss and illustrate
cal textbook for junior-, senior-, or graduateJevel
courses in the mechanical, civil, or chemical engineering fields. The book can also be used to supplement an intro-
the phenomenon of external pressure, this subject is only
ductory level textbook. The French philosopher Voltaire once said, "Common sense is not very common," and unfortunately, this is sometimes the case in engineering. Common sense is often the by-product of experience, and while both are essential to sound engineering practice, neither can be
mentioned briefly.
This book is not intended to be a substitute or a replacement of any accepted code or standard. The reader is strongly encouraged to consult and be knowledgeable of any accepted standard or code that may govern. It is
ix
--*
learned from books alone. It is one ofthis book's eoats to unite these three elements of "book learning," c6mmon sense, and experience to give the novice a better grasp of engineering principles and procedures, and serve as a practical design reference for the veteran engineer. Finally, I wish to thank Dr. John J. McKetta, professor of chemical engineering at the University of Texas at Austin, who had many helpful comments, suggestions,
and words of encouragement. I also wish to thank other engineering faculty members at the University of Texas at Austin for their comments. I must exDress thanks to
Larry D. Briggs for reviewing some ialculations
in
Chapter 4; and last, but certainly not least, I wish to express gratitude to William J. Lowe and Timothy W. Calk of Gulf Publishing Company, whose hard work and patience made this book oossible.
A. Keith Escoe, PE.
.{
j&ir,,
Piping Fluid Mechanics
The study of fluid energy in piping systems is a comprehensive subject that could in itself fill countless volumes. This chapter is primarily concerned witl fluid energy dissipated as friction resulting in a head loss.
Although this topic is popularly known in industry as "hydraulics," the term "piping fluid mechanics" is used here to avoid confusion.
Pr
- Pz = V,t=- vrt + (y. _yr;€1p p 28" c"
I and 2 refer to flow upstream (after the flow process) and downstream (before the flow process), respectively, and where subscripts
Pt
-
Pz
p
BASIC EOUATIONS
p where
29"
P:
g"
,llr. + ,1ll^
(l-l)
F: He: HE:
-
Yr)
I =
:
change in static head (potential energy)
friction 1o* in
!JlQ,
cm (kg)
density, lb./ft3 or g./cm3 pressure, lb/ft2 or kg/cm2 conversion constant, 32. 17 (ft-lb./sec2lbr)
gravitational acceleration
g/9" :
dY:
change in velocity head (kinetic energy)
:dz F
velocity, ftlsec or cm/sec
8":
change in pressure head
29"
(Yr -r-
:
Vt^- V' :
The basic equation of fluid mechanics, originally derived by Daniel Bernoulli in 1738, evolved from the principle of conservation of energy:
,]V r ,{E
(r-2)
:
32.2 fllsecz,
cm/sec2; 1.0 height above datum, ft, cm differential between height above datum and
reference point, ft, cm head loss, friction loss, or frictional pressure drop, ft-lbr/Ib., cm-kg6/g. energy added by mechanical devices, e.g. pumps, ft-lb/Ib., cm-kg/g. energy extracted by mechanical devices, e.g.
The following are expressions of the Bernoulli equation when applied to various incompressible and compressible flow conditions: Incompressible
flow-
p, - P.
- v.2 zE"
P
gc
Compre s sib le -i s othermal
turbines, ftlb6/1b., cm-kg/g.
Rewriting Equation l-1 along a fluid streamline between points 1 and 2 with steady, incompressible flow and no mechanical energy added or extracted results in
v,2
FJn
:
H X[
f low -
_[*l
[*l]
+F+HA+HE
+
(zz
- z,
2
Mechanical Design of Process Systems
Compre s s ib le -adiabati c f low
H [1 [' -
(,*J'.-"']
-
: xl' -FJ^ [*J] +(22-z)+F +HA+HE
.
where
\* /p\ l- | : l:l : general gas law \Prl \rrl k : .specific heat ratio (adiabatic coefficient), /o
t- lt-
Cp :
sPecific heat at constant pressure,
Btu/lb.-'F
C, :
specific heat at constant volume, Btu/lb--"F
Equation 1-2 is the analytical expression that states a pressure loss is caused by a change in velocity head, static head, and ftiction head. The most cofirmon units are "feet of head." lb. and lbr do not cancel out and the
expression is exactly "energy
(ft-lb) per pound of
mass."
In most industrial fluid problems, Equation 1-2
is
cumbersome to use, because the friction loss is the parameter most often desired. The friction loss is the work done by the fluid in overcoming viscous resistance. This friction loss can only rarely be analytically derived and is determined by empirical data developed through experi-
mental testins
.
Forcing a fluid through a pipe component requires energy. This energy is expended by shear forces that develop between the pipe wall and the fluid, and to a lesser extent among the fluid elements themselves. These shear forces are opposed to fluid flow and require excess energy to overcome. Figure 1-l shows a simple version of this phenomenon and illustrates how shear stresses increase in the radial direction away from the pipe center line and are maximum within the boundary layer next to the wall. Friction energy loss is a resuit of these shear stresses next to the pipe wall. Excess loss in energy occurs because of local turbulence and changes in the direction and speed of flow. As a fluid changes direction, energy is expended because of a change in momentum. The methods used to determine energy loss caused by wall friction are essentially the same, where the pipe component is treated as a straight piece of pipe. However, the methods used to determine energy loss caused by change in momentum differ, and a couple are described as follows.
Equivalent Length In this approach to determining energy loss caused by fluid momentum, a piping component is extended a theoretical length that would yield the same energy loss as the actual component. This length is called the "equivalent length" because it is that length required to obtain the same amount of friction pressure drop as the piping component alone. The major problem with a change in
dv oy
x+c
---[,
.
9e a"] or1'1
rf>
--
Figure 1-1. Shear stresses in fully developed flow. Shown here are imaginary fluid elements "slipping" over one another.
Piping Fluid
this method is that the equivalent length for a pipe component varies with the Reynolds number, roughness, size, and geometry of the pipe. All these par.rmeters must be analyzed in using this method.
Velocity Head llethod Since the excess head loss is mostly attributed to fluid turbulence, the velocity head method is widely accepted
and is replacing the equivalent length method in fluid calculations. Throughout this book, the velocity head ap-
Mechanics
3
into the piping system, the factor F in Equation 1-2 becomes the desired parameter. This friction loss is the work done by the fluid in overcoming viscous resistance and loss attributed to turbulence. The parameter F is composed of two components, pipe wall friction and losses for the various pipe fittings, pipe entrances, pipe exits, and fluid obstructions that contribute to a loss in
fluid energy. These latter losses are described in terms of velocity heads, K;. In solving for F in Equation 1-2, we first obtain pressure loss attributed to pipe wall friction, represented by
proach will be used. The velocity head is the amount of kinetic energy in a fluid, Y2l2g". This quantity may be represented by the amount of potential energy required to accelerate a fluid to a given velocity. Consider a tank holding a fluid with a pipe entrance shown in Figure 1-2. We draw a streamline
By adding values of velocity head losses to Equation 1-3, we obtain the lollowing for any piping system:
from point 1 of the fluid surface to point 2 at the pipe entrance. Applying Equation 1-2 at point 1 we obtain the followins:
-
1= p
\,,
-AP.'
aP,
=.: eyll] 2e. \d/ :
t". ILL
+
\u
\
(1-3)
.,,
)-r,l4I .6c
(l-4)
I
flld
g
And applying Equation 1-2 at point 2 we have
Pr-P2_Pr_V22
PP2g" in which the change in fluid pressure between points I and,2 is Y ] l2g, or one velocity head. A pressure gauge mounted on the pipe entrance would record the difference of pressure of one velocity head. This term is accounted for in Equation 1-2 by Y y2 - Y2212g.. Analyzing a simple conversion from potential to kinetic energy is an elementary procedure, as demonstrated. After the fluid passes through the pipe entrance
where is the dependent pipe friction of the pipe of diameter d over the length L, and DK; the summation of velocity head losses. Equation l-4 provides the friction pressure drop in a pipe for a steady-state incompressible fluid of fully developed flow with a flat veiocity profile.
Examples of this equation are given after the terms in Equation 14 are further explained. The term (flld) (pV2l2g") expresses the amount of energy loss attributed to shear forces at the pipe wall and is based on experimental evidence. It is a function of the pipe component length and diameter and the velocity of the fluid. Writing the relationship for friction pressure drop as a result of pipe wall friction results in
-'p' -
[L
pV']
t+qd
2i-
where Fp,
:
L: d:
'
'-J'
i.i"aion torr, pri length of pipe, in. corroded inside diameter, in.
The other terms are explained with Equation
1-1.
Equation l-5 may be expressed in various forms. To express flow rate in gpm (w) and d in inches use FPf
:
0.000217 fLW/d5
(l-5a)
Equation l-5 is the most commonly used relationship and is known as the Fanning equation. Dividing the equation by p/144 yields feet of friction loss rather than psl. Figure 1-2. Storage tank.
The reader is cautioned in applying the friction factor f, because it is not always defined as above and some au-
4
Mechanical Design of Process Systems
thors use 4f1 in place of f. If such factors are used, particular attention should be paid to the specific friction factor chart used. The friction factor f is dependent upon the dimensionless term expressing the roughness of the pipe (E/D, where E is the depth of the pipe) and the dimensionless Reynolds number
Nr"
:
dpV/M, where
l1,
is the absolute
viscosity of the fluid, inJb1-sec/ftz. The Reynolds number is the single most important parameter in fluid mechanics because it establishes flow regimes and dynamic sirnilarity. The relationship between the friction factor f, the pipe roughness, and the Reynolds number is shown in the classic relationship given by Moody in Figure 1-3. Figure l-3 may be presented in a more convenient form as shown in Figure 1-4, where the relative roughness of the pipe is based on a single value of roughness. This value of roughness must be an average value estimated to simplii/ the problem. The figures presented herein are the best available until more reliable friction
factor data can be obtained and better understood through use of new methods for measuring roughness.
Figure 1-3 is broken into three flow regimes-
laminar, transition from laminar to turbulent, and turbu-
lent. The Reynolds numbers establishing these zones are 2,100 for laminar, 2,100 to 3,000 for transition zone, and 3,000 or more for turbulent The basis for Figure 1-3 is the classic Colebrook equatron
| r1r,
: -.^.to8ro Idd 2.51 [- " **,rpi
I
for (3,000 to 4,000)
<
NR"
(l -6a)
<
108
For laminar flow the friction factor is determined by the simple expression
"64
(1-6b)
Nn.
.09 .08 .07
.05 .04
.06 .01
.o? .0t5 .04
^
:
.01
.008
=-
.006
.03
a
oo4 : 003 : 002
.0015
:
^^, -0008 -' .0006
.01
.009 .008
? 3 4 56 I
2 3 4 56 Blo5 2 3 4 56 € to7 \2 -q-s9l r, -If* , o i' n., ,' ir *4r = = f '. ff Figure 1-3. Moody friction factors. (Repdnted from Pipe Friction Manual, @ 1954 by Hydraulic Institute. Data from L. Moody, Frioion Faaors for Pipe Flow, permission of ASME.) z J 4 56 8 rot
R?ynotds Nunber n"
F.
#( -8u Piping Fluid Mechanics Pipe oiameter, in Fe€t
-/)
,=
.
Pipe Diafleier, in Inch€s
-,/
Figure 1-4. Relative roughness of pipe materials and friction factors for complete turbulence. (Courtesy of Crane Company [5]. Data from L. F Moody, Friction Factors for Pipe Flow permission of ASME.)
Equation 1-6a, which describes the friction factor for turbulent flow in pipe of any roughness, is a simple addi tion of the Prandtl solution for smooth pipe and the von Karman solution for rough pipe. The relationship holds for the transition between rough and smooth pipe. To solve Equation 1-6a for the friction factor f an iterative analysis is required because the function is nonhomogeneous and inseparable. There are several empirical relations of f expressed as an independent separate function of f G/d, NR.), but with today's micro-computers Equation l-6 can be solved more accurately and expediently with iteration.
-rll
Dimensional forms of Equation 1-4 are presented in Table 1-1 [1], where the equation is conveniently shown in various units that are used to solve fluid pressure loss problems.
NON.NEWTONIAN FLUIDS The Colebrook equation holds for fluids whose flow properties are dependent on the fluid viscosity. These fluids consist of all gases, liquids, and solutions of low molecular weieht and are known as Newonian fluids. In
Mechanical Design of Process Systems
Plessure Ol?p,
Table 1-1 Dimensional Forms Used With Equation 1-4
ne
[11
r, ana
= rate -APr or pHr L IrNr">2,ooo'r:[2 g nvz w {*-r^,.i + * rr 'l pt)pD pD2 e \ 'l uoQ' cQP dQ pv' /!& * ",. D4 pD D2 . "- \ D ' -L\J Row
Conventlonal units psl
w(Q)
psl
lb/h
(ft)
(gprn)
D
ln. in.
tb/h
tn. tn.
ln. ln.
-AP(H' e
I
p
ft
ft
lb/ft3 cp
ftls HV a
b
c
d e
ft
lb/ft3 cp
ftls
psi
Units and constants Metric units
(f9
inHrO[60"F]
ln.
(acfm) In.
in.
bar kg/s mm
in.
rnm
ft
a,b,c,d,e D
f
HI
K
9,266
mm mm
m
m
m
m
kg/m3 mPa-s(cp)
kg/m3
kg/m3
Pa-s
Pa-s
m/s bar 8.106
m/s
m/s
tb/f13
kglm3
ftls
cp
ft/s
ft/min
mPa-s(cp) m/s
in. H2O
bar
0.02792
8.106 x 106 1,000
ft
6.316 0.05093
64 1aY ^
= pipe diameter = \lbisbach friction factor = frictional head loss
-
(m) (m3/s)
cp
psr
50.66 0.4085
Pa
kg/s m m
lb/ft3
ft
50.66 0.4085 64.35 x p
t2
a=
number of velocity heads
ical behavior. Non-Newtonian fluids are those in which the viscosity alone does not define their rheological behavior. Sucir fluids are solutions composed of solid particles that ex_ pand. Clay and very dense slurries are examples of non_ )iewronian fluids. The flow properties of suih fluids are a function of the particle characteristics, e.g., size and flexibility and thermal expansion. Purely viscous non-Newtonian fluids are classified into dree categories: time-dependent and time-indepen_ dent and viscoelastic. A time-dependent fluid displays slo*' changes in rheological properties, such as thixbtr-o_ pic fluids that exhibit reversible structural chanses. Several ty,pes ofcrude oil fit inro this category. Anoiher rype of tinre{ependent non-Newtonian fiuid is rheooectic fluids- Under constant sustained shear, these fluidi. rate of srrucrural deformation exceeds the rate of structural decav. One such category of fluids is polvester. Rheqectic fluids are less common than thixotrooic flu-
x
379.0
1.273
183.3
1.273 x106
1.204
x
106
piF
Newtonian fluids the viscosity alone defines the rheolos_
ids.
ft
bar
(L/s)
lb/ft3 cp
2.799x10-7 1.801x 10-5 4.031 x l0-5 2.593 x 10-3 t2 t2 12 12 6.316 0.05093 9,266
loglqQ27etD+(?/NR"o)],'
2xttr
length frictional pressure drop
volumetric flowrate Reynolds number
velocity
106
1,000 1.273 1.273
2xlo5 HV = =
: =
m m
Pa
m
0.8106
0.08265
I
I
r.273 1.273
1.273 1.273
2
19.61xp
velocity head pipe roughness fluid viscosity fluid density
Time-independent fluids that are purely viscous are _ classified as. pseudoplastic, dilatant, Bingham, and yield-
pseudoplastic fluids. ln pseudoplastic fluids an intinitesimal shear stress will initiate motion and the ratio of shear stress with velocity decreases with increasins ve_ locity gradient. This type of fluid is encountered in iolu_ tions or- suspensions of fine particles that form loosely bounded aggregates that can break down or reform witL an increase or decrease in shear rate. Such solutions are aqueous dispersions of polyvinyl acetate and of an acrv_ clic copolymer: aqueous solutions of sodium carboxy_
methyl cellulose, and of ammonium polymethacrylatl; and an aqueous suspension of limestone. In dilatant fluids an infinitesimal shear stress will start motion and the ratio of shear stress to velocity increases as the velocity is increased. A dilatant fluid ij characterized by an increase in volume of a fixed amount of dispersion, such as wet sand, when subiected to a deforma_ tion that alters the interparticli distances oI its constituents from their minimum-size confisuration. Such fluids are titanium dioxide particles in waier or su-
':bl&,,
Piping Fluid
crose solution. Dilatant fluids are much rarer than pseudoplastic fluids. ln Bingham fluids a finite shearing stress is required to initiate motion and there is a linear relationship between the shearing stress-after motion impends-and the velocity gradient. Such fluids include thickened hydrocarbon greases, certain asphalts, water suspensions of clay, fly ash, finely divided minerals, quartz, sewage sludge, and point systems. Yield-pseudoplastic fluids are similar to Bingham fluids, but the relationship between the excess shearing stress after motion impends and velocity gradient is nonlinear. Fluids in this category are defined by their rheograms, where relationships between the shear stress and rate of shear exhibit a geometric convexity to the shear stress axis. Such fluids are many clay-water and similar
suspensions and aqueous solutions of carboxypolymethylene (carbopol). Viscoelastic fluids make up the last category of nonNewtonian fluids. The term "viscoelastic fluid" is applied to the most general of fluids-those that exhibit the characteristic of partial elastic recovery of the fluid structure. Whenever a viscoelastic fluid is subiected to a rapid change in deformation, elastic recoil oi stress relaxation occurs. Many solutions exhibit viscoelastic properties under appropriate conditions-molten polymers, which are highly elastic; and solutions of longcharged molecules, such as polyethylene oxide and poly-
acrylamides. Processes such as coagulation, oil-well fracturing, and high-capacity pipelines rely on polymeric additives to cause pressure drops. Viscoelastic fluids exhibit the "Weissenberg effect," which is caused by normal stresses and produces unusual phenomena, such as the tendency of the fluid to climb up a shaft rotating in the
Mechanics
7
(
100,000 the following empirical relations can be used for determinins the friction factor:
(Ni") b" where bn
:
n=
0.0019498 (n)-45"
(7.8958
Typical values for
x
"y
l0-7) (a") 182.1321 and n are given in Table 1-2 [3].
Values for "y and n not available in literature must be de-
termined by viscosimeter measurements. Figure 1-5 shows the rheological classification of non-
Newtonian mixtures that behave as single-phase flow. The reader is urged to refer to Govier [4] for further information on non-Newtonian fluid or other complex mixtures. Usually, the mechanical design of process systems does not involve non-Newtonian fluids, but knowledge of them and their peculiarities is a must if the need anses.
MULTI.PHASE
SINGLE PHASE
TRUE HOMOGENEOUS
fluid.
For any time-independent non-Newtonian fluid, Metzer and Reed [2] have developed the following generalized Reynolds number fraction: =
N*"
_
D'
U2-np
(1-7)
"l
where D : U : p : ^l : : n:
For
Np"
n:
=
PLASTIC C OILAIAI.II
pipe
9
ID, ft
average bulk velocity, ftlsec
density, lb,/fC generalized viscosity coefficient, lb./ft gc c 8n-r (see Table 1-1) sec experimentally determined flow constant, for a Newtonian fluid empirical constant that is a function of non-Newtonian behavior (flow behavior index), 1.0 for Newtonian fluids
I
:
//g"
1.0 and C : p/g", Equation 1-7 reduces to Du p/p for Newtonian fluids. For 2,100 < NR"
Figure 1-5. Rheological classification that behave as single phase fluids [4].
of complex mixtures
Mechanical Design of Proces: Slstems
Tabte 1-2 Rheological Constants tor Some Typical Non-Newtonian Fluids* ol Fluid 23.3% Illinois yellow clay in water
Rheological Constants n 0.229
of Fluid 0.863
0.67 % carboxy -methyf cellulose
(CMC) in water 1.5% CMC in water 3.0% CMC in water 33% \me water 10% napalm in kerosene 4% paper pulp in water 54.3% cement rock in water
o.716
0.121
0.554 0.566
0.920
0.171
2.80 0.983
0.520
1. 18
0.575 0.153
6.13
18.6% solids, Mississippi clay in water 14.3 7o clay in water 2l .2% clay ln \nater 25.0% clay in water 31.9% clay in water 36.8% clay in water 40.4% clay in water 23% Iime in water
0.331 * Reproduced by permission: A. B. Metzner and J. C. Reed, AICHE Jownal, l,434 (1955\.
VELOCITY HEADS Returning to Equation 1-4, let's focus on the term EKi. This term represents the excess velocity heads lost in fluid motion due to fluid turbulence caused by local turbulence at the pipe wall and change in flow direction. The latter is the greatest contributor to the DKi term. When a fluid strikes a surface and chanses flow direction. it loses momentum and. therelore. Jnergy. Considering the 90' elbow in Figure l-6, we see that the fluid changes direction from the x to the y direction and imparts reactions Fx and Fy, each a function of the pressure and velocity of the fluid. End conditions of the elbow determine some of the velocity head loss, that is, where the
fitting is a "smooth elbow" or a "screwed elbow." A smooth elbow is one that is either flansed or welded to the pipe such that a smooth internal srirface is encoun-
n
0.022 0.350 0.335 0.185 0.251 0.1'16 0.132 0. 178
0.105
0.0344 0.0855
0.2M 0.414 1.07
2.30 1.04
increased velocity head loss.
Analytical determination of velocity heads can only be accomplished in a few simplified cases. The values for velocity heads must be determined and verified empirically. Comprehensive listings of such velocity head (K) values are given in Figures 1-7 t5l, 1-8 [5], 1-9 [6], and 1-10. Using these values in Equation 1-4, you can analyze most cases of friction pressure drop for pipe under 24 inches in diameter. For pipe with diameter greater than 24 inches, an additional analysis must be made in solving for the velocity head term. This method, presented by Hooper [7] is called the "two-K method."
TWO.K METHOD As explained previously, the value of K does not depend on the roughness of the fitting or the fitting size, but rather on the Reynolds number and the geometry of the fitting. The published data for single K values apply to fully-developed turbulent flow and K is independent of N*. when N^. is well into the turbulent zone. As Nq. approaches 1,000, the value of K increases. When Na" < 1,000, the value ofK becomes inversely proportional to NR". In large diameter pipe ( > 24 in.) the value of NRe must be carefully considered if values of 1,000 or less are encountered. The two-K method accounts for this dependency in the following equatron: K1/Np"
: K- : d:
where K1
flow.
Rheological Constanis
tered by the flow. In a screwed elbow there are abrupt changes in the wall causing local turbulence and henie
K:
Figure 1-6. Reactions on an elbow induced by a change of
13I
+ K- (1 + lid)
(1-8)
K for the fitting of NR" : I K for a large fitting of NR" : oo internal diameter of attached pipe, in.
kxt
:i. a.t'- ;;t:
continued page 22
:::a*a;=-:;i{ilif/r td
nt-*":m Piping Fluid Mechanics
Represenlolive Resisfonce Coeflicients (K) for Volves ond Fittings PIPE FRICTION DATA FOR CTEAN CO'\AMERCIAL STEET PIPE WITH FIOW IN ZONE OF COMPIETE TURBUTENCE t/^n
3/q"
.o27
.o25
Nominol Size Friclion Focfor ( fr.)
.o23
I Y4"
1Y2"
.o22
.021
2V2.3"
.0r9
.018
FORMULAS FOR CALCULATING
.o17
"K"
.01 6
.01 5
8.10"
12-16"
t8-24"
.014
.01 3
.ot2
FACTORS'
FOR VALVES AND FITTINGS WITH REDUCED PORT
o.s(in9(, -
t/\2/^1 rz=
o'r
Ba
:
Kr= tr
,, Kz=
O
-
Formula
lA
K,- o r !sin
z , Formula
i(r
4
- trt + (r -
E
)2
tJ'|
"iG-p)\f"#
Kr lf
a4
k. Kr= j.n - 0(Formulaz 'Formula+) uhen d = r8o"
/.\
6(sin+(I - P)'? K, _ ,__]____184 2
|,
K.
a2\2
=
K,
E
Kz=
K,+O [o : (, - g') + (t - 9')']
Kr R4
^ Kr=SO *Formr.rla I + Formula
d,r
lJ \2 az_\d,J 12\ "
l
1I _au
Subscript
K"=
Kr +sin3[o.a 0
-
P\ +2.6 (t
-
I
dennes dimensions
and coefncients with reference 02)2)
SUDDEN AND GRADUAI. CONTRACTION
to
the smaller diameter. Subscript 2 refers to the larger
SUDDEN AND GRADUAT ENI.ARGEMENT
E;l
0<
+5".........K, - Formula
45"
r
= Formula z
0.
4to. . .. . . . ..K2
- Formula
3
45o<0< r8o-. . .Kr = Formula 4
Figure 1-7A. Selected Crane Company velocity head values. (Courtesy Crane Company [5].)
10
Mechanical Design of Process Systems
SWING CHECK VATVES
GATE VAIVES Wedge Disc, Double Disc, or Plug Type
TL€ fNr, r-L-r FI-/f F
Et# JLI I.-+ -ffa-rlf
. ts
= r,0 =
o.
...........
.
K' :
8
-
-/r
P< r and 0 < 45o ........K2: Formula B< r and 45"<0< r8oo...Kz - Formula
5
6
K:
K:sof,
rcof7
Minimum pipe velocity (fps) for full disc lift
Minimum pipe velocity (fps) for full disc lift
=)5vv
-a8!V
LIFT CHECK VAIVES GTOBE AND ANGTE VAIVES
r
If: B: r...Kr=6oo/z 9. r.. .K, = Irormula 7
E
If: B:r...Kt=l+ofr
Minimum pipc r tlocitr itp.; ior full .lisc Iifr : F p2 \,/ v
lf: lf
A-t.. Kr=sjfr
9=
tr r...K,:
B<
r.
.
.
;s fr K, = Irormula
7
Minimum pipe velocicy (fps) for fr-rll disc
: t4o B|V V TIITING DISC CHECK VALVES
l--4-lV I z++ll l-
l'F i
If
: A=r...lit=riofr t
Ftr-IF
L
If: B:r...Kr:S5fr
All globe ancl angle valves, hcthcr rcducccl scat or throttled, Ii: 13 < r. . .l(2: Formula 7
Sizes
zto 8'...K:
Sizes ro to t+'...K: Sizes 16 to 18". . .K =
Minimum pipe velocity (fps) for full clisc lift -
Figure 1-78. Selected Crane Company velocity head values. (Courtesy Crane Company [5].)
li:il- -:::i::
lift
8t'-n*" Piping Fluid Mechanics 40
l
+.[
830 :E
.4
20
llo
t.o 2.o 3.O 4.O 5.o
6.0
VBLoCITY-FPllxl03
< 45. ora ( 22.50 Kr = 2.6(1 - B'?)2 sin e lf d
ll 45" < 0 <
SHADED AREA UNDER CURVE CORRECTION FACTOR,
1800 or 22.50
FITTINC AND PIPE
K'=(1 -0"f
IS
CRITERIA FOR UULTIPLYING
A,BY lHE
VALUE OF
It
COI4PONENT .
CORRECTION FACTOR TABLB
. td,d=arcslnl-
d,ll=- 0 \21 /2 Figure 1-9. Correction factor.
Figure 1-8. Calculated Crane K-values for concentric conical diffusers are tabulated in Table l-6.
T./1 Dl ( _l_
\,-,/
,l
TWO.MITERED ELBOW
1.0
0 Figure 1-10A. Velocity heads for change of flow [6].
'*
11
FOR EACH
12
Mechanical Design of Process Systems
n =number
ot
1Eo
miters
or segments
smooth ell
mitered ell
.5
644+
I
1
t.o
1.5
R/o
Figure 1-108. Velocity heads for change of flow [6].
h*":ns Piping Fluid
2<.-
-V-
<*3 +s"(o
an
=
az/og
Figure l-10C. Velocity heads for change of flow [6].
'4
Mechanics
13
Mechanical Design of Process Systems
on=
9/og
Figure 1-10D. Velocity heads for change of flow [6].
Piping Fluid
\sri \7 tAl
| |I
aR = or
Ai= A2: A3
/ag
Figure 1-10E. Velocity heads for change of flow [6].
Mechanics
15
16
Mechanical Design of Process Systems
on
=
or/ag
Figure 1-10F. Velocity heads for change of flow [6].
k-...n* Piping Fluid
OR: O1/o3 Figure 1-10G. Velocity heads for change of flow [6].
'*
Mechanics
17
18
Mechanical Desisn of Process Svstems
o*= 02/o3
2----->
-_)>
Figure 1-10H. Velocity heads for change of flow [6].
3
k*--=* Piping Fluid
--v'.
.
---)t
-->2
OR= 01/O3
Figure 1-101. Velocity heads for change of flow l6l.
' 'drF'
Mechanics
19
Mechanical Design of Process Systems
-llt-
2--+
----)3
Kzg
on=
oz/o,
Figure 1-10J. Velocity heads for change of flow [6].
it -
'I[||,,'
Piping Fluid Mechanics
or:
o.'
/o3
Figure 1-10K. Velocity heads for change of flow [6].
21
Mechanical Design of Process Systems
Small pipe fittings have more surface roughness and abrupt changes in cross sections, making Kl insignificant at values of Nr" ) 10,000. For this reason, the new Crane method is recommended for pipe diameters 24 in. and less. Comparison of the methods for elbows is depicted in Figure 1-11. Table 1-3 lists Kr and K- values. The two-K method is preferred over the equivalent length method because in large, multi-alloy sysiems the equivalent length method could predict losses 300% too high, resulting in oversized pumps and equipment. With laminar flow, the equivalent length method predicts head losses too low. Also, in the equivalent length method, every equivalent length has a specific friction factor associated with it, because the equivalent leneths are derived from the expression L. = K D/t. The Hydraulic Institute's widely used K-factors are good for l-in. to 8-in. pipe, but result in errors in larger piping. The disadvantage of the two-K method is it is limited to the number of values of K1 and K- available, shown in Thble 1-3. For other fittings, approximations must be made from data in Table 1-3.
Table |-3 Constants for the Two-K Method I7l Filting Type Kl Standard (R/D : l), screwed Standard (R/D
:
:
1.5), all
typqs
90"
(R/D
:
This relationship applies to noncircular cross sections flowing full or partially full, oval, rectangulat etc., but not to extremely narrow shapes, such as annular or elongated openings, where the width is small relative to the length. In such cases the value of Rs is approximately one-half the width of the passage. The value of 4RH is substituted for d in Equation 1-4.
**"
: r,1*,
Thble l-4 provides hydraulic radii for various cross sections.
800
0.20
: l 5)
4-Weld
(22t/2") 800
o.27
5-Weld
Elbows
Standard all types
(R/D
(18") 800 : l),
0.25
500
0.20
500 500 500
0.15 0.25
1,000
0.60
1,000
0.3s
1,000
0.30
Long-radius
: 1.5), all types Mitered, 1 weld, 45" Mitered, 2 weld, 22rlz" (R/D
Standard (R/D screwed Standard (R/D
: :
1),
l),
Long radius (R/D : 1.s), all types
In using Equation 1-4 the geometry of the flow area must be considered if the area is noncircular. In calculating the Reynolds number and the diameter for a noncircular cross section, the hydraulic radius is applied: hydraulic radius
0.25
(90") I,000 1.15 (45') 800 0.35 3-Weld (30') 800 0.30
flanged/welded
:
800
2-Weld
elbows
PIPE FLOW GEOMETRIES
R11
0.40
1-Weld
Mitered
180'
cross-sectional flow area wetted perimeter
800 1),
flanged/welded Long-radius
(R/D
K-
Used as
etbow Tees
Runthrough tee
Standard, screwed
Long-radius,screwed Standard, flansed or welded Slub-in-type
200
1.00
150 100
0.10 0.50 0.00
p:
300
0.10
p:0.e
500
0.15
1.000
1,500 1,000 1,000
0.25 4.00 2.00 2.00 0.25
2,000
10.00
Full line size,
ball,
1.0 Reduced trim,
plug
Reduced trim,
p=0.8
Globe, standard Globe, angle or Y-type Diaphragm, dam type
Butterfly
Lift Swing
Tilting-disk
:
= 1.5 values for R/D 5 pipe bends, Use appropriate tee values for flow through crosses. Note: Use R/D
500 0.70 800 0.40 800 0.80
branch 1,000
Screwed Flanged or welded Stub-in-type branch
Gate,
Check
0. 15
800
1,500 1.50 1,000 0.50
45' ro 180'.
< - -8l
23
Piping Fluid Mechanics Screwed
Screwed tee
9d ell
Globe valve Screwod
Line
flow
Regular
D
K1
10
0.8
6 0.3
rfi-I|l
H
r\
Long radius
I
K
10
T
Branch
}J
flow 0.3
Flanged
1
4
D FlangEd tee Gate valve Screwed
Flanged 90oell
K o.2 0.1
0.3
Long radius
0.6
I D
o.4
t\\_t
Branch
flow
1
p!"..ffi Contraction
20
0
o'?FidG,i\
Square-odged inlet [24]
o.4
*Hl--
0.8
Regular screwed 45oell
p
K=o.b
0.6
X
ffi'=.err-r,rf(fia-r]
0.4 0.3
0.3
Inward ptojocting pipe
0.5
Enlargem€nt
/(=1.0
Lonq radius flanged 4soell
(:; *-1---lJ/,
0.3
K 0.00' 0.02 0.04
0.06 0_10
0.15&up I For
(,
0.1 0.5 0.28 o.24 0.r 5
0.09 o.o+
p= lmall diamete./larse dismerer K based on velocity in slnatter pipe based on main pipe
see
table
'Sharp{dged
K
for orifice. l40j
Hydraulic inltitote [24]
.........,......
crane
It2l
[,liller. based on water at 6
ft^
132]
Figure 1-11. Velocity head values for common piping components [1]. (Reprinted by special permission from Chemical Engineering, @ 1978, by McGraw-Hill, Inc., New York.)
'd
24
Mechanical Design of Process Systems E
Swing chock valve Screwed
F nninqfricrlon lactor for fllribl. m6.tl
v
n tLtLtt-
hc.
Il4l
_
flilj-ll-lH;E
4
Tvoictl
.T
,I
0.6 '1
24
K
0. 9 o.12 0.08
dimh'ioo3
Nomimr LDr LE u tL tize {in.l {in.l 1/2 0.520 0.250 314 0.750 0.275 0.04t04 t.000 0.187 r 1.500 0.200 r1n 2.O@ 0,161 2 2.962 0.143 3 4.000 0.081 4
106
Feynolds number, /VF"
Head loss in conical diffuse6
Flanged
4 6
10
1.2
tr9l
1.0
5
o.e
Angle valve Scre$red
6l-
4l-
Ir
,t-
P, des.
,I llIl 0.3
0.6
1
Head loss in circular
147l
63 Flanged
mite6
K= 1.2 (1 -cos0
1
Screw€d return bend
Pf0g cock
valve lr9l
Buttertly
valve ll9l
Flanged return bend 0
0
dk
Figure l-11. Continued.
to'
0.05 0.29
2o'
r.56
lo"
11.3
60"
206.0
anste ber@en pipe axis and plus cock axis
to'
o.24 o.52
20" +0"
1.54 10.8
6o'
I18.0
5"
d
is
angle between pipe axit and llapper plate
Piping Fluid Mechanics
where Y 1214a12 : 0 for incompressible flow since a?- @, the term ar2 multiplied by the fluid density pl is the bulk compressibility modulus of the fluid and gives
Table 1-4 \ralues ot hydlaulic radius (RH) for various Cross
Sections Cross Section
the pressure change for the fractional change in density. Values of the bulk compressibility modulus for various substances are given in Appendix A. The term a1 is the velocity of sound waves propagated in a compressible medium.
RH
As Equation 1-9 shows, the velocity of the fluid is compared to the fluid velocity of sound in the term V1'l 4a12. If this ratio is small, compressibility effects can be ignored because the error is the difference between this term and unity. This analysis is valid only for barotropic fluids, which are typical of most industrial applications involving flow of gas through a nozzle and the flow of water in conduits or over obstacles. Compressibility effects of a fluid are small when the fluid velocity is small, compared to the fluid sonic velocity. If V1/al is equal to 0.3, the error in the velocity is less than I % when using the incompressible assumption. For ambient air, this limitation corresponds to a velocity of 300 ftlsec without causing significant error. The phenomenon ofnonsteady flow is somewhat more complex than that of steady flow. The acceleration or deceleration of liquid particles immersed in a two-phase solution is one such example. The time required for the nonsteady phenomenon to occur is compared to the time reouired for a sound wave to traverse the flow in which substantial differences in velocity occur. If the time dif-
L-
IN/ E+=
0.153 Di
ferences are small, then the incompressible Bernoulli equation (Equation 1-2) may be applied.
PIPING FLUID MECHANICS PBOBLEM FORMULATION COMPRESSIBLE FLOW The preceding analysis assumes steady and incom-
:::ssible fluid flow. This is a reasonable assumption :jce most liquids are steady flow, but frequently the as.-nption is valid for gases. Because some liquids and all :-ies are compressible, a criterion is needed to deter-,ne what percent of error is incurred assuming constant :::1Slty. -\n estimate of the error can easily be made for a baro::pic fluid-a fluid whose density is a function of pres-
.-::. :
.:id
:
Sabersky and Acusta [8] have shown that for a Vr, static pressure R and density
stream of velocity mat
(1-9)
To solve piping fluid problems a firm understanding of basic equations and units is essential. The units should be carefully defined and used throughout the calculations. Thble 1-5 presents reasonable velocities for various services used in mechanical systems. These velocities are only guides intended to give the reader foresight for trial
values and are only for mechanical systems; for such values of chemical processes the reader should consult chemical engineering sources.
Viscosity Widely misunderstood and often improperly applied, viscosity is perhaps the most recondite of all the properties associated with fluid mechanics. However, a clear conception of this physical property is critical to the suc-
Mechanical Design of Process Systems
26
Table 1-5 Reasonable Velocities Feet per Second
Liquids
2to5
Service water mains General service water piping Boiler feed water piping Heat medium oils
4 to l0 6 to 13
2to6 2to6
Lubricating oils Gases Low-pressure steam heating
70 to
:
139.53 cp at 90'F
54.725lb^/tr
ij!-.
lb,-rT, (rry )r)cP /o.oooozol\ :2. iz, |1 r ., /= lbrsecr
Natural gas
100
150
to
(s4.72s)
165
165 to 400 100 to 150 330
r:
0.0017
70
Air, 0 to 30 psig
:ft2 sec
ft2
35
0.00001076e
7
cessful design of hydraulic systems and rotating equipment that transport fluids (see Chapter 6). Viscosity is the property of a fluid to resist flow. Consider how much more freely and easily gasoline pours from a container than does black strap molasses. In fluid mechanics terminology, the heavier, bulkier nature of molasses is caused by the fluid's high shear stresses. These high shear stresses make the molasses very resistant to flow. The fundamental measurement of flow resistance is the dynamic or absolute viscosity. In the cgs (centimetergram-second) system of units the basic unit of viscosity is the poise, which is equal to one hundred centipoises, (For a detailed explanation ofhow absolute viscosities of fluids are determined, the reader should consult a basic text on fluid mechanics.) The centipoise (cp) is now the standard unit of absolute viscosity, but because other units are still used, as illustrated in some of the examples scattered throughout this book, methods for converting to and from centipoises are provided. With the centipoise, one must be careful in using the English system of units when converting to the kinematic viscosity. Illustrating this conversion we have the following:
E fP
0.0017 -::-
40 to 60 30 to 50
Forced draft ducts Induced-draft flues Chimneys and stacks Ventilating ducts
z
p=
w
15 to 70
and process piping
Low-pressure steam mains High-pressure steam mains Steam engine and pump piping Steam turbine piping
p=
Thus, ifone has a fluid such as a fuel oil (see Example 6-1), which for a given temperature has an absolute viscosity of 139.53 centipoise, we calculate the kinematic viscosity, z, in the English system of units as follows:
il
centistoke
:
159.261 centistokes
sec
Since the kinematic viscosity is a function of the fluid density, the above value is only valid at the specified temperature of 90'F. In the metric system the kinematic viscosity can be obtained by dividing the absolute viscosity by the specific gravity. This is only for the metic system of units.It is a common mistake in using the English system of units to compute the kinematic viscosity by dividing the absolute viscosity by the specific gravity of the fluid. Equipment manufacturers often use other units of viscosity. One ofthe most widely used units is the Seconds Saybolt Universal (SSU). This unit represents the number of seconds required for sixty cubic centimeters of liquid at a constant temperature to flow through a calibrated orifice. For liquids of high viscosity a larger orifice is used and the unit applied is termed Seconds Saybolt Furol (SSF). It is customary to specify these units of viscosity at standard temperatures. The following are formulas for converting SSU's and SSF'S to centistokes. Below the value of 32 the SSU is undefined and below the value of 25 the SSF is undefined. Throughout this book, the centipoise and the centistoke are the standard units of absolute and kinematic viscosity, respectively. Where the need arises, the centistoke is converted to SSU. SSU to centistokes
absolute viscosity, centipoise
= i.0 lb-sec/ft2 = 478.7 poise = 4.787 centipoise : kinematic viscosity, centistokQ2 : & 8", for the English system of units
Wnefe gc = JZ.|t
w=
fr-lh aa---------a
lDrSeC'
mass density of the
t: :
,/
For32(t(99, For
fluid, lb./ft3
Seconds Saybolt Universal centistokes
t)
100,
6.2261
: - P7 t
o.zzu
- !1 t
:
*( ----L'
Piping Fluid Mechanics
with COz in steam. The properties of the mixture are as follows:
SSF to centistokes
::
Seconds Saybolt Furol
Rrr 25
( t(
5rt>40,
39,
p= p=
lR4
2.24r - -:- : t
2.16t
60
= - -:-t
v v
EXAMPLE l.l: FRIGTION PRESSURE DROP FOR A HYDROCARBON GAS.STEAM MIXTURE IN A PIPE An amine still reboiler boils off a hydrocarbon gas{eam mixture that flows in a 3M ss line connecting the :eboiler with an amine still tower. It is desired to deterrine the maximum pressure drop in the line as shown in Fieure 1-12. The sas is a small tract of amine immersed
Figure 1-12. Amine still reboiler hydraulics.
d
e:
0.01322 cp 0.085 lb/ft3 0.0015 in.
P
:
10 PSig
The velocity head approach is used in determining the friction pressure drop. The line shown in Figure 1-12 is coming off two nozzles on top of the reboiler and merging at a tee before entering the amine still tower. The dimensions shown are identical with both sides coming off the reboiler nozzles (exemplified by the word "TYR" meaning for both sides). To solve this problem, we must apply Equation l-4. To use this equation, we divide the connecting pipe into three components (see Figures 1-13-l-15)-an 18-in. f portion with W = 25,291 lbl hr a24-in. d portion with W : 25,291lblhr; and a24in. d with W : 50,582 lb/hr, Equation 1-4 is applied to each portion and the pressure drop for each is added to
Mechanical Design of Process Systems
-
FLUID ANALYSIS FOR SINGLE PHAS€ FLOW
coNFtq!84[!9X.
L,,
(z'.- a"\
y-
rerzr\H
r{z'-j"\ + (r'-et) ,
(=#l)
(o.,s$$
1'- z"
iE;G'dr;BrE-vEEcrw
=
E REYNoLDS
scttEOULE
tcs
p7
1, 1s.7
No=
ov
t
Ki= No oF ver-ocrri ems; DEpENDENT ptpE FRtcrtoN
K VALUES ILD = 5OK, D=rNStDE D|AMFTEFtfrll
PIPE ENTRANCE
x
=.ov/, = rt6
lL= o,ot32? cp = o,O85 Lb/cu tl y= 1, I L'l I' € = O,OOI5 in p
FOR COMPONENTS:
)*,
=
- tr'6
+i,+81# f"*",i,"'(##) =
SERVICE FoR sERvtcE
GAS OR LIOUID
LINE NUMBER IE"6 PoRTt oN
.
?1.x ta" u FFUSER (cs/{rRrc). t6" t R 90' ELL =
)
80 o,079 o, oza o,7
*=,..,u
f=
D: 17' 50 [p= o, O?9 v = *9,18'1
NpE= 690,49/
=
o,otl
W=
2sz9t
|
in.
psi
1y
".
Q=
tt/nr
Figure 1-13. Fluid analysis for single phase flow-gas or liquid.
PAGE
_OF _
Piping Fluid Mechanics
FLUID ANALYSIS FOR SINGLE PHASE
..r-
'
(i'-o') + (1'-t
tv/1i']1
""n #n"cr.z\
i,,''
SERVICE
FEASOMBLE VELOCITY FOR SERVICE
=
Gfi],,)
REYNOLDS
-
21,++2
LR ELt s
'tli =
2+076
++
*
^.,2 KI=NO OF VELOCITY HEADSiK= .ov72 fl prpe rRrctroH = DEPENDENT
FOR COMPONENTS:
rwo 9d
OR
NO= DVM'
K vALUEs [LD= soK,D=tNStDE DIAMFTERlft]l
)*,
GAS
+ (rg'' rr"\ = 2+'- o
raszgr\E(#c'"J
("
-
LINE NUMBER
coNFtquRAI!9!L
L,.=
FLOW
- K- o,1?o
322 o.o?s P= y lL=
o,ot
cp Lb/cu
= 21.C78 t' 6 = OOOI5 1n. /=p= - 23,5 ;n. o,O29 [p= y
= 21a12
ll
1si
191"".
€t+,t17.r25
o.oll Q=
w= ZS29l
tyn
flow-gas or liquid. Figure'l-14. Fluid analysis for single phase-gpm
J
Mechanical Design of Process Systems
FLUID ANALYSIS FOR SINGLE PHASE FLOW -
CONFI6URAT1ON
lt
Z''tt"
= 2,9l.1
cAS OH
LtOUtD
LINE NUMBER
k
Sh =
"4q
<2."
rs'srz'tiF (=za!=ai
fo,oa,iS
K vALUEs ILD= 50K,D=tNstDE FOF
)*,
=
h*l\ru.(ffi
DTAMFTER
tftll
COMPONENTS:
coMatNtNG
PIPE ExtT
FLOV'I =
TEE,
)*=
t2 2,2
r7,s84
lL= P= t= e=
*
O.ol32? co O.O?S Lb/cu tr ?-91'7 n' o,OOl5 in
04< !r- --:::_tn.
Ap= oQ6, 5'1, 884 V=
psi .11rl"""
NRE= l.o2A,35+. esp
t=
otol3
Q= 111r= So
Sg2
.L/rrr
--gpm Figure 1-15. Fluid analysis for single phase flow-gas or liquid.
Piping Fluid Mechanics
the other portions to give the total frictional pressure drop for the line (For velocity head value of concentric conical diffusers, the reader is referred to Thble 1-6). The calculations are as follows.
:
Lr
6.167
Table 1-6 K-Values tor Concentric Conical Diffusers
ft
d2(in.) d1(in.) L(in.) p
:
(6.72
x
10-4)(0.01322)
:
(8.384
lr1:50)r, 1+r.+tzr
\ tz I =DVP: p
(8.884
80
tl2
a secro.oasl k rr-
10-6)
x
Sch 80
3lc x
;lb' n-sec
Sch
690,491.450
f:
_2 ron,^ [{g "-
1-6a)
0.014
'0.014)-05
:
flPf =
(
(?.
8.452
+
: -2 logr0 [(2.317 x :
(3.072
x
10-5)l
10
5)
r'.l#
:I
0.373 0.225 0.099 0.009
(4e.487),
g
fr lh
H*)
S€C'lD6
lP1,
:
L. :
_\p.
12.758 3.000 10.661
2.469 0.957 Itlq 2.469 1.278 ztlz x lt/z 2.469 1.500 2.469 2.067 40
3.068 0.957 1V+ 3.068 1.278 3 x lyz 3.068 1.500 3.068 2.067 2tl2 3.068 2.467
tt
514,177.125 and
f =
0.014
0.022
0.436 0.297 0.131
0.055
3.500 12.474 3.500 9.796 3.500 7.957 3.500 3.292
0.406 0.237
3.500 14.816 3.500 12.944 3.500 8.221
0.454
0.143 0.013
o.
o8r
H ei
1
0.337 0.11 I
3.500 4.9@
0.028
lV+ 3.548 1.278 4.000 16.484 lUz 3.548 1.500 4.000 14.833 3t/2 x 2 3.548 2.067 4.000 10.668 zth 3.548 2.469 4.000 7.151 3.548 3.068 4.000 3.440
0.559
Sch
40
+ o.72ol - [(0.014X24.07s) t (23.s0) I (
.
44zf
!(, * *-)
fr lh S€C'lD1
c--,-..,&
lc 2.067 0.742 3.000
Sch
40
Similarly,
\R" :
Q.121
Sch
9-929 O.t 24.078
x
0.957 2x ll/c 2.067 2.067 1.278 3.000 7.556 llz 2.067 1.500 3.000 5.423
* ,"--'l ,rol
ft
0.036
1.500 0.546 2.500 10.999 3lq 1.500 0.742 2.500 8.720 1tl2 x 1.500 0.957 2.5W 6.235 lUq 1.500 1.278 2.500 2.545
Sch
,o.oss,
0.126
0.318 0.153 0.040
tlz
80
(l -4)
(0.014X6. 167X12) (17.50)
3lt 0.742 0.423 1.500 6.104 tlz 0.742 0.546 1.500 3.746
1.278 0.546 2.000 10.545 r.278 0.742 2.000 7.701 1.278 0.957 2.000 4.603
Sch 80 I r/4
40
-ro,
0.302 0.423
Sch
-8.537
0.014
Kr
0.225
1X
* _?r_] [3'7 NR"(f)"'l
-
,fl-05
tlc 0.546 ls 0.546
d(deg)
4s 0.957 0.423 2.000 7.672 1lz 0.957 0.546 2.000 5.898 3lc 0.957 0.'742 2.000 3.081
80
:
Let
x
x l0 6)-]!L It-sec
Sch
0.449 0.210 0.093 0.010
32
Mechanical Design of Process Systems
Table 1-6 continued
Table 1-6 continued
Size
dr(in.) dl(in.) L(in.) d(deg)
40 ltlz 1.500 4.026 4.000 18.406 2.067 4.026 4.000 r4.r74 4 x 2tl2 2.469 4.026 4.000 11.223 3.068 4.026 4.000 6.878 31lz 3.548 4.026 4.000 3.425 Sch
2.067 Ztlz 2.469 5x 3.068 3t/z 3.548 4.026 402
Sch
2.469 3.068 6 x 3tlz 3.548 4.026 5.047
40
Ztlz
s.u'l
5.000 17.338 5.047 5.000 14.940 5.047 5.000 1r.4r4 5.U7 5.000 8.621 5.U7 5.000 5.860
6.065 6.065 6.065 6.065 6.065
5.s00 19.08 5.500 15.810 5.500 13.228 5.500 10.682 5.500 5.310
0.609 0.345 0.197 0.055 0.088
7.981 r7.2s0 15.000 17.997 10 10.020 r7.2s0 15.000 13.946 18 x 12 11.938 17.250 15.000 10.199 14 13.250 17.250 15.000 7.662 16 15.250 r7.250 1s.000 3.823
wt8
10 12 20x 14 16
l8
std
0.023
4.A6 10.020 7.000 25.350 0.703 5.M7 10.020 7.000 20.807 0.514 6.065 10.020 7.000 16.409 7.981 10.020 7.000
0.295
5.047 11.938 8.000 25.511 6.065 11.938 8.000 2r.535 12x 7.98t 11.938 8.000 14.319 10 10.020 11.938 8.000 6.885
0.674
0.051
0.197 0.027
std
10 12 14 24x 16 18
wt
13.250 13.000 t6.042 7.981 13.250 13.000 1r.692 14x 10 10.020 13.250 13.000 7.136 12 rr.938 13.250 13.000 2.892
Srd
wr
26
x
std
wt6 16
6.065 15.250 14.000 19.150
7.98r 15.250 14.000
x 10 10.020
r5.U7
15.250 14.000 10.765 12 rr.938 15.250 14.000 6.793 14 13.250 15.250 14.000 4.096
0.449
0.214 0.059 0.005 0.604 0.356 0.157 0.046 0.011
10.020 11
.938
0.125 0.058 0.008
0.180 0.108 0.036 0.005
13.250
0.194
0.092 0.030 0.004
23.250 23.250 23.250
r5.2s0 23.250 20.000 1t.537 17.250 23.250 20.000 8.627 20 19.2s0 23.250 20.000 5.739
Sch
40
20.000 8.627 20.000 s.739 20.000 2.866
14 1,3.250 21,.250 20.000 11.537 22x 16 15.250 21.250 20.000 8.627 18 r7 .250 2r.250 20.000 5.739 ?0 19.250 2r.250 20.000 2.866
Sch
40
20.000 10.533
0.275
10.020 2t.250 12 1 1.938 2r.250
0.257 0.151
7.981 19.25Q 10.020 19.250 11.938 19.250 13.250 t9.250 15.250 19.250 17.250 19.250
0.496
l0
wt
3.068 7.981 6.000 24.168 0.726 3t/z 3.548 7.981 6.000 21.680 0.618 4.026 7.981 6.000 19.243 0.476 8x 5.V7 7.98t 6.000 r4.r52 0.229 6.065 7.98t 6.000 9.188 Q.O74
l0x
wt8
srd
0.537 0.388 0.205 0.100 0.035
Sch
40
L(in.)
std
403
Sch
d2(in.) d10n.)
Kr
Sch
12 r1 .938 25.250 14 13.250 25 .250 16 15.250 25.250 t8 r'1 .250 25 .250 24 .W0 9 .s94 20 19.2sO 2s.2s0 24.000 7.181 22 2t.250 25.250 24.0W 4.780 24 23.250 2s.2s0 24.000 2.388
0.169 0.079
0.026
.123 0.057 0.018 0.003 0
std
Wr
14
16
l8
30x
20 19.2s0 29.250 24.W0 12.025
0.174
24 23.2s0 29.250 24.000 7.181 26 25.2s0 29.250 24.000 4.780 28 27 .2s0 29.250 24.WO
0.044 0.014 0.002
Piping Fluid Mechanics
APt,
Table 1-6 continued
Size
dr(in.)
L(in.)
d1(in,)
@(deg)
K1
Srd
\\i
6.961 O.'
Total Friction Pressure Drop for Line
APl
16
: =
33
APr,
*
APr,
*
AP;,
:
:
(0.029
AP
+
0.005
+
0.061)
pst
18
20
_\
x
AP1
24 23.250 33.250 24.Un p.025 26 25.250 33.250 24.000 9.594
0.141
4.780
0.011
30 29.250 33.250 32 31 .250 33 .250
24.000 24 .NO
0.078
0.001
Std
\\'t
18
EXAMPLE t-2: FRIGTIONAL PRESSURE DROP FOR A HOT OIL SYSTEII OF A PROCESS TANK
used in the manufacture of roofing products. To maintain the coating mixture at the required temperature, external
20
24 23.250 35.250 24.W0 14.478 16x 26 25.250 35.250 24.000 12.025
0.207 0.128
7.181 4.780
0.032 0.010
2.388
0.001
30 29.250 35.250 24.000 32 3t .250 35 .250 24 .000 34 33.250 3s.250 24.000
24 26 30 32 34 36
1\l
6.695 O"'
A pressure vessel storage tank contains 6,000 gallons of filler coating that must be maintained at 370'F to be
16
Srd
:
22
23.250 41.250 24.000 22.024 25 .250 41 .250 24.000 19 .47 | 29.250 41.250 24.000 14.478 31.250 4r.250 24.000 12.025 33.250 41.250 24.000 9.s94 35.250 41.250 24.000 7.181
jacket coils are placed on the outside shell and bottom head as well as four internal coils inside the tank with an agitator. The tank is depicted in Figure 1-16 and the hot
0.4s4 0.339 0.161
0.098 0.053
0.024
:P,. = 0.005 psi '-. : 2.917 ft
\r. :
't:
rP.-
1,028,354.250 and
I
(0.013x2.917) (23.s0)
+
f = 0.013 2.201
(o.oss)
H
(s4.884F
-i1Fl",ooJ ft lb. r,.r r' --7-a-\J-.-/ S€C'lD1
Figure 1-16. Process surge tank. (Courtesy of Tranter, Inc.)
34
Mechanical Design of Process Systems
oil system in Figures l-17, l-18, and 1-19. It is desired to determine how much frictional pressure drop will be incurred for the entire tank so that pump sizes may be selected.
Bottom Head Hot Oil Supply
I
Hot Oil Entrance from the 2-in. Header and Flow Through Station 1. (Figure 1-U):
The tank is divided into two systems-the hot oil supply system and the hot oil return system. Each system connects to the three components-the four internal coils inside the tank, the outside shell jacket coils, and the jacket coils connected to the bottom head-and each of the three components must be analyzed separately.
6
gpm ,l/ "1,
30 spm
t
Bottom llead System A 2-in. pipe header supplies hot oil to the six inlet jacket nozzles and returns hot oil from six outlet iacket nozzles. The supply nozzles are designated by an S and the return nozzles by an R. We will analyze the supply system. The piping system is divided up into "stations," which are points designating flow change due to separating fluid. Each line following a station must be analyzed separately because the flow rate decreases after the flow separates in the tee. We will consider the pressure drop from point A to B, since that path involves more stations and the maximum amount of pressure drop.
Yt,, z.s' I
For Q
L o p
: 36 gpm : 26.5 in., p = 0.15 cp, e : 0.0018 :2.067, p = 58.7 lb/ft3 : (6.72 x 10-4)(0.150) : 1.008 x 10-5 lb./ft-sec (36)
'
sd (___u, ){_1.'"
min \7.479 gal/ \60 sec
:
3.442 ft.lsec
g=11h"x31a"
C=11h"x1, D=2"xEa" E=2" x1" F=2'x1112"
Figure 1-17. Process surge tank bottom head coils.
Pipiry Fluid Mechanics
___.1
Figure 1-18, hocess surge tank-shell coiis Qooking south).
35
Mechanical Design of Process Systems
rl
tl t^ JI r3-
qq.\
7sm
0l Il-
{t {t-\| \t
I
\l NI |\l t\l | \l
_l
t\ tt\
I
-@
Figure 1-19. Process surge tank-shell coils (ooking north).
fm&----* Piping Fluid Mechanics
Nn"
_DVp_ P "I
n
?8\o"*" (t.oo8
x lo )
L:
osD*
4.0
v_
-tD'
ft
.io\ '--'
sar
{
rc
I
\ltgi
rnin \7.479.9aU \60 sec/
ilrt I (J.JJbtrn.'t-......_l
n-sec
37
:
2.869 ft/sec
\144 in.'/l
:3,452,9\0
l{q!q'!)
I (1o
-z
s
:
roe,o
ffi
+
2.51
DVp
I
K=
Branch flow tee
aP,: _
.-
(dLL.
0.78
1.
[
90" LR ell Flow-lhru tee
I
or,^ ''
,.r6al
:K: :K:
_
[ro.o+orr+.orrtzt
I
Q.067)
.-^-. lb {r.6oe]' _^ ^-^.. fc I I ft, , l.fil = n'
=
0.126 n.t
Z Hot Oil Fl.ow from
Hot Oil Fbw from Station 1 to Station 2:
Station 2 to Station 3:
I 1ftr ll
I min min V.a79 ga| \60 sec
12.036)in., 18gpm
(ril!.lo Nn" : \r2 l 22t,657
:
t tt'.1
\144 in.J
r' o.ru sec rss.zr P fi'
(1.008
l8
I
x
10
4)
th
-j:' n-sec
I
sec' \r+4 ln.'/
lrql rr ft lb' -'--'-'sec2
..^. sal tlxl-l-ll '--'
I
I
()d. /)
APr,
0.186 psi
30
*,.orol
lbr
sec'lDf
., -Q,-*-Q,-
I
e8lJwtfi{-'
0.570 0.910
I
,rrta j:b:l'-
-
--l!' n-sec
K-factors
rh rr2 / rfi2 \ /5R?\::11 M)\2:L | -" I '-' ,ftr.- -. ss62 \144 in.2/
$rr :
4)
1.480
(2.067) *
[to.o+oxz.zoelt
10
,7U
D")# rzr
x
:0.040
0.46
+
287
I
a,sa.;, sec
[
(fl0.5
+ (-0.78)
\-
/
rzz
1
0.78
12
[/o.oora\ I z.st l\-0. i -2 logp 3r -
K-factors
:
67lr,,z.sost (1.008
:
K
_\
a,qsz,srol(D\
0.040
Pipe entrance
12
2.837 ftlsec
Mechanical Design of Process Systems
oore\ a l\ r:+ 1 * z.st [/o
1
(flo
-z
s
rnrsvltf
[-
'oc'o
1ft
I
I ft3 \/1 min\ 'oi" \2.+zs s"il \60 '*/ = / t e'z \ (0.864)in.,tfr1n}/
,,^, t"'
I
1
ca1
/
4.457 ftlsec
:0.M2 K-values
x
o 2-in.
ltlz-in. LR ell
Nn. =
t#)o,0.0", (1.008
o . - "'
[(9
t' - e'i],u,
=
* _ .
P4
:
|
0.607
1
(o0
-
0.607)]
(0.368)
_ o.o'
1)
or,,
.
2.51
I
* [ 3i tz26seo]flri
o.oar + 0.53
lr/2-in.
x f-in.
|
reducer
et-
:
p,)] _
-
0.8 sin [(6.23s)(0.593)1 0.166
0.611
: [,oq?!u1'uo]t't, * 0.u,,] .-^
.
lb .^ ^^-.. n, / r ft, \ {r.6J /)' .*r- h44 i" j-l
ftr
z1zz.z1
:
rocro
l\ o0s7
sin ,. _ 0.8 --- [c(l -
r.v
-
(J6. -. /)
APr,
-r
5
lb''4 /
K-values
Q*:18-:0.667-K:0.53
Dr:
x 1o-) .lb' ft-sec
:0.051
Flow-thru tee
-
*
0.368
0.8 sin [(5.423)(l
^R -
or.a
226,889.525
1u9'
Ir rr o\2 = l- -^"1 = \2.M7
:
A
!!y
Flow-thru tee
. o, 6 = 0.5lAn: Ar -_ _ = 1.0=K :0.87 Q*: *Q: = _:_ t2 A3 Dr:0.:rt+0.87:1.181
Sec' lDf
0.063 Ott
Z Hot Al
*r:I
Flow from Station 3 to Station 4: 6 gpm
(0.051x1.0x12) (r .049)
+
r. 1811
,l
r1
---A
t!'
h
l2x't
I
,
I
-spm
12
|
+6
rr lb
r,,,
,.t', fC / t t' sec \t+a
-oFm
fr-lh
I
@
S€C'-lD6
\
1"31
=
O.222 psr
Piping Fluid
E Hot Oil
Flow from Station 4
to Exit B:
(58.7)
rh ft;
Mechanics 39
(3.612F
rr2/ rcz\ **- |rfri".,I
tcrrr!jq.S€C'-lD; APq
=
0.405 Ott
Total friction pressure drop from entrance A to exit B: Path (Figure
L:2ft /
\/r -i"\
1ft3 t-l sal /4\ \"/ min t-t \7.479 ga| \60 sec/ -
_ 3.612 ftlser
(0.533)in.'(+)
a rsa.zr'tt'I {o't'lo,r.utl'sec' \12l :
@ @ @ @ @
A4.449
Z
Entrance
I
APl psi 0.186 psi
to station 2
0.126 psi
statioo 2 to station 3
0.063 psi
station 3 to station 4
0.222 psi O.zlO5 psi 1.002 psi
Flow from Flow from Flow from Flow from
station
Dot, =
1.002 psi = Total frictional pressure drop from entrance A to exit B
statioD 4 to exit B
Shzll mils-Soutft ride (Figure 1-18) Station
1^
1-17)
A thru branch flow tee
1-
(o0.5
=
0.055 35spm 2
I-values
.
l-in. x
3/a-in. reducer
sin [a(l - F1] _ ,. _ 0.8 _____7-_
: .
0.8 sin [(3.081X1 (0.361)
0.0'[8
3-90' LR ells
K
:
3(0.025X30)
:
:
2.25O
Pi1r exit
+
E* :
o.o+s + z.zso
&r, _ -
l(0.055x2.0)(12)
t
1q
- 0.601I
o.7 o" =:.r : 42 : 0.167 Qr Kr = -0.032 Header entrance = K = 0.78 station 1 : K = -0.03 K : O.75 : 42 Q: epm 'L = 10ft;/ = 0.15cp;d = 2.067in. p:58.7 lb/ft3;6 = 9.9613 V = 4.016 ff/sec; f : 0.020; Nr, : 402,829 APr : 9.195 *' Station 2-
1.0
to^szat
+ r.ooo = +
3.2esl
3.298
35 gpm 28 gpm
40
Mechanical Design of Process Systems
n. 1 Qr: ::] = JJ .-:0.200 Qr Kaz = -0'03 L = 5in. = 0.417 ft;d = 2.O67 in. Qa : 35 epm Y : 3.346 tusec; f : 0.020; Nn : 335,691 AP, : g.gg1 n"t Station
Station
5-
3-
9:1:o.soo 14
Qr L: 10ft Krz : 0.015 v = 1.339 ft/sec;,f : Nn":134,276 APs : 9.914 O.t
0.021
Friction pressure drop from station 6 to coil entrance
Q3
=
28 gPm
Q:.128
:o.zs
Qr L = 10ft d : 2.O67 rn. v : 2.677 ft/sec; K32 : Nr":268,553 f : 0.020 APr : 6.952 n.' Station
-0.036
43 21 gpm
I Tspm
I
14gpm
I
2
Q:1:o.rgr 2l Q: &z = -0.030
L:5in.:0.417ft; d = 2.067 ln. : 21 epm V = 2.008 ff/sec; f : 0.021 Nn' = 201'415 AP+ : g.ggt O.t Qr
o^:Qt=ro Qr &r = 1.28 x
K = O-129 K : 0.311 K : 0.048 K : 18(0.025) : 0.450 2-l1lz-in.90" LR ells, K = 2(30)(0.021\ : 1.2@ 1-1-in. 90" LR ell, K : (30X0.023) = 0.690 1-3l+-in. 90. LR ell, K : (30X0.025) : 0.750 Exit into coil, K : 1.0 Q = 7 gPm; L : 7 -25 f7 F.- = 5.168 !K : . For 2-in. { pipe, d 2.067 in.
For 2-in.
1tlz-in. reducer, l-in. reduceq l-in. x 3/a-in. reducer, r/+-in. plug valve,
lrlz-in.
x
L:7in.:0.583ft
K: V=
1.049
0.669 fl:/sec
Piping Fluid Mechanics
n.
Nr":67,138
= 0.333 QR::r \J3
f:0.023
AP
:
0.0M psi
o For lrlz-in. d Pipe, d : !.610 in. L:3ft K : 1.571 V : 1.103 ftlsec; Nx" : 86,195; f : 0.023 : AP 0.016 psi o For 1-in. { pipe, d : 1.049 in. L:Zft K = 0.738 V : 2.599 ftlsec; Nq" : 132,292', f : 0.024 AP : 0.055 psi . For 3/a-in. { pipe, d : 0.824 in L :2ft K : 2.2O Y : 4.Zll ft/sec; Nx" : 168'416; f:0.025
AP
=
is
!s\
llP
=
0.195 psi
+
station
+
0.001 psi
+ 0.052 psi +
i-!-Z
\--
1
+
2
(0.004
station
+
0.016
O.OOS
psi
:
2
-
3 +
station 4
0.055 + 0.330) psi
o, : Q' :
o.5ool
L = roft
Qr K:z = 0.015 14 gpm Q3 1.339 ft/sec; N3" AP 0.014 psi
: v : :
:
134,2'16:
f:
Total Drop for Shetl Coil on South Side
-
Shell
coils-Nonh side (Figure 1-18)
Sration
13 + 21spm
;'il]
I
I
r 14 gpm
2
d
0.021
Friction pressure drop from station 2 to coil entrance:
station 6
station 5
I-t" :
0.001 psi --/-
\-!-
station
0.014 psi
Station
0.330 pst
Toral frictional pressure drop from station 1 to bottom shell
.nil
Kr: -0.030 L: 10ft Qr : 21 gpm p:58.7 lblff; p :0.015 cp; e:0.0018; d : 2.067 \n. V = 2.008 tusec; Nr" : 201,415t f : 0.021 AP1 : g.g3g O.'
n. o" : lll = 1.0: K,, = 1.28 r)^ For 2-in. x 1-in. reducer, K : 2.538 1-in. x :/q-in. reducer, K = 0.048 3/4-in. plug valve, K : 0.450 Exit into coil, K : 1.0 For l-in. 90" LR ell, K = 0.690 For l-in. { pipe, d : 1.049 in.
4'l
Mechanical Design of Process Systems
:
: 4fr, V = 2.599f1/sec; f : 0.024 Q
7 gPm, L K 0.738
:
Ns.:132'292
:
AP For
2-i'].0
EXAIIPLE l-3: FRIGTION PBESSURE DROP FOR A WASTE HEAT RECOVERY SYSTEM A gas turbine manufacturer specifies that the maximum back pressure on the unit used in this system be 10 in. of water pressure, therefore, the waste heat recovery
0.079
system should be designed so that the frictional pressure
pipe:Q:7gpm,L: llft K:2.538 V : 0.669 tusec Nn":67'138.184 f : 0.023 Ap : 0.0t1psi
drop does not exceed 10 in. of water. The system is shown in Figure l-20.
Z
Turbine exhaust dntq
for outside air ot 6l)'F
Temp. ofexhaust gas
For3A-in.
opipe:d
:
L:
0.8241
V:
2 ft:
K
= 1.450
4.211 tusec
Nn":168'416
f : 0.025 : 0.245 psi
Ap
tt :
0.0759
L:
l2O
ft;
th
0.030 psi + 0.014 = \-!-\-.-/ station
+
1
(0.011
e=
psi
N""
VDP,
:
t'
station 2
+
0.079
+
0.245)psi
:
2.108
station 3
sr
L
AP
=
0.3'19
psi
:
O.OOOO+Z
x
Nn:
B{SS
STAC
t
0.03
cp
(commercial steel)
0.00015
10-5
'|
-lb ft-sec
a(4t.25)i".
sec
(2.108
=
=
131 fusec
\3,600 sec/
Side
Maximum friction pressure drop in supply system is incurred at bottom head coil line with AP : 1.002 psi.
V=
a = 0.0759 lb {--!t ft-hr
fl 1t.0)
Toml Drop for Shell Coil on North
.n
:
D
coil is
l-r AP
795"F;
.':. \0.4132) lb/n-hr --l= It-hr
Total frictional pressure drop from station 1 to bottom shell
sr
:
x
I | ftin./I {0.031) !ftJ \12
10
5)
-.!!rr-sec
662,224
i(
42'6 670 9a
4zV srD
Figure 1-20. Waste heat recovery system.
Piping Fluid Mechanics From Equation l-6a,
For 42-in. d portion,
, : log,o I n o!goo38j -:* 10.00001I + :-: -2 ri rttot / t
K.*r
:
0.770 + 3.161 From equation l-4,
f:0.0130
op = ILL*
D=
41.25
in. =
..
fL D
(0.0130)(120)
3.438
+ 0.340
_
rr)ey I2e,
, "-,1 1- +,zt1l ur = [(0.0130)(I20) t(3.44) L I
^,r..4
3.438
ior
K1/Np.
+ K-
(l + '/d)
straight pipe, 42-in.
..
fL d
{
(0.0130)(120
AP
:
For l0
rt"
2\32.2)
fr ".
(144)
sec'
ft x
4
ft x
42-Lrr.
{
o, nKr K- nK800 800 0.25 0.25 150 150 0.50 0.50 Kr
I r
R.un-thru tee
sec'
fr2
ln.' --:-
transition piece,
th
tsrtterfly valve
il
D:68.571 in.: L = 4.0ft: K:0.615
3.438
es and Fittings
0.75
950
( _
(r 3r .oo,12
-19,
30)
ii-\'alues
\:lr
to.oiU
0.271 psi
section
-
4.271
\d -
ft
From Equation 1-8,
t :
:
qso -" | (0.75) /ll I _lr\ = 0.770 662.224 \ 4t.251
* - [
0.005 psi
AP
=
0.005 osi t27.912t
i.De entrance at turbine nozzle
l .000 0.161 1.000 1.000
.lrste heat recovery unit entry duct
l-rck exit
'
0.140 in. H2O AP thru heating coils Total
rl-in.dx30-in.d
2132.2)
AP
:
Itirer K-values
(0.031r: (47.458), j , Itsec' o u,rl fr2 I :fr
:
t
psi
2 in. H:O
+
0.140
9.704 in. HrO
<
l0 in. allowed
=
sec'1144) = ln.'
in H,O ar 62.F '::::::L
7.564 tn.
AP
ff2
in. + 2.000 in.
OI
AP
:
3. 161
:rr
a rectangular duct,
i.=ab/2(a+b)
EXAMPLE I-4 PRESSURE DROP IN RELIEF VALVE PIPING SYSTEM
:-'r round pipe,
i. =
Di4
a+b 68.571
_
in.
:
2(10)ft (4)fr
l0ft+4ft
_ < ",,
r,
Equivalent circular diameter
Relief valve piping systems are designed to have minimum pressure drop. In this application the plant rules stipulate that the pressure drop will not exceed 3 % of the valve set pressure. The system is to have two valves, shown in Figure 1-21. The relieving fluid is Freon 114 and the flow rate is W :243,755lblhr. First we compute the velocity heads, or K-values.
Mechanical Desisn of Process Svstems The total pressure drop for 6-in. and 4-in. lines
Pr
:
3.869 psi
Set pressure
:
+ 5.935 205 psi
psi
:
:
Pr
9.804 psi
%^P:#:4.8vo>3vo Consider moving 6-in. x 4-in. swages above gate valves and making 90" LR and gate valve 6-in., as shown in Figure 1-22. Recomputing the K-values we have
K : 30 fi : 30(0.015) : 0.4s0 K : 8ft : 8(0.015) : 0.120 Entrance, K : 0.780 Tee, K : 0.900 6-in. 90' LR ell, K : 0.450 6-in. gate valve, K = 0.120 6-in. x 4-in. swage, K : 0.019 6-in. 90' LR ell, 6-in. gatevalve,
+
D*:
Figure 1-21. Relief valve piping system. For 6-in.
60
ft =
60(0.015)
:
:
60'
From Figure 1-7,
-
0.,141)(sin 30')05
0.194
4-in. d 90' LR elbow,
k:
30
ft
:
30(0.015)
:
=
1.019
0.450
4-in. gate valve,
8(o.ol5)
:
o.l2o
6-in. d line from entrance thru swage, Lo
:
5
B
: I :
Entrance,
1.0
K:
+r( = 8ft : 0.78
ft
\-r
LtK : 0.'78 + 0.90 + 1.019 : 2.699 AP : 3.869 psi; Np" : 14,931,929 V : 37.002 tusec; f : 0.01741 4-in. line from swage to relief valve, L4
Dr
V
=
:
5
ft
= o.oso+o.l2o =
0.570 5.935 psi; NRe =22.494.325 :83.973 ftlsec: = 0.01913
AP
f
10
ft
The pressure drop in the system in Figure 1-22 does not exceed 37o \p to the relief valve as the plant rules require, thus, Figve l-22 is the final configuration. Latet in example 2-5, we will examine the structural integrity of the system.
6:d,:4.@6=o.ao+ ' d2 6.065 0.5(l
:
205
0.900
6-in. x 4-in. swage nipple = 0
K:
line from entrance through swage, Lo
AP = 4.869 psi: Ns. : l4,g3l,g2g V : 37.N2 ft/sec; f = 0.01741 Vo AP :4869 : 0.024 = 2.470 <37o
6-in. tee
K:
@
z.zas
Flgure 1-22. Relief valve piping system.
The Engineering Mechanics of
: a. : AR : b. : c: d= D:
sonic velocity of sound waves in compressible medium, ft/sec rheological variable, dimensionless ratio of branch area to header area, dimensionless rheological variable, dimensionless experimentally determined flow constant where c plE" for a Newtonian fluid inside diameter (lD) of pipe. in.
f: F: g:
g"
:
Ha: He: k K KL n'
= : : = = Nr" : P: Rn : u= v: Y:
:
inside diameter (ID) of pipe, friction factor, dimensionless
ft
: 6: d
"y
e
angle, degrees ratio of smaller diameter of pipe fitting to larger
=
:
p= y=
cr
:
diameter generalized viscosity coefficient lb'/(ft)Gec) absolute roughness or effective height of pipe wall
irregularities, ft absolute (dynamic) viscosity, centipoise kinematic viscosity, centistokes angle, degrees
head loss, friction ioss or frictional pressure cm(kgr) droo. ft(.br) .
'. lb.
cm/sec-
English system conversion factor, 32.17
lbt energy added by mechanical devices, e.g. pumps, ft(lb)/Ib.", cm(kg)/g. energy extracted by mechanical devices, e.g. turbines, f(lbr)nb*, cm(kg)/g. specific heat ratio (adiabatic coefficient), Co/C, velocity head, (ft)(lb)/lb* velocity head for a large fitting at Np" = o length of pipe or piping component, in. rheological variable, dimensionless Reynolds number, dimensionless
l!lt9,
REFERENCES
g.
gravitational acceleration constant, 32.2 ftlseczl
pressure,
kgrlcrfi
hydraulic radius, ft, in' average bulk velocity, ftlsec velocity, lblt(, kgrlcrfi height above datum, ft, cm
45
Greek Symbols
NOTATION
al
Piping
1. Simpson, L.
2. 3.
L.
and Weirick, M.
L.,
"Designing
Plant Piping," Chem. Eng., April 3, 1978. Metzer, A. B. and Reed, N. C. A.l.Ch.E. Jownal, vol. 1, no.434, A.S.M.E., New York, 1955. Rase, H. F., Piping Design for Process Plazts, John
Wiiey, New York, 1963.
4. Govier, G. W. and Aziz, K., 5.
The Flow
of Complex
Mixtures in Pipes, Robert E. Krieger Publishing Co., Huntington, New York, 1977. Crane Co., Technical Paper No. 410 Flow of Fluids, Crane Co., New York. 1981. HVAC Duct System Design, SMACNA,
6. SMACNA,
Vienna, Virginia 1981.
7. Hooper, B., "The Two-K Method Predicts Head Losses in Pipe Fittings," Chem. Eng., Ang. 24, 1981.
8.
Sabersky, R. H. and Acosta, A. J. Fluid Flow-A First Course in Fluid. Mechanics, The MacMillan Company, New York, 1964.
The Engineering Mechanics of Piping
Static and dynamic analyses require clear and precise c.efinition of terms-their misuse can often lead to mis:-;nderstandings, a problem the engineer greatly appreciThe application of engineering mechanics to piping "tes. :s mainly referred to in industry as "pipe stress analy-.rs." However, the term is not comprehensive enough recause engineers are usually more concerned about :orces and moments exerted on equipment than stress. Cerrainly, stress is a concern and is discussed along with
rtier
These forces and moments are controlled by structural supports attached to the piping using pipe supporrs ro control forces and moments in the pipe and attaching components bring up two fundamental concepts-stiffness and f lexibility-which are discussed later in this chaDter.
phenomena in the chapter.
PIPING CRITERIA
-{nother popular term used in industry is "piping flex-:ility analysis." The word flexibility can pose a prob-em because in the stiffness method of analysis
In analyzing piping mechanics, the following parameters must be considered:
it is actu-
-:lh the structural stiffness of pipe supports, rather than :ieribility, that is important. For this reason the term -'piping flexibility analysis" is avoided. piping component is any constituent part of a piping -\ .-, stem, of any finite length of pipe-a valve, flange, el:\.\\\'. pump, or anything else within the piping system. llping is supported for various reasons-an obvious one -rng to counteract the force of gravity-and to begin to -:rderstand the applications we must start with some baa.: concepts. Consider a piping component as shown in Figure 2-1. i{:re we have a three-dimensional axis system with the : rmponent-a short length of straight pipe-subjected to
1. The appropriate code that applies to the system.
2. The design pressure and temperature. 3. The type of material. 4. The pipe size and wall thickness of each pipe 5. 6. 7.
rrces and moments about each axis. The forces and moare considered as vector quantities and often ex::essed in terms of resultant vectors. For convenience u'ill express resultant vectors in terms of a resultant :.ror operator defined as follows: ' :
8.
:.nts
::
;
\.\.2)
-je -J
: ,tll*-Z
com-
ponent.
The piping geometry including movements of anchors and restraints. The allowable stresses for the desisn conditions set by the appropriate code. Limitations of forces and moments on equipment nozzles set by API, NEMA, or the equipment manulacturers. Metallurgical considerations, such as protecting material from critical temperatures, like carbon steel below its transition temperature.
For any piping system, these criteria must be considpiping system, it is not always necessary. For example, a system having only two terminal points and pipe of uni form size does not require a formal analysis if the following approximate criterion is satisfied: ered and satisfied. While it is sufficient to analyze a
(2-1)
resultant force and moments change in magnitude
direction along the length of the piping system. 47
Mechanical Design of Process Systems
Figure 2-1. An element in a pipe wall is subjected to four SIrESSES.
onlv code that is different from the ASME codes is the Geiman DIN code, where the basis of yield is different' The code basis and theories of yield are discussed later' Reeardless of what ASME codes are used, the user is cauti6ned that the codes are written by ASME to be euidelines and not design handbooks. The intent of the lodes is merely to set minimum rules and procedures for desrgn. This does not include operation ofplants' Operationil problems are not intended to be governed by ASME codes. Such problems as bowing of the pipe and geysering are considered operational and are not consrdered as design Phenomena. Pioine codes-are not the only ones with which the desien'eniineer should be familiar. It would be expedient utia n.t-pru if he or she is familiar with ASME Section
(2-2)
o?w"" where
D, =
-y =
L=
: C: :
U
outside diameter (OD) of piPe. in' (mm) resultant of total displacement strains to be absorbed by the piping system. in (mm) developed length of line axis between anchors, ft (m) anchor distance (length of straight line joining anchors), ft (m) 0.03 for U.S. units 208.3 for SI units, in Parentheses
Usually. however. the piping sysrem has either more rhan two terminal points or not all of the previous cnterla are met, and a formal analysis is required' After the first five criteria are considered the next and foremost factor to consider is Step 6-the allowable stress of the pipe. To determine this, one must reter to the appropriaie code that governs the piping system-' The following are codes applicable to industrial piplng ln the United States: ASME 83l.
I
piping
Piping-governs -Power in the Power industries (e'g''
high-Pressure steam lines) ASME B31.3-Ct emical Plant and Petroleum
RefinerY PiPing-governs PiPing sYstems used in the chemical
and Petroleum industrY ASME B31.4-Zt qiid Petroleum Transportation
PiPing SYstems
ASME 831.5-RdiEeration Plnins . ^. ASME 83l .8-C,as Transmission and ulstrloution PiPing SYstems ASME Section |II-Nuclear PiPing' Most foreign codes are similar to the ASME (American Society of Mechanical Engineers) codes' particularlv as fai as the theoretical basis is concerned' lne
Also, the AISC (American Institute of Steel Construction\ Manual of Steel Construction is mandatory in the design of structural supports-a requirement that will be obvious later. 'The reader will notice a stark contrast between the ASME and AISC philosophies of codes' The AISC Manual of Steel Constiuaion is intended to be a design handbook and is considered as such. AISC' unlike ASME' covers all industries of steel construction, from the buildine of tall office buildings to major chemical plants ' Unlike ASME, the AISC codes give a commenta'ry on what bases are used in formulating the code and why much these bases were used' It cannot be emphasized too civil and mechanical crosses mechanics that engineering A States United in the known as aisiiplines ensindrine kniwleaee"of some of both is necessary to understand the overill perspective of piping mechanics' ln satisfuing Step 6 in the list of criteria, once the appropriate iodi is selected. the system must be analyzed io ditermine if any portion of the system exceeds the allowable stress given by the code' The allowable stress br the cide is' in the ASME and most foreign of fail"i;;; EoA... Uu."a on ttte maximu-m shear stress theory itrit tft"ory is based orfthe fact that a material yields "i". when the maxihum sheir stress equals the yield stress' data This theory is in good agreement with experimental for and rnO"i .,"ufv stati and iatigue stress conditions
vnl Di;. I and II.
reason has been adoPted' this --iince
tnowledge of thi different theories of yield is pip-ing noi dir""tly pertiient to industrial applications of further for Ill r."ft-i.., the reader is referred to Fairesstresses are rewhat note to pertinent is It discussion. cuired bv the codes in analyzing piping systems' ' An element of pipe wall subjected to four stresses ls pressure shown in Figure 2:i. The pipe is under internal and the four stresses are as follows:
oL oc
: :
longitudinal stress circumferential or hooP stress
The Engineedng Mechanics of
rR
Jr
: :
radial stress shear or torsional stress
The longitudinal stress is the sum of the following dlree components:
l.
Bending stress induced by thermal expansion. For straight pipe: oB
M : ,7 LM
Q-3)
For curved pipe:
oe: _M.| LM
(2-4)
stress induced by the weight of the pipe. (This stress should not be a consideration ifthe piping is properly supported and will not be considered in this analysis.) ,1. Longitudinal stress induced by internal pressure.
"' = Pi
:- =
lle
oBL
+
(2-6)
oP
circumferential or hoop stress is caused primarily by
::ernal pressure. Thus.
,- = P(D - 2Py) 2tE
(2-'7)
i ,: thin-walled cylinders op is negligible. However, for --::k-walled pipe, the following relationship may be --'d for determining the radial stress: rozPo rozri2(Pi -il --l- _- Gt:'5r
__ -
ic ,_
r,2P,
shere external pressure,
-T |
Po)
P6
(2-6)
-
lZm
::ie
(2-11)
stress range reduction factor
for cyclic condition
Total no. of full temp. cycles over expected life
< < < < <
7,000 14,000
22,000 45,000 100,000
Expansion stress, caused by thermal expansion, must not exceed the allowable stress range, oo, and is defined:
oe=[@s)2+4(o)2]
(2-tz)
The piping codes further state that the sum of the longitudinal stresses caused by pressure, weight, and other sustained loadings shall not exceed op. This also includes the longitudinal stress caused by internal pressure, op, defined above. When torsional stress becomes significant, as in many multiplane systems, the resultant fiber stress, or combined stress, is determined by the following:
t = llor+
op
*
[4(o1),
*
(o1
-
op)r]05]
(2-13 )
0, we have
PBIMARY AND SECONDARY STRESSES
rilP; _ rotr,.P, h: - ri2 (ro, - ar,)r
l::.ional or shear stress
f :
O.25 oe)
(2-s)
3ecause both longitudinal stress caused by internal pres.-re and bending stress act in the same direction,
49
Direct shear stress is negligible and is not considered when caused by the piping temperature, because local yielding or "creep" reduces the stress at piping components. Local strain hardening restricts the local yielding and prevents the material from rupturing. This phenomenon of locai yielding reducing stress is termed "selfspringing," and has the same or similar effect as cold or hot springing. The operating stress ("operating" is used because it can be either hot or cold) diminishes with time. This change in stress is compensated for by the allowable stress range, which is the sum of the operating and down condition stresses and remains practically constant for one cycle. This sum is obtained as follows:
ot : f 0.25 o" i
2. Bending
Piping
(2-9)
is (2-10)
torsion is generated in a multiplane system.
These two concepts are very important in analyzing piping mechanics problems. A more detailed discussion of the various types of primary stresses is given in Chapter 4. The reader is encouraged to review Chapter 4 for an understanding of pressure vessels, as well as this chapter for help in solving piping mechanics problems. Secondary stresses are called self-limiting or selfequilibrating because as they increase in magnitude, lo-
50
Mechanical Design of Process Systems
cal yielding causes local deformation which in turn reduces the stresses. Self-springing is an example of this ohenomenon. -
Primary stresses are not selflimiting because as they increase, local yielding does not reduce them. One example of primary stress is internal pressure. Under sufficient pressure a pipe will undergo local yielding and deform, but the stress will not diminish and the pipe wall deformations will be excessive and unacceptable. For this reason, it is necessary to assign lower allowable stress limits to primary stresses than to secondary stresses. This fact is extremely important, as prlmary and secondary stresses are evaluated differently' and have different allowable limits. It must be remembered that piping and vessel codes give allowable stresses only for primary sresses. Secondary stresses must be assigned allowable limits as shown in the following discus-
e
---:>
Figure 2-2. Stress-strain curve.
sion.
ALLOWABLE STFESS RANGE FOR SECOI{DARY STRESSES The most important secondary stresses are those induced by thermal expansion (or contraction) and surface discontinuities, the latter being more relevant to vessels. The most widely used approach in designing equipment' vessels, and piping is to keep the induced stresses in the elastic range. In the case of ductile materials, the elastic range is well defined by the minimum yield point. Ductilehaterials are often used in piping systems subjected to loads that induce secondary stresses. Materials that do not have a well defined minimum yield point are designed on the basis of their ultimate yield strength, which is the maximum tensile load divided by the original cross-sectional area of the specimen. The minimum yield point is the tensile load required to develop permanent deformation in the material. Materials that do not have a well defined minimum yield point are generally not used temperatures and in piping systems 'Thus, subjected to extreme to those materiapplies this discussion presiures. yield als with minimum Points. Consider the stress-strain curve shown in Figure 2-2' Here the metal specimen is loaded to point A and then unloaded. Because point A is the minimum yield point' no deformation occurs because the material is still in the elastic range. Now, consider Figure 2-3 where the material is loaded beyond point A' Because the minimum yield point is exceeded, plastic deformation sets in that permanently deforms the material to point B. When the specimen is unloaded, er is the amount of permanent deformation, denoted by point C. Point B' is the theoretical stress point if the material had not deformed to point B. Figure 2-4 shows a case where a specimen is loaded
Figure 2-4. Stress-shan curve.
The Engineering Mechanics of
inro the plastic region. For complete plastic deformation to occur, the entire area ofthe pipe wall must exceed the minimum yield point. This would not be acceptable in practice because of permanent deformation and the pos-
sibility of rupture. There are acceptable cases where the loads will fail between Figure 2-2 and Figve 2-3. This condition is shown on Figtre 2-4, where part of the pipe wall is in the elastic range and the other part is on the plastic region. For cases where the portion in the plastic range is small compared with the portion in the elastic range, the amount of permanent plastic deformation is imperceptible. For this reason, the distance between points A and B m Figure 2-4 is small compared to Figure 2-3 because the portion of material in the elastic range limits the amount of permanent deformation . Thus , when the spec-
51
imen is unloaded, residual stresses are developed that cause reverse yielding when the material exceeds the compressive yield point. This is shown graphically in Figure 2-5. The specimen is loaded to point A and an excessive load deforms it to point B. At point B, part of the material is in the plastic range and the other portion is in the elastic range. When the specimen is unloaded, the stresses in the material go into compression shown at point C. Residual stresses caused by the combination of material in the elastic and plastic regions make part of the material exceed the compressive yield point and the specimen deforms from point C to point D. Upon application of the same initial tensile load, the material is loaded to point E. Point E is larger in value and, thus, to the right of point A, because the initial loading of part of the specimen into the plastic range causes strain hardenB
I tl
ll
,l
,l
STBAIN
Frgure 2-5. Stress-strain curve.
Piping
=>
52
Mechanical Design of Process Systems
ing and, thus, increases the minimum yield point of the material. As excessive loads are applied, the minimum yield point E is exceeded and the material deforms to point F. As the material is unloaded again the initial process repeats itself and the stresses in the material move to point G and then to point H as the compressive yield point is exceeded. Point Q represents the stress in the loaded condition after several loading cycles, and point P represents the stress in the unloaded condition. It is possible that no significant plastic deformation will occur after many load cycles. However, should stress values of Q and P exceed the fatigue limit of the material, small cracks will propagate throughout the strain-hardened material. After the small cracks appear, further cyclic loading will result in brittle fracture failure. The stress magnitude P results from the specimen being unloaded when the load condition, point Q, is reached. Thus, since Q is the tensile stress opposite to the compressive stress P in the parallelogram OB'QR the sides OB' and QP are equal in iength. Therefore, Q : 0.5 B'. Fracture by strain hardening will not occur if the theoretical tensile stress B' does not exceed twice the minimum yield stress of point A, and the magnitude of Q does not exceed the ultimate yield strength of point A. When a ductile material, that is a material with a defined minirnum yield point, is subjected to repeated loading, a certain behavior occurs. When a component, such as a nozzle on a header pipe, is repeatedly loaded and unloaded, the strain hardening makes the material stronger from load cycle to load cycle. As the material becomes harder, it is better able to resist yield. However, the maximum point at which this repeated loading cycle can occur is 2oyp. The stress o : 2ovp is the limit ofthe maximum stress range. This process is called elastic shakedown. that is. the material "shakes down" to an elastic response, and undergoes deformations or strains induced by loads beyond the minimum yield point of the material. It must be noted that at elevated temperatures the value of 2oyp can be altered by hydrogen embrittlement. Carbon steel exposed to hydrogen at elevated temperatures can fail during elastic shakedown because the hydrogen combines with the carbon causing embrittlement. The relationship between the maximum stress range and the initial yield point can be expressed as
o1,s
3
where
This analysis indicates that the allowable stress should be based on the yield point rather than ultimate strength. The material's ability to revert into compression and
limit itself to the amount of permanent plastic deformation is termed "shake down." The material "shaking down" limits the amount of deformation and, thus, has an elastic response.
From this discussion, we see tlat there is a range of allowable stresses available. Direct membrane stresses are limited by oy, bending stress is limited by l.5oy, and a limited, one-time permanent deformation from A to B occurring from secondary stresses is limited by 2oy. Table 2-l gives recommended values for design allowable stresses. As shown in ASME Section VIII, Division I, paragraph UA-5e, different stress levels for different stress categories are acceptable.
FLEXIBILITY AND STIFFNESS OF PIPING SYSTEMS There are two basic approaches to piping mechanics-
flexibility and stiffness. The former approach is more common and easier to understand. Piping mechanics (more popularly known as "pipe stress") is often referred to as "flexibility analysis," but it will become obvious in the following discussion that such a term is not complete. In the flexibility approach, the piping configuration is made more flexible by using loops that allow the pipe to
Table 2-1 Allowable Stresses' Pressure Component Design Conditions l. Internal pressure . ....... oA 2. Internal Dressure plus therinal loading . ... . 1.25 (oa * op)
3.
Temporary mechanical
overload
.
4. Hydrotest
..... . . ...
l.33oa < oy
oo X hydrotest factor
Non-pressure Components Design Conditions
1. Pipe supports
and connections other
than
bolts
2. Bolting
.. ... .......
1.330a Per AISC Manual of Steel Construction considerable
savinss in material can be
incuried if high strength bols are utilized, such as Zoyp
MR : YP :
(2-1,4)
maximum local stress range not producing fatigue failure, psi initial yield point of the matedal at the operatrng temperature, psl
SA-193-87. Followins AISC guidelines in n6n pressure components
result in prudent economical desisn.
'
Courtes) of American Socier) o[ Mechanica] Engineers
will
The Engineering Mechanics of
displace itself, resulting in lower stresses, forces, and moments in the system. This method is often the most desirable when relatively inexpensive piping material is used (pipe elbows can be very expensive in alloy piping) and space is available for the loop(s). However, the stiffness method becomes quite important when the flexibility method is neither practicai nor economical. When limited space reduces piping flexibility or makes it irnpossible or undesirable to use flexibility loops, restraining the piping using the stiffness of pipe supports becomes the alternative. This approach is gaining popularity with the increased use of modular designs of petrochemical plants, offshore platforms, and other industrial facilities. The following is a summary of the advantages of both methods: St iffne s s Me
l.
2.
thod Ady anta
Piping
A piping element has six degrees of freedom, three in translation and three in rotation, as shown in Figure 2-6. The amount of force or moment required to produce unit displacement in each degree of freedom at points all along the piping element is described mathematically as the stiffness matrix. K. which is defined as
P:KU where we have an elastic element subjected to a set of n forces and moments
(2-ts) the corresponding displacement of each by the matrix
P1
is described (2-r6)
g es
Requires less pipe fittings and is thus more economical than flexibility method, because pipe restraints required are far less expensive than the number of fittings they replace. In alloy piping these savings are enormous. Requires far less space for piping, such as in modu-
Iar skid-mounted plants, offshore platforms,
53
and
Therefore, the stiffness matrix can be expressed
as
p (2-17)
U
which can be in pounds per inch or foot pounds per degree. The relationship
ships.
3. 4.
Method is safer because in case ofa failure, such as a leak in a weld crack, the pipe restraints can (and have) kept systems from blowing apart. Piping and system is more resistant to dynamic loads, such as vibration and seismic shock loads.
Flexibility Method Advantages
1. Utilizes simpler pipe supports, and requires less piping engineering skill. 2. Is more desirable in noncritical systems, e.g. exhaust and flare lines. 3. Many solutions do not require a computer. The problems can be solved manually. To better understand these two methods of piping me-'hanics, it is necessary to examine some basics of struc::rral analysis. Stiffness is the amount of force or moment reouired to :ioduce unit displacement. either translational or angu-
-.lr movement. The simplest concept of stiffness is to ::nagine using X pounds to compress a spring one inch. Thus, the spring stiffness is in terms of pounds per inch. This simple example illustrates translational stiffness. Rotational stiffness can be thought of in a similar manner as a spring that resists rotational movement, foot-pounds rer unit degree of movement.
II
(2-18)
P
is defined as the compliance or flexibility matrix and can be in inches per pounds or degrees per foot-pounds. Thus, the stiffness K ofa system is the inverse of the system compliance or flexibility, C, that is, the piping system becomes more flexible, or less stiff than its initial
configuration
.
The system stiffness matrix, K, is made up of elements that are either direct stiffness or indirect stiffness components. The direct stiffness component K;; is the value of stiffness at the point i when the displacement U1 is produced by a force or moment P acting in the direction of U1. The indirect stiffness Kij is the value
the point
of stiffness
at
j, with the displacement Uj acting in the direc-
tion ofj, due to a force or moment at another point i in the direction of i. The indirect stiffness can also be thought of as relative stiffness-those stiffness values induced by forces and moments in the system other than the point in consideration. It is the combined grouping of the complete direct and indirect stiffness values that form what is called the "stiffness matrix." Each direct and indirect stiffness is considered in the matrix when all other matrix components are zero. Such as the system described in the followins:
Mechanical Design of Process Systems
translational stiffness for a beam element fixed on one end and pinned at the other end is
P:
tmi
HniHtrHl iil] *11-u:J
Q-1e)
lH ft: e ft [:
where the values K11, Kzz, Fv:z, K44, K55, and K66 are known as direct stiffness values and all the other compon"rrt. u." known as indirect stiffness values' Each value of U represents a unit displacement. The components ol (a'tial the stifiness matrix are ditermined by the nature force, bending moment, shear force) of the force or moment inducin! unit displacement U at or arvay froT the point in que.iion. To eifectively see how these stiffness io-pon"nt, ur. utilized in practical applications'.we will consider each type of force or moment rnduclng olsolacements, thai is, each component of the P matrix coriesponding to each value of the U matrix' Table 2-2 lists in"'airect'uatues of stiffness induced by direct and indirect loadings shown in Figure 2-6. For analytic derivations, the rlader is referred to Przemieniecki [2]' To illustrate how these concepts apply to piping mechanics, let us consider both a 4-in. schedule 40 pipe and we a 10-in. schedule 40 pipe shown in Figure 2-'7 He,re a to. are considering two pipe spool pieces subjected me that force F shown. Referring to Table 2-2' we see
-n't :
3EI t_3
For the 4-in. PiPe, K4
:
x 106) ${r.zr) ------GD3 ini 3(29
in.o
:
S,Oal.OO
P m.
For the 10-in. PiPe, 3(29
Kro =
-
x lo) |rtoo.s) (48)' in
ln."
=
'
r26,497.40Y
l/+ The force required to move the 4-in. pipe
F
:
lh (5.687.66t .11 (0.25)
in.
=
1n.
in'
is
1.421.92 lb
To generate the same amount of force in a 10-in' pipe the same length would have to move
|,421.92 lb
zo,qsl.+o
:
0.011 in.
!ln.
Figure 2-6. Pipe element.
The Engineering Mechanics of Piping
Table 2-2 Stittness Properties ot Piping Elements
*"t
rl'>'*-
Ktt=Kr:?
->x
-(*--u
f
AF
r,,:r,,:4EL K:r:IQr:K5r=Iqr=0 Kzz=Kqz:6tr=lQr=0
-""/
_- = or,
tzEl il-+ e)L3
^44:(l+o)L:
,, :
-lzBl 11 1oy rr
,. : - tzEr ^" rJi) IJ-
^.-_____________ TT T/ f-l
&::ree:d#r,
Tu
,.
Ky :
Koq
:
6EI
.-=1+o)Ll
,=---.---=
/P t"t --(.4-=-Y/^-
f.r
.lffil
/,
o-------4 "(\YI t<----_T+ r\55
:
466
(4 + O)EI : .-);-L(r r:-=: 9,
Note: In all cases
-6FI Krs=K:r=illo)U
l2Er
(
: rqi = {1 + O)tr
l--------9)'
,/
\.t
Kla:K2a:0
K53
\-1._________J
A\l l,k r\
Kr::Kzs:0
^or
K..
t"
-
lzBr GALI
and
-K = cJ -:L
lorsronal sunness
Kes
=
Kso =
(2
-
a)EI
L(l + O)
56
Mechanical Design of Process Systems
g ,r, 10Q SCHEDULE 40
FOR ONE END PINNED AND THE OTHER FIXED K1o
K,, =
'
-3!.L-
))
K4
\
l1+olL'
a"q scHeoure
Figure 2-7. Comparative stiffness.
In other words, if the pipe itself moved because of ther-
mal expansion and theie was a restraint of a given spring ."tttuioing the movement, the 10-in' pipe would "onrt-t onlv have to rnonJ0.0l I in. to exert ihe same force as the'4-in. pipe moving r/+ in' Thus' the l0-in pipe is the 4-in' pipe, which is a -ore tltun 2i ti-es stiffer than the .igrifi"-t point because it indicates that the larger oiloine. the'less it must move to exert excessive forces Iria rio."ntt on nozzle connections and pipe supports'
the p^ipfi". ,fti, example it is obvious that the largeroften fail i*. tt'" *t"ut"t itte stiffness' Piping designersmove very
piping does not have to toiealizJ that larger -greit
ioads . This basic fact is important
much to generate
in ttt" OE ign of-pipe supports, particularly using the
-stiffness apProach.
iarrvine^the analysis further. consider the two piping shown in Figure 2-8 This situation is "oniit,itu,iont similir to Figue 2-7 in that one end is fixed and the other pinnedi'e., both systems have the same boundary The segment-B-C is flexible enough to bend """Jit'i"".. with enough rotatidnal flexibility to consider tut "ld^:: piping is -luu' a pinned j6int. lf the temperature ofthe moves B-C f, the segment M a: (-1.75)do,o'ft = -o.o70in'
The force required to move a 0.070 in. is
Fq:
(5.687.66)
th
I
4-in
tO.OUOr in. =
schedule 40 pipe
398.14 lb'
Figure 2-8. Pipe size makes a significant difference in nozzle loadins.s.
The Engineering Mechanics of Piping
The force required to move 0.070 in. is Fto
=
oz6,4s7.40r
a l0-in.
Itn. to.ozol in. :
schedule 40 pipe
Aluminum exchanger llange
8,854.82 rb
l ielding a moment of
vro:
(8,854.82)(4)
:
35,4r9.27tt-lbl2
:
l7,7o9.64ft-tb
at the nozzles A and B. The 4-in. force of 398.14 lb would nroduce a moment
\'r1
:
(3e8.14)
at nozzles
! :
na.ze
of
uv
A and B.
It is clear that the 10-in. pipe would exert moments ell above the allowable moments for most rotating and stationary equipment. To reduce the loading at the nozzle, the engineer is faced with two options-make the piping configuration more flexible or restrain the piping. To fabricate the piping configuration to within a tolerance of 0.070 in. would be well beyond the practical range of any fabricating shop. First, we will analyze a case where space is premium and there is not enough room to make the piping more flexible. This requires using piping restraints to transfer loads from the pipe to structural steel or concrete. Consider the piping system in Figure 2-9, where two aluminum heat exchangers are piped parallel to one another. Here we use the fewest 90' elbows needed to give the svstem enough flexibility to stay within the maximum aliowable stress range for the material at the given temperature. Piping restraints are then placed close to the heat 3\changers to transfer loads from the pipe to the steel instead of the nozzle of the exchanger. Now, we analyze the component that makes the system $ork-the pipe restraint at the equipment nozzle. The :estraint's function is to transfer forces and moments exerted by the pipe to the structural steel below, simultaneously allowing the equipment to move freely. This requires a more careful design of the piping restraint, as .\e are expecting it to do more. In this example the piping restraints must allow the exJhangers to move upward as shown in Figure 2-9. A restraint that resists moments by transferring the moments :iom the pipe to the steel is termed a moment restraining support (MRS). Different types of MRS supports are shown in Figure 2-10. An MRS can vary from a boiled plate connection shown in Figure 2-10A to a sophistiiated type in Figure 2-10C. MRS restraints' sophistica:ion is a function of how much rotation is resisted and iow much translational movement is allowed. The most u
Exchanger
Figure 2-9. An MRS support-restraint designed to reduce forces and moments on an aluminum olate-fin heat exchanser.
simple MRS restraint is the anchor, where the pipe itself or a pipe attachment is welded down to structural steel or immersed in concrete. In that case, it is resisting three degrees of freedom in translation and three degrees of freedom in rotation. In most applications, the moments at nozzle connections can become excessive, and it is often desirable to resist rotation in one. two- or tlree axes while allowins translational movement. Resistine rota-
58
Mechanical Design of Process Systems
tion along three axes is, if not impossible, wholly impractical. An MRS allowing two degrees of freedom in
Restrainl
-
KTX, KTY, KRX, KRY KRZ
translation and resisting three degrees of rotation is quite complicated, although practical, very useful, and economical when the situation warrants. In designing such restraints Teflon and other materials with very low friction coefficients are desirable. Care must be made in assuring that such material selected can witlstand the forces and moments being resisted. If the material used is not resistant to shear, cold flow will result, leading to uneven surfaces and an improperly functioning restraint. In the engineering of MRS restraints, the principles discussed previously must continuously be applied. No support or restraint can be expected to be infinitely rigid along the degrees of freedom that are being restrained. Placing MRS devices in front of equipment nozzles will not stop all loading exerted by the piping, because all restraints have a corresponding stifftress value for each deg of freedom, either lbs/in. for translation or ft-lbs/deg for
rotation. The engineer must also understand what assumptions are being made by the piping stress program being applied. Almost all computerized pipe stress packages consider an anchor as six springs, three resisting translational forces of 10e lbs/in. and three resistine rotational forces of l0e ft-lbs/deg. There is no infinitel! rigid anchor in nature, but 10e lbs/in. is sufficient to be called an anchor in almost all applications. In modular plant design it is often desirable for the engineer to enter the actual stiffness of any anchor or restraint to obtain an accurate model of the piping system being analyzed on the computer.
STIFFNESS METHOD AI{D LABGE PIPING
-=a'/ C
Fesl€inl =
KTX, XRX. KRY KFz
Figure 2-10. Various designs of moment restraint supports (MRs)-arrows indicate direction of allowed movement.
--=4
Large piping is rnore difficult to restrain than small piping because of the surface to be restrained. The terms "large" and "small" are quantified in the following discussion. The most common complication of restraining large piping is the phenomenon of shear flow, which occurs longitudinally and circumferentially. As illustrated in Figure 2-1 I , longitudinal shear flow transfers bending moments and shear forces to the equipment nozzle. In modular construction longitudinal shear flow does not become a problem until one starts using l0-in. pipe and larger. Shear flow can be resisted to some degree by making the attachment pipe size or structural member size close to that of the pipe, but is most often impractical. What is often desirable is to mount an MRS on opposite ends ofthe pipe, either top and bottom or offto both sides, depending on what space is available. In piping 30-in. and larger MRS restraints must be attached on four sides for the MRS effect to be effective. In pipe di-
The Engineering Mechanics of Piping Nozzle flange I
_>
Hequrres
Restraining pipe with MRS at AandB required with pipe sizes -normally 12" d and over
Uniaxial longitudinal shear flow nozzle tlange
D
Requires
Restraining pipe with MRS at A, B, C & D required with pipe sizes -normally -30 " d and over
Biaxial longitudinal shear flow around points A and B
Figure 2-11. Longitudinal shear
meters 8-in. and smaller, attaching an MRS on one side is sufficient for most modular construction. Circumferential shear flow, on the other hand, is not a lactor in most installations because torsion is very effeclively transferred to the structural steel by the MRS resralnt. Using piping restraints to transfer loads to structural iteel or concrete to lower loads at equipment nozzles is 'becoming quite popular and more widespread because is more economical in modular skid design.
flow-a
phenomenon of large pipe.
equipment, it is often more economical and desirable to design the piping to be flexible enough to reduce loadings on supports and equipment nozzles. For pipe racks, long headers, etc. this method is the only practical approach to solving piping mechanics problems. Tools used
in this approach include such well known devices
and
techniques as piping loops, cut short and cut 1ong, and expansion joints.
it
Also, where
erpensive piping materials are used, the stiffness method can help reduce the number ofelbows used for flexibility end, thus, reduce the cost of the job because restraints and supports are far cheaper than piping elbows.
FLEXIBILITY IIETHOD OF PIPING HECHANICS
In non-modular skid construction (block-mounted plants) and areas where there is ample space to place
PIPE LOOPS The most common types of pipe loops used today are shapes, "2" shapes, and "L" shapes. Curves for these shapes showing stresses plotted against the loop dimensions are shown in Figures 2-12 and the equations are as follows:
"U"
F1
=
A1B -ll-
tu,
t" :
in.o
60
Mechanical Design of Process Systems
rol t
,I I
8l
,l Ry
6 5
it 3 2 1
tof I
"I I
"l _l Ry
6
1 3 2
I
Figure 2-12A. UJoop with equal legs'
The Engineering Mechanics of Piping
1o
Ry
4 3
1
ro 9
I 7
Ry
5
4
'|
to
12 14 16 1A 20 22
24
Ay
Figure 2-128. Uloop with one leg twice the other leg.
Mechanical Design of Process Systems
to
I a 7
RY
5 1
3 2
I
Figure 2-128 (continued). UJoop with one leg twice the other leg'
10
9
a 7
6 Ry
4
2 1
180 ^
z&
Figure 2-12C. UJoop with one leg three times the other leg'
The Engineering Mechanics of Piping
6 Ry
5
"* o,
ooo
Fv
10 t2 tO t"o,
22242a303234
Figwe 2-12C (continued). U-loop with one leg three times the other leg.
Mechanical Design of Process Systems
to
I I 7
Rv
4 3 2
tao
oo
22o
10
I a
6 Ry
4
2
I
15
2O o, ,o 1,
25
Figure 2-12D. Uloop with one leg four times the other leg.
The Engineering Mechanics of Piping
'to
I a
2oo
300
400
500
500
700
800
Figure 2-12D (continued). UJoop with one leg four times the other leg.
a
=
-i1 n=*
6
Ry
4
Ab
Figure 2-12E. UJoop:
"2"
configuration.
Mechanical Desisn of Process Svstems
a 7 6
Ry
4 3 2 1
10 20 30 40 50 60 m
80
gOAv
IOO llo
l2O l3O lr|o 15O 160 17O
a
Ry
4
1
40o
A,
so
Figure 2-12E (continued). U-loop:
"2"
configuration.
t8O
The Engineering Mechanics of Piping
"=E
Figure 2-12F. U-loop:
"L"
configuration.
Mechanical Design of Process Systems
Figure 2-12F (continued). U-loop:
Fv: AvB{lb, oo: -L , , SIF
A"B P osi.
L - fr. D =
rn.
Thermal movement (in./100 ft)Eo 172.800
=
1.0 (Verified by computer stress analysis)
Loops such as circle bends, double offsets, and other geometrics involving completed circular geometry should be avoided because they are impractical, expensive, and unappealing to clients due to their complexity. If excessive looping is required, the stiffness method should be used to produce a practical, economical solution. The use of both the flexibility and stiffness approaches in areas, where applicable, can yield very attractive and appealing piping designs. In pipe racks, the "U" shape loop is invariably the most practical shape to use because of its space effi ciency. "U" loops are normally spaced together (i.e., lines running together on a pipe rack are, where practical, looped together as shown in Figve2-13). It is desirable to guide the pipe on each side of the loop and at every other support thereafter as shown in Figure 2-14. Make sure the first guide is far enough from the loop to avoid jamming problems. Usually, this distance is twice
"L"
configuration.
the bend radius of an elbow of the pipe size being used. If you cannot put piping guides on the pipe coming down from the loop, then put them on the inside ofthe loop as shown in Figure 2-14.
"2"
Other configurations, such as and "L" shapes, are used in the normal routing of piping systems. It must be remembered that when these shapes are anchored on opposite ends, the ratio of the shortest leg to the longest
should
fall in the range of 1.0 to 10.0 to avoid over-
stressing the pipe. When analyzing the shapes by computer, any ratio can be used, but usually the aforementioned range is valid for most applications.
PIPE RESTRAINTS AND ANCHORS Pipe restraints are used to counter forces of gravity, wind, earthquake, vibration, and other dynamic forces such as water hammer. The most common type is the gravity support, which merely restrains the force of gravity. A piping restraint can act in one or all degrees of freedom. As discussed previously, there are no restraints that are infinitely rigid-each has its own spring rate in each degree of freedom of translation and rotation. Even an "absolute" restraint has in each desree of freedom a rranslational stiffness of tOq lbs/in. aidior a rotational
The Engineering Mechanics of Piping
Line smallesl in size aod has least lhermal movement is placed on inside
Lrne tnat has greatesl lhermal movement and targesl size is placed on oulsade to allow lor movement
Figure 2-13. Optimum grouping of UJoops.
stiffness of 10e ft-lbs/deg. Such a restraint that restrains a pipe in all degrees of freedom is termed an anchor. Piping guides are restraints that counter movement in one or several directions but allow total freedom of movement in one or more directions. Total freedom is defined as a stiffness value of zero. An anchor, by definition, has some value of stiffness in every degree of freedom, even though the anchor itself can move. The movement occurs while the anchor is still resisting movement at a certain stiffness in each degree of freedom. Thus, the term "sliding anchor" in place ofa pipe guide is erroneous, because guides have a value of zero stiffness in one or more degrees of freedom. An anchor can restrain movement, although it may move. It is important to be cognizant of restraint terminology to avoid unnecessary confusion. The stiffness of a support is not only a function of the restraint material, but also a function of the structural steel or concrete to which it is attached. Even thoush very stiff in compression. concrete is not infinitely stifi. As shown in Figure 2-15, the pipe restraint has a stiffness value K,, the concrete a stiffness value of K6, and the soil a value of IG. Because Ka ) Ks, the concrete can sink or move in the soil if the concrete support is designed correctly or if subsidence occurs. Movements caused by soil conditions should be the responsibility of the piping engineer as well as the civil/structural engineer. The latter is responsible for limiting such movements as much as possible, and the piping engineer is responsible for entering these movements in the stress computer run or manual calculations. It was mentioned earlier that for a pipe restraint to be considered absolute in one direction it must restrain one billion pounds per inch of translation and one billion pounds per degree of rotation. However, very few pipe restraints in nature are so rigid (an anchor being a restraint in three degrees of translation and three degrees
)
Figure 2-14. Guides are necessary for controlling movement
r: loops.
of rotation).
If
the actual flexibility of the restraint is
modeled into the pipe stress analysis, more realistic reactions and moments are obtained. In the case of nressure vessels much work has been done in determining realistic spring constants for nozzles. For application to rotating equipment, the reader is discouraged from using these spring constants, especially on equipment made of brittle material such as cast iron. Also, these spring constants are to be used only for ductile materials. Nozzle loadings should be based on either manufacturer recommendations or applicable standards. For further details and discussion of nozzle loadings on rotating equipment Frgure 2-15. Conceptualization
of system stiffness. Each -::rponent of the system-pipe, pipe supports, concrete, and .::--has translational and rotational values ofstiffness (matri-.: ilbout each axis. These values can be modeled into the sys'.- as springs, -
see Chapter 6. To treat a restraint with elastic end conditions, only rotations are considered significant. Deformations induced by radial force and other translations are ignored, be-
cause their influence is insisnificant.
70
Mechanical Design of Process Systems
The basic relationship for rotational deformation nozzle ends is applying Equation 2-17 as
M " ler I e
..P
=
-
U
where K : M = e : F :
I : Dy kf
= :
of
Angle of Twist Longitudinal
(2-r7)
180 -l-l [DNkr I
KRX or KRY, ft-lb/deg
Circumferential
moment, ft.lb angle of rotation, deg
modulus of elasticity of vessel metal at ambient temperature, Psl moment of inertia of vessel rLozzle, in.a diameter of vessel nozzle, in. flexibility factor, referred to in piping codes as
"k"
The flexibility factor, kr, is a parameter that has had several formulations over the years. One widely used variant was that proposed by the "Oak Ridge ORNL Phase 3 Report- 1 15-3-1966 ." Since this document was oublished in 1966, several revisions have been made' the current ASME Section III Division I code gives detailed discussions on the flexibility factor. If one is desiening piping for nuclear systems. then that person str-oula only consult that code. Outside the nuclear industry the piping engineer rarely knows all the parametersthat are necessary to compute the flexibility factor of Section III. Also, the piping engineer in nomuclear work rarely knows which vendor will supply the piping components, thereby making many Section III parameters unknown. Therefore, the more elementary "ORNLI" factors are Dresented here, because they produce lower values for [, which, in turn, produce higher, more conservative values of K. These factors are as follows: Flexibility Factor
c","o" Longitudinal
= K.:
Circumferential
.. - : MD"K, " - tracransl : H,
:
K"
(|i
tD
:
^
^. -,,8"8
lr\:
where C1
:
C. :
:H: ,
MD"IC. .. " - {fadl?llSl EI
0'09 for in Plane bending O.2'l for out of Plane bending diameter of vessel or pipe header' in. diameter of branch' in.
D= = E = modulus ofelasticity. lb/in I : moment of inerria of branch. in.a KL : longitudinal flexibility factor K : circumferential flexibility factor M : apPlied moment, in -lbs Or : longitudinal angle of twist, radians O. : circumferential angle of twist, radians t : wall thickness of vessel or pipe header' in. tB = wall thickness of branch, in
Dg
2
In-plane bending refers to longitudinal bending in Ihe pipe header or vessel in the plane formed by the interseciion of the branch and vessel or pipe header centerlines' Out-of-plane bending refers to circumferential be.nding in a plane perpendicular to the vessel or pipe header. diameter. These rotational spring rates are necessary wnen the stiffness of an anchor must be considered in pipe
sfess analySis.
PIPE LUG SUPPORTS These are about the most common pipe suppo(ts' The lug can provide a means for spring hangers or simple clevis-rod hangers. As simple as these supports are' a failure by one could result in loss of property or lives Thus, their simplicity should not allow one to take them for granted thinking that any design will suffice' Tie following method is based on the Bijlaard analysis discussed by wichman et al. [3]' Consider a pipe subiected to a load P (lbs), as shown in Figure 2-16 The lug
\T/
Rotational Spring Rate r-onsitudinal
=
Circumferential
*.: #or*[ry*) :
R"
Figure 2-16. Pipe lug support for a pipe with internal pres-
suie-primary and secondary
stresses must be added'
The Engineering Mechanics of Piping
connection is free of moments because the pin connection at the lug hole allows the pipe to twist in all directions. The usual oversight in designing a lug support is not considering the primary and secondary stresses, which must be added together and compared to the minimum tensile strength of the pipe material. First, we will discuss the Bijlaard method, which is only concerned with secondary stresses. The pipe and 1ug geometries determine the attachment parametet B, and the shell parameter, k, by
^C^L,RU ' 2Rna
2Ru
r ff> r,,
: [' - ](ui -
L
*,)] ')(' (B,B)os Q-20)
rr
pq
< | .u
: [, - i(-
'ff),,
-
",] (Btp)o:
(2-21)
where K1 and K2 are determined from Table 2-3. For circumferential stress, od, the circumferential membrane and circumferential bending stresses are determined by .l
f" - (f' ( f.l : r \P/RJ \R.V
T
=
H (9 -
circumferenrial membrane stress
.,,".u'r.,ential
bending stress
Figure 2-17. Membrane force, Na,/P/R-, induced by radial
The membrane force, No/(P/R.), is determined from Figure 2-17 or Figure 2-18, and the bending moment, \1"/P, is determined from Figure 2-19 or F\gure 2-2O. Stress concentration factors must be accounted for in the surface discontinuity between the rectangular surface rfthe lug and the circular surface ofthe pipe. The memlrane stress concentration factor for Dure tension or :omoression is determined bv
t : r+l/ 6w/ \5
\0.65
:< :rd
I
(2-22)
the concentration factor for bendine stress is deter-
Sned by
=,*(-t'\" \9.4wi
(2-23)
; here w, the weld size, is given in Thble 2-4 for various :-ite sizes. These values for w are only recommended
load P [3].
Table 2-3 Radial Load P Nd
N,
Kr
0.91
1.68
1.76
t.2
K,
1.48
r.2
0.88
r.25
Md
Table 2-4 Recommended Minimum Weld Sizes for Plates Thickness t ol Thicker Minimum Size, w' ot Fillet Plare welded (in.) weld (in.)
t
3/ro
51rc 3/z
!2 5/s
72
Mechanical Design of Process Syslems
100
+ :H
:
(9)
'"'r"'o''"r
bending stress
The total longitudinal stress is thus found by adding the two stresses,
N" ,, ,, o"T-^o
6M,
*
(2-2s)
The longitudinal stress and circumferential stress represent the secondary stresses in the pipe wall. These
primary stress which, in the case of internal pressure in the pipe, is the pressure stress. The pressure stress is determined by stresses must be added to the
I €tE z l:\
'2t
OD:
P"GD) .
DSI
Q-26)
Thus, the total stress for each secondary stress is as follows: oT
= q6+
op
Q-2',1)
oT:qx+op where o1
<
Q-28)
2oa
1
oy
Often, with large piping, a simple lug will be overly stressed because of localized stresses at the lug-pipe connection. When the lug attachment dimension, c, becomes small to the pipe radius, a clamp is normally put around
Figure 2-18. Membrane force, N-6/P/R., induced by radial load P [3]. and the engineer should use whatever sizes are actually to be used in practice. The total circumferential stress, ox, is determined by using these factors in the following equation:
*: "(9 **,(9
(2-24)
The longitudinal stress, ox, is determined in a similar way. The membrane force, N*/(P/R.), and the bending moment, M*/P, are determined from Figure 2 -17 or 2-18 and Figure 2-21 or Figure 2-22, respectively. These parameters are used to determine the longitudinal membrane and circumferential bendins stresses. where
\ : (\) (i'l = r-onnituainal membrane r \P/RJ \R.V
stress
the entire pipe with the lug attaching to the top of the clamp. This reduces localized stresses at the pipe wall by adding extra metal. This same principle applies to vessel nozzle reinforcement, which is discussed in Chapter 8.
SPRING SUPPORTS These supports provide loading to a pipe that has undergone displacement. Simple supports are no longer useful if the pipe raises off and loads are transfered to other supports or fragile equipment nozzles. To ensure support for the pipe while it moves, a moving support is desired. The most practical device to fill this requirement is the spring.
Springs come
in two basic categories-variable
springs and constant springs. The former, which is by far the most common, provides loading to a pipe at a fixed spring rate, lb/in., but the amount of force to deflect the
spring varies with the amount of deflection. This force versus spring rate is a linear relationship and is the reason for a "variable" spring. The constant spring is a
74
Mechanical Design of Process Systems
Mx
T .ol
p
.30 .35 .40 45
.50
Figure 2-21. Bending moment, M"/P, induced by radial load P [3].
Mx
-T
Flgwe 2-22. Bending moment, dial load P [3].
M"/l
induced by ra-
The Engineering Mechanics of
spring that will provide the same spring rate for any force great enough to cause initial deflection. Constant springs are used in critical installations where forces or deflections induced on the piping system are critical. These springs are considerably more expensive than the variable types and are usually avoided by piping engineers when not needed. Constant springs provide constant supporting force for the pipe throughout its full range of contraction and expansion. As shown in Figwe 2-23, this constant support mechanism consists of a helical coil spring working in conjunction with a bell crank lever in such a manner that rhe spring force times its distance to the lever pivot is always equal to the pipe load times its distance to the lower pivot. Thus, the constant spring is used where it is not desirable for piping loads to be transferred to connecting equipment or other supports. Variable springs are used where a variation in piping loads can be tolerated. As an example, consider the folIowing example shown in Figtre 2-24. The spring is above the pipe and is attached to it with a rod and clevis. This arrangement is called a spring hanger. As seen in Figure 2-24A, the spring supports the weight of the pipe and insulation. As the pipe heats up and expands it
moves upward. The amount of deflection, the amount of excessive force as F"
where
:
K: A=
75
A, relates to
AK' lb
(2-29)
spdng constant of spring, lb/in.
deflection, in.
It is common practice to calibrate
the hanger in such a manner that when the piping is at its operating (hot or
cold) condition, the supporting force of the spring is equal to the weight of the pipe. This means that the maximum variation in supporting force occurs when the pipe is in the down condition, when primary stresses are nonexistent because of no internal pressure. Therefore, in the cold position, the suppo ing force of the spring is
F:F"+WP where
WP
=
(2-30) pipe and insulation weight
To reduce the amount
of variability, it is desirable to
use the smallest type of variable spring provided that the
deflections will not exceed those of the spring range. Typical spring sizes and ranges are shown in Table 2-5.
--F
(A) F=Wt In thls case, hot
_
(B)
Hot Condition
Cold Position
Flgure 2-23. A constant load spring support provides constant .rpport loading in critical situations.
Piping
= operating condition, cold = down condition
Figwe 2-24. The "cold" and "hot" loading positions ofa variable spring hanger.
Mechanical Design of Process Systems
.eB
sg
9
sss
s
!,i to
g$ f;
bE89 EE$f;9Ffr;S FN&SRREhR 83RE $EHTEESgEP
9383
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egfi E$$3m$Ege$$$$8$gE
s8E8 ?bEr
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5
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ao
It)
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ctt
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ao .(g
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e
8
8
a
ri I
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dE
8
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N&RNRREhE&
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EsEpp:::$FFSppi33$EEq EESF FPRESbS$8588839:P:&ft
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83SE33633bEFFrRR8$$E3 s S
9E
g8
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ss (, F F
()
The Engineering Mechanics of
It is common practice to utilize the smallest spring
size
possible.
In critical and large systems, spring loadings should be eYaluated by computer analysis. Often, in large systems, piping movements are not intuitively obvious and errors can result because the entire system must be evaluated if a correct analysis is to be obtained. In most systems, hand calculations are far too cumbersome. Occasionally, springs are used as moment resisting devices, as shown in Figure 2-25. In such an application, the spring preloads the pipe in a specific direction. As the pipe expands or contracts, the spring counters the rbrce created by the movement and, thus, reduces the moment at an end connection. Such a system in normal practice usually works in the operating mode but when ihe system shuts down the spring overloads the piece of equipment protected in the operating condition. Thus, if such a scheme is used, care must be taken to ensure that Cre protected items are safe in both the operating and Jown conditions. These schemes can be avoided by use
..'i MRS devices where space does not warrant piping t-lexibility. lrcation of spring supports is of critical importance.
\\-hile springs should be placed where they will be most 3fficient, often such locations are undesirable from tle itructural engineer's viewpoint. The piping engineer :hould always be cognizant of available structural steel Lrr concrete and loads to be placed on structures. Most prings are supported from above at either mid spans or at elbows. Many times it is desirable to support the pipe tiom below. When using this type of spring, one must be .autious of pipe movement, as excessive movement ( >
l/a in.)
will
Piping
77
cause such a spring to jam, as shown in Fig-
rre 2-26A. To avoid jamming, a guided load column is used to prevent such a problem (Figure 2-268). Springs are often used to support equipment to reduce nozzle loadings, which are discussed in Chapter 6.
EXPA]ISION JOINTS These devices accommodate movement
in
piping
caused by temperature changes. Such items range from
special slip joints that only allow movement in the axial
direction to corrugated bellows joints that can be designed to accommodate movement in several directions. It is the latter type that we will concentrate on, as they are by far the most numerous and complicated of expansion joints. Corrugated bellows expansion joints have a bad reputation with some users because of ignorance. Many bellows expansion joints have been incorrecdy specified and the consequences attributed to the device itself. This is unfortunate because this device is invaluable when either re-routing the line is impossible or cold spring or other alternatives are not available. The surest way to avoid problems with bellows expansion joints is to have the piping (stress) engineer specify the unit and to procure the unit from a reputable manufacturer. The bellows expansion joint is like the MRS device discussed earlier because the more the unit is required to accomplish the more complex is its configuration. The simplest corrugated bellows expansion joint is the single
= momenl generated bY movement at Pl A lvla
\ )
t"
= moment generated
by spring
)L2Nozzle
Direction oI Pt A movement
Figure 2-25. Utilizing a spring to counter a moment generated by piping is appropriate only when the spring movement, Ms, does ilot overload the nozzle or overstress the piping system when the latter is in the down condition and there is no movement at A. This condition is required after the operating condition is met.
Mechanical Design of Process Systems
: : Figure 2-26'. (A) Enough piping movement will cock load flange andjam spring. Note: arrows indicate direction ofmovement. (B) A guide load column shown here will prevent situation in 1a--;. ttreie arJvarious designs for guide load columns, but for pipe movement greater than t/+" one should consider a column with rollers or Teflon on top;f the ioad flange.
bellows type shown in Figtxe 2-27 A. This specific joint is shown with flanges welded on each end, but is available from manufacturers with pipe spool pieces on each end to enable the unit to be directly welded into a line. The piping engineer should try to utilize this type ofjoint whenever possible because of economy and simplicity of operation. The single bellows is free to move in all de-
grees of freedom except about the longitudinal centerline. In fact. no bellows expansion joint can accommodate torsion and any tendency for the pipe to exert a high torsional moment could seriously damage thejoint. External restraints are placed on the joint to restrict movement in one or more degrees of freedom. Such devices are tie rods or hinges that restrict movement or pressure thrust. Figve 2-278-E are examples of joints that are so restricted. Following the same nomenclature shown in Figure 2-10, we consider each joint in a threedimensional axis system. KTX, KTY, and KTZ are the translational stiffness values lb/in., about the X. Y. and Z axes, respectively. KRX, KRY, and KRZ are the rotational stiffness values, ft-lb/deg, about the X, Y, and
Z
axes, respectively. For all bellows joints, (1.0 x 10') ft-lb/deg, as previously srared.
KRZ:
ln Figure2-27 A, we have finite values for KTX, KTy, KTZ, KRX, and KRI the joint is free to translate about three axes and rotate about two axes. The bellows does
not support its own weight so this joint would not be desirable where each end exceeds the maximum amount of pipe span shown, as calculated by the following equation:
L:0.131
: modulus of elasticity of pipe material, psi I = moment of inertia of pipe, in.a P : design pressure (psig) A : bellows effective area. in.2 K : axial bellows stiffness (KTZ in F\gure 2-21) E
The maximum length of unsupported pipe implies that the unit itself is within this length. Preferably, the joinr is close to one support or nozzle to avoid excessive deflec-
tron.
Thejoint in Figure 2-278 has values ofKTX and KRy KTY : KTZ : 10e lbs/in. and KRX = KRZ = 10e lbs/deg. This means that the joint is free to translate in the X-direction and free to rotate in the y-direction and is rigid in all other directions. This type ofjoint is called a "hinged" joint and is self-supporting in the y-direction shown in Figure 2-27 . Placing high vertical loads on a joint must be approved by the manufacturer. and
The Engineering Mechanics of The joint in Figure 2-27C has values of KRX and KRY irut absolute values of KRZ, KTX, KTY, and KTZ. Nor-
nally, these joints are used in pairs to allow rotation lbout two axes similar to swivel or ball joints and not ellowing any translation. This action is seen in Figure 2-
t8. The unit in Figure 2-27D is a pressure balanced uniersal joint. It is free to move about all degrees of move:nent except KRZ and is restricted by tie rods that bal.rnce pressure thrust. This type of joint is very common r
aa
in engine exhaust systems. Figrre 2-278 depicts one of the most complicated expansion designs-an in{ine pressure balanced expansion 'oint. This joint eliminates pressure thrust, is self-suprorting, and does not require a change in the piping sys:em to install. It is desirable where structural supports .ire not available and a joint is needed because flexibility rs required of the piping.
Piping
79
Pressure thrust is the amount of force generated by internal pressure and is simply internal pressure times minimum bellows radius area (PA), lbs. This force can become quite high as the pipe size and the internal pressure increase. In many applications, the piping itself is anchored and the joint is allowed to compress when the thermal compression force exceeds the pressure thrust force. As seen in Figure 2-28, when movement in the form of lateral translation is desired (KTZ and KTY), tie rods are used to restrain the joint in the axial direction @). If tie rods are being used to overcome pressure thrust, then any equipment flanged to the joint
(KTZ:
should be able to withstand the load reouired to overcome pressure thrust. Generally. tie rods are only used to permit lateral movement. Bellows expansion joints can be restrained and combined in pairs or trios to perform certain tasks. It must be emphasized that just because a joint is free to move in
) A
{:,
c
n
,-T
-.Fz
.%^
Ftgure 2-27. Types of bellows expansion joints: (A) flanged-flanged end simple bellows joint; (B) hinge bellows expansion ::nt: (C) gimbal bellows expansion joint; (D) pressure balanced bellows expansion joint; (E) "inJine" pressure balanced self'-:oorting bellows expansion joint. (Courtesy of Pathway Bellows, Inc.)
80
Mechanical Design of Process Systems
lA: PG:
MOVEMENT HOT
TUEJ:
-LATERAL
lnt€rmedlaleAnchor Planar Guid6 Tied Univorsal Expansion Joint
Figure 2-28. Generally the use of tie rods is to allow only lateral movement. (Courtesy of Pathway Bellows, Inc.)
directions KTX, KTY, KTZ, KRX, and KRY does not mean that the corresponding stiffness values are small. As internal pressure and pipe size increase the values of KTX, KTY, KTZ, KRX, and KRY increase, because the bellows wall thickness increases to resist increased internal pressure. The bellows can be a single wall construction (single ply) or multiple wall construction (multi-ply) and the stiffness values vary with each manufacturer. Some people erroneously think that the purpose of using bellows expansion joints is to make the pipe stress analysis unnecessary. Such is definitely not the case, because values of stiffness in each direction must be en-
tered in each computer stress run so that
it
can be
vei-
fied that the displacement and piping loads are not
excessive to the equipment nozzles. As shown in Figure 2-28 a pipe can either be properly guided or anchored, and such restrictions should be modeled into the computer stress analysis. The piping engineer is encouraged to refer to the Standards of the Expansion Joint Manufacturers Association (EJMA) t4l in accessing piping layouts when using bellows expansion joints. Also, it is desirable to specify the joint such that the manufacturer is required to meet EJMA requirements. One should follow EJMA guidelines and requirements, and include modeling restraints and stiffness values in computer stress analysis to verify that attached equipment is protected. Expansion joints are not cataloged items to be bought at random but rather
sophisticated pieces
of equipment that must be
engi-
neered into the piping system. With this approach, the
user should not expedence any problems with bellows expansion joints.
PRESTRESSED PIPING Piping systems are sometimes prestressed to reduce anchor and restraint forces and moments. This prestressing of the pipe is best known as cold springing, but is also called "cut short," meaning that the pipe is cut short a percentage of the amount of thermal expansion expected. The opposite is true in cold systems where the pipe contracts, so the pipe is fabricated extra long, with the extra length being a percentage of the amount of thermal conEaction expected. This procedure is best known as "cut long." Some refer to cut long as "hot springing," which may cause confusion because it is not as popular as the term cold springing and to some it means hot forming, which hds nothing to do with fabricating the pipe extra long. "Credit" may not be taken for prestressing the pipe in computing the stress in the piping system. Several piping codes are specific about this and, if the piping is over the allowable stress range, one cannot cut short or long to lower the stress. However, credit may be taken for anchor and restraint reaction forces and moments. The procedure of cutting short or long involves a percentage of thermal movement. The whole purpose of the prestressing process is to balance the forces and movements between the down and operating conditions. Thus, cutting short or long 1007o (i.e., cutting short or long the exact amount of thermal movement) is normally not done. Exceeding 100% is not recommended and doesn't make good sense. Normally, the amount cut is 50% and should not exceed 66% of the thermal movement' The reactions, R6 and Rp in the operating and down condi-
The Engineering Mechanics of
tions, respectively, are obtained from the reactions R derived from calculalions based on the modulus of elasticity at ambient temperature, 8". The relationships are as follows:
n":lr-?*l& - \ 3 lEo
I
11
Bellows expansion joints should be avoided if a more economical and practical method is available for providing flexibility oi restraint to the pipe. ln many ipplications, only the bellows expansionjoint will suffice, e.g., movement and vibration in straight runs of pipe at elevated temperatures between different pieces of equipment can only be compensated by bellows joints. How-
thereby more expensive, other alternatives should be considered. Such alternatives lie in either the flexibility or stiffness methods Dreviouslv discussed.
ot
-t:
-
]. FLUID FORCES EXERTED ON PIPING SYSTEilS
whichever is greater, and with the additional condition
b
that ---:
<
4 where
1.0
X:
: Ep : Ee : R: E
: Ro : Rp
81
ever, as the joint becomes more sophisticated and
Ro: XR
R"
Piping
cold (or hot) spring factor ranging from zero to one, one being 100% cold or hot spring computed expansion stress. psi modulus of elasticity in the down condition, psi modulus of elasticity in the operating condition, psi maximum reaction for full thermal movement based on Ep which is the most severe
condition. lb- or in.-lb maximum reaction in down condition, lb or
in.lb maximum reaction in operating condition, lb
or in.-lb These formulations are not necessary nor desirable when computerized stress runs are made. All reactions that result from prestressing the pipe are much more accurately made by a computer. However, one is not always privileged to use a computet especially at remote sites, so these formulations will yield conservative approximations to feactions. The biggest legitimate objection to prestressing the pipe is that often it is simply not done by the pipe fabricator or construction workers. The orocess is often difficult, especially in large pipe, and is unpopular with fabrication personnel. When schedules get tight and people fall behind on the schedule, there is a tendency to overlook prestressing the pipe. To avoid such a problem, some large engineering companies issue cold spring reports that are signed off by inspectors. However, such reports get lost fairly easily, unless a rigid system is implemented to treat them as control documents. There is certainly nothing wrong with prestressing the pipe, except maybe a little extra paperwork.
When fluids move in a piping system, they import energy to the system when they are forced to change direction by the pipe. In other words, it requires energy to change the direction of a moving f luid . This fundamental fact is known as the impulse-momentum principle, exnressed as:
l)l \-]
ph
:
Mv,
-
Mv,
(2-31)
This states that the change in momentum in a system remains constant during the exchange of momentum between two or more masses of the system. Applying the equation to that of a pipe elbow shown in Figwe 2-29, we apply the principle to obtain:
Mvxr+DFxxt:MVy,
(2-32)
Mvyr+DFyxt=Mvy2
(z-33)
where t =
M= 6-
1
for unit time
force in horizontal direction exerted by the bend on the flowing fluid, lb force in vertical direction exerted by the bend on the flowing fluid, lb horizontal velocity component at bend inlet, ftlsec vertical velocity component at bend inlet, ftlsec horizontal velocity component of bend oudet, ft/sec vertical velocity component of bend oudet, ft/sec Wgi
g"
:
fluid
mass
weight of fluid in bend, lb, local acceleration due to grayity, approximately 32.2 ftl serz dimensional consiant 32.17 lb-ft/lb1sec2
:
the analysis of chemical rocket engines is suitable for estimating reaction forces. These calculations in such an analysis agree with those reactions comDuted bv other methods and have been found to be slightly conseivative. The method presented by Hesse [5] is desirable because of its simplicity and accuracy, and knowledge of the process fluid is limited onty to the specific heat ratio, k, and the molecular weight, M. The derivation and explanation of the formulation is given by Hesse [5]. Consider the nozzle shown in Figure 2-30. The reaction force developed by a fluid exiting the nozzle is given by the following:
F= Figure 2-29. Pipe reactions induced by change of momentum of fluid flowing through elbow.
[/
lo.t
',[' where \ Ca=
When applying Equations 2-32 and 2-33 to relief valves, the fluid dynamics of nozzles must be considered. The dynamics and thermodynamics of fluid motion through nozzles is a very involved subject and rather than investigate the various theoretical methods in this book, we will only investigate the various results and discuss their merits. Relief valves can exert enormous forces when fluids exit the nozzles. Often, the fluid exits the nozzle at speeds exceeding Mach 1. Numerous private companies, as well as the ASME and API, have developed procedures to approximate such fluid forces. The ASME B31.1 gives a method for computing the reaction forces exerted by relief valves. The main drawback to this method is that it applies to steam only, because Code 831.1 governs only power piping. Steam is one of the most comprehensively defined substances, with all properties well known and published, but such is not the case with many chemical processes. The 831.1 method requires that the properties of the substance be we defined, to the point of being rather cumbersome to use. The ideal method would require the fewest number of physical properties, but still provide the necessary data. One such method that is very easy to use is the ApI formulation in API 520 Part II, paragraph 2.4, which is used for gases or vapors. This formula loses accuracy as the flow rate approaches Mach 1, so another method is desired for predicting reactions at all flow rates in processes that have poorly defined properties. The aerospace industry has done much research in the study of fluid dynamics and thermodynamics of nozzle flow. Because relief valves operate in a closed system,
\/
\,-,
l="'.2 ,l l-i" ,lt\K-l/\K+u
\cac"A,P. I
I
*+tn-P.l
(2-34)
:
nozzle correction factor l/2 (1 + cos o) 1.0 for most relief valves nozzle discharge coefficient, which 0.97 < Cd < 1.15, normally Cd > 1.0 specific heat ratio CplC"
-
:
c=
nozzle inlet section throat-where critical condition exist = e = nozzle exit section ef = gffrat;rr exit section-where exhaust gas pressure first equals ambient pressure, Po
t
l/r, /
7l\-
t Figure 2-30. The relief valve mecharusm.
-'.--
The Engineering Mechanics of Piping
cv:
(rJ05 = 0.95 to 0.98 nozzle adiabatic efficiency nozzle exit pressure, psia 14.7 psia ambient pressure nozzle exit area, in.2 nozzle throat area, in.2
cause the process is considered adiabatic making the to-
tal temperature constant. Thus,
:
critical pressure
:
P,
l---I \K -f l/
rc =
G= T"
/"_,..-,f
- [r- {_z\:ll +u I
.T,
/r.
r\
I + l-.--1l
:
(2-34a)
ffir,, 't
M2 for adiabatic process
Substituting these exDressrons mto Equation 2-34, we
:
1 028A,P"
+
A"(P"
-
[-+ (#= P,)
(2-36)
Reaction forces produced by relief valves can become quite enormous and should not be overlooked. A structural failure of a relief system could well result in a catastrophe.
have
F
5
vc=V.=(skRrJo5=|\#',f
Figure 2-31 molecular weight of fluid, lb/mole gas flow rate, lb/sec, where
critical temperaiure
r,t
and
C.A,p"'[Rr.\k
:
r,. oF l-l + \K
'
critical pressure ratio, determined trom
G:
t)l
[' - (,:)*]]"' (2-35)
Equation 2-35 assumes that the flow is isentropic and in addition to relief valves, includes turbines, compressors, jet engines, rockets, injectors, ejectors, and atomizers. Most nozzles used in current applications are either convergent or convergent-divergent, also known as DeLaval or Level nozzles. Convergent-divergent nozzles are used for high pressure ratios and supersonic flow, and convergent nozzles for low pressure ratios and subsonic flow. Thus, relief valves are Level types that can handle high pressure flow. Critical pressure of gas occurs at the point where the fluid velocity becomes Mach 1. This pressure is obtained at the minimum area of the nozzle and this minimum cross section is called the nozzle thrcat in the DeLaval nozzle. In the convergent nozzle, the cross section of minimum area is the exit section. The critical velocity can be expressed in terms of the inlet temperature be-
EXTRANEOUS PIPING LOADS Vibration can be a real hazard in piping systems. Usually, vibration problems that occur with piping have two sources-pulsations generated by reciprocating equipment and wind. Pulsation shock phenomena on rotating equipment is briefly discussed in Chapter 6. The phenomenon of wind-induced vibrations on piping along tall towers is discussed here. Wind-induced vibration is caused by vortex shedding on the cylindrical surface of the pipe, and becomes a problem with piping more than about thirty feet long. Vortex shedding usually occurs with piping that runs up along the height of a vertical tower. Analyzing and solving vortex shedding vibration problems can best be handled by applying certain principles that include dimensionless parameters and experimental data. Sophisticated digital computer models are possible, and recently, vortex streets have been simulated with flow patterns around piping and structures. Such computer simulations are rigorous and expensive, so with current software they are impractical to use for all piping that may be exposed to wind. Several proposals have been made concerning vortexinduced vibrations around cylinders, but perhaps the most straightforward is the work by Belvins [6]. He developed a dynamic model for vortex-induced vibration using random vibration theory. The theoretical basis is a representative spanwise correlation and cylinder amplitude is presented as a function of the vortex forces. When the state of resonance exists, the amplitude of the correlated lift force on the cylinder is represented as a continuous function of cylinder amplitude. Also, at resonance, the spanwise correlation of the vortex force is presented as a function of the characteristic correlation length. This model is limited to the resonance of a singie mode with vortex shedding and a Reynolds number in
84
Mechanical Design of Process Systems
100
90 80 70 60
o"A,
10 8 7
6
Figure 2-31. Critical pressure ratro versus area ratio for various fluid specific heat ratios (k).
80 lOO
2OO
/rcO 600 80O
loOO
'clPa
(
(
the rate of200 Nn" 200,000, where a well-formed vortex stre€t exists. Figtre 2-32 shows flow regimes of fluid flow across stationary circular cylinders, and illustrates how the vortex streets tend to separate as the flow velocity increases.
which is the numeric constant between the resonant frequency of vortex shedding (f) and the cylinder diameter (D), divided by the free stream velocity (V). This is analytically written as
Between the range 300 NR" 300,000 thi region is called subcritical because as Nx" approaches 300,000, the boundary layer becomes completely turbulent and the vortex shedding effect is lost. One parameter used in analyzing vortex phenomena is the Strouhal number(s),
^
<
f.D Q-37)
For circular cylinders, the Strouhal versus Reynolds number is shown in Figure 2-33. In a structure, the ob-
The Engineering Mechanics of
ject of design is to avoid resonance. If the inverse of the Shouhal number < 1, where f is the natural frequency of the structure, then resonances with vortex shedding from the first, second, and third harmonics are avoided. This can be accomplished by adding mass, such as insulation, and putting pipe support spacing at uneven intervals. If pipe supports are spanned evenly, periodic wave motions can form, resulting in resonance.
Piping
85
The response of a right circular cylinder at resonance with vortex shedding is a function of the following: Damping
:
(2zs)2 6.
where 6.
:
reduced damping
_ 2m(2rl) pW
(z-38)
and
Etl_g
energy dissipated per cycle "| _ 4?r(total energy of structure) Mode shape : VW: i for a rigid cylinder) Aspect ratio : LlD, L = length between spans
RcGrMa OF urrsEpARArEo FLO{.
voRTrcas rfi rnE w^(€.
'rwo
nEGrMEs
lr
l'r
PERIOOICITY GOVERNEO
II{ tiIOH
R.
RII{CE BY
R. RING'
,,4.* -W
-u/////t
'Y
I/(E
3r|ol voRrEx
sritEt
LOW
VOR'IEI
IRAXSIIIOI NINGE
Eg-5-E!-l-3aq
lOO
wHrcH vofiTEr
PERTOOTCT'IY COVEFI|ED
TO
IUiBU.
rs Frrl'tl
3,'o..' i. <35, o.
e'
L^YE
IYi?Y,",li,t
i
BAS UIiOEROOXE
lt6%i!13i*,,*.*[i'"
voirEx srREtr rs.PP.REnt 3,5rro'< R. <
cO
t?l
R€'€SJA8LISITTEIT OF Tt1€ TURAU.
IENI
IORIET SIREE' II]AI EvrD€tT rx 3oo< i.? 3r|o: 'AS Ih'S IIME TIE SOUNDIRY LAYER
lno
THE uAr(€
Figure 2-32. Fluid flow regimes across circular cylinder l7l.
The amplitude Ay/D can be approximated by loading the pipe with a uniform wind load and using the maximum deflection as Ay. This can be used in Figure 2-34 to estimate the damping at resonance for a given aspect ratio. This damping is then compared with the natural frequency of the piping. The natural frequency of the pipe, especially for complex geometries, is computed by modal extraction computer analysis or any other dynamic computer software that computes the natural frequencies of piping systems. For short straight spans, the natural frequency can be determined by comparing values obtained from Table 2-6 and with the resonance damping frequency in Figure 2-34. In practice, the greatest problem with vortex shedding occurs on tall vertical towers when pipe four inches and smaller is uninsulated and left hanging without support. It has been found that once insulation is applied to the pipe resonance vanishes. The following simple guidelines will enable you to avoid the vast majority of wind-reduced vibrations:
l.
Increase the flexural stiffness of the pipe so that its critical velocity is above the range of moderate
winds. 2
.
Use damping devices to restdct the amplitude of
vi-
bration.
3. 4.
5. REVIIOLDS
U
E€h! R.
Figure 2-33. Strouhal-Reynolds number function for circular cylinders [7].
Reduce the effective length of the member by using
intermediate struts. Attach spoilers to the pipe to disrupt the flow near the tower surface; this impedes the formation of vortices and thereby eliminates the cause of vibrations. Span the piping supports at uneven intervals to prevent a periodic wave function from developing.
The analysis of wind-induced vibrations on tall vertical vessels is discussed in Chapter 4.
Mechanical Design of Process Systems
Table 2-6 Natural Frequency ot vibration ot Beam Elements Concentraled Load on Relatlvely Light Beam or Spring
Uniform Load on Beam Supported
Unitorm Load on Cantilever Beam
at Ends
ffi
. / \0.5 r - t l9l '- t\-Di
f: D:
f:
(3.55XD)-0
5
f :
(3.89) (D)
natural frequency of vibration. cycles per second maximum static deflection of member under its own weight plus any weights that vibrate with it
0.5
The Engineering Mechanics of Piping
or
r,rer r.re
= r stn
r3l s2/p#
Figure 2-34. Damping, d (dimensionless), versus amplitude, Ay/D (dimensionless).
88
Mechanical Design of Process Systems
EXAilPLE 2.1: APPLYIilc THE STIFFNESS SKID.IIOUIITED
]UIETHOD TO A IIODULAH
GAS LIQUEFAGTION FACILITY
Figure 2-35 depicts the preliminary piping design of a gas liquifaction plant mounted on a skid module. Space is severely limited, as the equipment and piping are limited by the structural steel skid supports, so such devices as piping loops are unthinkable. Expansion joints are not
allowed by the client, because high-pressure hydrocarbon gas is highly combustible and an expansion joint failure would mean certain gross property damage and possible loss of human lives. Therefore, the piping engineer
must utilize the stiffness of pipe supports to transfer loads from the piping to the structural steel rather than to the equipment nozzles. This transfer of loads is not total, but enough to guarantee that the equipment nozzles loadings will not exceed allowable levels. For the stiffness method to work, the piping configuration must be flexible enough for the piping itself to be within allowable stress limits set by the applicable code. This is the first significant criterion, because if the piping exceeds the allowable stress range in any part of the geometry, the system design is faulty. Conversely, the piping system can be well within the stress range and the equipment nozzles still be overloaded. Thus, the piping itself must have a certain amount of flexibility to be within code allowables. The piprng supports must be stiff enough to protect equipment nozzles from excessive loads. Here our case has been stated; adding additional flexibility is not acceptable. From computer calculations the original configuration in Figure 2-35 is found to be overstressed and the expansion stress exceeds the ASME 831.3 allowable stress range provided in Equation 2-4 for 3O4 SS pipe. Therefore, the piping must be changed to bring the maximum stress within the accepted stress range. This analysis includes the nozzle movements shown in the figure. Each nozzle is considered as an anchor. Figure 2-36 shows the final configuration after several iterations are made to determine what configuration would best suit the structural limitations set by the module skid. This configuration is found to have a maximum allowable well within the stress range of ASME B3 1 . 3 . To achieve this acceptable stess, a limited amount of flexibility must be added to the system. Thus, regardless which method is used-flexibility or stifftiess-a certain amount of flexibility is required to make the piping system operate properly. Once we have obtained the minimum flexible configuration required, we now focus our attention to the equipment nozzles. To consider this question, we must distin-
guish between the types of equipment. The heat exchangers HE-A and B shown in Figures 2-35 and2-36 are aluminum plate exchangers, and the cold separator and power gas volume tank are made of reasonably thick-walled stainless steel. Thus, the critical items are the aluminum heat exchangers. The line between points l0 and 25 in Figure 2-35 must be cut because the relative Z-movement between these points overloads the nozzles at points 5 and 30, creating a very high y-momenr and Zmoment, because the pipe wants to move in the -Z and *Y directions. These movements can be accommodated
by using certain structural devices, such as shown in Figure 2-37. Even though flexibility has been added to the system to get the piping within the allowable stress range, the equipment nozzles are still overloaded by excessive moments above the X, Y, and Z axes-M;q, My, and Mz. To counter the movements of the piping at the nozzles numbered 5 and 30 at HE-B and A, respectively, variable springs are placed to support the pipe while allowing the
pipe to move at the same time. One spring is placed at point 20 with a simple Y support added at point 56. These additional supports help reduce the moments at nozzles 5 and 30, but not enough. So, we must add MRS restraints (see Figures 2-9 ard 2-10) in pipe members 5l0 and 30-35. Each MRS is designed to allow nozzles 5 and 30 to move upward but to transfer moments M;, Mv, and Mz from the pipe to the structual steel below. Also, each MRS allows pipe members 5-10 and 30-35 freedom to nove along the axis so that we have the following restraints at each MRS: KTZ, KRX, KRY, and KRZ of Figure 2-38 (see Figure 2-10). Thus, we have
one translational and three rotational restraints, each with a stifftress value K in lb/in. or ft-lb/deg. The pipe and exchanger are free to translate along the X and Y axes. One can readily see that the MRS restraints must allow nozzles ar points 5 and 30 to move upward, as the exchangers are bolted down to structural steel higher up on
the units. Restraining the nozzles from moving upward would anchor the unit at the nozzles and at the support point causing the exchangers to rupture. Pipe members 5-10 and 30-35 must be allowed to move along the x-axis for thermal expansion. We now have the conceptual model of what the solution looks like and the next step is to finalize the details. The MRS restraints are resisting forces and moments shown in Figure 2-38. It is necessary to design the restraints such that each has enough stiffness to transfer the loads to the steel and protect the nozzles at points 5 and 30. We will now compute the support stifftress values KTZ, KRX, KRY, and KRZ. Once these values are determined, they can be input back into the computer run and verified to be sufficient for the nozzles.
The Engineering Mechanics of
\,zr/
\/W \\ \\\ \\\ \ \
\
\\ \'"
\\--l \p't 'a2
,r^
o
ao
o '4
q
z o_ tsJ
-4
7
"3 2:1
7^
, t
e-:x
$-
4e. 2l/o o.,
Piping
89
90
Mechanical Design of Process Systems
F
o o ',',
ao
ct
N
o .D
IL
9 z
The Engineering Mechanics of Piping
@ GnTNNELL slzE a rYPE
@
venncr
91
D
suPPoRT(sEE F|GURE 2-9)
@ GR|NIELL stzE 10 rYPE
D
SPR|NG
Figure 2-37. Plan view of location of MRS supports.
OHAr{GER suPpoRT
TO OF
ENSURE PFOIEC'IoN CAF8ON STEE
L COSPONENTq
OISIRIB(IIION OVER
LE GIH
\\
---
rtrslrL^r
--' +
€IIDE STSE SOPMRT PIPE
Flgure 2-38. Two-axial translationfree multiple moment restraint support
(BIAX-MMRS). Arrows indicate rections of freedom of movement.
d!
-_4
DIATES ASSEMELY }IOUSING
Systems
Mechanical
-tb )o lb ioo ft-rb
ro -x ' ;> [ rr-r-owso TRANSLATE tt !x otngcrtots
For Torsion
:
T
12,800 ft-lb
For Shear
+ Rr + 3(R + r)
4(R2
._ _
4(10.976
+
. I"igit'1 :"it jotffi''.
12)
9.545
+
8.297)
316.194)
=
(12,800)ft-rb
,r:a: Tc
:
1.975 in.
----
(r.,J
(*,
)
4oJ0 in.o
12,563 psi
For Tensile Stress
A_T-- $-Q.?
I-
.'_-*
q
1.20 t! 8.40 in.'
p_ "- : A :
I
=
r+t prt
Shear Distribution At Point
r,
A-
O
:
22.83"
For a circular .thin-walled cross-sectron'
rl4lc,
(r,roonb
"=+:+i: : rs
521-648
(ry)
in.'?(r.e75) in.
Q
:
(40.49) in.a (0.432) in.
--'\-n 16'
psi-max at neutral axis
:
-(1,100 lbx3.0) ft
Mz
=
-9,500 ft-lb
Mn : :
o
R(Mx,
M, :
10,308
ftib
M
-
700
ft-lb
:
-4,000
(-4,000)" + (-9'500)tlo
10,308 ft-lb
625 + 5.76 I
ftlb
At Point 5
o 4
(1,100) (7.635) (40.49) (0.432)
For Bending
Mx
2R'zt cos
Q
=
=
=; = ----r,j/ti.-= = 1o,114Psi
480.143 psi
2t9.588t (0.432) cos (67.166') (
/.^.rn'l\
At Point
83")
B-
1,100) (3.215) _ ' _ (40.49) (0.432)
lY \ln/
(0.432) cos (22
202.182 psl
c-
A:?)R'lo=r=
480.143 psi
=
3.215
=
7 '635
The Engineering Mechanics of Piping
<- rfi, .-- ll A ll --+ -;. <- {l lt __}
-r' l-, '
6r:1o,jr4+i/tg
oi:
Point
= r. + rr = 480,143 + 12,553
'
= 13,043.143 psi
* lf--lf __-f o:1oJ14 -143 lt e <--ll ll ------) O=seflpsi
{_
r = 13,043.143 psi
l_ rr----.lr <-- ll c ll ----+ 6r=uspsi <-rL_-Jr+ ____+
o=
= 12,765.182 psi
ox
oy - o"'l', 1ot 2 *-t\[/o* 2 I ",^Yl rov-0 [h0,257\':
2 -l\ 2
o
:
l
(12.5) (0.322\
lot f (13,043.14311
:
17,000 psi < 19,143.614 psi allowable stress, so, try 8-in. d Sch 40. o"11
Bending ro.ms ir-ru
ll?:"
\ft/
I43 psi
=
9,138 psi
o : l4,lll.\57
+
:
)
r:
r
8.625
-: 4
?1? : :L = := JI'.U
KTX
psi
<
Torsion
:
or KRX
<< | -
x
g
'
It^
(72.5)in.3
=
109
9.138 psi
o
:
l,200 lb
870GJ
:
r+r
Psr
or KRY
:0
(72.5) in.4
:
4(2s.0
x
106)
*
(zz.s) in.o
(36.0) in.
233,611,1ll.l in.Jb/deg
:
KRZ
2(29.0
:
540,766.5 lb/in.
x
=
19.467 .s92.6
106)
ln-'
(36.0) in. 116,805,55.6 in.Jb/deg
:
-:*
fr-lh qeg
(72.5) in.4
--1
KRY = Tensile Stress
9,658 psi
(36.0)3 in.3
in
t4.313)in.
:
17,000 psi allowable stress
0.120
12(2s.0
:
:
2,800)ft-lb (12)
psi
+.JlJln.
2
KRX -_ KRZ
7,358 psi
(|
520
]
16.81 in.3
o
7.501 psi
. = (1 +l2EI' O)LJ
-t 19,143.674 psi
For ,4312 GR TP 304SS,
+
7.358 psi
[\21
-
lo,2s7+
11.039
7.501 [h.sor\' ^ -- .lo' 6 = -|1J! ll '--'l + {9-658)rl 2
KTx
Point A is the most critical point.
_
:
(l.100) ( l 1.039)
r = rs + z1 :
Stress Elements
,-,
A, Q :2(\8.59'17) (0.322) cos (22.83)
Therefore, use 8-in. Sch 40 A-312 TP3G4 SS pipe for the 3-ft pipe spool piece. From these calculations, we see that the minimum pipe size for the MRS is an 8-in. Sch 40, 3.0 feet in height. The stiffness values for an 8-in. Sch 40 pipe are as follows: From Thble 2-1, we have
r=202.182+12,563 7
Shear
1o,2s7 psi
9,133,196.3 ft-lbldeg
94
Mechanical Design of process Systems
Entering these stiffness values into the computer run. we see thar lhe nozzle loads fall very sharply it points 5
and 30. Further reduction in loads can be obtained bv adding springs abo',e the MRS restraints to counter ; negative moment above the Z-axis. Using springs above these supports is not always necessary, but in this case they are required because of the large vertical movement of points 5 and 30. A weight run should be made to verify that the springs do not ovedoad the nozzles durins
therefore making such a unit sensitive to external loads. Always be careful when subjecting rotating equipment or vessels made of light material to excessive nozzle loads. In the final analysis the pipe loadings transferred by the MRS to the steel must be considered by the structural engineer. who must design the loundation accordingly. Sometimes it is necessary to model the stiffness of the steel foundation members when nozzle loadines become
critical.
shur-down.
The MRS restraints vary in design and are conceptually shown in Figure 2-10 and Figure 2-39. These iupports are made ol interlocking sliding plates wirh eaih sliding surface coated with high-strength Teflon. The precise details of such supports vary and are customized for each application. Looking to other parts of the piping system, we notice that nozzle 75 on the cold separator has a high moment about the negative x-axis. This moment is attributed to the aluminum exchangers (HE-A and B) moving upward and the cold separator shrinking downward. Because space is premium and we are "locked-in" and can't add any more flexible piping, we add a spring at elbow 65 pulling downward to counter the exces5ive neqative xmoment at nozzle 15. The spring is sized ro b6 acceptable for operating and shut-down modes. Table 2-7 lists the forces and moments at each equipment nozzle. Upon reviewing Table 2-7 , you will notice the disparity in nozzle loadings. The aluminum heat exchangers,
HE-A and B, have lower loads, especially moments,
than does the cold separator or power gas volume tank. This is because each has acceptable loadings that are different. The cold separator is made of 23la-in. plate stainless sreel. which makes rhe loads shown easilv acceotable. {The method of determining whether such-loads ire acceptable on pressure vessels is discussed in Chapter 8.) Such loads would be very unacceptable lor the aluminum heat exchangers because aluminum cannol withstand nearly as great a load as steel and is not very elastic,
Figure 2-39. The BIAX-MMRS installed and in operation olant facilitv.
Table 2-7 Equipment Nozzle Forces and Moments Heat Exchanger A Heat Exchanger B Process Vessel A Process Vessel B
t44.7 279.O
126.2
-
38.5
-255.9 -624.6
299.2
-2437 .8
0
0 854.4 94.6
293.9 684. I
0 0
914.O
-6175.0
2440.0
877 .1
-210.5 -553.4 4501.9 3163.0
210.5 553.4
8217.6 3306.8
ar
The Engineering Mechanics of
EXAIIPLE 2-2: APPLYING THE FLEXIBILITY IIETHOD TO A STEAiI TURBINE EXHAUST LINE A client has added a steam turbine to a chemical plant and has piped up the turbine with make-shift parts and existing pipe, plus a newly purchased bellows expansion joint. When the turbine technicians determine they cannot cold align the turbine with the exhaust piping, the client decides that the piping must be rerouted, but requests an evaluation of the system, which is shown in Figure
240. The system is modeled with a computer software package, and the results indicate that a moment about the yaxis in the magnitude of 31,000 ft/lbs is exerted on the turbine exhaust nozzle under operating conditions. Such a load is well above any turbine allowable. The reactions
Piping
95
along the other axes are moderate and the problem of alignment must be solved. The extremely high y-moment is caused by the thermal expansion of the pipe member extending along the z-axis from point 95 to point 145 almost Ze in. With this expansion along the positive z-axis, the pipe rotates about the positive y-axis from point 20 through the expansion joint at point 45 to the elbow at ooint 75. This torsion is transmitted to the turbine nozzle it point 5. Thus, the adjustable base elbow support at point 31 is entirely useless in resisting this vertical moment and the expansion joint at point 45 transmits all of the torsion motion to the turbine nozzle at point 5. An earlier section discussed the fact that these joints are totally rigid in torsion-a moment about the axis is parallel to the longitudinal axis, which in this example is the y-axis. In fact, with the vertical moment as great as 31,000 ftlbs the expansion joint at point 45 will either be destroyed or have a short service life because the bel-
li
lri
ii
i
d-o.^*
.u""'"'
Figure 2-40. Original piping configuration of 20-in. 0 steam line for turbine exhaust: temperature psia.
:
300"4 pressure
:
16
Hg
96
Mechanical Design of Process Systems
lows are not designed to resist such high torsional moments. Thus, the diagnosis is to avoid the high torsion and stop the .8-in. movement at point 135. To do this- economically with minimum alteration to the piping, a bellows expansion joint is added at point 123 and.the shoe on the dummy leg is stopped in the *z direction (i'e'' movement in the 1z direction is stopped, and the vessel nozzle at point 85 is protected by the joint at point 123 ' An expansion joint is sized based on the manufacturer's standard dimensions for a 20-in. pipe and the joint stiffness values are as follows:
KTX KRX KTZ
: KTY - 1,500 lb/in. = KRY : 200 in.-lb/deg : l2O lblin.
These values are provided by the
joint manufacturer'
The problem of turbine alignment is directly related to the inabilitv of the turbine technicians to adjust the pipe because of the pipe's inflexibility, which is caused by the suided base elbow at point 3l . The base elbow support is ieplaced by a spring depicted in Figure 2-41 and modeled into the compuier siress program. This mn is made with the added ixpansion joint at point 123 and. the spring at point 3. ihe following results were obtained from the computer run:
Turbine nozzle (Point
: : Mx : Fx
46.51bs,
Fy
:
-530.8Ib, Fz
634.l lb
=
5)-
:
343'9 lb, Fr
:
1,978'2 ft-lb' Mz 1,198.4 ftlb, MY ftlb 2,430.0 745.3 ft-lb, Mr
:
Vessel nozzle (Point
85)-
F" = -46.4Ib, Fv = -3,311.8 lb' Fz : -3,348.5 lb, Fr : 4,709 9lb
Mx
: :
5,968.7 ft-lb, MY
5,0?6.0 ft-lb, MR
:
=
9,742 0 ft-lb Mz ' 12,501.9 ft-lb
The loadings at the turbine nozzle are acceptable' (The basis for conaluding this is discussed in Chapter 6') The reactions at point 85 seem excessive and would be for a steam turbin;, but considedng the vessel is five feet in diameter and made of 3-in. plate, these loads are not ex-
cessive. Pressure vessel nozzle loading analysis is covered in Chapter 4, but one can deduce that pressure vessel nozzles tan withstand much greater loads than most tvDes of equipment. ''The svstim is implemented and in two days the turbine will be fired up and operating well. The concluding remarks are that the expansion joint at point 45 is accom-
plishing nothing and the capital expended for its purriu. wa$;d' ln fact, it would not hurt to move the "hu." unit, but this is not necessiuy since the high torsional moment has been eliminated. The expansion joint at point 123 was specified and ourchased for those stiffniss values previously listed' the final configuration is shown in Figve 2-42
EXAilPLE 2'3: FLEXIBILITY AIIALYSIS FOR HOT OIL PIPING
A olant in a remote area of Brazil has an emergency need for a hot oil system. The plant manager has deter-
mined that a 3-inch Schedule 40 pipe is to be u-sed' based on plant requirements and available pipe trom local to design the piping and ensure it will ioui.".. w" not be overstressed. There are no electronic computers available anywhere near the plant and all calculations must be made without a stress program' For a hot oil header extending over some distance the flexibility approach is the practical method in this applifit" iiit" it to operaG at 550'F at 50 psig For-aj"ution. in. Sch. 40 pipe, d :3.50 in. A layout is n-rade o{ the system and preliminary loop is shown in Figure 2-43' The piPe is ASTM A-53B PiPe.
it"
SPRIN6
I'
Y
1':l
.7
V
Figure 2-41. Sketch of spring that replaces base elbow^supoon: installed load :713 lb. operatlng load = /uJ rD'
ipring :
300 lb/in.
i
-":
I
= 3.73o5 :
8.oo: Rv
:!:I:z.so La4
The Engineering Mechanics of Piping
*f--ttt
97
t I
,-tt^\.
,"_'-wJ_\ tN:z
Dlf,Ectro{s
Figute 2-42. Final piping configuration of 20-in. steam line for turbine exhaust: temperature 300"F, pressure
=
:
16 Hg psia.
From Figure 2-12A, Ah
B
:
(4. I
l)
(_2.9._q
0
=
(29.525t (30\ =-njaf =5u.urt "
220
x ltr) _ 689.8
r72,800
From Table 2-1 and ASME 831.3 the allowable stress is
oe
:
1.25(20,000)
+
0.25(18,100)
:
29,525.0psi
The available steel in the plant in the area the hot oil header is to be run is spanned 4.5 m or 14.76 ft, making tlre anchor points spaced at 18 m or 59 ft. Thus, = 59.0 ft. We change
At:98
The maximum bending stress is oB
: - = A,B [q] \L/ : 17,7M.9 psi
on
tzzol toss.at tr.sol
L = 30 ft between guides. Solving for the distance between anchors. we have
r^
:
rr7.704.9\lL-'l '
\L/
(98) (689.8) (3.50) j-r:-l : ---10 :
6.0
+
7.886.7 psi
Rx =
<
o^
30.0
L',
This is based on
: Ia:
l<
Solving for total length
_
Qe,s25) (30) 7,886.7
L',
1t2.3
112.3 fr 15
ft
(between supports)
ft
:
7.5 supports
&:
L'
5.0'
Mechanical Design of Process Systems
Figure 2-43. (A) Initial piping configuration; (B) final piping configuration installed and operating.
Therefore, place a loop 6 ft x 6 ft (arbitrary dimensions) every seven supports. One could increase L' by making the loop larger (increasing Ia and La'1, but space limitations in this application prevent it. See Figure 2-43. The shess intensification factors (SID in the code were made equal to one because computer stress runs have verified that the curves are conservative enoush to make SIF : 1.0.
EXAMPLE 2.4: LUG DESIGN Referring to Figure 2-16, a lug is to be designed for a pipe with the following parameters:
t = corroded pipe wall thickness. rn. c
-'2 n
rrff< r.u = wlth ; >
8-in. { Sch. 40, C.S. 5A-1068 : -350'F, Pr = 500 psig P : 2,000 lb
:
3/s
in.,
L:
R5?5+?qRt R.: ---- ; --'=
4.t52in.
:
p: 0:
2tlz in., and the lug has l/z-in. d
mean radius, in. From piping properties in App€ndix
L : l.z) ln.
,
['
-i(' -u,t),' - nr ] to,o,lo'
L,
B B
hole
R. :
:
tt2
T
C
cr
: ft> t,u [' - i(,! -')rr - r,r] rB,B,ro,
Pipe
Let
0.188 in.;
Nd P/RM
Md
-
-.
P-
:
0.19 0.15 0.11 0.16
Fisu.e 2-17 Fisure 2-19
for Nd -* K, : for N; - Kz : for Md -- K, : for M" - Kz :
1.48
1.20 0.88 1.25
The Engineering Mechanics of Piping
*' : Eql[I t [P/Rml [R,tl
(2,000)
= ,' r, (4.1s2) (o.322) =
lotl _ ,", : tu," t:t -i- :_ lrnrOl t-P l[-i,l A.yzt"
{6) (2,0q0)
or,ao
Ci.rcumferential Stress,
=
E.*,.5.j2
: :
(1.38) (2,842.30)
K"
o7
+
(1.36) (rs,o4s.72)
P- -
*.:llolEl =,r' t [P/R,l [R,tl
10,186
:
r..^r r-. | tz - tPltt']l -
=
qx
:
:
31,032.62 Psi
:
<
:
oP
40,000 psi
>
31,033 psi
78
_ area)
oB
2,000
r(0.5)2 4
Oolt allowable)
25,000 psi
The distance from the lug hole centerline to the lug of AISC Table 1.16.5.1, p.
-'-"
2.000
2(0.25) (2.50)
:
1.600
f*:0.707Eoe: E = Joint efficiency
f* :
14,140.0 psi
(2,000)
(4.rs2) (0.322)
Weldsize
: *: ft f* : 0.113 +
r/c-in. weld is acceptable.
ta\t
/n ,....-r'2'000) \0.322),
EXAIIPLE 2.5: RELIEF VALVE PIPING
14,467.03
-. NY .. ox:K"itooti
+
edge is to be a minimum
:3,739.87
[rp]
ox
2(20,000)
Oolt or pin
-' P f,:-: ZvL
Fizure 2-18
[ur,-l
3g,5g6.Ot O.t
Weld Size
Fisure 2-2r
6M-. -.-^
+ or :
5-51.
Longitudinal Stress, o; R-
oO
Thus, a lug with these dimensions is acceptable.
os
t-ril
Nx -.
: or : o-t
t/+-in. weld,
.. x': t, + [-1l" = t-.lz1o.zzztlo" = r'36 lr,+w-l l*rcrr:l
!1r
12oa =
I t l'" =, * I n q.r.r loo5 r.38 + ls.uwl lr:rroC =
:'
:
Bolt shearing stress
[-, I
Pi
Total stress
6,196.43 psi
Using greatest value of o1,
24,309.65 lb
Letw :
(500) (7,981) 2(O.322)
:
o{
"t=*"Y*",ry od
_
2,842.30
SYSTEM 6M"
(1.38) (3,739.87)
Examine Example 1-4 relief valve system for external loadings induced by valve discharge. The gas properties
+
(1.36) (14,467.03)
k:c1c":1.451
:24,836.19 Primary or pressur" ,1r"a,
are as follows:
: o. = I 2t
N:
243,755 lb/hr
Ar =
28.89 in.2
T": M:
294"F 170.9
=
754"R
Mechanical Design of Process Systems
100
Experimental data from Blevins[6] support the following formulations:
I : I :
[r"ln' l__:l
IMl
I l ^ lrr.+srt
Cc:
\2451105
0.025 for large pipe
A
| ' l* v.45u I
't
0.1443 (1.15)
0.15 damping factor for small pipe (4-in.
|
I zs+ \n'
\r?ot
c
(>6-in. d)
.^
D
o.o7 [^ (6. + 1.9)52 [-'--
L:
30
{
ft, l-in.
d<)
o.7z (6,
+
lo'5
(2-39)
1.9)Sl
Sch. 40 pipe
For a uniformly loaded member with simple supports,
:0.055
-
5WL3 384EI
From Figure 2-31 or from the following we determine P" and P" as
G p-: ' ccA,-
61
710 =
(0.055) (28.89)
42.6t3
6
(0.99X1.1s)(0.98)(28.89)(42.613)
[
0.45r
)#[,
v.4stl I
_ l_ryq)l-,",,1" \42.613/
I
I
+(28.89) (4)
:
2,385.879 lb
:
1.68 lb/ft (30)ft
50.40 lb
12.569 in.
:
r- =
3.55 (12'569)u r
(2,385.879) lb (8.5)
ft :
The reactions at the vessel nozzle are discussed in Chap-
cvcles/sec
. 4mzf 'pDp:
(2-38)
0.076 lb./ft3
0.140
.= '1) --
EXAIIPLE 2.6: WIND-INDUGED VIBRATIONS OF PIPING @ Schedule
l.trut
20,279.9'12 ft-lb
ter 4, along with external loadings on vessels.
A l-in.
:
For air at 60'F,
Reaction moment at the vessel nozzle is
MR
:
W
From Table 2-5,
:
[zrr.+sr,l_r F
0.0874 in.a;
=
D =14
F
I:
where
40 pipe is to run up a process
tower, and it is necessary to determine what span intervals are needed to avoid vibration resonance caused by vortex shedding induced by wind external to the pipe. Piping designers have the line supported at 3O-foot even intervals. The first problem with the layout are the even intervals for the supports. Piping spans subjected to vibmtion should be in uneven intervals to prevent sine wave oscillations that would be symmetric and pedodic, and thus self-destructive.
i-th tn :0.004& ll.
ft )- _:L sec2
Air velocity under investigation sec
6,
:
13.037;
Nn
:
2.54
x 1ff
From Figure 2-33,
S
:
0.18
rnus,
fi
Damping
: =
o.tzo
tul#I"
:
tr.utt
:
25 milhr
:
36.65
ttl
Heat Transfer in Piping and
RD
Values from Figure 2-34 indicate we are close to resoftrnce, as we are within an L/D ratio of 5 and L/D = 30. Thus, we should experience resonance at 25 mph for the l-in. S Sch 40 bare pipe. The line should have more supports added at uneven intervals closer than 30 ft and the previous analysis repeated for a range of wind velocities . Such a problem can be approached with a computer program based on experimental data. As is obvious, vortex shedding vibrations is still a sub_jective phenomenon based on empirical data, but this example should assist one in protecting piping surrounded
R(x, y,
:
z) : fi ro
T t U
w
Z
z^
by vortices.
OR
I{OTATION
A: C= D: Ep : E" :
oc OL
area, in.2
compliance, in./lb or deg/ft-lb diameter, in. modulus of elasticity in down condition, psi modulus of elasticity in operat-
ing condition, psi F = force, lbs G modulus of rigidity, psi I moment of inertia, ft' polar moment of inertia, fta J K stiffness, either translational (lb/in.) or rotational (ft-lb/deg) stress concentration factor for bending stress concentration factor for pure tension or compression KTX : translational stiffness along Xaxis, lb/in. KRX : rotational stiffness about Xaxis, ft-lb/deg KTY = translational stiffness along Yaxis, lb/in. KRY : rotational stiffness about Yaxis, ft-lb/deg KTZ : translational stiffness along Zaxis, lb/in. KRZ : rotational stiffness abovt Zaxis, ft-lb/deg L: length, in. M= moment, ft-lb P= force (lb) or moment (ft-lb) in stiffness matrix Pi= internal pressure, psig P"= external pressure, psig Pn: internal pressure evaluated at radius R, psig R: reaction, lb
o" OR
OT
oy
X,
+Y,+Z
reaction in down (non-operating) condition, lb vector resultant operator inside radius, in. outside radius, in. torsion, ftlb thickness, in. displacement, in. weight of fluid, lb. weld size, in. section modulus, in.3 section modulus of mean section radius, in.3 bending stress, psi circumferential stress, psi longitudinal stress, psi pressure stress, psi radial stress, psi torsional stress, psi yield stress, psi forces
or moments acting only
in +X, +Y, or *Z
4M-X, -Y,-Z :
K= K:
101
shear stress, psi
T
F,M +
Equipment
direction, respectively forces or moments acting on.ly in or -Z direction, respectively
-X, -l
REFERENCES
l. 2.
1
5.
6. 7.
Faires, V. M., Design of Machine Elements, The Macmillan Company, New York, 1965. Przemieniecki, I.5., Theory of Matrix Structural Analysis, McGraw-Hill Book Co., New York, 1968. Wichman, K. R., Hopper, A. G., Mershon, J. L., Welding Research Council Bulletin 107, Local Stresses in Spherical and Cylindrical Shells Due to External Loadings, Welding Research Council, New York, 1979. Expansion Joint Manufacturers Association, Inc., Standards of the Expansion Joint Manufacturers Association, Inc., New York. Hesse, W. J., Mumford, Jr., N. V. 5., Jet Propulsion for Aerospace Applications , Second Edition, Pitman Publishing Corporation, New York, 1964. Blevins, R. D., Flow Induced Vibration, van Nostrand Reinhold Company, New York, 1977. Lienhard, J. H., "Synopsis of Lift, Drag and Vortex Frequency Data For Rigid Circular Cylinders," Washington State University, College of Engineering Research Division Bulletin 300, 1966.
Heat Transfer in Piping and Equipment
Providing thermal energy to process systems and
5,000 centipoises or more. Such high-viscosity fluids are quite common with coating mixes used in manufacturing roofing tiles. Tracing such viscous mixtures with several tracers has proven to be so inferior to jacketed pipe that the disadvantages ofjacketed systems are offset. With a viscosify of 4,000 centipoises, one should consider jacketed pipe.
maintaining desired temperatures are key responsibilities of mechanical design. Although they border on chemical engineering, the concern here is with the mechanical as-
p€cts
of
process systems, and not with the processes
themselves. (Chapters 2 and 4 illustrate how mechanical design borders civil engineering in a similar manner.) Process systems require thermal energy for various reasons, and the most common are to accelerate chemical reactions; to heat products and services so the products remain liquid and do not clog piping or equipment, such as with asphalt and roofing materials, viscous fuel oils, and syrups; and to cool products and services, for example to protect epoxy from polymerizing. In piping systems there are three ways to transfer heat to the process service-tubular tracers mounted externally to the pipe, jacketing the process pipe with a larger pipe forming an annulus in which the heat transfer fluid flows, and electrically tracing the pipe. We will discuss the first two types of transfer systems.
Most jacketed pipe is limited in commercially available sizes. Normally 8-in. by 10-in. is the largest size
JACKETED PIPE VERSUS TRACED PIPE The difference between traced pipe and jacketed pipe is obviously the heat transfer area available on each. The two types are depicted in Figures 3-1a and b. Jacketed systems offer more heat transfer area, but are expensive and can be difficult to maintain. One common nroblem is cracks that develop from the thermal stresses that are incurred. Such cracks, which are difficult to locate and re-
pair, can cause the heat transfer and process fluids to mix, which can have catastrophic resulis. However. the disadvantages ofjacketed pipe must be weighed with the economics of adding tracers. A proven guideline is to use jacketed pipe for process fluids with viscosities of
front vi6w
Figure 3-1A. Traced pipe.
103
104
Mechanical Design of Process Systems
Figure 3-1B. Jacketed pipe. (Courtesy of Parks-Cramer Co.)
Heat Transfer in Piping and
Equipment
DIMENSIONS COMMON TO ALL
stzE
o
tPs
tPs
u
Y2t1Y1
Y2
1r/a
2.56
1Y2
2.56
\/+
2
3.44
1t2
,l
1Yarz
'|
1l2x2l2
3OO
T NPI
.oD
Dia.
BC
RF
K
OD
4.25
0.62
3.12
2.00
0.75
5.00
0.62
3.88
2.84
0.75
4.75
3.62
0.75
6.50
3.62
0.62
No.
Vq
6.00
0.75
%
6.00
0.75
Dla,
BC
RF
K
4.88
0.75
3.50
2.OO
0.88
6.12
0.E8
4.50
2.88
0.88
0.75
5.00
3.62
0.6E
0.75
5.00
3.62
0.88
1L/2
,
7.00
0.75
4.12
0.69
7.50
2
3
4.69
1
7.50
0.75
6.00
s.00
0.75
8.25
3x4
3
4
4.44
1
9.00
0.75
7.50
6.19
0.94
4x6
4
8.50
1.00
4.31
6xE
6
I
8x10
8
10
4.31
4.88
1 1
1Y2
11.00
I
0.88
9.50
No.
6
2x3
L/^
0.8E
5.EE
4.12
1.00
I
0.68
6.62
5.00
1.12
'10.00
8
0.8E
7.88
6.'l9
1.25
12.50
12
0.88
10.62
8.50
1.44
'L00
13.00
10.62
1.62
'15.25
12.75
1.88
'13.50
0.88
11.75
10.62
1.12
15.00
12
16.00
1.00
14.25
12.75
1.19
17.50
16
.Flanges of higher pressure class and other facings available.
Figure
LB:
Holeg
Holes
I
3/tt1Yz
150 LB.'
3-lB.
Continued.
Figure 3-1C. Expansion joints for jacketed pipe. (Courtesy of Parks-Cramer Co.)
105
106
Mechanical Design of Process Systems
DIMENSIONS 150 LB., DUCTILE IRON. STEEL FLANGE DIMENSIOIiISi OD ID
Holea
A
srzE
tPs
lns.
mm.
No.
Dla-
BC
RF
1Y1r2
1Y4
6.00
152
4
o.75
4.75
3.62
1t/2f,Y2
1Y2
7.@
178
2
M
0.75
x
T
lns.
mm.
U
TIPT
24.OO
610
3.44
3/t
4.12
o.75
25.00
635
6.00
5.00
0_88
25.38
645
4.69
'I
3/q
7.50
190
4
3x4
9.00
28
8
0.75
7.50
6.19
1.00
26.00
660
4.44
'|
4x6
11.00
279
6
0.88
9.50
8.50
't,12
26.50
673
4.31
,l
6x8
13.50
3/$
8
0.88
'tl.75
10.62
't.19
27.U
4.31
1
16.00
406
12
1.00
14.25
12.75
1.38
u.25
470
4.8
1Y1
8x10
I
All dimensions in inches (ins.) unless otherwise noted. 'Flanges ol higher pressure class and other facings available.
Figure 3-1C. Continued.
carried in stock, but larger sizes can be specially fabricated. When a jacketed system is selected, a careful stress analysis should be made to ensure that the system is not overstressed. (Chapter 2 covers such stress analyses.)
TRACIilG PIPING SYSTEMS When process fluids have low to moderate values of viscosity 1g 4,500 cp), it is best to trace them with tubes containing hot or cold fluids. The tracing can be done with or without heat transfer cement around the tracer tubes (Figure 3-2). We will consider two methods for analyzing both systems. Usually, steam or hot oil is used to trace systems. Hot oil is used when the fluid to be traced is hotter than saturated steam at typical operating pressures, which would be about 350'F and above. Hot oil systems are some-
what simpler than steam-traced systems, because steam traps and condensate return lines are unnecessary. However, hot oil can be expensive and if there is ample auxiliary steam available for tracing, steam is favorable for moderate- to low-temperature systems. When there is much piping to be traced, steam at the available temperature and pressure may condense into hot water before tracing the entire system. For these situations, only hot oil can be used. Thus, hot oil is used in tracing applications where steam is either not practical or not available. There are many types of hot oils marketed by various chemical companies as heat transfer fluids.
It is most
desirable and should be mandatory to use
heat transfer cement in tracing tubes on process piping, because it provides more heat transfer area. Heat transfer cements are available in all major countries and in
some of the larger Third World countries. However there are times of expediency in which traced systems must be installed without the cement.
Heat Transfer in Piping and
Equipment
1O7
Traced Piping Without Heat Transfer Cement The modes of heat transfer in a system without heat kansfer cement are natural convection through the air space inside the insulation, and to a much lesser extent, direct radiation between the tracer and pipe or equipment. Since the tracer tube and pipe surface have very little surface contact, conduction is minimal. Any effect of film resistance to heat transfer between the air space outside the insulation and the inside insulation surface is negligible. The procedure for tracer design without heat transfer cement is outlined in the foliowing steps (see Figure 3-3 for parameters) :
l.
Assume a value of air space temperature equal to or greater than the minimum temperature of the process temperature inside the pipe.
Tr = aclual insulation thickness
Figure 3-3. Traced pipe with one tracer under bottom without
HTC.
2. Estimate the natural convection coefficient,
h",
from the tracer to the air space from Figure 3-4. 3. Calculate the equivalent cylindrical insulation thickness, T", as
'"'\ 4.
: {q'r=l)'" {9': =t) 2l\Di
(3-
l)
I
Determine the outside film coefficient of the insulation to atmosphere, h., from Figure 3-5 and calculate Uo from the following:
T] kt
1
u. Di
:
ho
=
ki
:
T"
=
(3-2)
h.
inside diameter of pipe insulation, ft outside film coefficient from insulation to atmosphere, Btu/hr-ft2- "F thermal conductivity of insulation,
Btu/hr-ftz-'F
T,
:
Uo:
equivalent thickness of cylindrical insulation, actual insulation thickness, ft overall heat transfer coefficient from the air space to the atmosphere, Btu/hr-ft'-"F
5. Formulate a heat balance around the air
ft
sDace.
solving for the temperature of the air space. q:
- L) a: Q: ) (r)(Qr) (v,xA")(t"
(hJ(AJ(n)(tt
Figure 3-2, Various traced pipe configurations: (A) single traced pipe, with tracer under pipe, with heat transfer cement (HTC); (B) process pipe with two tracers with HTC; (C) one tracer on top ofprocess pipe with HTC; (D) process pipe with three tracers with HTC; (E) jacketed pipe.
where Ao
:
h,
:
A, :
(3-3)
(34)
t")
(3-5)
outside insulation surface area, ft2lft outside surface area of tracer tube, ftzlft convection film coefficient from tracer or heat transfer cement (HTC) to air space,
Btu/hr-ft
-'F
108
b
.c
Mechanical Design of Process Systems
1.o o.9
o.a o.7
oo,ouTstDE D|aMETER OF CyL|NDER ltNcHESl h: NAIURAL
h.
.^.
CONVECTTON
FtLM COEFFICTENT
Figure 3-4, Natural convection on horizontal cylinders.
.o.25
o.5lt-l
9
a: 7
6 5
35710 Figure 3-5. Heat transfer outside horizontal pipes.
152030
50
OUTSIOE DIAMETER OF INSULATION IINCHESI ho=COMBINED OIJTSIDE HEAT TRANSFER FILM COEFFTCIENT
Heat Transfer in Piping and
: heat transfer per lineal foot from air space to atrnosphere. Btu/hr-ft Qz : heat transfer per lineal foot from tracer to air space, Btu/hr-ft L : temperature of outside air, oFoF ti = temperature of tracer fluid, "y : safety factor; 1.3 for piping systems without
Qr
HTC, 2.0 for piping systems with HTC, 1.5 for vessels without HTC, 2.5 for vessels with HTC
Traced Piping Wlth Heat Transfer Cement One mode of heat transfer in a system with heat transfer cement is conduction from the tracer tube through the pipe or vessel wall to the point of the wall most distant from the tracer. The thermal distribution of such a sys-
tem is shown in Figure 3-6. The other mode of heat transfer is the natural convection from the tracel and the pipe or vessel wall to the air space. Thus, the air space temperature is lower than the minimum process pipe or
wall temperature. The contribution of radiation from the tracer and pipe or vessel to the inside wall ofthe insulation is negligible, as is the film resistance to heat transfer on the inside insulation wall. The procedure for tracer design with heat transfer cement is as follows:
1. Determine the scheme of tracers to be applied using Figure 3-7. Calculate the metal wall area (equals wall thickness) A*; the outside surface area of insulation, Ao, the outside surface area of pipe, Ao, and the outside surface area of tracer tube or heat tfansfer cement
(Hrc).
.
Assume a value of the minimum pipe wall temperature, to, equal to or greater than the minimum process f luid temp€rature. 4. Assume a value of air space temperature, ta. 5. Estimate the natural convection coefficient, h", 3
from the HTC to air space. 6. Calculate T" using Equation 3-1. 7. Determine the outside film coefficient of the insulation to the atmosphere, h., from Figure 3-5 and calculate Uo from Equation 3-2. 8. Calculate the average pipe wall temperature tp and estimate t}le natural convection coefficient from the pipe or vessel to air space, ho, from Figure 3-4.
=
o
COLO SURFACE TEMPERAIURE
Figure 3-6. Heat transfer by radiatlon.
109
vessel
2.
lf ta > ti, then the system is adequate. The maximum spacing of tracer tubes for cylindrical vessels is calculated in the same manner except that a flat plate approximation (T. = t) is used to compute the heat losses, or Q values.
Equipment
',{s-J[(!e"" I-e#9]
It2I
F
110
Mechanical Design of Process Systems
Figure 3-7, Temperature distribution of a two tracer system. (Courtesy of Thermon Manufacturing Co.
9. Formulate a heat balance around the pipe or vessel wall and air space and perform an iteration analysis solving for t" and te with the following steps:
: Qz: Qr
(u.)(,\)(r" (hJ(At)(tt
:
(2Xq)
Q+)
(r)(Q:)
Qn
-
t")
- t") (hPxApxtp * t") (I*)o.u,, * ,,,'
:
= = k : n, : Q: = Q4 : Ap ho
(3-e) (3-10)
Qz+ Q:)Qr where Am
(3-6) (3-7) (3-8)
(3-l
t
temperature of air space, 'F ambient temperature,'F length of heat flow through metal, ft pipe temperature at point nearest tracer, 'F pipe temperature at point farthest from tracer.
.F
Likewise for traced systems with HTC, for traced vessels, the maximum tracer tube spacing for traced vessels is calculated by the same procedure, except that the flat plate approximation (Te : t) is used to compute the heat losses, or Q values.
l)
cross-sectional pipe wall area (equals pipe
Condensate Return
thickness), ft,/ft outside surface area of pipe, ft /ft convection film coefficient from pipe to air space, Btu/hr-ft2-oF thermal conductivity of vessel shell material,
Steam differs from hot oil in that condensate is formed by loss of heat energy. During energy shortages, the use of condensate return lines is normally justified. Considering the use of 1/2-in. tracers, normally a l-in. conden-
Btu/hr-ft2-'F number of tracers, dimensionless
a ltlz-in.
heat transf€r per lineal foot from pipe to air space, Btu/hr-ft heat transfer per lineal foot from tracer to
pipe, Btu/hr-ft
sate subheader
will handle condensate from 2-8 tracers, 9-20 tracers, and a 2-in. sub-
header from
header from 21-50 tracers. With a condensate collection and return system the steam supply pressure should be at least 100 psig. Even though these rules of thumb are well tested in field practice, the reader is encouraged to calcu-
Heat Transfer in Piping and
late the condensate load for his particular needs. Consider the following analysis:
:
Total heat loss from steam tracer Qr For systems with HTC (by adding Equations 3-'7 and 3-9),
Qr:
Qq+Qz
(3-12)
For systems without HTc,
(34)
Qr:Q:
The steam in the tracer is assumed to enter the system as saturated steam at an initial temperature or pressure. Considering the amount ofheat loss over a given temperature range, the condensate load from n tracers on a given process pipe is
,ir
: $, nnfc
(3-13)
rum
where hr8
:
Equipment
11
1
enthalpy of vaporization (also called latent heat of vaporization), Btu/lb
The steam in the tracer is assumed to transfer energy as heat for a given mass of steam under constant pressure. A typical condensate return system is shown in
Figure 3-8. When collecting condensate, care must be taken to prevent water harnmer caused by the mixing of condensate at different temperatures and pressures. To prevent water hammer in condensate systems, spargers and steam separation kegs should be considered. To size the condensate return lines, as well as the tracers themselves, use the methods presented in Chapter I for line sizing. In systems where a large quantity of condensate is formed by steam flashing, a condensate return
pump may be required. Normally, condensate return pumps are the horizontal centrifugal type. Pumps and their applications are presented in Chapter 6.
STEAM SUB
E
HOR.
COND. HOR.
SEEDETAIL A(TYP.)
SEE FIGURE 3
COND HOR.
SEE
OETAIL
A
(wP.) OETAIL-
Figure 3-8. Condensate return header in tmcer system. (Courtesy of Thermon Manufacturing
co.)
112
Mechanical Design of Process Systems
Jacketed Plpe
for Dy'D"
Figure 3-9 illustrates details ofjacketed pipe. Forjacketed systems, it is customary to assume a temperature drop over a given length of pipe for hot oil. In applica, tions of hot oil heating a viscous fluid such as asphalt, 100'F drop per 100 ft, or I 'F per foot, is quite common. If one is not familiar with a given service, then a heat balance must be made, like those done for tracers, However, using a temperature drop over a given lenglh of pipe simplifies the analysis and has been proven in practice, because all examples cited are from actual, successful operating systems. The following steps illustrate one such method of designing jacketed pipe: Compute the overall heat transfer coefficient, U, by the following relation:
For an annulus, the hydraulic radius, Rs,
l.
N*"
:
:
Y%
D:4Rs ._
Nr"
: o.o2o Nr;'Nr
,1-
9d
rooo
"LP) ($
(3-18)
(3-19)
NC"
(3-20)
and thus Nru"k
(3-2r)
2. After solving for
the overail heat transfer coefficient, determine the amount of heat transfer from the relation
(3-r5)
r.86(NrJ"'(N",)
d.o
in which
tt
hr:
-
0.2
(3-14)
[h':
where
Dr-i
Rs
' .D-
u = Er*r+ln(ry'r'* ll-r kzr h
>
k$'"
(3-
l6)
q
:
UA(LMTD)
where
0_17\
(oeJ
A:
outside area of inner tube. ft2. and the LMTD is based on the assumed rate of heat loss per unit lengrh of pipe.
o socror.t
LR
PE(rcESS IINE
PrJ:1r2, 2r3,3t4,/rt 6linl
(3-22)
ptt= t'ga,&1,4,€
Figure 3-9. Standard fabrication details for jacketed piping.
Heat Transfer in Piping and
Equipment
113
END OF JACKE'T DETAIL
v2t. ss n
BING
PROCESS LINE IPI JACKETIJI
CUIOE
PrJlinl
z'z
31
OETAII- BANS PLACEO EVERY rEN FEEi OF PR@ESS IINE
GLJtoE BAR Srz€linl
z t" i,u
r4r15 -2 rrYi6-r
4
4t6
BAi
-le'9r-
-t
PFOCESS LITIE
rrNE srzE prJ
li.L
ll
Figure 3-9, Continued.
In
to€
in tong
114
Mechanical Design of Process Systems
The LMTD is solved using the following formula:
_
(GTTp)
-
(UrTp)
/1-r1r
, /crro\ ]n l-l
\rjrTD /
where
LMTD : logarithmic GTTD LTTD
: :
To facilitate manual calculations refer to Figure 3-10 [1]. The concept of the logarithmic mean temperature differ-
ence is widely explained in most basic engineering textbooks, so its explanation will not be presented here. The reader is referred to Kern [2] or Ludwig [3] for a formal
description of the significance of the LMTD. mean temperarure difference
greater terminal temperature difference lesser terminal temDerature difference
3.
Once the amount of heat transferred is determined from Equation 3-22. assuming a given temperature
tm
Chart for Solving
90
MTD Formula
80
GTTD.LTTD -"- _ GTTD t-o8e LrrD
,\,rn
70 60 ^o@
.c,*
50
.rk@'
to,4
40
i5
tll o
E
F
t E
J
Greater Terminal Temperature Difference
Figure 3-10. LMTD chart.
(O
1978 by Tubular Exchanger Manufacturers Association. Repdnted by permission.)
Heat Transfer in Piping and
drop, the amount of flow rate ofthe heating fluid is determined by
q
:
1
15
jacket (outside the tank) and exits through another side heating the vessel's contents. This can be seen in Figure
)-tzrirCoAt
where rir At
: : :
(3-24) hot fluid flow rate, lb/hr specific heat of hot fluid, Btu/lb-"F hot fluid temperature drop
From this formulation we determine the flow rate required.
4.
Equipment
Using Figure 3-11, the amount of pressure drop in the annulus is determined and added to the Dressure
drop in the whole sysrem (which includes the piping connecting the annuli). The pressure drop for the piping other than the annuli is determined by using the methods presented in Chapter 1. Chapter 6 shows how to select and size the pumps to handle fluids that usually require jacketed services, such as hot oil.
Before we analyze in detail these various components, we must first look at the overall heat reouirements of the vessel to determine how much heating surface is required. The controlling criterion in determining the amount of heating panel surface area of a vessel is the transient state, i.e., how much surface area is required to heat a given mass of fluid of specified properties to a
specified temperature within a specified time. Figure 3-13 illustrates a control mass inside a oressure vessel. Consider two transient boundary conditions in the vessel-the fluid resting at steady state and the fluid moving through the tank at a given mass flow rate. Thus, the following two criteria must be established before the heat transfer area required for a process vessel can be determmeo:
1. A vessel shown in Figure 3-13(a) contains a static fluid of X gallons at an initial temperature, Y'F. How many degrees of temperature per hour will the fluid mass rise for a given surface area of
Once the flow rate is determined, the hydraulic analysis made, and the pressure drop judged adequate for the size ofpumps selected, the jacketed system details can be
2.
designed.
Typical jacketed piping components are depicted in Figure 3-9. In extensively jacketed systems, valves can be procured that have jacketed spaces built in. These types of valves are recommended for services where jacketed pipe is required (p > 5,000 cp). Some of these valves are shown in Fieure 3-9.
clamped-on jacketed coils? Using clamped-on jacketed coils shown
in Figure 3-13@), how many degrees of temperature per hour will be transferred to a given mass of fluid of defined properties flowing through the vessel at a constant mass flow rate with an initial temoerature of Y'F
These two criteria are established bv considerins the following relationships:
:
Vessel and Equipment Traced Systems
Q
Systems that require piping to be either traced or jacketed likewise require similar components for vessels.
and
The complexity of traced components depends on the viscosity of the process fluids being handled. For highviscosity, non-Newtonian fluids special items must be added to vessels, such as agitators that are composed of blades and usually powered by electric motors. There are many reasons to use agitators, and one of the most common is to keep suspended particles in a non-Newtonian fluid evenly distributed to prevent particle settlement on the tank bottoms. There are two basic types of heating and cooling devices used for vessels-internal and external iackets that fit on the inside and outside of the vessel, respectively. These jacket types are shown in Figure 3-12. The hot fluid (normally steam or hot oil) enters one side of the coil and flows through the baffle (inside the tank) or
Q
:
mcpat
(3-2s)
UA(LMTD)
(3-26)
Equating Equation 3-25 to 3-26, we obtain
At
:
UA(LMTD) mCp
(3-27)
The U value, or overall heat transfer coefficient, is calculated on the basis of whether the panel of heat tracing tubes are clamped on outside the vessel or located inside the vessel. These overall heat transfer U values are determined through extensive laboratory tests and accumulated field experience. The U value used in calculations should be that recommended by the heat transfer panel manufacturer, as various panel designs are available and the calculation of the U value analvticallv can
116
Mechanical Design of Process Systems
rh" x1" s,ch.40 Jackeled Pipe ol jacketod pipe (tiw 2010: lengrhs) and inclsde live 1" o.D. x.065" wal tubing jumpplus overs entrancs and exit losses. Warer @ 60'F. (16"C,) curves based on 100 l€et
tt; I
=
A
P-inchesoluater I
Flgure 3-11A. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
't
Heat Transfer in Piping and
Equipment
,a" x1Y2" Sch.40 Jacketed Pipe curues based on 1oo reet or racceled p'pe (rrv;20 o_ 3d" O o r 06s' wal lubing iump_ lengths, ano Include 'ive €xit losses. Water @ 60'F O6'C) overs plus €ntrance and
dl
o =
Figure 3-118. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
117
I 1
18
Mechanical Design of Process Systems
f, fi
{. 1" x 2" Sch.40 Jackeled Pipe curyes based on 100 leel ol jack€ied pipe (livs
20{"
rive t4" o.D. x .065" wall lubrng jump_ rengrhs) and 'nclude and exii losses. water @ 60'F- {16'c.} overs plus entrance
E J I
o = J
g
A P- inches
of water
Figure 3-1|C. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co')
Heat Transfer in Piping and
1Y4"
Equipment
x2" Sch.40 Jacketed Pipe
Cutues based on 100 leet ol jacketed ppe (lve 20:0" lenqths) and include live 74'O.D. x .065'walrlubrnq jump overs plus entance and exit Losses. Wate. @ 60"F. (16'C.)
d
A
P-psig
<'
ut
o =
A
P
-
inches ol
water 3
Figure 3-11D. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
119
120
Mechanical Design of Process Systems
1r/a" x
2V" Sch. 4O Jacketed Pipe
ot jackered pipe (Uve 2010' r;'O D. ! .065" wdl tJbrng jumplengrl^sl dnd r clude rive'eet overs pr!s entrance and exl rosses waler @ 60,F. (16.c ) Curves based on 100
AP-psig
t 'to
= J
Figure 3-11E. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
Heat Transfer in Piping and
1Y2"
Equipment
x2t/2" Sch.40 Jacketed Pipe
Curues bas6d on 100 teei ol jackered pipe (live 20!0" lenglhs) and incrude nve ya" O O x obs" wrll ruo,rg tuhpovers plls enrra.ce a.d ext losses. water @ 60"F. (16'c)
lD I
=
Figure 3-11F. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
12'l
122
Mechanical Design of Process Svstems
2" x 3" Sch. 40 Jackeled Pipe Curves based on 100 leel ol iackeldd pipe (iive 2010" lenolnsl and nclude live 1" O.D. (.065'sall rubnq_Lmpovers plus entrance 3nd exit rosses water @ 60.F. 06"c.)
E
6 = J
A
P
-
inches ot water
Figure 3-11G. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
Heat Transfer in Piping and Equipment
3" x 4" Sch.40 Jackeled Pipe curves based on 100 leer
ol jackeled pipe
(tive 20'0"
l6n9rhsj and Include l,!e I" o.D ^ 064 rali rlbr.g tuhp. overs plus enl.ance and exil losses. Water @ 60'F. (16'C )
d
A
P
- psig
o
I
=
Figure 3-11H. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
123
124
Mechanical Desisn of Process Svstems
3" x 5" Sch. 40 Jackeled Pipe CLNes based on 100 leel ol iackeled pipe (live 2010" lengihs) a.d include live 1" O.D. x.065" walllubing jumpovers plus enirance and exil losses. Waler @ 60'F. (16'C.)
o = J
A
P
- inches ol waler
q
Figure 3-1 11. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
Heat Transfer in Piping and Equipment
4" x 6" Sch. 40 Jacketed Pipe Curues based on 100 leei oi jacketed pipe (uve 20'4" lengrhsl and ,ruluoe lve I' O D ^ 065" $Ell rlbrnq tunp. overs pius entrance and exn losses. Water @ 60'F. (16'C.)
E
o =
A
P
-
inches ol
wate. q
Figure 3-11J. Engineering data pressure drop through jacket. (Courtesy of parks-Cramer Co.)
125
Mechanical Desisn of Process Svstems
6" x 8" Sch. 40 Jackeled Pipe curues based on 100 ieer
oi
iackered pipe (nv€ 20a0'
lenglhs) and inclLde nva I O o r 065'war' ruo ng Lmp overs plus enlrance and exil losses water @ 60"F. {16"c.)
AP-psig
7
,LENT )aa:
-:,-:
t -
j:
o(
7., o(
E, o(ra
lo
=
=, a
7
':: AM tN/ \R
::::l::::l:
::::l::.1:.::1.::t,:
Park :s -l ,fal ne JACKETET
NG
l,ill A
P
- inches ol
SYST :l\4S
r: t
COMPONENTS
'
1
,'1,,,,1,,
water q
Figure 3-11K. Engineering data pressure drop through jacket. (Courtesy of Parks-Cramer Co.)
Heat Transfer in Piping and Equipment
8" x 10" Sch. 40 Jackeled Pipe cu.ves based on 100 ieet ol tackeled prpe (rve 2oro, leng l-sl aro incrLde trr- t" o D. r 06r" do r_b'.q tu-p. overs pL!s enlrance and exrr tosses. water @ 60.F {16.c )
AP-psig
-/;; !r:::r'
i,? ,/..:
T FTOW
JT
i:,1-,:
h-0b,
F=
.1-=:
t1=
/. /
I
l::::
F= t.-
t:
lv
=, (r.
c
)1
@
7/.
o, =
o =
/ ul
L AMINAR
A
I
:l
Pe
:::l't
':r:i::::l
k s-l fame I
,l
I
i. coMP ONEI {TS !l
:;::l ::l ...1..1
A
Figure
3-1
1
L.
P
-
inches ol
:
:::.[] .. .t.._ .
.
.1.-.
water q
Engineering data pressure drop through jacket. (Courtesy of parks_Cramer Co. )
127
128
Mechanical Design of Process Systems
Moderate bracins for mediurn agitation -cooditions. All 5rac6 are from vessel wall and no circumIereotial rings are used.
Brrc$ 6ay be weldcd ot
bolted, Hemocd edgc pcr mounting lug detail, page ,{4. desirable.
Flexible hoses desirable her€ w-hen possible aod wnen lorces are Severe. Also particularlv imoorc ant, foi altematirig heiting
ano cooltnq
conorttons.
Speial bracing.for heavy aertauon conorarons,
Figure 3-12A. Heat transfer internal plate or panel baffles inside a vessel. (Courtesy of Tranter, Inc.)
Heat Transt'er in Piping and
,/ w*\ \ \ / _-.--\r\1
'ffiFt* \-*'/ ,(?,''l \t\ l[ [ l\ l\
Equipment
129
C=2%" MlN.
e
I I
A
D ----v
3RD. S€T OF CHANNETS USED WHEN B DIM. EXCEEDS 7T'
HEADER SIZE
OVER,AI.I WIDTH I(NO. OF PLATECOTL-|) (CJ.3',]
Figure 3-128. Schematic depicting how heat transfer panel plates heat up or cool down process fluid in tank. (Courtesy of Tranter. Inc.)
L-3S Luqs (typ)
ffi N Figure 3-12C. Heat transfer panel plates designed to curved surfaces. (Courtesy of Tranter, Inc.)
fit
on
Mechanical Design of Process Systems
lead to erroneous results if the exact details of the Danel design are not known. Most panel manufacturers hesitate to reveal such detailed features, so the U values on the low side are recommended for situations where the panel manulacturer does not have a recommended U value. With high-viscosity fluids such as tar and asphalt at temperatures of 300-700'F. a good U value lor lnternal baffle panels is 9.60 and for external clamped-on panels a
value of 4.00 is reaSonable. After a U value has been selected, Equation 3-26 is solved, revealing the net temperature change per hour. The second criterion involves the mass flow rate ofthe fluid through the vessel. To estabiish this criterion, Equations 3-25 and 3-26 are solved tosether to determine the temperature rise. The analysis o-f both criteria is
L 35 Llgs (typ) Cuslomer shoutd instatl
same
al iifre ol instartairon.
This sketch shows tine conlact pfovrded by the 1?,,
iq -i-
Figure 3-12C (continued). Heat transfer panel plates designed fit on curved surfaces. (Courtesv of Tranter. Inc.)
to
graphically illustrated later in Example 34. Once both transient conditions I and 2 are satisfied bv the selected heat transfer area, the detailed design of the baffle panels (both external clamp-on and inteinal) can be designed. This is best shown by example and done so in Example 3-5. Further applications of Equations 3-25 and 3-26 are given in Example 3-6. In this example a material handling problem is analyzed in which both steady state and transient heat transfer conditions are considered. After reviewing Examples 3-5 and 3-6, the reader is encouraged to always consider transient conditions of heat transfer in similar situations. Transient criteria, as revealed, usually govern to a large degree.
Figure 3-12D. Vessels with typical external heat transfer plate panels. (Courtesy of Tranter, Inc.)
Heat Transfer in Piping and
Equipment
131
Figure 3-12D. Continued.
-'-- -*-i fluid x gallons
v'F
oF/min
Figure 3-13. Two schemes in which the heat transferred must be considered: (A) conrol rnass scheme; (B) control volume scheme.
132
Mechanical Design of Process Systems
HEAT TRANSFER IN RESIDUAL SVSTETyIS
lleat Transfer Through Gylindrical Shells Heat transfer through pipe supports, vessel skirts, and empty branch piping connections to hot or cold headers can cpuse critical stress problems as well as damage to equipment. Excessive thermal deflections can result in unacceptable loads on rotating equipment and vessel nozzles. In cryogenic service, vessel skirts can fail by brittle fracture if the transition temperature point between alloy steels and carbon steel is not considered. This section discusses the analysis procedures for analyzing heat transfer in such residual components as vessel skirts and pipe supports. The methods used have been tested with empirical data and have been used for several years in design practice. For derivations to the following method on heat transfer through cylinders, the reader is referred to the author's paper [4]. Vessel skirts are normally insulated on the inside and outside surfaces as depicted in Figure 3-14. In cryogenic applications, there are many reasons why a heat transfer analysis of the skirt is desirable. The primary reason is the one previously cited-to protect carbon steel components from fracture failure. Another reason involves economics-a tall skirt made of alloy steel is much more expensive than a similar skirt made mostly of carbon steel. Also, we will see how the skirt can actually deflect as a result of this heat exchange. Consider the skirt in Figure 3-14. The vessel is at either an elevated temperature or a cold temperature denoted at the shell-skirt juncture as t.. Thermal conduction
and convection are the controlling modes of heat transfer. The convection can either be considered as natural or free convection, or in the case of wind, forced convection. It has been found that using the free convection coefficient is the most desirable in many cases, since vessels are normally surrounded by other equipment and structures, making free convection more applicable. Assume that the temperature inside the skirt is the same as ambient temperature and wind chill factors are not present. Air seepage under the skirt and open apertures on the shell allow for equilibrium to be established with the outside temperature. The first step is to determine the free convection film coefficient for the outside surface of the oressure vessel skirt insulation. In normal conditions. the air temoerature inside the vessel skirt. ti. is assumed five degrees lower than the outside ambient, ts. The free convection film coefficient is found by iteration using the following equatrons:
,, - [r, ln(r2lrr) -, qlnG!lt2) "--[ kl!r+
ta
=
(Ua/ha
5)(!
-
t5)
No,
=
[d3lgB I At |
NN"
:
C(NG.NP.)-
hl.s : G"i,NN,)/d
@l
flll
= =
+
,
1 l-' * k* -h.J
ln (r+/r:)
t5
(3,600)2]tp2
(3-28) (3-29) (3-30)
(3-31) (3-32)
insulation metal
.f Figure 3-14. Vessel skirt insulation detail. Sometimes the inside insulation is left off.
Heat Transfer in Piping and Equipment
133
For free convection of cross flow around cvlinders. the following constants hold [5]:
l0 < Nc.Np. < 10e, C = O.525, m : lOe
<
Nc,Np,
<
10", C
=
:
O.129,m
tlc Pipe being analyz€d slub pi6ce
)13
-pip€
These relationships are valid for applications for the refining, petrochemical, and gas processing industries. Now, for a cylinder with insulation on both sides, we use the final value of ha-5 after performing iterations from Equations 3-28 through 3-32 in the following equatrons:
^-
"
z
/2"r,.,\
\U,q,/
r tltt tr"'rrl [
l
I
r
l" (t ,ttj
\[
/
^ - ll:+l lroho,ttn . t5) - k2', l\KmAny' [
, [ ,, - (t/'i)lll
l]L
z
1-3'll
tl" {r./rr)
: ztQ
I"
(3-34) (3-35)
Substituting these parameters into the foliowing equation, we obtain the temperature distribution down the skirt length:
.
2(t.
, *
Zt
e-oo
5 =
(3-36)
"zrauJ
The difference between the process temperature inside the vessel and the outside ambient temperature is the main driving force of heat transfer. It is analogous to electrical EMF driving force or the potential energy of height differential from which a fluid is dropped and turned into kinetic energy. The degree in significance of convection is inversely proportional to the insulation thickness. The air around the outside insulation surface is in a state of local turbulence and for this reason the variance of the Grashof number down the outside insulation wall is insignificant. Experimental measurements confirm this fact. The reader will see in Examples 3-7 and 3-8 how to apply this method to vessel skirts. Piping that is supported by piping sections is treated in a similar manner to vessel skirts. Such piping supports are shown in Figure 3-15 in which the pipe supports and branch lines are subject to thermal gradients from a hot or cold process header. Figure 3-15a shows a stub piece used as a piping header support. The temperature gradient through the stub piece must be analyzed to determine if the Teflon slide beneath the base plate will be protected from the elevated temperature inside the process
Fragile piece ol
equipment
U
Figure3-15. (A) Stub piece used as header support: (B) process line is connected to a turboexpander. The line is supported by a short section of pipe welded to a base plate; (C) branch line from a header (hot or cold) connected through a shut-off valve to a ftagile piece of process equipment.
If the process header is in cryogenic service, the stub piece must be analyzed to assure the design engineer
header.
that the carbon steel structural members are adequately protected from temperatures below the transition temperature. Shown in Figure 3-l5b is a common situation in which a process line connected to a turboexpander is supported by a section of pipe welded to a base plate. If the pipe stub deflects enough (shown by 61), the thermal deflec-
134
Mechanical Design of Process Systems
tion could induce a sufficient bending moment on the turbine to cause serious mechanical damage. Figure 3-15c shows a branch line running from a hot
where c and m are determined as previously for skirts
or cold pipe header to a fragile piece of equipment. Even though the valve on the branch line is closed, the residual temperature distribution through the branch line may be enough to cause the pipe to deflect and damage the equlpment. Referring to Figure 3-16, the procedure for determin-
tj :
ing the temperature distribution through the empty branch pipe or pipe support is similar to the case of a vessel skirt. First, solve for the free convection film coefficient on the exterior surface of the pipe insulation. To do this, use the equation for the overall heat transfer co-
h,j
= (k"r.Nr")/d
- t.) + t" Atj : t3 - ti < 2'F
ur:
,"
(;)
,, ,"
(,:)
- r( \ k-
-n;/] ,
(3-37)
(u3/h;) (ti
: l=l
(r,
-
to)
+
(3-39)
follows:
2nk1
^
;"{$
t
/ r- \ r kJ, t't - ---tT l--^J lrrtr"tt:
(3-40)
rn
t
t',
(3-29)
Once Atj criterion is met, we can proceed with the final iterative value for the film coefficient, h.. With this final value. we solve lor the parameters Q, Z. and Z as
efficient:
1,,
(3-32)
(3-38)
to
(3-41)
lll \r,
o Once Q and Z are known, we solve for the temperature distribution with
No,
=
[d37,gB( lAt
l) (3,600),]/rr,
(3-30)
(3-31)
Nr" = C(Nc,NpJ'
ts
=
900'F; ; 300'F
dia., sch.40, cs 3-in. calcium silicate
Figure 3-16. Empty branch pipe with one end uniformly subjected to three temperatures.
tx
2(t. - Zte 'ao =-++L I + e2"au '
5
=
(3-36)
You will notice that the form of the final solution. Equation 3-36, is the same for the skirt problem with insulation on the inside and outside shell surfaces as the pipe problem with insulation on only the outside surface. The difference in the solutions is because of the boundary conditions, i.e., a cylinder with insulation on both inside and outside surfaces versus a cylinder with just insulation on the outside surface alone. The solutions to the basic differential equations are affected by these differences in boundary conditions. For further information on this subject, the reader is referred to the author's paper
t4l.
For cases of tapered vessel skirts the cylinder section can be approximated by using an average diameter. This
approximation is very close to actual results because skirts should not taper more than 15" (see Chapter 4). As a consequence of heat transfer along vessel skirts and pipe connections, thermal deflections will occur. The deflection equations are the same regardless of whar case is considered, whether it is a shell with insulation on the inside and outside surfaces or a shell with only external insulation. The values of Q and Z are determined from the appropriate equations of each respective case.
Heat Transfer in Piping and Equipment
The thermal deflection equations are dependent on the type of material considered since the coefficient of thermal conductivity is the governing property of the particular material being considered. Thking a differential ele-
ment of a shell, we solve for the amount of thermal deflection by
dL :
Since the temperature varies over the shell length, we inregrate Equation 3-42 to obtain the total deflection, 6, as
o= jar- = JL crrrr(xr dx
with d(t) in Equation 3-43. Then, the product of a(t)t(x) is integrated over a length L and we obtain the thermal deflection function for each particular material. For carbon steel, the expanded thermal deflection equation is as follows: (2.496
x l0 ,22)& -
Z) arctan
(elo0
5;
106e0.5
+
(2.496
x lo-)(t, (l09Qo 5(l
(2.496
Z)2(e2l-ao5
+
{rr,,
(2.055
x
l0-3) 1t. * ZY leuoorr l06eo5(1
(1.06 x l0-6) 106
(_ l8(t,
'Ir
+
e2lao
-
z),
sech (LQo 5) tanh(LQ0 5)
+
5)
-
1;
arctan [sinh(LQ0 5)]l
-
+
4Zi,-
Zt
tr
"..] ZrLl arcran rerq" )l + l^i. tv-' )
[sech(LQos.; tanh(LQo
-
87r,
- 2f
,a"--
/
Residual Heat Transfer Through Pipe Shoes Heat transfer through plate surfaces is much simpler than more complex surfaces, because they can be handled with one-dimensional equations that are simple to use. Based on Figure 3-17, we consider the heat balance down throush the shoe as follows:
1)
\l
+
+ arctan [sinhtLQo'y]l
s
etLao
i 5i
-2, [;L..,* r.'o"r] * z,r] -l
B-441
For practical applications in the refining, petrochemical, and gas processing industries, sufficient accuracy may be obtained by omitting the last term beginning with (6.536 x 10-?) in the calculations. Similarly, for stainless steel, the thermal deflection equation is as follows: 6.,
,
2&
-
Z) [8.96 +
(4.1
Ix
10
(106)Qo
5
)Z]
arctan
(eLQ0
(3-45)
Like Equation 3-44, Equation 3-45 can be adequately handled using only the first three terms. The use of these equations will be demonstrated in the examples.
- zr
e:Loo
|
)
5)
e2LQo
-------l1
..
42t.
l0o
t0-
(109
+
x ro ,7]L
x ro ,z'L
(6.536,l0-?)
't---
(2.Oss
(3-41)
The function, c(t), is the coefficient of thermal expansion for the particular material being considered. Values of the thermal expansion were curve fitted over a large range of temperature and a relation in terms of temperature was obtained for various materials. The function for t(x) is obtained from Equation 3-36 and is substituted
+
+
(342)
@(t)t(x) dx
2[5.89
+
135
5)
Figure 3-17. Pipe supported on a shoe.
136
Mechanical Design of Process Systems
/Heat conducted rhrough\
\
shoe to base
plate
(Heat loss by convection from'l shoe to outside l
/- \
air
.-t
Writing in equation form, we have for one-dimensional, steady state flow:
k.A,
l:l = hJp(ar)
(D'
go"F
(3-46)
sos'r 8o3'F
For the conduction process, At : ti - tp For the convection process, At : tp - to Substituting into Equation 346, we have
Ue.
=
8O3"F
-
l=hoAp(tp-r.)
Solving for to, we have
'-888'F
8sa"F
. _ k-A.t, + hoApl-to'^.F 'n- 1L.a. + trrl"I-r where
A. : Ao = h^ = k: L:
(P
x length of shoe) x 2,
(3-47)
Figure 3-18A. Thermal gradient through pipe clamp, clevis,
in.2
\ length of shoe. in 'z free convection coefficient for shoe to air,
Base width
and supporting rod.
Btu/hr-ft2-'F thermal conductivity of shoe material,
Btu/hr-fc"F shoe height, in.
Like the analysis for cylinders, the free convection coefficient, h., can be substituted with a forced convection coefficient. However, most pipe shoes are surrounded by enough obstructions to prevent a direct wind from blowing on the shoe for any length of time. Figures 3-18a and 3-18b show thermal gradients for various simple pipe
A'
:
0.131
From Figure 3-4, ht Calculating T",
h {D' \Di
supports.
*
2t) /
/r rr\
r. = l=l u.
i
EXAMPLE
3-l: STEAM TRACING
DESIGN
Determine the steam tracing requirements for an S-in. Schedule 40 gas-vapor line with a minimum process temperature of 140'F. The piping insulation is 2rlz in. caliium silicate, 9-inch nominal IPS. The system is to be designed for an ambient temperature of 0"F and a 15 mph wind. The tracing medium will be 150 psig steam,
aid tlz-in. copper tubing without HTC will be used for
kr
:
following:
A" =
3.63
ft
=
0.41e
:
=
2.5
0.256 ft
0.08
From Figure 3-5, h"
U. =
=
o.+rs
(2.0X0.04)
:
4.5 (assuming At
:
50'F)
0.292
Formulating a heat balance for t}re system we have the
following: Qr (ah space to
tracing. We first try using two tracers running alongside bottom of process pipe. Calculating the areas we have the
ft'?
Q2 (tracer to
atm) :
air space)
:
(0.292)(3.63)(140) : 148 Btu/hr (2.5)(0.131)(2)Q26) : 147
Btu/hf
The assumed number of tracers is inadequate for 1 1.3.
:
Heat Transfer in Piping and
Equipment
137
I.=9OO"F= PROCESS FLUID TEMPERATUBE
rr i-1 n-l
I
t___
olo
3
ol I
I
I
H_-
o
'{"1 ltll!'1-
*---l
'-
Figure 3-188. Thermal gradient through PiPe clamP support.
D.
Trying three tracers, we have
Qr :
Q: =
:
in.
D" + 2ti :8.0
:
0.667 ft;
=
+ 2(2.0)
12.0in.
:
1.0ft
148 Btu/hr
221 Btu/hr
Since Qz
> (f)Qr,
0.667
2(0.167)
,n [o.ooz
[
A" =
2.095 ft'?lft;
A-^ :
o 216
EXAIIIPLE 3-2: HOT OIL TRACING DESIGN A 3-in. schedule header contains asphalt which is to be maintained at least to 445'F. The 3-in. header is to be traced with hot oil (Ce : 0.50 Btu/lb-'R p = 58.7 lbl ft3 at 475"F). Determine the size and number of hot oil tracers required to maintain the asphalt at a minimum temperature of 450'F. For asphalt, Cp : 0.368 Btu/lb"F at 500"F. For most applications, l/z-in. copper tubing is the standard size for tracing operations. We select a l/z-in. 18 BWG gauge steel tube, At : 0.131 ftlft, k^ : 27.5 Btu-ft/hr-ft2-'n First we will try one tracer, 3.50 + 0.50 :
+
the system is adequate using three
tracers.
Di :
8.00
4.00 in. :
0.333
ft
:
12
Ap
=
o.ol8 fr:
ft :
At :
hr"
=
0.33[ffiu'.*r,,J:
tr"
:
hr"
I 5.059
=
0.203 rt
0.131 ft'?lft
ft
r't,
+ eh,:3.992 + (0.90)(1.185) :
1-0203+ u" 0.1
I
t' - j1 2n,
0'690
0.345
0.667
0.916 ft2lftl'
-
2(1.0)
+ zro.roull
5.059
= u^:0.449
Now performing a heat balance we have 350'F and tn, : 490"F. Using Equations 3-6 through 3-11 with 70'F ambient,
t, =
138 qt : n,
Mechanical Design of Process Systems
- 70) :
(0.449)(2.095)(350
_ 0., (sso -:sojo" = 0.s
\
263.383 Btu/hr-ft
z.z:o
I
: q2 :
: 258.680 Btu/hr-ft Q.25)(O.131X550 - 345) : 60.4248tts/hr-ft q3: (1.383X0.916)(497 .50 - 345.00) : 193.191 qt
-
qr =
(
1.375X0.916)(520
qa
=
jt
< 2qt
Qt
t)1 sl
(ffi/ -
Consider t"
ro
-
350) = 214.1l5 Btu/hr-ft
:
ott'tsso - +ro'
172.174 Btu'lhr-ft
<
2q3
: qz : q3 : qt
0.5
(::L
roo)"'
:
(0.449)(2.095X300
:
216.351 Btu/hr-ft
(
129t = No balance consider t" : 350'F and to, : 456"p
qq
q2 = Q.236)(0.131)(550 q3 = (1.375X0.916)(500 (0.449)(2.09s)(350
: 350) : 350)
I 'tt s\ 9" = Qt 1:::--: -1(0.018X550 \u.J+),/
jq <
2q3
Consider
r,,
=
:
70)
-
263.383 Btu/hr-ft 58.583 Btu/hr-ft 188.925 Btu/hr-ft
450)
=
286.957 Btu/hr-ft
No balance
t" = 345'F
and te2
+10" = os(try#, =
:
2.25
-
445)
:
301.304 Bruihr_ft
No balance
Since we have reached the minimum desirable temperatures for q and to, it is clear that the system will not balance using one Uz-in. tracer. Therefore, we will use two t/z-inch tracers. Referring to Figure 3-2b we consider the
:
4.645
in.
0.387
ft
0.720
ft
ti:2in. :0.167ft
Q.364)(0.131X550 - 300) : 77.421 Bttlhr-ft 1.454)(0.916Xs50 - 300) : 266.373 Bttlhr-ft t)1 \\ q^ = t2) l-::-:l (0.018)(550 - 450) = 286.957 Btu/hr-ft \u.J4)/
qt =
-
: D" = 8.645 in. :
r.+s+
70)
q4
D;
- ruul : 2.364 '- l))u -'-' : 0.5 0.5 \ I
:
\u.J+)/
following:
300"F and te2 : 450oF.
h,
hp
tr1 sl
(2t l_:i_:- l{0.018X550
350) = 58.583 Btu/hr-ft
No balance
=
70)
=
q4
9z
-
Btu/hr-ft
25
/ssn - rso\o :r.375 hp:0.5(""ffiJ t2.236t(0.t31x550
(o.449)Q.095X345
445'F
Di * 2tr , iDr + 2t,l ' = _-_2 lnl\D, l|:0.224
_ '1"
A"
:
2r(0.360)
:
2.262 ft'?lft
h,":033[sffiffi,,t:,,,, h- :
hr.
+ eh, :
1.996
+
(0.90X1.185)
| * -l = U^ = 0.390 u" -0'224 0.1 3.063 t^ : 2tr(2.323) - 2(0.886)(2.323) : : 0.873 ft r, : t' = 2n,
0 873 2(2)
:
3.063
10.479 in.
= o.ztsft
A. = 0.018 ft: Ap = 0.916 ft?/ft consider t" : 350'F and to, : 490'F h, : 2.236i hp : 1'375 q : (0.390)(2.262)(350 -'t0) : 247.010 Btu/hr-ft q2 : Q.236)(0.131X550 - 350) : 58.583 Btu/hr-ft q3 - 1.175 )(0.916X520 - 350) : 214.ll5 Btuihr-ft A, = 0.13t fP/fl:
(
r,": o.s({q::g)'" = 1.383
9a
=
/rt.\
t2\Qt l '1j". | (0.018X550 1d/ \u.z
-
490)
:
544.954 Btu,/h.:
139
Heat Transfer in Piping and Equipment
Consider
L
350'F and tp2 : 500'F
:
(2.236X0.131)(550 (1.375)(0.916)(525 -
(0.390X2.262X350
9r
9:
q. -
70)
:
: 3s0) : -
58.583 Btu/hr-ft
V=
220.4r3 Bt'tlhr-ft
V=
500)
=
454.128 Btu/hr-ft
5o
I
-,"tut
(100)f(454.128) Btu/hr-ft
=
VDP ^, _
Nn"
m
Q
{e38 08)ce
45,412.8 Btu/hr
=
Nn"
: _
22,706.422 Btulhr
:
(c08.2s7)
= -, _--
908.257 lb/hr
t ,r, .i, \ I--nr lz.+s 4l lll . rr / \ou mln/ \
'
hrz
:
1.86(NnJr"(N,)'' (P)'i3
=
t.ezy gpm
A jacketed pipe shown in Figure 3-1b is to be analyzed. The process fluid to be heated is a film coating mixture used in the manufacture of roofins tiles.
ln (ry'rr)
,
(e38.08)ce
kz,:
lb/ftr: C-
l+l [o/ nr -^
: D
-
hr.,
7
Btu
hr-fr-'F
,654.733
4 026
=
to.:+r,oB-tu,
/ rr'\
'" t,-rJ
1.86(3.242)r
=
0 336:
r (7.654.733)r
L= '
loo
(H)
rt
'
f',, = 2.415-Tnr-rt'- - f
1
h:
+
For hot oil in annulus, [6] recommends
For film coating in inner tube, 95.909
1.0. Thus, we have
'(#)(10)#.F
1.0
o=
=
/, , -,lo \
ofChapter 1 and size pumps to handle the hot oil. (Chapter 6 discusses how to select the pumps required to distribute the oil in the system.)
EXAMPLE 3-3: JACKETED PIPE DESIGN
(3-16)
H [:)."
N".:f
Thus, we see that two l/2-in. tracers containing hot oil flowing at I .929 gpm is adequate to maintain the asphalt at a minimum temperature of 450'F. The next step in the design is to do a hydraulic analysis using the principles
ra
i
Laminar flow
In most instances, the ratio plpw
(58.D*
ra ht z
3.242
<< 2,100 +
l\ ill *p
For laminar flow, we have [2]
22,706.422 Btu/hr for each tracer
(0.5) Btu/lb-'F (50)'F
I t4.026)in. Ull,n.7 '- lb 160h,secl sec 1,, '" ""ttr \ /
b'rL\
or, q
#h
(+,J F*r'J (,-r',J Hg)
(j.781)
Therefore, the system is balanced. For 100 ft of pipe,
:
500'F; k:0.1
3.781 ft/sec
qr>2qandq2+q3>qr
9r
Co at
247.010 Btu/hr-ft
3s0)
t1'7 al (2x2) l^'-:j" l(0.018)(550 \u.l r6/
p=938.08
:
0.34
Btu -
lb-'F
NN"
:
0.020
Di/D.
^9,'*"1,,(*]'
:
0.664
>
0.2, and Perry
140
Mechanical Design of Process Sysrems
For the annulus,
Rs
D
.
Now,
hydraulic 1361r,
:
4Rn
:
1.566
3 033
=
in. =
0.131
--
2 250
.-
0.392 in.
ft
For hot oil flowing at 0.5 gpm
Nr" ''
:
:
q
"* ( : 0.75t Rr'' "ts
UA(LMTD)
q
:
k
_
oil, At =
toH
-
toc
:
100'F and,
.' - ..r. Btu th-'F '
Iu
rorR-r,'l
,0.,r,a"
required
ricpat
For hot /rCo
^, "p,
7.80)ftr(72.135).F
It-nr-
q-hr -- 6,381.625 lI ,, ,n" heat transfer
]9:99: - ),0n.24r (0.1s)( L566)
(4o.ro7r
q
'\|i2.+ co / ,0.r, lb-'F
.nr m:-:
Btu " n7r "' ' hr-fC'F/fr n
6,381.625
0.5
Btu
Rtrl
=
127.$21! hr
ooo).F
lb-'F'
Now,
Nr" =
0.020(5,01 r.24D0.8(z.s3s)'t3
_ NN,k
1^
(0.*U*)*'
:
ze.r2r
Err' (29.121){0.071) ntu
D
0.131
hr-ft'/-"F/ft
th
ft
ftr
=
Btu rs.rs:hr-fC-"F
rr -
:
|13.033) + L
For t/z gpm,
(3.033) ln (2.2so/2.0r3)
2.4rs
1 l-' -, 15r$l
ft']-hr-'F
q:
A-
1.178
fPlft
:
:
outside surface area of inner tube
117.800
ft, for
100
500'F and
t. :
459'P
:
459'P
For hot oil,
ton
:
550'F and
LMTD
:
to.
72.135"F
I1,771.400 Btu/hr
Thus, 0.5 gpm is a sufficient flow rate to transfer the required heat to the film coating mixture.
ft ofpipe
In hot oil applications it is common to assume that the hot oil decreases in temperature 100'F per 10 feet in jacketed and traced systems. For the film coating mixture,
:
Rr"
'
or
heat transfer area
tcn
lh
(0.5) _= (t00)oF I- = (235.428) _: hr lb-'F
Ri,r
A:
0.271 gpm required
EXAMPLE 3.4: THERMAL EVALUATION OF A PROCESS TAilK A coating surge tank contains 6,000 gal of fill coating mix (see Figure 3-19). Two problems musr be solved: (a) how many degrees per hour can be obtained from a clamped-on jacketed system, when the fill coating mixture is static; (b) how many degrees per hour can be obtained from a clamped-on jacketed system, when the fill
Heat Transfer in Piping and
Equipment
141
= (92X0.8) = 73.60 ftz shell = (379.347X0.8) = 303.478 ft'?
Flanged and dished head @0O gal
f.1.537 ol
4-internal heat transfer panels
12.82 lb/gal cP=
o'g+
: :
4(107)(12)/1,14
35.667 ft2
The overall heat transfer coefficient, U-value, supplied by the panel manufacturer for applications to the fill coating mix is as follows: Process Conditions (as determined by process engineers
COATING MIXTURE
or client for desired capability of tank): Initial temperature of coating mixture = 360'F Final temperature of coating mixture = 400'F For internal panels, U : 9.52 Btu/hr-ft2-'F For external clamp-on jacketing, U : 4.00 Btu/hr-ft2"F Substituting into the previous equation for At we have
-'^, _ -
(9.52x35.667)(LMTD)
+
(4.0X377.078XLMTD)
(?6,110 ooxo 34l
at:7.410'F/hr COATING MIXTUR€ AT TEMPERATURE t
Referring to Figure 3-19 we can now determine how fill coating mix will rise using external clamp-on jacketing on surfaces of the flanged and dished head, the vessel shell, and four internal panmany degrees per hour the
Figure 3-19. Coating surge tank.
els just considered:
Q -
:
(60)
oal min lb ":' (12.82)'gal :hr" (150)'min -
x 0.34 Btu (t lb-'F'
coating mixture is flowing through the tank at 150 gpm ar 360"F.
Q
From Figure 3-10, we have
LMTD
: (550-360)-(450-4oo)
: and Q : with Q
,
,
[sso '" t4so
-
:104.869'F
:ool 4ool
mceAt
UA(LMTD)
UA(LMTD)
-
{6.000)gal(12.82)
39,229.20(t
-
UA(LMTD)
:
39,229.20(t
gal =
:
+
(9.s2)(35.667)(LMrD)
LMTD th
360) Btu/hr
Now,
1,847.862(LMTD)
DLp
m
:
360)'F
:
=
2L.230(t'
-
360)
39,229.2O(t'
-
:
8)(LMrD) 39,229.20(t'
-
360)
(4.0)(377 .U
-
360)
360)
Now, 76.920.00 lb
Using heat transfer panels shown in Figure 3-12 we compute the toial available heat transfer area as follows:
(550-360)-(450-r')
|'"t450-tl 1550 -
3601
-
21.23(t'
-
360)
142
Mechanical Design of Process Systems
Solving for t,
wP:
(21.23r' (110.394t',
-
1
,642.80)
39,841.956)
ln (450
-
Or el.0
:
eln
WP:
"t
A
(450
-
t')Y
I
0,68
in.'?
:
4a(W)
length (see page 145)
A = 2(O.4125)'? + 2(O.412r'1 : A 0.681 in.'l ^'' WP -1.158 in.
366.12'F
366.12'F - 360"F :
D : 4RH :
6.12'F
The amount of heat required for the system is
0.681 in.2
0.862 in.
The equivalent circular cross-sectional area : 0.584 in.'?
=
r(0.431)'?
The hot oil properties are as follows:
UA(LMTD) (9.52)(3s.667)(LMrD)
+
(4.0X377.078)(LMrD)
,
_ 550"F -
450'F
500'F {since we anticipale in the plates)
OI
Q
:
W: a:0.4125 in. W : effective heat transfer
where
Thus, the temperature rise is
: Q:
cross-sectional f low area
A:2Yr+2wY
=
After several iterations, t' :
Q
:
(450-r')Y
in which 2.718
at :
: (--.Jo*t*
r')
* ,642.80) Letting y _ - 39,841.956) we have 1.0 : ln (450 - t'y (21.23t' (l 10.394t'
wetted Perimeter
=
Velocity of hot oil through baffles
1,847.862(LMTD)
Now,
LMTD
=
1550
- 390) (450 - _366,12) = . lsso -:oo ln |
1t9.789.F
I
[4s0
:
-
p:
58.7 lb/fc
k:
0.071
Cp
:
:
in which Q 1,847 .862(129.7 89) 239,832. 162 Btul hr is the heat transferred to the coating mix.
EXAMPLE 3.5: THERMAL DESIGN OF PROCESS TANK
7.913 ft/sec
Btu/hr-ftl"F/ft
o.5o Btu/lb-'F
366.12l -l
'a =
:
0.15
/^ +. ..rD/rl-nrl ," . \ c- lz
'\
1Co I -
0.3b0 tb/lr-hr
The maximum pressure drop permitted through the internal baffles, which are connected in parallel, is normally 10 psi, thus
*l\Re -- VDp
The coating surge tank of Example 3-4 is now analyzed for detailed heat transfer requirements. The flow rates through the various types of heat transfer jacket
-
(7.e*)
r-t
l-
l'
l,rr.r, \ll ln./
(0.862) in. {-.1.
sec
plates are desired.
0.360
g (lql..'*) rr-
\ I nr
Ib
ft-hr
lntelna! Baffle Plates Film Goefficient Some of the plates used are shown in Figure 3-12. Looking at Figures 3-20, 3-21, and 3-22 we determine the hydraulic radius as follows:
Nr" =
N"':
333'661
f
(0.360)
,j:lh
lu.v/lr-
(0.501 Btu
Rr :j:
't
/
Heat Transfer in Piping and Equipment
From Kern
29 BTU/hr-t12-"F/fl ri :0.44in =O.O37 tt
143
K23:
[],
- : = ro.o27r ([) ,t-.,., I
/tl-
r. = {0.027)
r. =0.545 in = O.O45
,N,,,' ' (uJ"'"
thn
tt
Btu
'hr-ft2-'F/f
llrt l2 in.i
ro.aozrin.
I
\
x 1.
. = qsl R? Btu
(333,661f
8
(2.535)1/r (1.0)
is the film coefficient
hr_fd_.F inside the jacket baffles located inside the tank
Actual Internal Baftle Hot Oil Plate
Film Coefficient Exte?nal to Baff les-Forced Convection The coating mixture inside the tank is in a state offlow across the baffle plates made possible by agitator blades powered by an electric motor. From Perry [61.
rtt =
U.U9
i r\ir-:r.r.o\." /c-J'' "I l-ll l!l p \DJ \ / \k/
Approximated as Circular Tubes Figure 3-20. Cross section of panel plate tube approximated as a
'h9'^ ni =
("il'kl'
number of internal baffle plates
:
(3-48)
cylinder whose surface area is equivalent to the heat trans-
fer of contact area.
4
For coating mix, 10r < NR" < 2 x 106 The properties of the mix are as follows:
p: A
=
k=
95.909 lb/ft3 6,000 Co
:
14,400 lb/ft-hr
0.1 Btu/hr-ft-'F
Other properties related to the internal baffle plate approximated as a string of cylinders with diameters equal to four times the hydraulic radius of the trapezoid plate sections shown in Figures 3-20 and 3-21.
\6 =
angular velocity of agitator, revolutions/hr
\. -
56
/-^ \ 11 lgel'nl min
\ lhr
:
3360 revrhr
/
Lp
:
diameter of agitator plate
Dj
=
10.0
ft
D" = 0.862 in.
:
65
in.
:
5.42 ft
HEATING AREA: A. t= STRAIGHT SECTION BETWEEN CHANNELS
Figure 3-21. String of tubes.
144 k: h,q
Mechanical Design of Process Systens 0.071 Btu/hr-ft2-.F/ft
-
0 0e (oo
r-)
+:r't:'log.o ['s [(o
^[ h:.+
:
or
'qs
eoqJ'^'
,
r4){ r4.4oo)1,
lT -
[i^] o^- *
{lJ2l l]),'
(0.I) l
t\2/
,
110.0/
\41
Now, to solve for the overall heat transfer coefficient, U, we must develop the appropriate equation.
=
the overall area of plate
L=
length of plate,
W:
:
I
lr;h1
,
,
J
(1.0)
18.334 Btu/hr-ft2-.F for all four baffle plates
Let Ao
E'l I u * r" rn tr,rr,r - _r l 2ur k, h,
for these baffle plates,
,, " -it\
n=
7, for which
7o
[(jJto
--l
.
to:'
i:]
LW
I|
width of plate
- art"'
o
+
(0.045t ln (0.431 /0.32b)
I 18.334
[(0.326X949.883)
Referring to Figures 3-20 and 3-21 we have
e
:
UAa
(tr
-
ta) for baffle plate
Ar :
u = 29.492 Btu hr-ftr-'F
sr
The baffle plate area for all four baffles is determined from the baffle plate manufacturer's dimensions, as follows:
LW : wetted area : 2oD rL where W : werred perimeter (WP) LJ
| = '2 D" + r' . n = number of flow circuits
=
Length of channel per
baffle
To account for the residual heat transferred through the plate connecting the hexagon tubes we consider to be the equivalent radius of a cylinder that is the total surface
A=
surface area
2210.431)i"
area of the baffle plate separating the hexagon tubes. Now,
A:
lt.672 fe
D, :
For all four baffle plates,
r'
Zor'
,o,u, distance between channels (Frgure 3-21)
rsl.72t rr) {.:-tf) ln./ \rz
A=
It
Heat Duty of lnternal Baffle Plates
UA.
{f
I - t1) 2T(tr
r" "-T-
finl-2
4(tr.672) ft2
46.690 ft2
For hot oil the anticipated temperature through each plate is 100'R as stated earlier, thus
From above,
-
2trlJ
\.r lzr
1t,
-
r" ln (r./r)
ta1
q:
I L
Kt I
UAAT
Rr', q - (29.492J, "-1:1, (46.690)ft, nr-It'- -f
ta) n
--f
q
in which
U:
:
ft
= Dt 2tr
q=
-
51.'123
:
137,698,1a8
(100).F
f.! nr
Outside Heat Transfel Jaeket Plates
D,Iq*r"lntr./r't * hrII k: [r,hr-z
:
J
In the case of external jacket plates, the heat transfer parameters are based on the dimension, shown in
I
Equipment
Heat Transfer in Piping and
-tgure 3-22, because it is this surface that is in contact rth the vessel wall. Consequently we can analyze the ^ : xfiguration in Figure 3-22 as a tube with circumfer::re'e of W. Hence, we have the following:
: .rhere rr :
i;r1 =
Y7
where
1.375 in.
At =
tube cross flow area
At =
r(0.219)1
:
0.151 in.':
tube inside radius, in. Velocity of hot oil through outside plates
:iom above,
|
: = ;
175
Yz
=
0.21C in. or
D,
:
9.433 in.
:
:
V2
3.134 ftlsec (determined from process data)
internal cross flow area of baffle plate plate manufacturer's data)
The tube equivalent flow rate for the length W mapped :nto a circle or radius rr is by the continuity condition of iluid mechanics,
145
I
(3.134)
vr-
sec
(0.62) in.,
o.Lsrin:
= 6.448
-
:
0.62
ln.2 (from
:sec
vDp I'r (6.448)
lll'l a in. sect0.438r I \12
(0.360)
=
Nn"
in.i
,s8
7, 'g i{rylecl in.1 \ | hr /
lL tt-hr
138,150.85
Solving for the over-all heat transfer coefficient, U, we have
w= 1.375 in 1.,1o.
:
PCo
h,,
:
(0.027)
k
w = eflective heat transfer area For approximalion, analyze the ligure as a tube with a 2Tr
circumference
j = 'l.375
in which, rz = O.219 in., or D2
= 0.438
=
w
=
2.535
(H1.ol ,rrr,rro r5)0s (2.535),/, (1.0)
h',,- = 77.260
in.
Btu
hr-ft2-'F
Equivalent llow, 13 1341/|) 111
=
Perry [6] gives the correlation for heat transfer for jacketed walls to the agitated liquid as follows:
6.448 fusec
Thus for the equivalent tube, rz = 0.219 in. rs = 0.219 + 0.109 = 0.328 in. r+ = 0.328 + 0.375 = 0.703 in.
''
c,
h
: "(;)t')1'(9^k)'
where, tq
5
Dj
k Equivalent Cylinder
LP
N, Figure 3-22. Panel total flow cross section. Contact length w is mapped into an equivalent circular tube whose circuinference equals w.
(3-49)
film coefficient at vessel wall (see Figure 3-22) inside diameter of the vessel, ft = 10.0 ft 0.1 Btu/hr-ft-'F diameter of agitator = 5.42 ft angular velocity, or rotation of agitator 3,360 rev/hr 95,909 lb./fC
146
Mechanical Design of Process Systems 14,400 lb/fi-hr
.u=l t
speciflc heat of coating mix viscosity at bulk temperature, lb/ft-hr viscosity at wall temperature, lb/ft-hr see Table
3-l
(0.703 )
samples.
For a disk. flarblade turbine agitator we find values for a. b, and M from Thble 3-1 as follows:
a:0.54,b = 2A,M:0.14 since40 ( l38,l5l < 3 x 105 following:
,*,(,*)[
(14,400)
, =
U
14.060
:ltr+,+ool]"' lto
II
I lr
: 8.141 Btu hr-ftr-'F From manufacturer's drawings, the shell jacket plare
A,
heat transfer area,
A:
is
37,043.82 in.'?
Now, area of channels in all nine jacket shell plates clamped-on to outside of shell
A' :
q
l-
(0.73) ln (0.328/0.219)
ln r0.703/0.328)
257
.249
ftl
Ar = 100"F for (s.42t(3,360.0X9s.909
+
14.06-l
A' :
substituting above values into Equation 3-49 we have the
h,,. '
)
l(0.2t9)(71 .26)
Laboratory tests were made on the coating mix and the results showed that p6lp* : 0.65. Since the coating mix is a non-Newtonian fluid, it is strongly recommended that the physical properties be deterrnined by a qualified Iaboratorl,. the ratio p5lp* should reyer be assumed to be I .0 for a non-Newtonian fluid without laboratory tests of
fluid
(0.703
-
{8.14lr
hot oil-coaring mix servicc Rr'
' .nr-It':i-_r25t.24o1ft t -
(100)'F
or ,o.ur',o,o
q=
Btu
209
.414.44
Rr,'
--: nr
hr-fC-'F
Thus, II
_
Heat Duty of Jacket Plates Clamped to Bottom Vessel Head The bottom head panel sections are depicted in Figure
l-17. In Chapter 1, Example 1-2 we analyzed the hydraulics for the hot oil flow through the panels mounted Table 3-1
Values of Constants for Equation 3-49 Feynolds Number
Agitator Disk, flat-blade
Range
: V: : V:
7.315 fi/sec 5.237 ft/sec
0.14
40
Heat Duty for Bottom Head Inner Panels
2lt ,/3 2h
0.24 0.14
80
Similar to the shell panel plates above, we must compute the equivalent tube diameter and equivalent velocity. As determined above the equivalent radius is
Paddle
Helical ribbon
0.633 Vz
turblne Propeller
innerpanel outerpanel
2lz
0.54 0.53 0.54 0.36
turbine Pitched-blade
on the tank. From this analysis we determined the following velocities required to obtain l0 psi pressure drop through the panels:
0.21 0.
l8
x
105
8
rr :
0.219 in.
Heat Transfer in Piping and
S.lce the bottom baffles have the same flow area as the .rell plates, the cross flow area of the equivalent tube is
q'
i = n(0.219) in.2 :
in which
I
0.151 in.2
-
uA
at = (8.s90). lr)-hr-ftr-'F Btu
re cross flow area inside the plate channel is found
1r.+r+)n,
147
lroo;"r
for both two inner plates
h,
::om the manufacturer's catalog to be 0.31 in.2. Since
Equipment
:e
equivalent tube circumference is equal to the contact ::mension, w, as above we must compute the equivalent
..locity. Thus
Heat Duty for Bottom Outer Panels (7.315)
-quivalent velocity
= Y.
=
-:' sec
0.151
(0.31)in.2
tcutvatent \ etoclt\
in.'z
{
/r\ r58.7 rr3.600 l-l
I
lt/sec
)
322,453.78
.:
(0.027)
l9J11l r:zz.+s:.28)0" {2.535,r
'r { 1.0)
\u.4J6/
:..:152.2ll
Btu
/^ ^--\
- {0.027) lfffl
'hell
film coefficient is the
same as
for the
Thus,
(0.703) (0.73) ln {0.70Ji0.J281 mt(02lrr(15, rr1- -
,' - |
*
f'n,
:
29
*
.l.l+,SlO
in. (1.375) in. (2)
,, "
-, u
heat transfer area of bottom head plates from rhe manufacturer's data the flow path length is 388.231 in. for one half of the head, hence,
:
1,067.635 in.2
ft2
heat duty
:
area of the two inner head plates
ro.703 r ln
(t.trr:,
29
/^ -^^\ /urI
lu
\0.328/,
2s
34'l
rn lo \0.219/
'
I I'
r+.st+)
: o.lg+ Bt' hr-ftr- "F
A:
heat transfer area
A=
4(1,014.389) in. (1.375)
in. =
5,579.140 in.2
OI
A=
OI
'1.414
--!$nr-rI'--t
| 0.703 _ tO) 9,( t 16:0l,
I 14.914)
A:
1 = (18$.231)
,nr-lt'-'f :tu^=
r
I
Eli, ' r, :8.590. :i^= nr-tt'-'t
A: q:
1t6.303
Thus,
Btu -. : t+.gt+hr-ftr-'F
Let
h,, =
panels,
(0.703) ln (0.703/0.328)
rz.lo..lss.:41)0b r2.s35) '(1.01
\0.438/
Similarly as for inner panels,
hr-fP-"F
The vessel-side
i.r.
lu. /f
0.160
h,2 '-..
r
0. 151
10.75l,(0.438r
Nn.
\-
(5.237rt0.31
-
q
:
38.'144 ft2 for all four outer panels
UA
At =
(6.394)(38.7 44)( 100)
=
24,772.333
ry hr
148
Mechanical Design of Process Systems
Total Heat Duty of Tank At maximum flow
rates the total heat duty is as fol-
lows:
q=
Btu
137,698.148
+
,
hr
209,414.44
internal
shell side
panels
panels
Btu hr
6,368.11
+
24,772.333
two nner
q=
Btu
EXAIIPLE 3.6: TRANSIENT AND STATIC HEAT TRANSFER DESIGN
hr
Roofing shingles are made by adding asphalt, filler material, granules, talc and adhesives to a plastic-glass sheet, which is the basic component of the roof shingle. The process is shown schematically in Figure 3-23. Granules are added last, after adhesives and talc. The sheet must be cooled so that workers can handle it with gloves. Cooling is accomplished by water sprays, circulating water through the rollers, and using radiant heat transfer to the surroundings. The sheet, once cooled to the desired temperature, is cut into specified dimensions by mechanical cutters and then packaged into boxes for
Btu
hr
four outer
panels on
panels on
bottom head
bottom head
378,253.631
P!! hr
From Example 3-4 the total heat duty required is
q-t
=
shipment.
There are two aspects to this problem-static heat transfer and transient heat transfer. First, we solve the static conditions and then the transient case to determine how fast the sheet can be cooled with the coolins svstem designed in the static case.
23g,832.rc28: nr
Now,
q:
Thus, the minimum hot oil flow rate in pipe header supplying the total hot oil to surge tank is 10 gpm, the actual flow rate is 16 gpm.
rh cp At
Static Heat Transfer Analysis Elr"
373.253.631
{0.50)
Rrrl :t:
"-
7,s65.073 (
tb-'F
l00toF
The static criteria to be determined are as follows:
l! nt
1. Specific heat of the composite sheet (Table 3-2).
2.
Mean temperature of the sheet leaving the granule
section flhble 3-3). Elr'r
239
flnln
,832.162
::: nt
(0.50) Btu { 100).F tb-'F
4.", :
7,s65.073
5s.7
:
4.796.64
th
nr
P nr
/r.+a gur\
\ri/
!ftr
Table 3-2
Specitic Heat of Composite Sheet Leaving Granule
lb 0/o by wt. 6.30 L9785
Component wt., Glass mat
16.067 gpm
87.32 96.08
Asphalt
120.58
Filler 4.796.640
th
:nr
58.7.]9'
n'
=
7.48 gall
\- r/ f
Granules Thlc Adhesives q4R
)q t;0-
I
:
Cp
0.2
2',7.4220
o.4
3"t.8682 30.1740 1.9200 0.6375
0.217 0.20
318,42 10000
C, = 10.187 gpm
I 2.03 6. I
Component
0.299 Btuilb-'F
o.2 0.50
o/o
ol
Cp
o.395'7 10.9688 8.217 4
6.0348
4.0128 0.3188 29.9483
Heat Transfer in Piping and
3.
Table 3-3 Mean Temperature ol Sheet
80'F 400'F
(1.978s)(0.2X80
+
=
-
t^) + (27.422)(0.4)(400
.8682)(0.22)(400
-
t.)
(30.17398X0.2)(t. - 80) + (1.92)(0.2Xt(0.6375X0.5)(r. - 80) 31.656 - 0.396 t,
-
:
(37
0.2 o.2 0.5
80"F
10.969
6.035 t. 25.50
-
where
t. :
t^ +
-
3332.402
482.',784
313.633'F
+
-
8.331
0.384
t. -
t.
30.720
149
Heat to be removed from sheet and amount of wa-
ter required.
Leaving Granule Section Q = mcp At for each component Temp. of component Component prior to mixing Cp Eo by wt. 0.2 1.9785 80'F Glass 400'F 0.4 2'7.422 .A.sphalt 400'F 0.22 37 .8682 Filler Granules Talc Adhesives
Equipment
30.17398
r.92 0.63"75
-
t,)
0.319
t- :
313.63'F (from Table 3-3)
At:313.63 -212 = Specific heat of sheet : weight of sheet
:
101.63"F 0.299 Btu/lb-'F
0.9375lb/ft2
Thus, the amount of heat to be removed per square foot is mCpAt
=
(0.9375X0.299)(101.63)
=
29.49
:
3.0
t.
.t 2t
Btu/ft'?
b. Sensible heat loss through rollers Btu/hr
+ -+ 80) 4387.520
+
a.
x
106
c. Heat loss through forced convection and radiation of heat passing through air medium is determined as follows:
At
:
:
313.63 90 223.63"F = temperature difference between sheet and ambient air
-
t ] |I
FINAL COMPONENT
Figure 3-23. Process of manufacturing roof shingles.
'150
Mechanical Design of Process Systems
For convection,
Q:
For 600 shingles/hr (or 144,000 Btu/hr) the heat removal would be : (144,000X0.9375)(O.299)(313.63 - 125)
hAAt
= h."^ :
For flowing air, h,in Use
h. =
removal>
Thus. Total heat
=
t2
s.708
fr2
For vaporization,
Qv
|
=
Heat removal requtled
and the cooling system is adequate.
For radiation,
h,
7.614 mm Btu/hr
23 Btu/hrtfP l"F
/6R {r ";:-'(l)
A
: 2 Btu/hrlft2/.F 50 Btu/hr/ftrl.F
,l
:
29 Btu/ft,
104,400.00 Btu/min
For water, h1,
- t':")l (tr t - tz)
q:
:
1,000 Btu/bb
F.Fo lo(tr"
At 600 fpm, we have,
J
Fe:1.01 F": e = h. : (0.90)(1.0)
0.90; o
:
0.173
x
10-8
1r)4 400
;*;
-
104.40 lbi
min
-
amounl of water required
Thus, 104.40
h,
:
gpm =
1.857 Btu/hr/ft,/"F
g mtn th
=
12.518 gpm
8.34:
gal
Thus, the water pump to be used is to be sized gpm at a terminal exit pressure of 200 psi.
Total Heat Removal
:
: Q = h1A(At) :
hr
h" + h.
23.000
+
1.857
=
24.857 Btuthttfet"F
(24.8s7X5.708) (223.63)
Btu/hr
=
3r,729.464
for
13
Transient Heat Transfer Analysas This method is based on the Fourier analysis of unsteady-state heat conduction. The following assumptions are made:
l. Water Required for Cooling Let Qv
:
2.
solid. heat removed by vaporization
The heat removed for a sheet 6 feet wide moving at 100
ftlmin Qv
:
The composite sheet is approximated by a material of average conductivity. The sheet is infinitely long and is an isotropic rigid
is (100)(6) frrlmin (29) Btu/ft2
:
17,400 Btu/min
For a sheet velocity of 600 ftlmin,
= 104,400.00 Btu/min Qv : 6,264,000.00 Btu/hr Total heat removal : 6,264,000 + 31,'729.464 Qv
Q=
+
3,000,000
9,295 ,729 .464 Btulhr
Figure 3-23 shows a view of the roofing slab. Assuming that the material is a composite sheet approximated by an integral sheet of average properties, the temperature distribution is at all times symmetric about the midplane of the slab, thus x = 0 at the center of the sheet. From Fourier's law of conduction,
Q
AI
= -k-dX
The heat transfer across x = 0 is zero and at the midplane of x : 0 the sheet behaves as a perfect insulatoran adiabatic surface. Consequently, the solution to this problem applies to a slab that is perfectly insulated at one
Equipment
Heat Transfer in Piping and
k p Cp
Iace, initially at a known temperature, to, and then exposed on one face to a
fluid at a constant temperature,
Temperature of the sheet
:
= 314'F
Gmperature of the spray water
:
tr.
t"
90'F
:
r = 0.90(0.094), .070
125'F.
0.:314-9O=224"F
l c.
,=r
|
=
125
-90:35"F
rn.
:
:
150
in. in which
L:
:/:z
For
V.
0.094 in.
:
=
o.ott
3-24, NF"
300
=
0.25 min
0.90
0.2146
min
=
15 sec
400 ftlrnin,
ft
:
0.375
min
=
22.5
sec
Btu/hr-ftl"F temperature of the water. Thus,
:
hr =
The length of the cooling section and the velocity of the sheet are both fixe.d. The only parameter not fixed is the
Fourier number
From Figure
ft
400 frlmin
k o'30 : hL= (300X0.094) Np.
:
150
For water, Surface coefficient (worst condition)
1.070 ft'?lhr
r = 26.'756 = 2'7 sec for 90'water Approximate length of sheet exposed to nozzle splay : 150 ft Velocity of sheet : V, For V, : 600 ft/min, 600 ftlmin
3/ro
:
or
35 =-=0.156 224
Thickness of sheet
U.UO/
1
ti
Here we are spraying water on the sheet and we wish to determine the time required for the sheet to reach
0,L=o
0.30 (0.9375)(0.299)
151
:
d7 L-
r:
NroL2
:
o.oo417
ct
I
m/L2 Figure 3-24. Heisler's main chart for the infinite slab [7].
152
Mechanical Design of Process Systems (o oo4l7j(
'a
(Nr o),"o
|
o7o'
0.505
(0.094)'
For a Fourier number of 0.505,
(*).,,-,, Let
t" :
l)5 Jl+ -
:
oo,o
lequirad water temperature
r t,\
in which
uo
t* = -11.86"F
=
Thus, for a cooling section of 150 feet long, the sheet moving at 600 ftlmin cannot be cooled to 125'F since the theoretical value of t* is below freezing.
At V,
= r=
{Nro),.u.r
ln\
l;l
:
and is well below the freezing
temperature of water.
lts 314 -
lyzed, -200"F, - 100'F, and -50'F. The skirt is made of Type 3(X stainless steel and is insulated on the inside and outside as shown in Figure 3-28. The insulation is sized for the most extreme process temperature that the vessel will be exposed to, -200"F. Data used in the example are given in Figure 3-25. First, determine the natural convection film coefficient for the skirt. The temperature inside the skirt, ti, is assumed to be five degrees lower than the ambient temperatute, t5.
Lr-tn, O.3"75 min :
.,.
[', 'L(no,r
I [7.r1s
Assume h4,5
+
=
O*4,
*
u'i,r:.',n)
*
iJ-'
r l-, -hJ
0.275
u4:0.093
499
= =
0.0063 hr
(0.0063X 1.070)
.:
--j--- =
^: (u.u94r
0.7568
0.180
r
t*
and
t* :
83.51'F for a
sheet velocity
of 400 ftlmin
Thus, the sheet can be reasonably cooled while moving at 400 ftlmin. If a velocity of 600 ftlmin is desired, additional water sprays must be added. However, one must balance the sheet velocity against the cutting machines and workers' capability to handle the additional material. It is found in most roof shingle plants that 400 ftlmin is an optimum velocity. As demonstrated, the transient heat transfer analysis is mandatory in evaluating a system.
EXAMPLE 3-7: HEAT TRANSFER THROUGH VESSEL SKIRTS Calculate the temperature distribution down the length of a vessel skirt. The vessel contains a cold process fluid that varies in temperature because of cyclic process conditions. Three operating temperatures are to be ana-
4 = 55'F
= 60"F = 3048-in. :2.573lt /, = 367,b-in. = 3.073 ft f3 = 37%-in. - 3.135 ft /4 = 435//6-in. : 3.635 ft A^ = (tt - r,2) = l.z0glt, F - 1(460+ 60) = 0.00'1923 1 = 0.07633 lb/tt3 p = 0.04339 lbfit h k*, = 0.01466 Btu/h ft "F kyz 8.0 Blu/h ft.F ka t = kg-'q = 0.14 Btu/h ft'F G t1
NP'
= 0'712
Figure 3-25. Cryogenic pressure vessel with internal and external insulation on the skirt.
Heat Transfer in Piping and Equipment
,. =
(tr
[*J
- ts) + ts
#[",('[4
-
['-h
.
\0.275i
:
63sx0 27sx-1 69)
ra-1nl.2gsr
s8.31'F
l'3 t
L-t5:58.31 - 60 = -1.69"F \o, = [d37,gB( Atl)(3,6o0)2]/p,
I
,,1.
|
d
Nc,Np,
C=
:
=
2te
213.6tt)
=
andm
:
:
1,14g,9tt,ttt
14
r
Iturr\t-t
55.00
ln
t-l \3.073/
1.126'7
57.781'F
-299'P
-
2(t.
r/:
-
=6s'1o2
Zle*oo
5
5
+z
C(Nq,Np,)-
= n.1 ' =
:
0.129(l,148,969,155)r/3 (fqi,
I.") d -
IOOqII ti - l#l
58.31
(-s)
-
135.
(0.014661(l35.ll) 7.27
-60:
58.29
=
t. _
11
:
0.2125
s8.29"F
t." _
For a cylinder with insulation on both sides,
.:[ffH][dil.*-.19] z
r+r
I
/z.sz:\
[l '" \'otr-/ r.1267 ft'?
!
r
.
(
rl ';T#"'J
+
57.781
t, : -50"F
(-215.56x2.89). + 5? ?Rl l + (2.89t^
Figure 3-26 shows these distribution curves. The axial deflection of the skirt will now be calculated using the first three terms of the stainless steel deflection equation (Equation 3-45). The hyperbolic terms in the equation are not necessary when the steel temperature is greater than -300'F or less than 1000'F,
_ *._ ^
2(t.
-f
t
|
100'F,
-515.56X2.89)r + (2.89)"
and for
0.02
57.78.1
Similarly for:
r _
I I t_ = t_t"ro. [(8Xl.2oe, li
(-515.56)(2.89)-+ 1 + (2.89y'
t, : -
:4.275
Q:
Q For t. :
I + e2*qo
N", :
0
[ \3.13s/
z:?
7.27 ft
(1,613,720,723)(0.7 12) > loe
0.129
:
:
'(;-.,Jll
Z:65.1O2"F1ft2
Na,:1,613,'720,723 where
sa.:
-
|ln
6T)' Q2.2)(0.00r923)(r.69)(3,6tJ0)21 (0.04339f
l(7 .27)3(0.07
- t, ll
- -, 'f5)
:l /o.osl\l{-))+bU
153
-
Z)ls.sa + (4.i1
(2.055
x
x
10-3)Zl arctan ielo0
l0-3\z2L
100
(2.055
x l0-rxr" - Z)2(e2oto' - l) 106 eo 5(1 * e2lao )
5;
154
Mechanical Design of Process Systems
EXAMPLE 3.8: RESIDUAL HEAT TRANSFER A section of carbon steel process pipe is shown in Figure 3-15c. Three conditions will be analyzed for process fluids at 900"F.600'F and 300"F. the basic analysis is the same as used in Example 3-7 beginning with the iteration procedure to find the natural convection film coefficient. Note that it is assumed that the temperature inside the empty pipe header, t1, is 130'F and that the ambient temperature. t.. is 60'F
U:
: :
[(r: ln (r1r')/k.) + 13 ln (r3lrr)/ki + '/h"] (0.s26 In (0.26710.2527)t25) + 0.526 ln (0.526/0.276)10.027
: Let U3
-200 -160
120 _80 Temperatur€,
.F
_40
0 m 40
,
[sech rLQ05) tanh (LQ05)
rElt
.,82rt,
- 2f ,a'-
/
\l
NNu
t. : : 6.5 -200"F. Q =
: 6., : 6,,
t
arcran [.,inh rLeOstfll
ezroo:
65.16.F
:
C(Nc.NPr).
0.525andm:r/+
+ ela
t
1.1267,2
+ 0.00004 +
0.00718
fr :
0.4t77 (U3/h;)(ti
1
+60
:
t3 t3' = 65.16 Let
0.08616 in. see that
for the worst case ofts =
struction and considerable material savinss could be ob-
72.35
:
-7.19'F
too large, try another tdal valve for hn.
57.781 and L
0.00013
-t.)+to = (0.073110.4177)(130 -
'72.35"F
.I L'L
-200'F that -20"F is obtained at x : 1.75 ft. At about 2.0 ft and below, the skirt could be of carbon steel contained.
0 '0137
0.525 (10,623,181.44)\ra = 29.97 (k"i,/d)NN" : (o.ot466n.052) 29.57
0.00701
From Figure 3-26 we
'
1.0 Btu/hr-ft2-'F
where,
--l - - -Zt tr arcran reLo"'tl - 4zlt. l;'". tQ"' )
For
h"
At=t:-L=5.16'F }'16, : [d3e,gB( lAt l)(3,600t]/r., : (1.052t(0.0763r2(O.O01923)(32.2) x (3,600F(s. l6)l/(0.0433eF : 14,920,198.65 Nc,N", : (14,920, 198.65X0.7 12) : 10,623,181.44
Junctron temperatures.
\ to o) [0,, _ 2,, 106 t","
: Ut :
+'/h"]
r
t: = (U:/h")ftr - to) + t,, = (0.07371 1.0)(130 - 60) + 60 :
60
Figure 3-26. Temperature distribution for the three shell-skirt
(1.06
[12.565
+ r/h.l
h"
:
t3
:
V:
0.49 Btu/hr-ft-'F rt(.r2.565 + r/0.49): 0.0687
Btu/hr-ft
-'F
(.0.0684'710.49) 70
At :9.781"F Nc, :28,279,559.99 Nc.Np, : 20 ,r35 ,046 .7 |
Nr, h"'
= \, =
At:'
:
+ 60
0.4901 Btu/hr-ft-"F (0.0684710.490r) 70 69.'781 69.779 =
-
:
69.781'F
+ 60 =
69.779"F 0.1
0.002'F <
60)
Heat Transfer in Piping and Equipment
= a = a =
h
0.49 Btu/hr-ft-'F 2?rki/[kMAM
2r (0.027
)I
(0.52610.27
z
(r4 .233)(3s4 .3s2)(1 .497)
ln (ry'ra)]
[25 (0.0387
6)l
:
) In
O.272
Z tx
fr
(2.496
2
= | [2rl(k.A.)][r3h.(t3 - t") - kit3/ln (ry'rJl : I l21rt[25 (0.0387) [0.s26(0.49)(69.78 60) -0.027 (69.78)/ln (0.52610.276)1 : -| -2.607 | : 2.60'1"F1ft'? : zlQ : 9.587'F + Z ^= t2 (i. - Zt.'oo1lt 1-.:roo51; : iZ t,, - 9.587)e''0 "'7'o 5/11 + e2r'02?210s)l +
For
t, :
9.587
(
(600
-
0.0008 2706.95
x
(6.s36
+
109(184.902)
x 10-')
[558,494,713.0
2000884.26
+'74,115,250.451
6".
:
0.0155
ft :
0.1860 in. axial deflection
This example shows that residual heat through a closed branch line can be significant enough to cause thermal movements, which can result in high stresses. These thermal deflections are particularly important when space is limited and the piping system has little flexibilIty.
(l.3l3l
+ 9.587 (1.313),.1 -'
Curves depicting t, are shown in Figure 3-27. Unlike Example 3-7, the slopes of the curves change much less, almost approaching straight lines. Axial temperature gradients along a section of piping produce thermal deflections. The pipe support will now be analyzed for thermal deflections. The surface temperature, ts, of the branch pipe at the point of the contact with the header is 600'F. The average temperature inside the pipe may be calculated from the 600"F curve in Figure 3-27 which shows a temperature at a distance x of five feet to be 294'F.
t; =
10-3)(125 ,565 .623Xr82.902)
1
-. |'' : I.780.83 (1.313)'r q^ \87 tl + 1.313)'?1 For t. : 699'P r,' = 1.180.83 0.313). + 9.587 lr + (l.3l3y'l For t, : 399'P
ll+
x
(0.521
+ +
900'F,
580.83
x ltr)
(0.521
I
4
155
-
E
E E
+294)t2:447"F
Through the process of iteration, h. : 0.68 Btuihrft-'F at the average internal temperature of 447"F. This was obtained using the natural convection iteration technique described in Example 3-7. Using the same techniques, Q = 0.2719 ft 2, Z : 66.7916'Flftz, and Z : 245.6476"F. To calcuiate the axial deflection, substitute these values into the expanded thermal deflection equation for carbon steel, Equation 3-39. Note: Values for the arctan used in the equation must be calculated in radians. Calculate the arctan m degrees and convert to radians in which the relationship is 2zr radians : 360 degrees. Using equation 3-39,
X distanc€,
ll
Figure 3-27. Temperature of a branch pipe connected to
a
header through a closed valve plotted from the pipe to valve connection every six inches for a distance of five feet in Figure
3-15C.
Mechanical Design of Process Systems
156
EXAMPLE 3.9: HEAT TRANSFER TIIROUGH PIPE SHOE
Rtrr /< rs ;- z\ 126.0), ": r.-l irr r750) "F nr-rr--r \ t++ In. /
ffi
A l2-in process header shown in Figure 3-28 is supported by a shoe 14-in. long. The process fluid is at 750"F and it is desired to determine the temperature of the bottom of the shoe base plate where Teflon is mounted to accommodate pipe movement. The Teflon cannot withstand a temperature in excess of 400'F. Referring to Figure 3-28 and using Equarion 3-47 we
0) [126
hr-r''c (1ffi]
#" _
: k,,, : L: h"
h=
k.A.r, + hoAplto .D (k,A. + h""AI) 3.0
Btu/hr-ftl'F for
+
(,-,-ttt{,"J
Bru /nz t_t
(3.0)
(3 0]
r,'(,i)r, rm,'-
in.,\ tt. ^l t_t ttl "^ . /ro.o\ t2 \ / 'J
hr-ft'z-'F \144 in.J
have
,'r'
rP
.
306.303'F
Thus, the Teflon on the base is adequately protecte. The amount of heat loss through the shoe base plate :.
carbon steel in still air
q =
26.0 Btu/hr-fr-'F
h"Ap (tp
t")
-
in (r.0) l:u - frrz in.J:) ",,' {rob.J'3 '- -'hr-ftr-"F '\r++
,
10.0 in.
A. = (0.375X14) : 5.25 in.2 Ap : (8.0)(14) : ll2 in.,
=
-
e').F
504.706 Btu/hr
L:90'F NOTATION
t
y'lgscu
ao
5"cAlcruM srLrCATE
A- = Ao : Ao : At =
INSULATION
/-
to =9oo F
A_
D: :
D;
D,L= I
P=0.375in
ho' :
= ht :
ho BASE }IIDTH
=8in Figure 3-28. Heat transfer through pipe shoe.
h4-s
of metal in pressure vessel shell or pi5
ft2
outside surface area of insulation, ftzlft outside surface area of pipe, ft'?/ft outside surface area of tracer tube or HTC
ft2lfr specific heat, Btu/lb-'F outside diameter of a pressure vessel, ft diameter, ft, in. inside diameter of pipe insulation, ft, in. outside diameter, in. inside of outer ring of annulus, in. outside diameter of inner ring of annulus. :: inside diameter of tracer tube, in. acceleration of gravity, 32.2 ftlsec2
h-
oin
area
:
natural convection coefficient at OD of ::: piping insulation, Btu/hr-ft2-'F corrected value for h", Btu/hr-ft'?-'F convection coefficient, pipe to air space, B:hr-ftr- o F convection coefficient, tracer or HTC to "..: space, Btui hr-ft2-'F convection coefficient between the outsj.: vessel insulation and ambient air, Btu/hr-::-
Heat Transfer in Piping and
X: Z: Z=
\5' = corrected convection coefficient, Btu/hr-ft2ki = ki =
k, : L=
: N51. : Np. : Np" : Q: Qr : Qz : Q: : Q+ : t" : t; : tj : t, : N6.
to,
tj(
:
t5
=
t3,
t3' :
t4,
t4' :
: At' : Atj' : U3 : At
U+
=
insulation conductivity, Btu/hr-ft-'F thermal conductivity ofair inside empty pipe,
Btu/hr-ft-"F thermal conductivity of vessel skirt or pipe,
Btu/hr-ft-'F length of branch pipe, ft Grashof number, dimensionless Nusselt number, dimensionless Prandl number, dimensionless Reynolds number, dimensionless heat transfer factor, ft 2 heat transfer from air space to atmosphere,
distance of plotted temperature points along the vessel skirt or piping, ft heat transfer factor, 'F/ft2 heat transfer factor, ZiQ, 'F
0: 6.,, 6,, : ?: p: p:
volumeric coefficient of thermal expansion,
,IK
axial deflection of carbon or stainless steel skirt or pipe, in. safety factor for traced pipe absolute viscosity, lbift-hr densiry, lb/ft3
heat transfer from tracer to air space, Btu/hr heat transfer from pipe to air space, Btu/hr heat transfer from tracer to pipe, Btu/hr
ftr-'F
157
Greek Symbols
Btuihr
air space temperature, oF process fluid temperature, 'F air temperature inside the vessel skirt, pipe support or branch pipe, 'F surface temperature of the branch pipe at contact point with the header, or operating temperature in a pressure vessel, "F temperalure at distance x along the vessel skirt, pipe support or branch pipe, 'F ambient temperature, oF temperature and corrected temperature at OD of the pressure vessel insulation, 'F temperature and corrected temperature at OD of the pressure vessel insulation, 'F tr - t in piping example, ta - t5 in vessel skirt exarnple, 'F t4 - ta' in vessel skirt example, "F t3 - t3' in piping example, "F overall heat transfer coefficient at OD of pipe insulation, Btu/hr-ft'?-'F overall heat transfer coefficient at 14. Btu/hr-
Equipment
REFERENCES
1. Tubular Exchanger Manufacturers Association, Standards of the Tubular Manufacturers Association
QEMA), sixth edition, New York, N.Y, 1978. 2. Kern, Donald, Process Heat Tiansfer, McGraw-Hill Book Company, 1950.
3. Ludwig, Ernest E., Applied Process Design for Chemical and Petochemical Plazls, volume 3, second edition, Gulf Publishing Company, Houston,
4.
Texas, 1983. Escoe, A. Keith, "Heat Transfer in Vessels and Piping," Hydrocarbon Processing," January, 1983, vol.
62, no.
l,
Gulf Publishing Company,
Houston,
Texas.
Chapman, Allen 8., Heat Transfer, third edition, Macmillan Publishing Company, New York, 1974. 6. Perry, Robert H. and Don Green, Perry's Chemical Engineers' Handbook, sixth edition, McGraw-Hill Book Company, New York, 1984. 7. Heisler, M. P., "Temperature Charts for Induction and Constant Temperature Heating," Transactions of the A.S.M.E., vol. 69 (1947), pp.227-236.
5.
The Engineering Mechanics of Pressure Vessels
The specifuing, design, and construction of pressure containing vessels varies all over the globe. Each adopted code that has been used for any significant length of time has proven to be workable because its use has resulted in safe, economic designs. The main differences in codes are the theories of yield that are used for determining maximum allowable stresses, material spec-
ifications. and basic procedures. With increasing international competition and cyclic economic conditions, there is a growing need to emphasize economics and familiarity of foreign codes, and avoid unnecessary overdesign that relies on only one set of codes and standards. This chapter emphasizes the optimization of economics and safety. If you choose to be conservative in your design, you can be; however, if you are bidding in a highly competitive market, you can use these methods to produce a safe, economical design. International competition and economic condltions have caused engineers to restructure their thinking that a good design uses only enough material that produces a safe and economical product. Thus, this chapter's philosophy is to optimize engineering design within code rules, whatever the code. Overly conservative design that results in excessive material use becomes unproductive and expensive when one is competing in the world market today. A thorough treatment of vessel engineering and its concomitant aspects of static and dynamic phenomena would fill several volumes. To present this broad subject with clarity. various physical phenomena are briefly discussed and references are made to sources that give detailed theoretical explanations. lt is not this boo-k's purpose to give a trearise of static and dynamic problems. but rather descriptions of proven practices. The theory of these problems is always available, but proven solutlons are not-hence, the reason for this book.
159
The first problem you face in designing a vessel containing pressure is how to physically make the components and assemble them. In the petroleum refining industry (CPl-Chemical Process Industry) and allied industries, the most practical and economical method is welding. We will refer to welding later in more detail, but first we will look at the vessel from a pure engineering viewpoint assuming perfect welds with given efficiencies. Some have proposed bonding pressure vessels together with glue, as is done with aircraft components. The main disadvantages to bonding are
1. Clean surfaces are required for
assembly.
2. Glues that exhibit high tensile and
compressive
strengths are very expensive.
3.
Chemical bonding, especially in thick-walled vessels, takes much longer than any welding process.
Another form of assembly that has been even more seriously considered than bonding is threading components and screwing them in place. Even though this may appear to be simple, the process becomes enormously expensive with large diameters. Thus, welding is the most practical and economical means of assembling pressure vessels for the foreseeable future.
DESIGNING FOR INTERNAL PRESSURE The two factors that must be considered in the desisn for internaf pressure are crr??ponent thickness and quatiry of weds. Before either of these two factors can be addressed, you must know what the vessel is to contain. This chapter only considers gases and liquids. Vessels,
160
Mechanical Design of Process Systems
silos and bins containing solids are discussed in Chapter
In the design for liquids under pressure, the most severe condition of coincident pressure and temperature expected in operation must be considered in computing shell thickness. This is fairly universal in codes throughout the world. The intent ofthe statement is that the most frequently occurring liquid level should be considered. For example, if a vessel is filled to a certain level "A' 75% of the time and a higher level *8" 25% of the time, level "A' should be used for design purposes. The normal liquid level to be used for vessel design and its quantitative value should be determined by the process engineer. For upset conditions each code allows an increase in allowable stresses under temporary conditions, and you should consult whichever code is to be used for exact amounts allowed. It is recommended that a value of 30 psig or 10% be added to the operating pressure for design pressure. This practice varies with each company throughout the industry. Once the internal pressure is determined it must be decided how the vessel is to be welded. The factors affecting this decision are as follows:
l. 2. 3.
Size of vessel-whether rolled plate or seamless pipe is used. The toxic nature of the fluid to be contained. The economics of fabrication as to whether a full joint efficiency is necessary.
One can appreciate the degree of types of welds required for a vessel. A slug catchel which acts as a scrubber handling a non-toxic substance, does not require the same caution as a vessel containing cyanide gas. The quality of a weld joint is determined by a radiographic inspection. Full radiography includes a complete X-ray inspection (1OO% for butt weld and 907o for single-welded butt joint) and spot radiography implies 85 % for buttjoints. See Thble 4-1 for maximum allowable efficiencies for arc and gas welded joints. The reader is strongly urged to consult whatever code happens to govern. Listed in Thble 4-2 are the joint efficiencies for the various welded combinations for pressure vessels under
ASME Section VIII, Division I[1]. Any discussion on designing for internal pressure must include maximum allowable working pressure, which is the maximum gauge pressure permissibie at the top of the completed vessel in its operating position for a designated temperature. This pressure, MAVr'P, is normally specified on two conditions*new and cold (ambient) (NAC), and design. "New and cold" implies the MAWP for a new vessel (non-corroded) at atmospheric condition, and "design" implies the vessel corroded at
design temperature and pressure. The value of the MAWP at the two conditions gives the exact range of temperature and pressure that the vessel can withstand if the owner decides to use it in another application. The reader is cautioned to consult his respective code on the practice of using a vessel for another application. The following example illustrates how the MAVr'P is applied: An ASME Section VIII Division I vessel is made of SA 240-304 SS, design pressure : 500 psig, design temperature : 150'F. The vessel has a shell thickness of 1.00 in. and a ioint efficiencv of 1.0. MAWP (NAC) =
(18,800)
x
(1.00)
x
(1.00.)
(21.00)+(0.6)x(1.00) 870.4 psig
MAWP (Design)
:
(18,300)
x
(1.00)
x
(1.00)
(21.00)+(0.6)x(1.00) 847.2 psig
The 18,300 psi is obtained by linear interpolation of the allowable stress values in Table UHA-23 of the ASME Code. The vessel owner knows the maximum allowable pressure for the shell at the new and cold condition as well as the design condition. It is a common practice to limit the
MAWP by the head or shell and not by the flanges or openings, only the MAVr'P is determined by the flanges or openings when the vessel is to be reapplied in another application or a design oversight is made. Finally, in computing the minimum thickness of the shell or head, mechanical allowances must be considered. In the manufacture of heads, the metal is thinned on forming the section (a forgery process). This forming allowance must be considered when the nominal thickness is specified. When a minimum thickness is specified to the head manufacturer, the forming allowance is not considered because it is the manufacturer's responsibility to ensure the minimum thickness.
DESIGNING FOR EXTERNAL PRESSURE The design for external pressure of vessels is fairly standard in the ASME and codes of other nations. The procedures for determining minimum shell thickness, spacing, and section properties of stiffening rings are straightforward and simple. Because there is much published material on external pressure design, the subject is not discussed here. The reader is ursed to consult the oressure vessel code to be used.
The Engineering Mechanics of Pressure Vessels
161
Table 4-1 Maximum Allowable Joint Efficiencies for Arc and Gas Welded Joints [11 Degree ot Examination (a)
Fully No.
(l)
(2)
(3)
Type ol Joinl Description Butt joints as attained by double-welding or by other means which will obtain the same quality of deposited weld metal on the inside and outside weld surfaces to agree with the requirements of UW-35. Welds using metal backing strips which remain in place are excluded. Single-welded butt joint with backing strip other than those included under (l). Single-welded butt joint without use of backing strip.
(4)
Double tull fillet lap joint
(s)
Single firll fillet lap joins with plug welds conforming to UW-
t7
Radio"
Limitations
graphed
(b) Spot
Not Spot
Examined
(c)
None
1.00
0.85
Examined 0.70
(a) None except as in (b) below (b) Butt weld with one plate off-
0.90
0.80
0.65
set-for circumferential joints only, Circumferential joints only, not over 5/a in. thick and not over 24 in. outside diameter l-ongitudinal joints not over 3/8 in. thick. Circumferential joints not over s/r in. thick (a) Circumferential joints for attachment of heads not over 24 in. outside diameter to shells not over
0.60 0.55 0.50
t/2 in. thick (b) Circumferential joints for the attachment to shells ofjackets not
(6)
Single tull fillet lap joints without plug welds
over s/a in. in nominal thickness where the distance from the center of the plug weld to the edge of the plate is not less than 1r/2 times the diameter of the hole for the plug. (a) For the attachment of heads convex to pressure to shells not over s/e in. required thickness. only with use of fillet weld on inside of
shell; or (b) for attachment of heads having pressure on either side, to shells not oyer 24 in. inside diameter and not over t/+ in. required thickness with fillet weld on outside of head flange only.
0.45
162
Mechanical Design of Process Systems
Table 4-2
Joint Elficiencies for Arc and Gas Welded Joints per ASME
T1 = T2 =
Joint Types H, C, and L Type 1 Joinl (ASME UW-12) Type 2 Joint (ASME UW-12)
Asterisk (+) denotes which joint type governs.
Welded Head (Non-Hemispherical)-Welded Shell Head Thk. Calcu. Shell Thickness Calculations E. Cir. Stress E. Long Stress
Radiograph
L-
Type
C-
Illustration of weld joint locations Typical of Categories A, B, C. and D-see ASME Section VIII Division I.
H'
T1
T1
T2
I .00
Spot
1.00
0.85
0.90
L00 Spot None Spot
Spot
Spot
Spot
Spot
None
None
Full
None None Full
Spot
Spot
0.85 I I I I
None
I
Full
1.00
Spot
0.85
I I I I
I I
None 1.00 Spot
I I
Spot
Spot
Spot
Spot
spot
Spot
Spot
None None None
None Full None Full None Full None Part *L
I
100
Spot
Spot
Spot
I
I
Spot
0.85
I
I I I
Full
I
Spot
I
I
I
None
I
Full
1.00
Spot
0.85 1.00
Weld soverns in circumferential stress calculations.
I I
I I I I
V
0.85
0.80
0.80
100
i'[echanics of Pressure 'FL^ rrI E-^r-^^-r-^ LrrSrrr!!rur6 rr.
Vessels
163
Table 4-2 continued Welded Head (Non.Hemispherical)-Welded Shell Head Thk. Calcu. Shell Thickness Calculations E. Cir. Stress E. Long Slress
Fadiograph Type
L' C' None Part None Part
None Spot None Spot None None None None *L
Tl
H.
f2
Spot
None
Full
0.85
Spot
Spot None None Full None Spot None None
0.85
iii!
0.80
II rl YI
0.70
O.70
ii
0.70
0.6s
0.80
0.65
Weld governs in circumferential stress calculations.
Welded Head (Hemispherical)-Welded Shell Radiograph
Head Thickness Calculations
TYPE
H=Tl H=Tl H=T2 H=T2 L- C' H' C=Tl C=T2 C=Tl C=T2 Full Full Full 1.0 0.90 0.90 0.90 FUU Full Spot t { Joint
FullFullNoneiiii Frrll sn^IFrrll ' "" _____i!::_____i_
Full Spot None Full None Full
Spot Full Full 1.00 Spot Full SDot { Spot Full None i :------------- _--------=--:- | spot Spot tu i Spot Spot Spot 0..85 Spot Spot None Spot None Full Spot None Spot I
f2
0.85
0.80
T1
T2
I r
0.80
100
None
Full 0.85
None
Full 0.70
0.p0
t|
Spot
None
Tt
0.90
Full
Spot
Vo
!ll!
Full Spot Spot O.ps 0 p0 0.90
None Full None Full None Full None Spot None Spot None Spot None None None None None None
Shell Thickness Calculations E. Long Stress
E. Cir. Stress
0.80
0.80
100
0.85
0.80
100
164
Mechanical Design of Process Svsterrrs
Table 4-2 continued
Shell Thickness Calculations
Radiograph
Type
H=T2 H=T2 Tl C=T2 0.90 0.90 0.90
H=T1
H=T1
C=Tl
Full Full Full
Full
l
C=r2
00
C=
E. Cif. Stress o/o o^n
E. Long Stress 12 1.00 0.90
T1
T1
Spot
Spot Spot Spot None None
None
0.85
Full
I .00
0.80 0.90
Spot
None
0.85
Full
1.00
0.80 0.90
Spot
0.70
Head-Welded Shell
Seamless Head Thick. Calcu. Radiograph
E. Cir. Stress
TYPE
T1
Full
Full
1.00
0.90
Full Full
Spot
0.85
0.80
Spot
Full
L00
0.90
Spot
0.85
0.80
Spot Spot None None None
Shell Thickness Calculations E. Long Stress
None
1.00
0.90
T2
1.00
0.90
0.85
0.80
1.00
0.90
0.85
0.80
I .00
0.90 0.80 0.65
+ I I
0.80 i
None
I
Full
1.00
Spot None
0.85
0.70
0.90 0.80 0.65
I
i I
0.85 0.70
0.65
* C weld governs on head and longitudinal
*L
stress calculations. Weld governs on shell circumferencial stress calculations.
Seamless Head Thickness Calculations
0.80 ! C Weld go\ern5 ior head dnd longnudinal slre,s calculalion\.
Head-Seamless Shell Shell Thickness Calculations E. Long Stress
0.85
0.80
The Engineering Mechanics of Pressure Vessels
Table 4-2 continued Seamless (Non-Hemispherical) Head-Seamless Shell Head Thick. Calcu.
Shell Thickness Calculations E. Long Stress
E. Cir.
Stress Full Fart
1.0
1.00
0.90
0.85
0.80
0.70
0.65
Spot
\one
Seamless (Non-Hemispherical) Head-Welded Shell
Shell Thickness Calculations Radiograph
Head Thlck.
TYPC
Calculatlons
Full Full
Full Full Spot Spot Spot Spot
c' Full Spot
1.00
0.90
I
I
r00
Part
0.80 I
Spot
I
85
I
None Part
None
None
Full
i
I I I
Spot
Radiograph Type
0.90
I I
Full
Full
0.65
I
t
0. 70
0. 65
Welded (Non-Hemispherical)-Seamless Shell Head Thick. Calculations Shell Thickness Calculations
-Tl 1.00
E
E. Cir.
120.90
Stress 100
1.00
0.90
6 -)
0.85
0.80
1.00
0.90
0.85
0.80
1.00
0.90
0.85 0.70
0.80 0.65
Part Spot
I
None
I
I
Full
I
Part
I I
Spot
0. 80 I I
None
Full
None None
Part
None
Spot
None
None
*H
1.00
E. Long Stress
85
None
None None
Full Full Spot Spot Spot Spot
100
Part
None
Full Full
E. Cir. Stress
100 85 100
----:v
0.70
-U. 65
Weld governs in head calculations. + C Weld governs in loogitudinal sfress calculations.
6)
165
166
Mechanical Design of Process Systems
DESIGN OF HORIZONTAL PRESSURE VESSELS The analysis of horizontal pressure vessels converges on the design for internal pressure and vessel supports. This chapter only considers metal, cylindrical vessels, and focuses on the supports of horizontal pressure vessels.
L. P. Zick [2] of the Chicago Bridge and Iron Company developed the method of analyzing supports for horizontal cylindrical shells in 1951. We will not derive the method, but rather summarize it in a seneral discussion along with guidelines and useful praciices thar make the design of such items more straightforward. Horizontal vessels should be desisned to withstand internal and external pressures. and support reactions produced by the vessel weight and additional loads from ladders, platforms, piping, etc. Zick [2] showed that supporting horizontal vessels by more than two saddles is not only inefficient, but incurs additional undesirable problems. Figures 4-1 and 4-2 illustrate a horizontal vessel supported by two saddles.
-- - '\
/'\-
,\l ---,..T.,-
.
>\.----r<" ]''..- 9--7 Figure 4-1. Horizontal vessels are r = mean radius, ft
supported on saddles. The saddles can be supported on concrete piers shown in Figure 4-2.
LONGITUDINAL BEITIDING STRESSES
A horizontal vessel supported on two beams is the same as a beam overhanging two supports. The maximum longitudinal bending stresses occur at the supports themselves and at the center of the vessel, as shown in Figure 4-3. Zick [2) and Brownell and Young [3] give a detailed derivation
ts
of the equations for longitudinal
bending stresses at the saddle and at mid-span. This analysis is summarized in the following:
At
Saddle
qr =
longitudinal bending stress at saddle
oa1 allowable stress in tension. psi o"r = B = allowable stress in compression. psi Figure 4-2. Horizontal vessel with saddles on concrete piers.
For tension, 01
:
Eoan
where
+
op
E:
welding joint efficiency
op
pressure stress, psi
=
The allowable stress for compression is based on the accepted formula for buckling of short cylindrical columns, which is
/"\i,\[, - (,1,'*,(i)] \-rt \;i f
or the allowable stress in compression is o1
<
Bl2
where
r D
= radius of cylindrical shell, in. thickness of cylindrical shell, in. modulus of elasticity of shell, psi B factor in the ASME vessel code, psi
The Engineering Mechanics of Pressure Vessels
2A :
Referring to Figure 4-3, oy occurs at either lBl6 + 0l2l degrees or zero degrees at the shell acting in the longitu-
arc, in radians, of unstiffened shell in plane saddle
effective against bending
dinal direction. This only applies to unstiffened shells. The vessel must meet the allowable with or without ores-
At Mid-span
sure.
":-t*-[..(,
l-
*'-
I *ll,AL 3L +
o:
"41ll
I +
longitudinal bending stress at midspan
The longitudinal bending stress at midspan has the same
IJ
(4-3)
(4-r) Thneential Shear Stress where
A, H, L, Q, r, and t.
= 0:
CA
are defined in Figure 4-3. corrosion allowance, in. angle of contact of saddle with shell, degrees (Figure 4-1)
* l
\r2
l.
_ _ /r- "r"- - rrr-tAr\ L-H (0.r8)Q
lA-)
l
n
For shell stiffened by ring in the plane of the saddle,
|
o3
<
ze
u\ /
0.08ou1
\ --il \ .-11--T-
-
N
l-/
zT\-[ll ll/r\rr., | \lll ffi-[" V-t-+ 'Y
I
|| tt/
Figure 4-3. Bending moment diagram for a horizontal vessel developed by Zick l2l.
(4-4)
168
Mechanical Design of Process Systems
;&p
Figure 4-3. Continued.
The Engineering Mechanics of Pressure
I I
I
Figure 4-3. Continued.
Vessels
169
17O
Mechanical Design of Process Systems
z z
6
o.os-
= =
o z
z UJ
) t-
zgJ ,'u o'o2= E
1.O
RATIO A/r
The Engineering Mechanics of Pressure
L
Unstiffened shell with saddles awav from head (A
If A/r>1,
>R)
where d
a
/L-H
1=
r,#
r! :
tangential shear stress, located at an angle of B/20
g
& B in
,j.
Shell stiffened by head,
15
=
1
0sin0
1t
2
cos P
,
sin 0 R
.ltu\ \-/
of (l9l2O)P
. - r(#)'+
(4-7)
2cos2B (4-12)
^/^\:i srnpcosp,
.lslnpl
a
as shown.
Q lsin o[ "- sinocoso \l + tin r(rr-C{)1" \"-" ""oso/l
o,
:
\B
I
circumferential comDressive stress
This stress is located at the horn of the saddle If o; ( outr, it is not necessary to take credit for the wear plate.
-1. Shear stress in shell,
q [.in rI o- rino.oro \l - r(t5-CA)tn \" - " +.sindcose/ I
(4-S)
06 is the same as 05 and also is located at (19/20)0. With rhe shell stiffened by the head, then
3
sin 6
-[
shear stress in head
an angle
o6
(4-11)
(4-6)
degrees
This stress occurs only when t}re shell is stiffened by the head and when the head is located less than one shell radius from the saddle. The rnaximum shear is located at
"6
ot710
,o-r,
.. rq],
O.42Z2e-a
/
',r'here
.
K6:
then K6 : K3/4 Otherwise, use Figure 4-3.
:in," I '(\7r-@+slnqcosd/ (;
then deg
171
If A/r < 0.5,
-2A'l
''v- - 11-ctr \ L+H
:
Vessels
0.8o"1
o7
<
l'50
ou1
Additional Stress in Head When Used as a Stiffener
"s
-
Circumferential Stress at Horn of Saddle 08 S
sin']"
3Q I 3'-1u
-
6e,1
Lr .o, + sin "
cos
I
(4- 13)
"l
oall
For shell stiffened by head the maximum circumferential stress at horn of saddle is,
IfL>8R,o7: 4( -
CA) (b
+
-a 1.56(r(r
-,'QIu = 2(r -
Wear Plates-Ring Compression in Shell Over Saddle
-
CA))u)
p.s)
(t
CA)'?
If L < 8R, o
:
-a
@ _
oe
12&QR
L(t
-
_
CAf
(4_lo)
:
-
CAXb
+
1.56(r(t
{\7r-q+slnacosq/ '1':'"
-
Ca;101
}o"(0.5o,
ring compressive stress in shell over the saddle
This stress is located at O
:
7r
(4-14)
172
Mechanical Design of Process Systems
This stress is compressive and acts in a radial direction between the saddle and shell. The limitation of this stress IS
Longitudinal Bending Stress
0.5ori"ra
ot T op : o' i,DP a
where oyi"rd
:
the yield strength of the saddle material (metal or concrete)
For thin wall vessels with large diameters, it is desirable to locate the saddles close to the head, where A = ID/4, using the stiffness of the head. Although arbitrary on what a thin shell is, and Zick [2] does not define the term, a shell is generally regarded as ',thin" when D/t > 100, where D shell diameter and t shell thickness. For shells where D/t < 100 and the distance from the head tangent to head tangent is rather large (approximately L/r > 10), the saddles are best spaced when the longitudinal bending stress at rhe saddle, or, equals the longitudinal bending stress at midspan. o2. Undei no circumstances should the distance from the saddle center line to the head tangent, A, exceed 0.25L. A listing of allowable stress criteria is siven in Thble 4-3. Each of the previously menlioned stress values should be evaluated with this table and the appropriate
:
:
code.
Wear Plate Deslgn One of the first things to consider when designing a horizontal vessel is the need for wear plates. Too often these plates are "auromatically" included with no lhought given to their necessity in each application. Wear plates involve material and labor expense and are a waste if not needed. Wear plates are not required if two criteria are met: The circumferential stress at the horn of the saddle must be less than 1.5 times the allowable stress, and the ring compression stress in the shell over the saddle musr bi less than one half the minimum yield strength. These cri-
teria can be written as follows: o1 oe
02 +op =
ff
02
o4 E. where
E = joint efficiency
'o'' r
Tangential Shear Stress
Location ot Saddle Supports
ir
Table 4-3
Allowable Stress Values
1 7.5 o^x ( 0.5 o, 6n
Table 4-4 shows minimum allowable shell thicknesses required for horizontal vessels without wear plates. The values are based on using a fluid 1.75 times the weight of watet and the metal has a minimum yield of 30,000 psi and an allowable stress of 17,500 psi. For vessels in seismic regions wear plates should always be used to minimize stress concentrations at saddle plate-shell juncture.
q4 06
03' o5'
< <
0.8
oall
0.8
Circumferential Stress at Horn Saddle
o7
<
1.5
o"1
Circumferential Stress at Bottom of Shetl
q
oe
0.5
(or1-i") *
Compressive Yield
Zick Stlffenang Rings When the Zick stresses in a vessel become excessive and the location of the saddles no longer is a factor because the stresses are below the allowable stress, then two options are available-increase the vessel wall thickness or add stiffening rings. Almost always it is more desirable to add stiffening rings because it is cheaper to add a few rings than go to a larger size shell thickness, particularly with expensive alloys. Also, if the vessel is subjected to external pressure , the Zick rings can act as external pressure stiffening rings as well as Zick rings. Referring to Figure 4-3, if two Zick stiffening rings are located on each side of the saddle, then Ln,n :
l.Jb Vfl, It
Lr* :
r, ft
The stress in the ring is
_- _ -KuQ nAWhere
KuQr , n7,
= l-/c for ring in the plane of the saddle, tn.' z : I,-,/d at saddle horn at tip or flange of
I*-
Z
: "
n
r K6
: : : :
stiffener ring, in.3 moment of inertia of stiffening ring about axis x-x, in.a (includes wear plate thickness if one is used) cross-sectional area of stiffening ring, in.2 number of stiffener rings per saddle mean vessel radius, in. previously defined
The Engineering Mechanics of Pressure Vessels
175
Table 4-4
Minimum Shell Thickness Required lor Horizontal vessels Without Wear Plates
lD (in.)
78 8
l0
84
90
r/r
r/s in.
t4
108
120
132
144
lllro in.
I
5/r in.
rYrt in.
9/ro in.
?ro in.
?/x
in.
20 30 40 50
156
I
l6 l8
114
in.
_r-
t2
102
96
t2
ll/rc in.
tn,
r/+ in.
60 lYro in.
65 Not€s 1. The above table is based on the following: a. vessel is tully loaded with a fluid of specific gmvity of 1.5. b. The ratio of the shell outside radius, R., to shell thickness, t, is R-lt c. vessel weight is computed with not€ (a.) and hemispherical heads. d. Vessel material has the following properties: d,i" y,.rd = 30,000 psi and o.rr* = 17,500 psi 2- In seismic zones 3 and 4 wear Dlates should be used.
>
'72.
Is/r6 in.
78 in.
I
in.
I
in.
174
Mechanical Design of process Systems
In compression, oro is negative,
oleAB(0.5o., In tension, o,6 is positive, o'e
*
oo
(
o.1 [tension]
where B
= o", : op
:
ASME compressive stress (see ASME Section 8 Division
l)
compressive yield stress (see ASME Section g Division 2) internal pressure stress (includes wear plate thickness if one is used)
In defining the parameter K7, it must be noted that the Zick stiffening rings can fit on either the inside or outside of the vessel shell. Many clients object ro the rings
strengthened with stiffener or web plates. but often too many are used. which increases laboi and material costs. In the past, saddle plates have been purposely over-designed to guard against uncertainty. This is no longer required, since literature on flat plate theory has increased with mounting experimental data. One such organization that has engaged in extensive research is U.S. Steel [4]. Figure 4-4 shows a typical saddle configuration for a horizontal vessel. Section A-A shows that only an effective portion of the member will resist compression. shear. and bending loads because when rhe member is loaded, the outside fibers ofthe web plates and the center of the saddle plate -shown by rhe sh;ded areas in Figure 4-4-go into the plastic range. The rest of the plate area
is still in the elasric range because of residual
being external to the vessel surface because of aesthetici. However, after insulation is applied, the rings are no longer visible. We will consider rhe rings in both ways. The constant K7 is defined as follows:
b":KL
For a ring in the plane of the saddle-
where b"
Kr:
+ 1.0 0.340, 0.303,
0 0
0.250,0
: : :
(4-15 )
=
120"
combination of these loads (see Figures 4-5,
150'
4-6, 4-7, 4-8,4-9, and 4-10). c, b, s, or a combination of these characters, plate buckling coefficient for compression,
i :
180.
K. :
For rings adjacent to saddleFor internal rings,
Kb
:
\:
Ks
:
-1.0 (o.271, l.0.2r9, [0.140,
=
Kz:
0
0 0
: : :
120"
150' 180'
plate buckling coefficient for sheaq
We now have
-a
4(t - CA)[b" +
_
-1.0 (0.27 | , 0
10.2t9, {0. r+0,
dimensionless plate buckling coefficient for bending, dimensionless dimensionless
For external rings,
X
effective width, in. plate buckling coefficienr for either compression, shear, bending, or a
K; =
where
Kr:
stresses
that were created by non-uniform heating during rolling or welding. Presently, this "effective" area can be determined only by experiment. Equations 4-9,4-10, and 414 are used in saddle design as follows:
0
o
: 120. :150' = 180'
STEEL SADDLE PLATE DESIGN Once the shell conditions have been met. the saddle plates must be analyzed. The main phenomenon encountered with saddle plates is local buckling with the plates undergoing bending, compression, shear, or any combi-
nation of these loadings. Normally, saddle plates are
1.)K.
;:--.
1.56{rrr
rf L >
-
CA))o'] (.4-9)
8R
o 4(t
-
CA) tb"
+
1.56(r(t
-.lt*'gl.,rrL L(r - LA)' 4ft
-
cA) tb.
+
<
CA)
fI (4-10)
8R
1.56G(t
'(
-
-
CA)f
I1
7t- (\
5l
cos ol
sln a cos
-l
(4-r4)
The Engineering Mechanics of Pressure Vessels
175
d" t/ll
lffl b
- b"-:l fI t---------1
I
\r
.,-.-lN
I
'.-lF 1l"'l*" '-ff I *lJL.._"1 -
|
-.T----
sections A-A and B-8, shaded areas are in the plastic range.
elevation view
Figure 4-4. Horizontal vessel saddle support detail.
Figures 4-5 to 4-10 are courtesy of United States Steel Corporation. USSC makes no warranties, express or implied, and no warranty as to the merchantability, fitness fot any particular purpose, or accuracy of the information contained in any material reproduced herein from its Steel Design Manual. In the event of any liability arising out ofthe publication of such material herein, consequential damages arc excluded.
--'t------------- -
I
--r --i
cAS€
--'l-----------_---l CISE 4
r- -F
F-
I
l
j
5
_.1-...---------.1= casE 5 F -l
ri\ E E
\\'
---\
i\
loaoEo
EDGES
FtXE0
z.
LOADED EDGES SIMPLY SUPPORTEO
I
\\. ta.'a
Figure 4-5. Buckling coefficients for flat plates under uniform compression. (Courtesy of U.S. Steel [4].)
3
176
Mechanical Design of Process Systems aaTro oF EENDING STBESS
-TOU\IFOR\,I COVPBLSSION ST-8ESS,
LOAD ING
\l
T--
EDGES
SUPPonTED
UNLOADED EDGES FtxED
.] t7/
tl
-t!ft. {PU8E BENOING)
jr:=-2l3r,r
5.00
\
\-V {, = 1/3r, Y -tK
2.OO
F----E y H "=o
't.00
Fry]= !l r, = r/3f I E/
0.50
\t_-_____tr/
Ir
UNLOAOED Sll\,4PLY
3H. ,.1
MJNII\,4UI\,IBUCTI.NGCOLfFICITNI.'I,
r-r____-_r_: F= f: = f, t=
I,
rp,,.. . -... "^iiil.* --.....,--jtoN)
4.0
Figure 4-6. Buckling coefficients for flat
.VALUES
GIVEN AAE BASED ON PLATES HAVING LOADED EDGES S{I\4PLY SUPPORTED AND ARE CONSERVATIVE FOR PLATES
plates under compression and bending. (Cour_
HAVING LOADED EDGES FIXED.
tesy of U.S. Steel [4].)
n
i j
Figure 4-7. Buckling coefficients (Courtesy of U.S. Steel [4].)
for flat plates in
shear.
LONC EDGES FIXED,SHONT ED6ES SIMPLY STIPPOfi TEO
The Engineering Mechanics of Pressure Vessels Figure 4-8. Buckling. coefficients for stiffened plates under uiform compression (one longitudinal stiffener at mid-point).
t
0.6 0.8
177
1.0 2.O
,Courtesy of U.S. Steel [4].)
2.2
14
I
13 12
i
z
tl I
tr U
o o
z
= f F
1.O 1.2
1.4
34
2.8 30
3.0
2A
4
6
810
12 14 16
NONDIMENSIONAL PABAMETER,
18
O
I
26
j
24 22
: o (, =
-
20 18
t6
12
5
35 40 45 50
NONDIIUENSIONAL PAsAMETER. d
55
Figure 4-9. Buclding coefficients for stiffened plates under uniform compression (two longitudinal stiffeners at third points). (Courtesy of U.S. Steel [4].)
178
Mechanical Design of process Systems 0.6 0.8
1.0 1.2 1_4 1.6 1.8
2.O
2.8 3.0
F
I
z q n
o Figure 4-10. Buckling coefficients for stiffened plates under uniform c_ompression (three Iongitudinal stiffeneis at quarter points). (Courtesy of U.S. Steel [4].)
j
F
NONDII\,4ENSIONAL PARA]\IETER, d
no web plates are used then b" : t,. It is very comfor engineers and designers to use the we6 plate width, b, instead of b". This is wrong. The only time b" : b is when t, = b, as is true for a solid concrete saddle. With steel this never happens, as values of b can be as great as 24 in. and obraining plate that thick is impos_ sible (ar least on this Dlanet). Values ofb" depend upon K, and t,. Since the value of t. is known, the real independent variable in Equation 4-15 is K,. Once again referring to Figure 4-4. we analyze the
If
mon_
saddle configuration for end (boundary) conditions. Sec-
tion B-C is considered fixed-fixed in Fisure 4-5. since it js stiffened by sections A-B and C-D. S=ections A-B and C-D are considered fixed-free since the outer web Dlate is not stiffened by another section. The fixed-free condition is the most critical because it is more susceDtible to buckling. and rhus ha: a lower value oi the plaie buckling coefficient than the fixed-fixed case. [t is interestins to note that the plate buckJing coefficient for uniforri
compression for the fixed-free case, when multiplied by
t., yields approximately the effective width, b", that is used for residual stress. In other words, if a member is known or suspected to have residual stress and is sub-
jected to compression, bending, shear, or a combination. the plate buckling coefficienr is equal [o rhe effecr:ve width that is determined by the residual stress crirerion, which is as follows: d,t,
ti-
ldit.+2r*(b-l)l
(4-16)
The general equation in which the saddle plate stress distribution is defined is as follows:
o{:
K,
zr2
E
\,
rztr--l- 4ld'1"
\\/
(4-17 a)
The Engineering Mechanics of Pressure Vessels
shere di
:
saddle plate length normal to vertical axis
thickness of saddle plate, in. effective width of saddle plate that is perpendicular to the web plate, in.
of
stiffener (web) plate, shown in Figure 4-4. modulus of elasticity, psi Poisson's ratio effective saddle width, in. saddle plate thickness, in.
with
d.=d,(0.25+0.91\)
Substituting the elastic buckling stress
in
\:lll
Equation
-1-17a into
\dJ
o,
, or:6y-7
J(r
a column, psi
Horizontal Reaction on Saddle
-
,. oy'l-l Jol /")
;; ;; "' ,l[
\7-D
o,,
2
o.l2
(4-17b)
gives the relationship of the plate buckling stress in the inelastic range. This equation is based on the conservarive assumption that a plate will always buckle before the yield stress is reached. However, U.S. Steel [4] states that plates will deform plastically without buckling because of strain hardening. This process is similar to the "elastic shakedown" described in Chapter 2. In most applications, as already cited, saddle plates are reinforced with stiffener plates. A simplified analysis can be made to design saddles by using
n(A,
A, n
maximum unit load the stiffener can carry as
1o.,
= or-
where Fs
:
o*2
/, \2
Fs:
179
: : :
+
2b"t.)o.
force is as follows:
- ^h * cos 0 - 0.5 sin'z0l l't-lJ+sInPcosP.l
l9)
is As, shown in Figure 4-11 and calculated as follows:
Ae
: iRl l;l t,
where R
:
outside vessel radius
t 1 Figure 4-11. The load distribution on a saddle.
(4-
The effective cross section to resist the horizontal force
(4-18)
buckling load for compressive loading, LBq section area of stiffener, in.2 number of stiffeners
As shown in Figure 4-i 1, the load Q has a horizontal component exerted on the horns of the saddle. The saddle must be designed to p{event the horns of the saddle from separating. To accomplish this make sure that the minimum cross-sectional area at the lowest point on the saddle can resist the horizontal force component. This
R/3
180
Mechanical Design of Process Systems
SADDLE BEARING PLATE THICKNESS .Designing bearing plates for saddles requires knowing what type of foundation the vessel will rest on. For concrete the following analysis applies. Consider a bearing plate with the dimensions shown in Figure 4-12. From ACI Standard 318-77 par. 10.16.1. the allowable bearing strength on concrete is
o=
@10.85
'J
e,r
/,r
\o
s
(3
(4-20)
For bearing on concrete (ACI 9.3.2.e)
:0.70
0 a;
:
3000 psi
in which
o
:
(0.70)(0.85)(3,000)41
,
:1:-3,L,,: \Ar (,A
L-1,1"
l-"
Table 4-5
Bearing Plate Thickness Values tor Various Saddle Loads L1 L, Q.ax (tbs) t (in.) Bp (psi) o,(psi)
17 26 30 33 36 39 42 45 48 s4 s7 60 63 66 69 72 76 84 95
r4-1rl
4 2,858 0.165 42.029 108.852.563 4 5,043 0.178 48.490 162.100.694 4 8.103 0.2t0 67.525 t85.744.857 4.25 .13l 0.241 79.365 213,447.893 4.25 16,007 0.277 1U.62r 232,042.324 5.'75 20,418 0.350 91.050 320.269.t3r 5.75 25,387 0.3?6 lo5.t22 344.024.233 5.75 33,523 0.4t7 129.557 367.1-1.7.375 5.75 40,154 0.442 145.486 39t.528.914 5.75 s9,549 0.508 r9r.784 439,028.224 5.75 68,777 0.531 209.846 462,776382 s.75 84,203 0.573 244.067 486.523.,736 5.75 101.759 0.6t4 280.908 5t0,270.399 5.7s 114,664 0.637 302.145 534.016.463 6.75 t28.417 0.715 275.721 637,918..163 6.15 143,003 0.738 294.245 665.0.1s.973 6.75 174,748 0.794 340.639 701,285.2,75 6.75 210,035 0.828 370.432 773.70r.873 6.75 2s0,290 0.850 390.316 873.271.364
Using a factor of safety of 1.6, Equation 4-21 becomes Thus, the maximum stress in the bearing plate is
,' :
*=r,
r
rs.63 A,
(eir2Mtl!)"'
Using a minimum yield strength of 30,000 psi we have the allowable stress for bending, per AISC recommendatron, o.n
:
0.66
o,
:
0.66(30,000)
:
riq\/bj
op
=;
M= ,\2r"1\tl
"
-,
(4-))\
lil \6i
19,800 psi
Qt" lo'.,n. ,: I\24.600 Lrl where b : Q:
BP:
A-)
7l
Lz
load on saddle, lbs bearing pressure
Table 4-5 depicts values various saddle loads.
Q ao' = LrLz
of bearing plate thickness for
DESIGN OF SELF.SUPPORTED VERTICAL VESSELS Ar=LrLz Az=LoL+ Figure 4-12. Bearing plate dimensions.
Today's tall, cylindrical process towers are self-supporting, i.e., they are supported by a cylindrical or conical shell (skirt) with a large base ring attached to a con-
The Engineering Mechanics of Pressure
,'rete foundation or steel structure with anchor bolts embedded in the concrete or steel. Normally, a vertical \'essel must be at least thirty feet tall to be classified as a "tower." This height is used because thirty feet is the old first wind-zone demarcation in code use. However, smaller vertical vessels are governed by the same design criteria, but are not usually referred to as towers. The various phenomena that affect towers in normal operation make their design complex and worthy of experienced engineering personnel. Therefore, towers should never be taken lightly by any design office, because a failure could result in massive loss of material and possibly lives.
MINIMUM SHELL THICKNESS REOUIRED FOR COIIBINED LOADS High-speed electronic computers now provide detailed, exact solutions to complex mathematical probIems, and so have replaced the "strong arm" approximations of yesterday. An example is solving the equations of the moments of inertia and section modulus. Before the advance of computers, the following expressions were used to quicken computations on a slide rule or a small electronic calculator:
I = nR3t; exact: I: #,o""
.I
Z
:
A=
rRztt exact
?Irt;
= z = ,a (gd
exact: A:
l,o" -
ar'"'D
D,)
|
4-15 |
(.4-26)
Using R as the mean radius minimizes the error and using R as the outside radius results in considerable error. Solving for the thickness or stress with the exact formulations involves iterative analysis, which is a key attribute of today's computers. The minimum shell thickness required for internal or external pressure alone is often not sufficient for addi tional stresses induced by bending moments and weight loads. Bending stress is a result of static wind, dynamic wind gusts, vibration or seismic response spectra. In design the engineer takes the largest bending moments induced by one of the following: wind, vibration or seismlc. Referring to Figure 4-13, we analyze the stress element depicted. The maximum stress resulting from internal pressure occurs along the x-axis, i.e., the hoop stress is twice the longitudinal stress. Wind, vibration, and/or seismic forces cause the shell to bend about the z-axis, so
181
the internal stress in the circumferentiai direction is com-
bined with the bending and tensile (or compressive) stresses. Writing this expression we obtain,
"= -(.*J'H-(x) where
Z: A:
(4-27)
section modulus of the shell cross section, area of the shell cross section, in.2
in.l
Substituting Equations 4-24, 4-25, and 4-26 into Equatior 4-27 produces
,
: * (ryf - (":zlur.. _
-
- \4,/=
,(
\
to
\nrtO"
2w *
, h- iLr, _
"io^lra
ipo\ /
= \",tnt
"J
@-zB)
-t DitrDr D,:t/
\
(4-29)
Ot1
or
'
to o"t'.1 /po\ / \ - \+r/- \norD,-r D,rrD"r - D,2r/
2w \ * t1
,(
(4-24)
D'a)
Vessels
(4-30)
= \""fr5
Referring again to Figure 4-13, we summarize the following:
1. For the tension or windward side,
'
/po\ / \ +t
-
/
\rrr D"
ro
-
o"v
D,tt D"2
lzwl+ DJ/
\
-
D,2t /
(4-31)
\"(D"
or 16 D.M . - /.o\ I \ ' \+, /- \ro{D" --J,DJ + D-l-,/
- /zw\ \"r(DJ-D)/
2.
t4-1)\
For the compression or leeward side,
/po\ i \4tl
-
o.r,a
ro \Tt(D" + D,XD.r
lzwi
\"(D" + D)/
I
)
D,r)/ /4-11)
182
Mechanical Design of Process Sysrems
o u,
U'
o -3
ttGt q) o
tt, lo
th at
l--lo
l-
3lt ld"d l^'l -
'
clF
ll,
stN =ll x l= 1t--l --r'l tr
,. f---l -\'l II< l<-l /
l
ll' 'E'
/
l<1_
-
I
^i^ Lo-l I
> E-
s-^
o i.;
ci
Nls
o
" lci r \ | lr
tk
/ irlol
o"
*
--41ll < lr>- I
I
q)
o
tt
to C'
EO
bp
!'
o.
f
3 ielo Rl+--i- ",* ;l*
,ll lll - !l < l
"
x
^r
^"-'l= i' Ii.- - l'' ' oo- +
' {i ll I' -rdo[
Rlr
x
!:J
t€ I
a,l
o rl) E(/, o o-
E" O,o
3 5x
^, i rine* )
o r
i -tu
r N "_12 ^lil+ .Jt ql I/ - +;l it I:+
il= "-1 - ' f---------1r
Fl_
-\1il
..-t-''_ Ir
t-l I
Y\ . pl*
x ol o- td
o
a9 or l: !:
(1,
U'|,,l
q)
IL
The Engineering Mechanics of Pressure OT
._ - /ro\
'
\4"/-
/
ro
o.rra
\""(DJDJ(DJ
lr*\
\
+-3/
(4-34)
\"r(D" + DJ/
3. For
vacuum vessels the maximum stress occurs on the compressive side, such that Equations 4-29 and 430 become
- l2wl \"(D. + DJ/
(4-35)
Vessels
183
the cost-plus contractors seek to standardize designs and use lower pressure vessel code allowables. As with wear plates on horizontal vessels, most lump-sum contractors would elect to omit them whenever possible to save material and labor costs. This phiiosophy is becoming increasingly popular with recent economic upheavals and
increasing international competition. Types of skirt supports are shown in Figure 4-14. Figure 4-14b shows the most common and desirable skirt, since the shear is eliminated by the type of attachment. This type is used primarily on short vertical vessels. The skirt is designed to resist loadings caused by bending and the tower weight. Writing the expression that describes this we obtain
and
ro o"r',r \ .' - /po \ / \4")-F',D.+ qnD"' i-DI/ _l 2wl
\"t(DJ
Substituting Equations 4-25 and 4-26, as before, we obtain (4-36)
DJ/
16MD. 7r't(D" + Dr(D"2 +
l6MD"
SUPPORT SKIRT DESIGN
no(D" +
The design ofvessel skirts is one area in which designers disagree philosophically. Lump-sum contractors seek to use higher allowables and thus less material, whereas
2W
Di)
irr(Do
,
(4-37)
+
D,)
2W
5tD"'+ D-5 "'@. + D)
Once again, Equations 4-37 and 4-38 must be solved by iteration. Normally, these equations do not govern the skirt thickness, as the reaction of external bolting and
IAINIGHf CIRCULAF CYLINDBICAL SKIBT
t,/
l\l Jt tE, l
16I
(4-38)
EXTEiNAL LAPPING SKIRI
Figure 4-14. Skirt designs.
i
184
Mechanical Design of Process Systems
compression rings is not considered. The stresses in the skirt shell that result in compressive loading on the compression ring and bolting chair can be quite high in appli-
cations where external chairs shown in Fisure 4-15 ire used. See Brownell and Young [3], for a derivarion ofthe reaction expression. The skirt thickness required to re_ sist the reaction of external chairs or comp;ession ring for a chair of the type in Figure 4-15 is determined ai
follows:
see below
= N=
operating weight, lb empty weight, lb number of anchor bolts
(4-3e)
: skirt thickness, in. : radius of skirt, in. : bolt spacing, in. or 28 in Figure 4-15 = uplift bolt load, lb : radial distance from outside of skirt to bolt
t
r m F.
B G11
:
circle, in., Figure 4-15
The minimum initial bolt load required to maintain compression between the base plate and compression ring exist when o" 0. Thus, using Equation 4-40 and substituting o. 0 we have
Anchor bolts are one of the most important aspects of tower design, and, unfortunately, are often not taken seriously enough. Consequently, many problems related to towers during construction or operation can be linked to anchor bolts. Wind and seismic loads are dynamic and result in cyclic loading of the anchor bolts. For this reason, I will only present the method for analyzing preloaded anchor bolts. Initial preload is significant since pre-torquing the bolts reduces the variable stress range the bolts experience during cyclic loading. The tower weight and bolt load allow firm contact between the compression ring and concrete or steel such that the support base rotates about the neutral axis of the contact area, as shown in Figure 4-16. Referring to this figure we see that under a moment M at the base plate-concrete juncture the maximum and minimum stress is _
:
8M
[oJ
- (**J
f,to"t
-
o,r;
I,=#(D"4-D,4)
:
D.-
N(D", +
D,1-
W,
____:
N
(4-40)
(4-41)
The required bolt area is
[*")-
*'
No,
ANCHOR BOLTS
where A"
-' f,:
gusset height, in.
Equation 4-39 is normaily the controlling criteria for a skirt with external chairs. Howeveq for a skirt with or without external chairs, Equation 4-38 must be satisfied.
" = H).
yessel weight, lb
WE
:
,=176[#r]",,, where
Fi :
W: W. :
(4-42)
: bolt circle diameter, rn. : allowable anchor bolt stress, psi M : in.lb
where BC ou
Equation 4-42 is one of the major differences in designing a tower under a lump-sum contract versus cost-plus. Most cost-plus designers use vessel code allowable stress values that are based on a factor of safety of 4:1. This large a factor of safety is intended for components containing pressure. Thus, using vessel code allowable stresses for bolts leads to large anchor bolts, which is undesirable because more concrete is required and larger
bolts are much harder to torque, requiring bigger wrenches and being more susceptible to galling. To keep anchor bolt sizes down follow AISC euidelines for bolting- since anchor bolts are purely stirctural in nature. Table 4-6 provides the allowable stresses for boltins
per AISC
l5l. Type 4325 bols and ASTM Al93-87
high-strength bolts are used in most applications. A307 bolts are used where bolt loadings are not large and the bolt size need not be massive. When bolt sizes get large (231a to 3 in.) or it is desirable to reduce the bolt size. then Al93-B7 or A325 bolts are used. One can see from Table 4-6 that A325 has more than twice the allowable stress value as A307 bolts. The extra cost of the hieh-
strength material will still be less than rhe addirional c6ncrete and labor costs associated with a larger bolt. Certainly. if one pays more for high-strength stleel, he should be permitted to use the larger allowable, as given by AISC. Normally, 40,000 psi is used with A325 and 193-
87 bolts. The spacing of anchor bolts is another critical parameter. Spacing the anchor bolts too close to one another
The Engineering Mechanics of Pressure Vessels
f*-
r? lzA,l
185
"---|
1I IT
t[ liill
Iil J IIL
r-*-l
F-r:-'-_i
k----il--+l
NOTES: all dimenslons in inches BTHK to be evaluated by
eouations 4-57 or 4-60 all welds to be size
BOLT
SIZEABCBH 'I
'l
tl'
'l1la 1q8 1112
11la
2
2tl+ 21h 23lq
"t"
CHLLJMNP 31lz 31la 3 6 9e 51lz 5 3{+ 6 Ye 53lq 51lc 31lz 3 5112 33t+ 3qo 4 6 4t 6 33lq 4318 7 4q 61lq 53lq 4 41lq 41la 4112 8 3lq 6112 6 7 6tlz 4eh 4alc 43lq 9 1 Stlq 51lz 6 10 1 7112 7 Telc 7112 53lq 5718 6112 12 1 7 13 11/e 81lc 74c 64a 6 '14 11lq 8112 I 61+ 6{e 71lz 16'l1la98r/+777slq
GH
31lz 'l4a 14q 1112 2 3{+ 148 17k '1518 21k 4221s1c2112 41lq 21la 2118 148 2sla 2sl+ 4tlz 21lc 21la 2 5 2112 21lz 2th 31lq 51lz 24c 23lc 21h 31lz Sslc 3 24c 23lt 34a 61lc31l+334118 Srla 4112 61lz 3rlz 3 7 3glc 31lc 31lz 4gla
4e 9e 4e llz 112 5lB 3lc 3l+ 4e 1 11k
31lt 33/e 33lq 41le
41lt 5 51lz
53lc
64a 71lz
8
Figure 4-15. Typical designs and dimensions of chair and base plates
74s3 731rc3
1'tlq th 7112 1lq 81|q4 5h6 9 '12 {e 13 {e 144rc8 16 1lz 18 llz
3 3 5
6 7 9 10
186
Mechanical Design of Process Systems
ANCHOB BOLT
MAXIMUM TENSILE UPLIFT FORCE- q
FOUNDATATION
MAXIMUM COMPBESSIVE
JI
FORCE = nFc
zt<
E. I I
I I +-
COMPRESSIVE
TENSILE FORCE DISTRIBUTION
FOBCE
CENTROID
DISTRIBUTION CENTROID
Figure 4-16. Anchor bolt loading force distribution.
prevents the strength of the bolting in the concrete from becoming fully developed. It is advisable to set the bolts at least 18 inches apart. To accommodate this minimum spacing a wider base ring with gusset plates can be used or the skirt can be tapered with a conical skirt. As shown in Figure 4-14, with a tapered skirt the apex angle should not exceed 15 ".
factor. The modulus of elasticity of steel is approximately 30 x 106 psi and that of concrete approximately 2.O to 4.O x 106 psi. Defining the ratio of the two as n. we wnte
BASE PLATE THICKNESS DESIGN
since E.
Base plate design involves the loadings passed on from the tower to the foundation. The base plate is a circular ring plate used to distribute these load-s around the cir-
and
cumference of the bolt circle. Anchor bolts normally vary in diameter from one to three inches-bolts smaller than one inch are more likely to strip or shear off; bolts larger than three inches require large wrenches and create excessive problems for construction personnel. For these reasons it is desirable to attemDt to adhere to the one to three inch size range. In the case of a concrete foundation, the relative strength of the concrete to steel becomes a significant
F
(4-43)
F
E. :
:o" os €s
and e,
=
e. because os(induced)
=
of the base plate-concrete bond we noc(induced)
have
(4-44)
Listed in ?ble 4-7 are values of the moduli ratio n and the various concrete mixes from Brownell and Young [3]. Figure 4-16 shows a detail ofthe compressive force of the concrete, F", multiplied by the value of n shown opposite the maximum tensile stress, Fr of the base plate steel.
The Engineering Mechanics of Pressure Vessels
187
Table 4-6
Bolis, Threaded Parts, and Rivets Tension [51 Allowable loads in kips Bolts and Rivets Tension on gross (nominal) area Nominal Diameter. d. in. ASTM
Fi
Designation
Ksi
3la
20.0 44.0 54.0 23.0 29.0
0.7854
0.9940
6.1
0.4418 8.8
13.5
19.4
16.6
23.9
0.6013 \2.O 26.5 32.5
'7.1
to.2
13.8
18.
8.9
12.8
r7 .4
22.8
13ls
11lz
1.227
1.485 29.7
1.767 35.3
11la
Area (Based on Nominal Oiameter), 0.3068
A307 bolts A325 bolts A490 bolts .\502-l rivets A502-2,3 rivets
'l1la
4s
in.'?
15.'7
19.9
34.6
43.'7
54.0
65.3
77 .7
42.4
53.',1
66.3
I
22.9 28.8
?8.2 35.6
80.2 34.2
95.4 40.6
43.1
51.2
The above table lists ASTM specified materials that are generally intended for use as structural fasleners. For dynamic and fatigue loading, only A325 or A490 high-strength bolts should be specified. See AISC Specification. Appendix B. Sect. 83. For allowable combined shear and tension loads. see AISC SDecification Secl. l 6.3.
Threaded Fasteners [51 Tension on gross (nominal) area Nominal Diameter. d. in.
F, Ksi
F, Ksi
Ksi
A.r6
58
19. I
4572. Cr. 50
65
ASTM
Designaiion
1
Ft
11ls
13/8
11la
'l1lz
0.3058 0.4418 0.6013 0.7854 0.9940 1.227 1.485 A588 A,149
92 8l
d
I
lr/:
120 105
2t .5
5.9 6.6
8.4 9.5
23.
I
7.1
10.2
39.6 31.7
12. i
I
7.5
l l.5
r5.0
19.0
t2.9
16.9
2t.4
26.4
3.9
18. r
23.0
28.3
23.8
3l.l 3.1.5
12.6
r
23.4
28.4 31.9 34.3
1.767 33.1 38.0 40.8
Thc abole lable lists ASTM specified nulc.iul\ !!ailirblc in round blr sr(xk rhat lrc genrr!lly intcnded lirr u\c in rhreaded appljcaoons such rs rie rods. cross bracing and similar uscs The rensile capacir! ol thc lh.cadcd porlion ol an upsrl r(xl shall bc largrr lhan lh! b( ) lrca rrnrs 0.6F.. F, = specified minimunr tensilc strcngth oflhc lasrener nutcrill. t. = 0.llF, = allowable tensile srress in rhrcldcd iasrener.
Table 4-7 Design of Supports lor Vertical Vessels Values of Constants
C" 0.050 0. 100 0. 150
0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600
0.600 0.852 1.049 1.218 1.370
q,
C", Z, Function of k Cr
3.008 2.881 2.772
andJasa
Average Values ot Properties ot Three Concrete Mixes
ZJ 0.760
2.66r 2.551
o.418
0.7'79 0.781
7tlz 6
2000 2500 3000
5
3750
o.'766 o.7'7
|
0.776
1.765 1.884
2.t t3
2.000 2.113 2.224
2.000
0.438 o.427 0.416 0.404 0.393
1.884
0.381
0.783 0.784 0.785 0.786 0.785
r.765
0.369
o.784
1.&0
Water Content oi n U.S. Gallons 28-day Ultimate 30 x 106
0.490 0.480 0.469 0.459
a Ana 2.333 2.224
1.510
[31
Sack ot Cement
per 94Jb
63/c
Compressive
Streigth,
psi
Ec
Allowable Compressive
Strength, psi
l5 t2
800 1000
10 8
1200 1400
'188
Mechanical Design of Process Systems
Equation 4-44 is shown as a linear proportion by the straight line shown in Figure 4-16. Even though the tensile strength of the bolt is, by Equation 4-44, equal to the ratio n times the concrete allowable comDressive strength. it is not necessarily evenly distributed about the neutral axis as shown in Figure 4-16. This "offset factor," known as the "k Factor," is determined from
os (d
- kd)
noc
:
kd
(4-53)
f (ER)(SFC)
After computing an initial value of k, this process should be repeated five times in order to converge on a value for k. Once a value for k is determined, we now solve for the maximum induced stress at the outer periphery in the concrete,
I
ork =
(4-4s) oq.*,
: (sFC)t*X**]
tro"
using
Equation 4-45 is solved by iteration using the following steps: Thke values for C", C,, Z, and j in Thble 4-7 for a
L
=
D"
-
(skirt OD)
, ln.
(4-s4)
(4-s5)
given value of Z. Normally, k = 0.333, C" : 1.588, C. = 2.376, Z = 0.431, and j : 0.782 to start the process. Then the following equations are solved:
we solve for the base plate thickness, BTHK,
rt--/\
(4-46)
where ou1 psi
(4-47)
By using Equation 4-56 one assumes no gusset plates on the base plate-skirt connection. To reduce the required base plate thickness in Equation 4-56 the additional strength of gusset plates can be used, because with the gusset plate stiffening the base plate at the skirtjuncture. the base plate between the gusset plates can be considered as a rectangular, uniformly loaded plate with two edges simply supported (at gusset plates), a third edged fixed (skirt side), and the fourth edge free. The deflections and bending moments are tabulated by Timoshenko [6] and are shown in Thble 4-8. The process of using gusset plates to stiffen the base plate is begun by making the number of gusset plates equal to the number of anchor bolts. Doing this we write
/^^\ M _ (W,r(z)l!!l " lt)l .. lBcl
rJrl;l
BrHK = L
:
[tf,]"'
(4-s6)
allowable working stress for base plate metal,
\'.1
(Ah)N
''
r(BC) F
Ir =
/ -\
(4-48)
rt,r l!91c,
\2/
fc:
fi +wE
BPW
:
base plate
width, in.
Bpw:(D.)-(Di)
(4-4e)
2
tz
=
BPW
F
-
(4-s0)
t;
(4-51)
(c.)(1,000)
=
NG : let NG:
modulus of elasticity of base plate metal, psi compressive strength of concrete, psi, denoted in
:
5U=
Thble 4-7 as o" f,
J|L = --
(h
-
where SFC :
circle and
/^l (Enxt ))
-/IIat NG + N bolts
(4-57)
RAT:!SG
(4-s2)
(]Jrc.r
number of gusset plates N bolts
M- :
compressive stress on concrete at the bolt
M,'
:
1E,1o"1.""(SG)'?
(4-58)
lE,1o"1."-(L)2
(4-59 |
The Engineering Mechanics of Pressure
Maximum Bending Moments in a Bearing Plate with Gussets [61
{' = b/2\ \v
=r
/
0 0.0078f"b,
o.0293f"bl 0.0558f"b,
0.w72f.b, 0.123fJ2 0. 131f"b,
0.133f"b,
:
= :=
bt2 I
Typical designs and dimensions of chair and base plate designs are shown in Figure 4-15. The compression plate thickness is determined by
I rr,rc I
-0.500f"1,
-o.428f"t, *0.319tP
f^^ :
t _____________
-o.124f"t2 -0.125t"t2 -0.125f"1,
gusset spacing (x direction) inches.
bearing-plate outside radius minus skirt outside radius (y direction) lnches.
where
A
BS : Fi : o.11 :
where
:
lortalo
'
(4-60)
x
The gusset plate thickness is determined by the following:
:
M,
or
Mr
This iteration can be repeated as many times as desired to reduce the base plate thickness. In normal practice, it is unusual to use more gusset plates than anchor bolts. The bearing pressure on the base plate must be checked to prevent exceeding the allowable compressive stress of the concrete. Computing the uplift force on each anchor bolt we have,
--'
.
o^ -_
96MD" WF ,, a P:; N'''
A" A.
12MD"
DSI
21,
o" ( 1,200 psi for-.weight and wind where, M : ftJbs
where
A" = t-
r[(D")'?
-
(D)'?]
4
r[(D")a
-
64
. *:
[+r'a
\4-@l
gusset plate thickness, m. gusset plate width, in. (A in Figure 4-15) gusset plate height, in. (see Figure 4-15)
] - [w. I [.o"j
["o*l =
(1.33Xo"r)(0.55)
and
€ : w = 2F* : M: D.r :
where o"1
weld size
(4-65)
smaller of the allowable stress values for the base plate and skirt metals moment at base plate induced by wind or
seismic forces, in.-lb outside diameter of skirt, in.
ANCHOR BOLT TORQUE (4-62)
There have been many recipes proposed for the computation of bolt torque over the years. The mystery of bolt loads is unveiled by such authorities as Bickford [7] and Faires [8]. Their extensive research into bolt loading produced the following recommended formulation:
T:
CDFi,
where (DJa]
a],,2/F \
=0 - l"'i=' I,J|.ru
(4-61)
N1D"z
N" WF ----:: + -----: +
(F,)ta
by
Fw
in.-lb/in.
-
The minimum skirt-to-base plate weld size is determined
[_oJ
M
(4-63)
l
BSI
bolt uplift force, determined by Equation 4-61 allowable stress of compression ring metal, psi
where tc: Gw: GH:
ornN
-
and C are dimensions in Figure 4-15 1.25 nominal bolt size
18,000 Gw ta
Where o"1*n,; is determined by Equation 4-55, using the greater of M, and M, we have
::-
l4('.rr(A
-o.22'7 f:r2
-0.119f"F -0.125f"t2
0.133f"b,
189
COMPRESSION RING AND GUSSET PLATE DESIGN
Table 4-8
M,
Vessels
C: C: D= F1
:
in.lb 0.20 bare steel 0.15 for lubricated bolt nominal bolt diameter, in. anchor bolt uplift force, lbs
(4-66)
190
Mechanrcal Design
ol
Procg55 g151snlt
2.3<+<2.6
groutl-i
-f--
Boltom of sleeve or top of concrete
concrete
L = 17Du
Figure 4-17.
"J"
and
"L"
type anchor bolts are used for small vessel..
In most tower applications, Fel-Pro C5A is a very common bolt lubricant. The field of bolt desisn and bolt lubricants is almost as involved as tower desien and the
interested reader is relerred to the excelleni work of Bickford [7]. Figure 4-17 shows the two most common types of anchor bolts, "J" and "L." For large towers where large loads are anticipated, the bolt in Figure 4-18 is used.
orout -,L
T_
WIND ANALYSIS OF TOWERS Analyzing wind loading on towers requires combining loads induced by wind, internal or external pressure, and weight. Such an analysis must be made to ensure that the tower shell thickness is sufficient to withstand the combined loads. Wind and seismic analyses are completed separately, with their respective bending moments being used to determine the tower shell thickness values at each section. Before examining the design criteria, let's consider the following terms: ow
op
o"
= =
:
stress due to wind or earthquake stress due to internal or external pressure stress due to weisht
concrele
Figure 4-18. Straight type bolt-used for large vessels, cially towers.
espe-
The Engineering Mechanics of Pressure
Referring to Figure 4-13, we see that the stress ele:lent in the shell is affected by the combined loads more ::r the longitudinal direction than the circumferential di:ection. However, for the longitudinal axis the internal rr external pressure stress is governed by the relation
-4t
(4-67)
: : : :
,rhere D P op T
mean diameter of vessel, in.
internal or external pressure, psi Iongitudinal stress, psi shell thickness less corrosion allowance, in.
There are two conditions where Equation 4-67 is used to combine stress values:
L. Combination of wind (or earthquake) Ioad, intemal pressure, and weight of vessel. For windward side,
\'s:qw+op-o*r ,rLs
:
op
-
ow
+ op-
:f and only
- owr
- o*,1 ) o"1E where ou1 : allowable stress in tenslo, for a given material at a given temperature and pressure E : weld efficiency
o*,1
if
l oo
) 1oo-o*-o*,1 l>
lool
oo
Another form of Equation 4-71 may be determined by rewriting the equation as
)
op
o*,
or
-
0.40
E
W69)
l
o*,1
(4-70) (4-7
t)
reversed and
|>
Equations 4-70 and 4-71 hold,
Inwhrchfi{
which is true for most applications, when the internal pressure stress is greater than that induced by the weight of the tower above the section. However, for a few cases, the stress induced by the weight is greater than Ihat induced by internal pressure for low-pressure thickivalled applications. The thick walls at low pressure could be for controlling tower deflections due to wind. For these limited cases the allowable stress is that determined by UG-23 (b) of the ASME vessel code, which is known as the B factor. The B factor is commonly associated with external pressure, because the case of the weight stress exceeding the internal pressure stress is rare, but it must be emphasized that the B factor is the allowable value of stress for longitudinal compressive loading like that encountered in towers. Thus, the B factor is more comprehensive than its external pressure application would indicate. Therefore, if Equation 4-71 is o.,
If
(4-68)
Comparing Equation 4-68 with Equation 4-69 we have ow
loo-o*-o*l < Bfactor
P(R,
For leeward side
(4-72)
191
such that the leeward side governs, then
lo* -f
PD
Vessels
_ -;Rl W
-TI
pn,tl r [: w - t.zo L fSp" I
(4-73)
Equation 4-73 is another form of Equation 4-71, in terms of the vessel dimensions, where W is the total weight of the tower above the section being analyzed.
2.
Combination of wind (or earthquake) load, external
pressure and the weight of the tower-
On windward side OWS
= O*-Op-O"n
On leeward side
OLs:
-O*
op - O*,
For most applications with external pressure we have ols
>
ows
| - o* -op-o*, ) rw-op-owt oo*0 Since the value of oo is for external pressure, we must apply the B factor in Equation 4-67 . After these criteria are satisfied, we turn our attention to the determination of wind loads that induce o".
192
Mechanical Design of Process Systems
WIND DESIGN SPEEDS The procedures for determining wind design speeds for structures, towers, and stacks varv from Counirv to country, depending on how well records have been kept. The wind velocity is a function of the temperature gradient and terrain roughness. The first representation of a mean wind velocity profile in horizontaily homogeneous terrain is the power law, first proposed in 1916. This law
2.
used are as follows:
states
,t: r.\r:)" : Q:
where Vo
Z. =
Z=
(4-74)
3.
mean wind speed at a reference height Z reference height (normally 33 fr orl0 m) a constant dependent upon roughness of
(a) Importance Coefficient, I, a hospital or nuclear plant would be designed moie conservatively than a barn on a farm. (b) Variation of wind speed with building height and surrounding terrain. (c) Gust response factor. (d) Velocity pressure coefficient, K2. Test a model of the tower and its surroundings in a wind runnel. Even though rhe 1972 ANSI stindard does not mention this, the 1982 version sDecifies certain requirements lor wind tunnels.
terrain height above ground
Other proposals have been made to determine wind speeds. Simiu [9] states that the logarithmic law is a supenor representation of strong wind profiles in the lower atmosphere. What is relevant to the reader is to be familiar with whatever standard is used. The discussions and examples presented in this text are slanted toward those standards in the United States. However, the technioues and base principles of engineering are applicable to all countnes. In the United States there are four basic codes soverning wind- ANSI A58. | 1982. the Uniform, thi Basic,
and the Standard Building Codes [10]. The ANSIA58.1- 1982 differs from the ANSI-A58. I - 1972 in that
three optional methods of determining wind design loads on a structure are given [11]. These options are as fol-
lows:
l.
ing hit by one is extremely small; however, nuclear sites are designed to withstand tornado winds. Using site and structure factors calculate the design wind speed. The factors on rhe ANSI l98Z tesr
Choose a design wind speed (50-year mean recurrence interval) off the U.S. map provided on the document. The national map is a graphic display of isopleths (lines of equal wind speed) of the maximum values of the mean speed for which records have been kept. i.e.. basic wind speeds rhat can be expected to occur within a particular period. This "particular period" is called the return period. The problem with a nalional map consisting bf isopleths is that localized wind speeds can vary as much as 30 mph over the speed shown on the isopleth (particularly in mountainous regions).
Hurricanes are fairly well accounted for on these maps. Tornadoes are considered to be nonexistent, because it is not economically feasible to design an entire building for tornado wind speeds. The reason for this is that the probability of a structure be-
These three options are new to both the ANSI-ASg. I standard and to the three building codes-the Uniform. Basic. and the Standard. The larrei three codes do not au-
tomatically adopt newly revised ANSI standards, thus making for inconsistency in wind code provisions in the United States. The basic wind pressure in the ANSI-A5S .l-19j2 rs q3a= pv2l2
:
:
0.00256
: V36 :
where q.s
(0.5X0.00238)(5,280/3,600fV30
v3o
@-'75,
basic wind pressure at 30
ft,
above grade
lb/ft, basic wind speed, mph
The effective velocity pressures of winds for buildings and structures, qF, is
9r :
KzGrQ:o
where
K2 = velocity pressure coefficient that depends Ge
:
(4-76
t
upon the type of exposure and height Z above the ground dynamic gust response factor
In the 1982 ANSI-A58.1 Code the effective velocin pressure for wind is partially a combination ol Equarion. 4-7
5
: I:
qz
V=
and 4-76, 0.00256 KzGV)2 basic wind speed, mph importance factor I
\417)
:
A value of V can be approximated for the United States from the isopleths shown in Figure 4-19. One of the major differences between the ANSI A58.1-1972 and 1982 is how the velocitv Dressure coefficient, K2, is determined. In the 1972 Cod'e the value ot
J -
The Engineering Mechanics of Pressure
Vessels
o; -; b \-\ .E e. oot;9
\\ ;] \
\\
b9;.0 *-t!cb ; !b69
3. iaEg o-i=H9
a'*-w* * ird\
ii:# .s i
"E /\,r\ *i *tid
\px i4'
^;it 9\i !ii.s -
\F 9!.o : R: '-+!-€ 2 : \8. E i a; f : ]{ .: IEE:
)
P
I"
i-'q -i Hf;n* s :,'' s 18 ;:
g;ni: I-* l(U*963
$ " !;i;
: ; ; :
o-!o
8
6
let
o
6 r. E'=-
i" f i:.E ?i 4:' ig >iif o -6
r
6 o
No
5
z
-:
z O
J
.9 TL
E
.l
!L
:
rl' I jll\
193
194
Vechanical Design of Process Syslem,
Table 4-9 Velocity Pressure Exposure Coefficient, Kz
[1 1l
Height above Ground Level, Z 0- l5
o.t2
20
0. 15 0.1'7
25
30
40 50
0.19 0.23 o.27
60 70
0.30
o.37 0.42 o.46 0.50 0.57 0.63 0.68 o.73 o.77 0.82 0.86 0.93 0.99
0.33 o.37 0.40 0.42 0.48 0.53 0.58 0.63 0.67 0.78 0.88 0.98
80
90 100 120 140 160 180
200 250 300
350 400 450
1.1
t.24
K7 is a linear function of the height Z from heights of thirty to nine hundred feet. This results in a triangular wind distribution on the tower. In the 1982 Code the value of K2 is a parabolic function (can be approximated with a step function) for wind loading depicted in Table 4-9 and for dynamic gust response, K7 is governed by lhe power law, Equation 4-74.
,r*
lz\2'
\r,)
@-78)
forZ <
15 feet
where values of Z" and d are given in Thble 4-10. The parabolic function is a reflection of the old classical approach used in the ASA 58.1-1955, but is a more refined distribution. The treatment of K2 in the dynamic gust response analysis is a new development in U.S. codes. The force exerted on a tower immersed in a movins fluid is a function of the properties ol the tower shapi and properties of the fluid. The fluid properties of importance are the viscosity, density, and elasticity. Writing this relationship in functional form we have
F = f(p, Y, I, p, a)
1.46 1.52 1.58 1 .63 1.67
19
1.29 | .34 1.38 1.45 1.52 1.58 I .63 1 .68
|
1.87 1.92 1.97 2.01
2.10 2.18 2.25 2.31 2.36
1.',79
2.O5
2.12
=
l8
velocity of sound
|
1.81
1.88 1.97
2.
.'7
1.7 5
2.4r
=
0 in our case, because winci
speeds are extremely low compared
to sonic
speeds
This equation shows that there is a relationship dictated by the dimensions of the parameters involved. Applying dimensional analysis makes the equation
-tpvt, -t;
forz > ls feet
Kz=
l.
1
where a
r.32 r.37
| .24
1.16 1.28 1.39 1.49 1.58 1.67 1.75
1. 16
1.20 .27
1
1.06 1.13
1.05
r.07
500
0.80 0.87 0.93 0.98
P(Y2!2
,}:.
where each of the two components is a dimensionless parameter. The equation can be solved for the first dimensionless combination by
r _ - /pvi\ pv+-'\r/
(4-19
Equation 4-79 implies that the parameters F/(pVri: (pYllp) have certain definite values that will be equa. if a geometrically similar body with the same orientatio: is moved through the same fluid or another fluid fo: which pVflp has the same value as the first body. Tsi such bodies are said to be dynamically similar and dr namic similarity is the key to wind tunnel tests. Assumins and
that p has no influence on the force F, we can deduce
fror
The Engineering Mechanics of Pressure Vessels
Table 4-10 Exposure Category Constanls [111
Equation 4-79 (see any basic fluid mechanics text) and obtain
Exposure Category B
3.0 4.5
D
10.0
c
2
orF:
Cp
pYz12
195
7.0
4
Do
1500 1200 900 700
0.025 0.010 0.00s 0.003
(4-80)
where Cp is a dimensionless empirical constant. Equation 4-80 states that, for a body of given orientation and shape that is immersed in a moving fluid, the force experienced is proportional to the kinetic energy per unit volume of the motion of the fluid (p/2)V2 and a characteristic area f2. Cp is a dimensionless quantity that characterizes the force and
is called the /orce coefficient. Two bodies that are immersed in moving fluids are said to be similar (geometric similarity) if their Reynolds numbers are equal. Then the flows are dynamically similar and have equal force coefficients. The Reynolds number pVl y. is called a similairy parameter. Figure 4-20 shows the influence of the Reynolds number, corner radius, and surface roughness on the force coefficient on various bodies. The values of Cp are determined empirically and are shown in the figure. Sometimes this coefficient is referred to as the drag or pressure coefficient. Kuethe and Schetzer [12], use the Kutta-Joukowski theorem to show that the force per unit length acting on a right cylinder of any cross section whatever is equal to pVf and acts perpendicular to V. The symbol f is circuIation flow about the cylinder and | = r'DV. The KuttaJoukowski principle is exemplified in Figure 4-211131. Here the pressure distribution around the cylinder is maximum ninety degrees to the air flow. Depending upon the relative stiffness of the tower sections and mass distribution. this perpendicular lorce vector can cause a phenomenon known as ovaling, which will be discussed
r/h =
O.O21
1.8
---j ''--!1,
r/h = 0.167
lz' 0-4
(b)
1.2
,-"-01
I I I
t/h=
0.333
o.4
1.2
later.
In computing the wind forces on a tower, Equation 480 takes the following form in using ANSI A58. 1- 1982:
F:
q2GCpAg
whele qz
_
:
G: Cp
=
Ar =
t/h=
(4-81)
wind pressure at height Z, EgrJation 4-77,
lb/fc gust response factor for main wind-force resisting systems of flexible structures force coefficient cross-sectional area of tower and other attachments, ft2
The gust response factor, G, when multiplied by the mean wind load, produces an equivalent static wind load
tO. 2
4
8105
4
2
ato6 2
4
8tO7
Ae sanded
---Smooth -
$rface
(d)
srrface
Figure 4-20. The curves depict the influence ofthe Reynolds number, corner radius, and surface roughness on the drag coefficient, square to circular cylinders; r is the corner radius and K is the sand grain size [9].
O.5
196
Mechanical Design of Process Systems
112
p!2
Figure 4-21. A sequence ofpressure fields forming around a cylinder at Nq6 = I 12,000 for approximately one third of one cycle of vortex shedding (Flow-Induced Vibration by R. Blevins. @1977 by Van Nostrand Reinhold Company, Inc. Reprinted by oermission.)
that would induce deflections equal to those of a gusty wind. MacDonald [14] refers to this approach as a quasistatic loading analysis. Quasi-static means that at any instant the stress and deflection induced in the tower are the same as if the instanlaneous mean wind load were aoplied as a static load. Thus. the significanl factor is identifying the single highest peak value of instantaneous mean wind speed, or that is, predicting the future worst peak value. Baker and others found at the end of the nineteenth century that there is a simple relationship between the gust frontal area and gust duration. This relationship provides a means of determining the size of the gust, and is illustrated in Figure 4-22. The figure indicates that the worst wind condition for a Darticular tower is not necessarily the maximum value of the wind velocity, but rather the highest wind speed of the particular size of gust capable of totally enveloping it. To compensate for this in a simple quasi-static analysis, ANSI A58.1-1982 gives rhe gust factor as
tJ:
L,.o.l +t
where
p:
lp
+
\p
11
1
?tr.,/s
Table 4-1 1
Probability ol Exceeding Wind Design Speed P" = 1- (1 - P")N Annual
Probability Design Lite ot Structure in N years P, 1510 15 25 50 100 0.10 0.100 0.410 0.651 0.'194 0.928 0.995 o.999 0.05 0.050 0.226 0.401 0.537 0.723 0.923 0.994 0.01 0.010 0.049 0.096 0.140 0.222 0.395 0.634 0.005 0.005 0.025 0.049 0.072 0.118 0.222 0.394 D_
probability of exceeding design wind speed dunng n years, where P : l-(1 - p.)" annual probability of wind speed exceeding
_11
\r2 |
+ 0.002ci
e-82)
structural damping coefficienr (percentage of critical damping). For normal working stress conditions, 0.01 < P < 0.02 for towers.
a
given magnitude (Table 4-l l) exposure factor evaluated at two-thirds the mean height of the structure
S:
=
2.35(C,- )0 5 (Zl301rt"
structure size factor (Figure 4-23) average horizontal dimension of the building
or structure in a direction normal to the wind.
ft
(see Example 4-2)
The Engineering Mechanics of Pressure Vessels
r97
l'--4-l ^,--l
Iv MEAN VELOCITY: V
|-J
OUnOt'O".?
EFFECTIVE GUST DIAMETER
GUST DURATION 3
5 )165
15
tt
Figure 4-22. Diagram of relationship between gust duration and gust diameter.
For a tower with many obstructions, such as piping, ladders, platforms, and clips that are comparable in size to the vessel, the gust response factor can be determined by:
"
r.:
s
0.9
:r[o3ora
^ 0
20
30 r0 5060
80
t00
200
300 a005006008001000
hlftl
Figure 4-23. Structure size factor, s [l
l].
2000
= "--\/t.zsp n r<
6
r.l.:zr,),s \' ' * 1+ o.oolc/
,I
i
I
i
(4-83)
The gust response factors given in Equations 4-82 and 4-83 are for flexible structures, such as towers, where the height exceeds the minimum horizontal dimension at least by five to one or the structure exhibits a natural frequency less than one. The fact that the tower may have a natural frequency less than one is significant. Simiu and Scanlan [9] point out that for natural frequencies greater than one, the response spectra are dependent on the structure's height. However, for natural frequencies less than one, the spectra distribution has little influence on structural response, and the magnitude ofturbulent fluctuation components, such as wind gusts, at or near the natural frequency of the tower could significantly affect the structural response. For this reason Equation 4-82 should be used for towers with particularly low natural frequencies. Figure 4-24 shows a plot of wind gust velocity versus the structural response of a structure. The cyclic loading
I
198
Mechanical Design of Process Systems
platform
Figure 4-24. Quasi-static structural response spectra versus wind velocity [ 14].
DE
= effective diameter of area resisting wind
induced in the tower can result in fatisue failure of various vessel components. Equation 4-81 contains the last parameter that must be defined, Ar, the total cross-sectional area of the tower and attachments that are perpendicular to the wind. This area is computed by first determining the equivalent diameter of the area facing the wind. This can be expressed AS
De
:
+ 2(vessel insulation thickness) + (pipe OD) + 2(pipe insulation thickness) + (platform projection)
(vessel OD)
*
(ladder
projection)
(4-84)
Equation 4-84 does not consider extraneous equipment attached to a tower, such as reboilers. The engineer must
Figure 4-25A. Effective diameter can vary with height.
add the OD of the reboiler, plus twice the insulation thickness, plus any other equipment diameters to Equation 4-84. Doing this and multiplying by a length over which D" is effective determines As. Figure 4-25 shows the effective or equivalent diameter.
FJ,
WIND-INDUCED MOMENTS After the wind pressure distribution is obtained from
Ma+F"(2,-Z;+F,"rb
+ (F" + M. + (F, + Md + (F, + Mb
-
FbXZb Z") Fb + FcXZc Fb
+ F,r" Zd) +
-
+ F. + Fi(Zd
Equation 4-77 , the distribution of section force vectors is obtained from Equation 4-81. The force vectors, shown in Figure 4-26, act through the centroids of the pressure
or in a general equation,
distribution sections. Referring to Figure 4-26, we see that the wind moment distribution is obtained from the wind force vectors through the following relationships:
M" = M"-1 * (2" -z 4n_t'Ll,t,, -r\-p 1
i:
l
-
Fdtd
Z") + F"t"
-t c;
n
(4-85
r
The Engineering Mechanics of Pressure Vessels
199
insulation OD
d = plattorm angle Figure 4-258. Wind area and force calculations for conical sections.
/i = section length, ft Qi : wind shear at each section juncture Mi : moment induced by wind profile, in.-lb
WIND.INDUCED DEFLECTIONS OF TOWERS Thll process towers and stack are treated like cantilever beams in computing deflections induced by wind. Like a cantilever beam, when the tower deflects it translates and rotates at the same time. These translations and rotations are most expediently computed by the method of superposition. The three cases to consider in the superposition are a cantilever beam with a uniform load, an end load, and an end couple. These three cases and their accompanying equations are shown in Thble 4-12. The first case of the uniform load reDresents the wind load on the side of the tower, the second case o[ the edge load represents the wind shear at the various shell sections, and the third case of the end couple represents the case of couples produced at the shell section junctures by the translation and rotation of the upper sections. This combined loading is shown in Figure 4-26. Adding the three cases we obtain the following: 6,'
=
llY{*!{,*M') Er\8 3 2l
where
61
!1
W1
= : : :
lateral translational deflection of section length of section i concentrated wind load (wi/), lb
wind profile, lb/ft
(4-86)
For rotation we have /n- I \
l\-r.l
^,
_\?,'l
Er, \6 *q,r,_,,) 2 l
Total deflection
"=F
o
"{w,r,
,s
:
+F
(4-87)
y
,t.
(4-88)
WIND-INDUCED VIBRATIONS ON TALL TOWERS Chapter 2 discussed the phenomenon of vortex shedding inducing vibrations in piping systems. This chapter focuses on the nature and techniques of analyzing vortex
i,
in.
shedding. Over the years many researchers have made wind tun-
nel tests, proposed various analytical procedures, and conducted field tests of various structures subjected to wind loads. Wind-induced vibration was first noticed on
Mechanical Design of Process Svstems
Table 4-12 Cantilever Beam Formulas Formula 1
Uniform
w--.'
Load
dITTtrM
End Load
1i
T-
^
6EI
:
Q/' 2El
=
T-)
:vd EI
=
w/,
l
2
,-\ 4
End
Couple
^
wl2 6EI
:
w!2
, , Mo{ -2EI-Er'
wf' 8EI
Qi, 3EI
lul{ 2ET
iw{ -, wr +M)
EI\6
'
A:0t,
I\- olr A=
tall stacks by Baker at the turn ofthe century. Since then, many advances have been made in the field of aerodynamics allowing designers to adequately design tall structures. This chapter discusses tall process towers and Chapter 5 discusses tall stacks. The differences between the two will become more clear in the following discussion. Staley and Graven u5l summarized the state ofthe art of wind vibrations. Their studies indicate that even though vortex excitation of higher modes has been obtained in wind tunnel tests, existing free-standing stacks have always been observed to vibrate during vortex excitation at a frequency and with a mode shape associated with the fundamental mode. Furthermore. the shaDe of the dynamic lorce amplitude or existence of nearly constant frequency over the height of the stack (or "lockin") implies that dynamic response will almost entirely be induced by the first mode. Staley and Graven concluded that all higher modes should be neglected in the dynamic analysis and that the frequency and associated critical wind velocity ofthe fundamental mode should be considered. For this reason the Rayleigh method is the industrially accepted method because it is used to determine an approximate value for the lowest natural frequency of a conservative system based on an assumed confisuration of the first mode.
\2"1 "tw.t I'+ w/ I'+M| Er, l\6 2
\
|
What is clear in wind tunnel tests and field observations is that at low Reynolds numbers the tower is dynamically stable, vulnerable only to forced vibrations and at higher Reynolds numbers a possibility of self-excited vibration will be present. From many field observations it can be concluded that the first peak vibration amplitudes occur at the critical wind velocity Vr, which corresponds to a Strouhal number of 0.2 with the forced vibration as the basic source of excitation. Thus. it is sisnificant that the peak amplitudes of vibration determined by forced vibration theory are in very good agreemenr with field observations. This will be seen later in this chapter in Example 4-4. Even though the Rayleigh method is the industrialll accepted method for the present, there are other methods used to describe the vibration phenomena of tall process towers and stacks. One such method was devised by N. O. Myklestad, a great pioneer in the theory of vibrations. The Myklestad method used in cantilever beams is essentially a Holzer procedure applied to the beam problem. Its strong point is utilizing field and point transfer matrices to obtain relations that govern the flexural motion and vibrations of lumped-mass massless elastic beam systems. This method is used in such applications as aircraft wings where the structural component is sub-
The Engineering Mechanics of Pressure
jected to high Reynolds numbers. Since we have already delineated the difference between cylinders subjected to high and low Reynolds numbers and the fact that modes higher than the fundamental mode can be neglected, the Myklestad method has lost favor to the Rayleigh method. We are primarily interested in forced vibration peak am-
plitudes of relatively low natural frequencies. Although the Myklestad analysis is excellent for relatively clean aerodynamic surfaces such as wings and missiles, its practical use in process towers with attached ladders, platforms, and piping is questionable. Even for stacks. low Reynolds numbers allow for the fundamental mode to dictate. Before the Rayleigh method is applied to our analysis, let us summarize some basic precepts. Equation 4-80 calculated the pressure force exerted on a cylinder by a static wind. When dynamic effects settle in maximum actual amplitudes, these amplitudes often exceed those under static conditions. The net result is to multiply Equation 4-80 bv a masnification factor. To understand the
Vessels
2O1
magnification factor we must consider some basic principles. Consider Figne 4-27 in which a system with a single degree of freedom is subjected to viscous damping and an externally imposed harmonic force. The spring is denoted by stiffness k, the friction coefficient by c, mass by m, displacement by x, impressed force as F sin cJt so, we have
-X+.x +ki:
(4-89)
Fsin
From the theory of differential equations we know that the solution of Equation 4-89 is the superposition of the general or complementary solution of the homogeneous Equation 4-89 and the particular solution of the same relation. Writing this in equation form we have
X=X"*Xp where X" is the complementary function and Xo is the particular solution. This classical differential equation is
T" *, = ]+ r|",1
lr-eol
I* i -7- -, I
,-il]ur= ,=
--l[:
r6" _L-
-r
r-i-
14.=s\"
4_.=o"lr,-.+r,.1
6!
-r
I
I_-r
l)'.
olFrt ==
[.
,r
6.
4_; qlL,.+r,-,+r, .l
.L A
4-.=qlq.,+ r'.+t'-..r.-"1
IA L*
Figure 4-26. Schematic diagram of wind loadings and deflections of a tower.
202
Mechanical Design of Process Systems we have
x., fStru"t = forcing function
f
damper-represents tower's stiffness
Figure 4-27. The vibration of a tower is modeled as a sinsle degree of freedom. which i5 exposed to an exrernally impos=ed harmonic force and subjected to viscous damping.
(.4-9t)
"T -,,f-1_12r*
The maximum actual amplitude X of forced vibration is obtained by multiplying the static deflection X,, b1
fraction X/X,,. The fraction or ratio X/X* is called the dynamic magnification factor, D. These formulations indicate that the nondimensional amplitude X/X,, and the phase angle, 0. are functions of the frequency ratio r and the damping factor f and are plotted in Figure 4-28. These curves indicate that the damping factor has a large influence on the amplitude and phase angle in the frequency region near resonance. From Equation 4-91 we see that at resonance the dynamic magnification factor, D, is inversell proportional to the damping ratio, or
n-'
I
solved in numerous sources and will not be delved into here. See Vierck [6] for a complete discussion of the solution. The final solution takes the form of the followlng:
X(t)
:
e t''(A
cos (,Dt
+
B sin
ropt)
X., sin (c,rt - d)
{t -l t+ (r'tt
t:
(4-90)
c/c, 2(mk)ri2 is the critical damping factor that is the criteria for critical damping such that I : nonvibrating motion : overdamping I : harmonic vibration : underdamping a few percent of c. for a tall, slender structure such as a tower static deflection of the spring acted upon by the fbrce F/K c,,,/o : frequency ratio of forced vibration frequency to free vibration frequency
U
E E
P
K M Letting
and tan 0
X:
.(T
I -r
-l t+ (2rt
Freouencv
r.tio.
=
(;/o
Figure 4-28. The dynamic magnification factor versus the frequency ratio for various amounts of damping. (From Slructural Dynamics by M. Paz. @ 1980 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.)
The Engineering Mechanics of Pressure
The damping ratio, €, is not known and extremely difiicult to measure at best. A practical method for experimentally determining the damping coefficient of a system is to initiate free vibration, and measure through decreasing amplitudes of oscillatory motion, as shown in Figtre 4-29. This decrease or decay is termed the logarithmic decrement, 6, and is defined as the natural loga-
rithm of the ratio of any two successive peak amplitudes, X1 and X2 in free vibration. Expressing this in equation tbrm we have
^x,
203
The force coefficient can be readily obtained from Figure 4-29. Equation 4-92 yields the maximum transverse force per unit area of the projected surface of a cylinder at resonance. Equation 4-93 may be rewritten with the velocity in miles oer hour as
F=
0.00086(CrD)(H)V1'?, for air at 50'F
(4-94a)
0.01I l3pCrDVr'?(dH)
(4-94b)
and
F= x2
The evaluation of damping from the logarithmic decrement is given analytically by
X(t) :
Vessels
Ce-fdr cos(@Dt
-
cr)
It can be shown [17] that the dynamic magnification factor, D, and the logarithmic decrement, A, are related using the previous expression as ^T
(4-92)
These equations apply when the top third of the tower
is the controlling length. Often, the top fourth of the stack may be best to use as the controlling length. An example ofthis would be a section on top ofthe tower that is one fourth the total tower height and is significantly greater in diameter than the section below (see Example 4-4). Thus, for the top foufih of the tower Equation 4-93 becomes
F=
0.00065(CrDXd)(H)Vr'?, for air at
50'F
(4-94c)
and
Most research data available for practical use are presented in terms of the logarithmic decrement, 6. Table 413 provides values of 6 versus D for various structures. These values are acceptable for use process towers and stacks.
in actual design of
Applying the dynamic magnification factor to Equation 4-80 we have CeDpV2fz
(4-93)
0.07728pCeDVr'?(dH)
where d =
H= Vr : Vr :
T: p:
(4-94d)
outside diameter of either upper r/: or r/+ of tower, ft total height of tower, ft first critical wind velocitY, 3.40d/T, mph first period of vibration, Hz density of air at any specified temPerature,
lb/ft
F
z = 9
h 6
Figure 4-29. The Reynolds number versus the drag coefficient for a circular cylinder tet.
Mechanical Design of Process Systems
Table 4-13 Conservative Values for Logarithmic Decrement and Dynamic Magnilication Factor for Tall Process Towers Logarithmic Decrement
Dynamic Magnitication
6
D
Factor
Low damping: rocky-stiff
soil, low-stressed pile
0.052
support, or structural frame Average damping: moderately stiff soil, normal spread
0.080
High damping: soft soil, fbundation on highly
o.t26
stressed friction piles
A:
B
:
Structural
25
Coefficients l1
Steel frame
Reinforced or prestressed concrete
Low stress levels (a) 0.005 ( c ( 0.010 (b) 0.005 < c ( 0.010
Working stress
(a)0.01
C. =
c":2(Mk)05=28I).' ' \386/ C:
Near yield
(a)0.M(c(0.06
(b)0.0s
critical damping factor
"
D.M:
k: W=
damping factor
=
lbi-sec ln.
tower stiffness, Ib/in.
^ tLl \c./ : r/6 tower mass
c tower stiffness, lb/in. total tower weight, lbr
For tall, slender towers of constant diameter, the first period of vibration is given by the expression
the static equilibrium point. For the potential energy o; the system, the reverse is true. Thus,
T:
(K.E.)-,,
(l/0.5l)(WHa/gEI)o
where
g= H:
5
(4-95)
32.2 ftlsec total height of tower, ft
The Rayleigh method applies only ro undamped systems, but is found to be sufficientlv accurate for comDuting the fundamental frequency of process rowers. e;en though towers have varying shell thicknesses down the Iength that result in unevenly distributed mass and stiffness. The Rayleigh method is basically the conservation of energy, i.e., the total kinetic energy of the system is zero at the maximum disDlacement but is a maximum at
= (PE.).,- =
total energy of the system
will readily yield the natural frequency of the system. To estimate the period of vibration using the Rayleigh method the tower is considered as a series of lumpec masses. These lumped masses are determined by consid ering the weights of The resulting equation
1. Shell and
heads
2. Trays and internals 3. Manways and nozzles 4. Insulation and fire proofing
The Engineering Mechanics of Pressure
These are summed for each section and the overall :ower is considered as lumped masses at the centroid of :ach section along its entire length. The assumption is nade that the stiffness is constant along the entire length Jf the tower; an assumption that greatly simplifies the ;omputations for the various deflections of the section :entroids. The more sections, the greater the overall ac.-uracy achieved. Such a beam with lumped masses is shown in Figure 4-30. For such a simple, one-mass, vibrating system, Timoshenko et al. [19] have shown that rhe angular natural undamped frequency (rad/sec) for such a system is
-
lewv\o'
(4-96)
\wv'/
Integrating Equation 4-96 numerically across the section centroids of the tower results in
- :
+ Wzyb + ... + W,y.)/(W1y] + w2y3 + ... + w"yillo 5
(4-e7)
,"
(4-98)
[BOMry"
or T_
[(i -")/(,8 *,,)]"
The section weights, Wi, are computed by using cumulative weights down the tower. Summing moments about the base in Figure 4-30 we obtain the moment distribu-
tion in the tower as follows:
Mr=0 /-
+ M,-\21 = W, lKr
-\ K2l
M,
: wr () * *, * nJ + w,(?. . *,(?)
\2
, Kil )l
* *,lvr-*,\ -\ 2
I
205
") (4-9e)
The moments obtained are used to determine the deflections induced by vortex shedding. The method of deflection computation is based on the area-moment (conjugate beam) method applied to a cantilever beam. In this method the slope of the elastic bending curve of the actual beam is equal to the shear at the same point on the conjugate beam, which is an idealized beam corresponding to the actual member. The deflection y of the actual beam (or tower) at any point relative to its original position is equal to the bending moment at the corresponding point on the conjugate beam that has the same M/EI area of the actual beam. Figure 4-31 shows weights of the vessel sections distributed about the section centroids along with beam lengths used in the analysis. The conjugate beam method of computing deflection is demonstrated in Table 4-14. For an indepth analysis of the method the reader is referred to Higdon et al. [20]. The examples presented at the end of this chapter will clarify
this approach.
OVALING Ovaling is a resonance phenomenon more common in stacks rather than process towers. However, towers exhibit this phenomenon mostly during construction, before insulation and appurtenances are added to the vessel. To avoid ovaling, the designer should consider the following guidelines. The cylinder is considered as a ring that has a natural freouencv
u. = w, lI1 +n.
Vessels
''-
7.58r.
of vE
6oDt
Figure 4-30. A tower modeled as a sectionless beam with distributed lumped masses.
(4-100)
Mechanical Design of Process Systems
Table 4-14A Vibration Deflections Based on the Coniugate Beam Method
,f
+*t*t
+ t'+ t-, I r_,
L, l- 15
+
{
+
+
I
I
+
l)
' -1. |
w.w"vqq
Xs, = o,
r,
Mr
P
t4r
M,
E'It
ZE)l)
S,
+A, = A,
Pt*l.z:
ia, + e,\ \?/
Itt
Lr=Pr M2
=
W1L1
RI+R'
, -'
rr
2
19 EzI:
/v.
M,\
\E,I,
Err,/
52*41 :,A2
t?,
2
XL2: M1
:
W1(L1
*L)
-
+ w2L2
-2
R,
+R.
I:
M: E:I:
irur,\E.I-
xL2: 53+A.4
= Aj
M,:Mi r+Li
r
i
\-w Ll l:
l
Lo=l+R" 2
'.
14i14) xL3 =
Sa A,=Aa
/eo +
lrl
2
xl-o =
shells,
FT
r '2_ Ri +Ri+r
\E,
+
rli+
|
M, I E,l,/
s'
+D
/Ai +
Irl
2
I. v. /u.-' M"\ s" E"r. \E"I" E"I"/ xLn: M"+L"
xFw, L,l
Co_mputation
A"
lil
S"
of lateral y deflections. For formulas of y
see Table 4-16C. bending moment diagram oi conjusate beam slope of real beam elasric curve -- shear of conjugate beam moment diagram of real beam : load diagram of conjugate beam y1 fu)(12), in.
deflection of real beam
:
:
pt
Pa
Ai*ri
xL; :
S:=Ar
2
:
Ptr ps:
Pr
el
xl-a =
xl-i = S
M"+r
pt
So
/ M,*,
For cylindrical
Ptl p+:
P2
S1
Mr lM.,M.\ EoL, \E5I5 E4I4/
-v
r:
* ir:
\21
2
wr(Lr + L2 + L1) +W2 (L2 + L3) + W:L,
:
Pz
52
M, \ E,I,/
XL3:
a.\
/a, +
=
P1
p
Pi
*
irr+r
: I
Table 4-148 Beam Method-Section Break Method Deflections Based on the Coniugate Vibralion
lttrttl w" Mi Mr
w'r li
:0
Ir
w.{
Y "Y
V
V
Ds, = o,
M/Eili Mr ErIt
V
Mr -
^
sr
p = M;d2xlE;11
Pi
= Mrdx/Eili
+Ar:Ar
/e' +
l?l
2El1
xLq:P1
/-
Mj-
W,lr(r
+ ^\ r(?l
\21
Ir = W,Lj
M,
/vt, M2\
EtI,
\t'313
s2
+ A,
=
A/
l'212l
{rf
2
:
\2
r!\-w,fIL$,\ 2l '\ 2 l
Er
Wr(Lr + Lr) + WrL2
\2
W1(L1
t"
I
+
L2
+ Lr) +
'
2r..
xL2 =
52
Mrl
/Mr\E.I.
53+A*:4,
Err',/
lA, +
lrl
2
Ri u,' = w l/! +R, +Ri*w,(R,+ 2l '\ 2 :
Ir
MJ EoL
M,:w(q+*,**.*&\ 2l \2
It, r, \ lrvrl f, wlrl \E4I4 E4I4/
xL4:
15 l&
E:I:
ra+45:Ad
Po*/r: = lr
\)
I
xL4 =
P4
54
/tut, , tuto \ \E+ E.L/
6
s5
+
Dsi
f,L,+a"\ lrl xL5:
xL5 =
P3
/eo + ,+,\
2
+w,l&+n.+!l '\2 2l
Ps
*ro = rs
P5
55
+ &l -\21
+ w.lR.
lvl" = lvl^ r+L",
W,-l r,sr --,
I,
M"
/tut"-,
Ik
\EJ"
tnl" -, E t/\
_jI 2
L" =
P^
2
xL":S" M.+
r
= M"+L"
y = (pi)(12) ft
ttz
Pr*t.,:/:
Aql
xL3 =
2
W2L2
't pt :
xL2 = P'
_M,
M, = w,lR' , R,
Pt
S"=A" @ : ebrupt section break k : n + (number of abrupt Infigureabove,k=n*1
section breaks)
Mechanical Design of Process Systems
Table 4-14C Centroids ol Shell Volumes
-
b(4a
-
3t)
':'(T i
Conical Section
3H(D": v
6[{D"r
- Di) + 8Hr@., - Di") tano -Dit - 2H{D., - D.,) randj
k-t--l
The vortex shedding frequency is given by
f,"D
0.2v
where
v
:
process columns, because these vessels usually hare (4-101)
many external, attached appurtenances. What is more commonly done with towers is to stiffen up shell sectiont to offset ovaling resonance. See Chapter 5 for more information on ovaling.
45 mph or 66 fps
If for any section of the tower fi < 2f,, ovaling vibration is imminent. The resonance wind velocity that would
CRITERIA FOR VIBRATION ANALVSIS
theoretically induce ovaling is 60 f.D
where s
=
Strouhal number
(4-1o2)
:
0.2 for this application
To counter ovaling vibration, ovaling rings or helical strakes are added. These normallv are not oractical for
While there is no absolute parameter available for determining whether a vibration analysis is required, there are certain guidelines for designing towers.
1. If the critical wind velocity, V1, exceeds 60 mpf. then a vibration analysis is not required. Very feu cases of severe vortex excitation have been ot served for wind velocities in this ranee.
The Engineering Mechanics of Pressure
Vessels
209
2. If the first critical wind 3.
z- 4-_}
q-
+-
velocity, V|, is greater than the wind design speed, a vibration analysis is not required. The limiting minimum height-to-diameter ratios H/ d are as follows: H/d H/d
H/d
4.
)
columns
) )
(4- 103)
I
The Zorilla criterion for vibration analysis is as fol-
LD, 20
+
\
vibration analysis must
ZW
be performed
" -' analysis shouldr, vibration <,^, (- ". o_.-'il
25 < 5.
(4-lo4)
vibration analysis need
--LDI
not be performed
If
the total force on the tower induced by the first critical wind velocity V1 does not exceed l/rs of the operating (corroded) weight W or
1"
:oViHd ')"
w
i :
.1+_
13 unlined 15 lined 15 process
lows:
+ q
+-
stacks stacks
> >
1
o15
(4- 105)
Further guidelines and procedures for stacks are disin Chapter 5.
cussed
q-
SEISMIC DESIGN OF TALL TOWERS
++-
There are several ways to analyze earthquake forces imposed on a structure. The procedures outlined in the Uniform Building Code [10] are the simplest and most straightforward, but do not account for all of the signifi-
'--+---1
r+_ Figure 4-31. The vibration ensemble in which each section weisht is located at the section centroid.
cant dynamic properties of structures. Large, complex structures, such as so-story buildings, nuclear power plants, large dams, and long suspension bridges, require
a more thorough dynamic analysis. Fortunately, the UBC method is accurate enough for most tall, process tower/stack design problems and is presented here. In seismic analysis the design spectrum is not a specification of a particular earthquake ground motion; it is a specification of the strengths of structures. For this reason the tower must be ductile enough to absorb energy without ultimate yield. This implies that for the structure to absorb energy that exceeds maximum design conditions the overall structure deformation will be ductile
210
Mechanical Design of Process Systems
I : g=
rather than brittle. The result is that while more risorous analyses are very helpful in determining design ciiteria.
practical design procedures are simplifications of the complex dynamic phenomenon used as'.quasi" static criteria applied with elastic srress limits. The Uniform Building Code 1982 [10] requires thar all freestanding structures in seismic zones to be desisned and constructed to with5tand a total lateral force t-base shear) given by
V:
ZIKCSW
: I : K : c : s = =
where Z
(4- 106)
seismic zone factor (see Figure 4-32) occupancy importance factor : I for all process towers and stacks structure type coefficient structure period response factor slte structure interaction factor total operating weight of tower above ground
The structure type coefficient,
K= K=
K, is as follows:
t,h.n
>
1.5
tskin
^l : L
(4_107)
15"rF
-sec T = structure period of vibration, sec, with c","" : 0.12 where
For short, stiff structures, such as horizontal vessel supports, in lieu of making a period calculation, the response factor C may be taken as equal to C."". For most industrially accepted design methods, the effects of the soil-structure interaction are considered. This is done in the Uniform Building Code by using the ratio of the fundamental elastic period of vibration of the tower, T, to the characteristic site period, T,. Formulations used to determine the fundamental natural period ofvibration for seismic response vary as to the type of structural cross-section considered. The generally accepted equation for towers of uniform cross-sec-
tion is 'l--
:
1=
17.65e v
and for
E
:
29
where D,,,
:
where LI
E_
.
fundamental period, sec total heighr, ft weight per unit of height, lb/ft shell thickness, in. modulus of elasticity, psi
!
\D",i
(4- l09
r
106 psi,
For a tower with uniform cross section and tapered (conical) skirt the following relationship can be used in computing the fundamental period:
= 2" (o qod)" 6=
(4-111
)
the calculated deflection at top of tower induced by 1007" of irs weight applied as a laleral load
With towers of varying cross sections and attaching equipment, a method used to determine the fundamental frequency was developed by Warren W. Mitchell in an unpublished work [21]. The solution is based on the Ravleigh method ofequating porenlial and kinetic energies in a vibrating system. The resulting formulation is readill useful in computing fundamental periods of cylindrical. tapered-cylindrical, and step-tapered-cylindrical structures common to the petrochemical industry (CpI). The formulation is as follows:
,: ln)' \,F-4DfEo, + \100/
where
a.y
T H w
lrql" \EIei
x
l[)'^1tz*o'' r
mean diameter of tower, ft
w
t.re
/ \, t::-t0-")
(4-110)
where
The structure period response factor, C, is determined by
ft
32.2 ftlsec2
When Equation 4-108 is applied to sreel wirh a value of E 30 x 106 psi we have
r
2.0 for vertical vessels on skirt supports 2.5 for vertical vessels on skirts when
moment of inertia,
(4- 108)
E
: =
(4 Il2r
period, sec overall height of tower, ft distributed weight (lb/f0 of each section concentrated loads attached to the tower at any level, that add mass but do not contribute to the stiffness of the tower modulus of elasticity (106 psi) for each section
coefficients for a given elevation depending on the ratio of the height of the elevation above grade to the overall height of the tower (h,/H)
The Engineering Mechanics of Pressure
Vessels
3 E
xllo ollR
;llo ll0 o||o ;''ll,ro
Ell' !l]f; tl
"ll: oLJ
nt
.€
ol ol Ll
65 !o 6
6l
-R5C
NI
ol
6l
R
-
211
212
Mechanical Design of Process Systems
:
Ao, A.y
differentials in the values of a and .y, from the top to the bottom of each section of uniform weight, diameter, and thickness. 6 is determined from each concenttated mass. Values of and "r are shown in Table 4-15.
a. 6.
In applying Equation 4-ll2 the following factors
VERTICAL DISTRIBUTION OF SHEAR FORCES For towers having an overall height-to-base-width ra-
tio greater than 3.0, a portion of the total earthquake
force. V. shall be applied ro rhe top of the tower aciording to the following relationships:
should be considered: For,
n Ifa tower's lower section is several times wider in diameter and shorter than the upper sections, then the tower's period can be more accurately determined by computing the upper section's period, assuming that the tower is fixed as to translational and rotational displacement. If a tower's shell diameter or thickness is
significantly larger than that of the supporring skirt, the period calculated by Equation 4-112 may be overly conservative for earthquake design and a more accurate method may be desirable. D For conical tower sections the Mitchell eouation can'coefficients not be used because of lack of data for the a, B, and 7. The Rayleigh equation (Equation 4-97) is more comprehensive and ubiquitous in application. Once the fundamental period of vibration is determined, the numerical coefficient for the site structure interaction (seismic site-structure resonance coefficient),
S, can be determined. As previously stated, the soilstructure interaction is considered in most industrially accepted methods. The value of S is determined by the following formulas: For T/T,
S
=
1.0
For T/T.
S
:
1.2
(
1.0,
T
+:T,> +
0.5
/ \. ITI'
l:l
\T,i
(4-l l3a)
h
;<3.0,F,:0 h
3.0<: < 6.12. F. = l) h
6.12, F,
;>
where F,
V=
F^
0.3
E)' \r,/
(4-l l3b)
s > 1.0 (c) (s) < 0.14 The characteristic site period, T,, falls into the following
sec
When T. is not properly established, S is taken as 1.5, except when T exceeds 2.5 seconds, S can be determined by assuming a value of 2.5 seconds for Ts.
total force applied at top of structure overall height of tower, ft diameter of tower, ft total base shear from Equation 4-106
14-1
l5
r
\-w
r, LJ "I\
where F* : W* = h, =
:
lateral force applied to a mass at level x, lb weight of mass at level x, lb height of level x above the base (normally measured from bottom of the base plate of the tower), ft the sum of the products of w" and h, for all the masses within the structure, ftlb
The seismic moments are computed from the following expression:
M:
V, L, _,
where
Lr,-, :
*
(4-116)
F*,C;
length of section below shear force,
ft
Ci - L,lZ for a cylinder /.\f 2 ^zrrr' + rr'l ^21
tlme:
0.5 < T. < 2.5
(4-ll4)
0.lsv
tt/ 1, : (V F,) """
Ewh
I T,
TV
The remainder of the total seismic force is distributed and applied to the mass distribution in the structure according to the following equation:
1.0,
0.6
:
h: D=
:
0.07
c - lil lrl-+ \+/Lri+rlr,+r;I
foracone tsee Figure 4-33r
For an illustration of seismic analysis, see Example 4-3.
The Engineering Mechanics of Pressure Vessels
213
Table 4-15 Coefficients for Determining Period of Vibration of Free-Standing Cylindrical Shells Having Varying Cross Sections and Mass Distribution' nx
h"
H
H
I .00 0.99
2.103
8.347
2.02r
8.12l
0.98 0.97 0.96
1.941 1.863 1.787
7
0.95
1
0.94 0.93 0.92
1.642 1.513 1.506
0.91
1.440
0.90 0.89 0.88 0.87 0.86 0.85 0.84 0.83 0.82
1.377 1.316 1.256 1 .199
0.988 0.939
4.930 4.758
0.81
0.892
0.80
0.847 0.804 0.762 0.722 0.683 0.646 0.610 0.576 0.543 0.512
0.'79
0.78 0.'77
0.76 0.75 0.74 o.73 0.72 0.7
|
0.70 0.69 0.68 0.6'7
0.66 0.65 0.64 0.63 0,62 0.61
0,60 0.59 0.58 0.56 0.55 0.54 0.53 0.52 0.51
'vi,cher
.'7
t4
1.143 1.090 1.038
7.898 .678 '7 .461 7 .248
l .000000 1.000000 1.000000 l .000000 1.000000
0.50 0.49 0.48
0.0998 0.0909 0.0826
0.9863 0.9210 0.8584 0.7987
0.95573 0.95143 0.94683 0.94r 89
0.46 0.45 0.44 0.43 0.42
0.0'749
o.74r8
0.93661
0.0678 0.0612
0.9309'7
0.41
0.0442
0.6876 0.6361 0.5872 0.5409 0.4971
0.40 0.39
0.0395
0.4'7
6.830 6.626 6.425 6.227
0.999999 0.999998 0.999997 0.999994 o.999989 0.999982
6.O32
0.9999't I
5.840 5.652 5.467 5.285
0.999956 o.999934 0.999905 0.999867 0.999817 0.999154 o.999614
0.3 8
4.589 4.424 4.261
0.9995'76
0.31
0.999455 o.999309
4.1o2 3.946
0.999t33
0.30 0.29 0.28 0.27 0.26 o.25 0.24 o.23 0.22
'7
.O3'7
5. 106
3.794 3.645 3.499 3.356 3.217
0.998923 0.998676 0.998385
o.37 0.36 0.35 o.34 0.33 0.32
3.081
0.998047 0.997656 0.997205 0.996689
0.481
2.949
0.996101
0.453 o.425 0.399 0.374 o.3497 0.3269 0.3052
2.820 2.694
o.995434
|
0.993834 0.992885
0.17
0.99183 0.99065
0. 15 0. 14 0. 13
o.2846 o.2650 o.2464 o.2288
2.OO89
o.2122
1.61'7'7
0. 1965 0. l8l6
1.52'79
2.57
2.3365
2.2240
2.1r48 1.9062 1.8068 1.7107
0.99468 r
0.98934 0.98789 0.98630 0.98455 o.98262 0.980s2 0.97823
1.4413 1 .3579
0.97 573
0.1676 1.1545
I .217 5
0.97W7
0.1421 0.1305 0.1196
1.2002 1.1259
0.96688 0.96344
1.0547
0.959'73
rormura:
r- ,, E wA. . ,ruiE t {#l ti--S;;-
0.97301
pB
o.21
0.20
0. l9 0. 18
0. 1094
0.0551
0.0494
0.0351 0.0311
0.455'7 0.416'7 0.3801
0.888& 0.88001
0.0185
0.2552
0.0161
0.2291 0.2050 0.1826 0.16200 0.14308 o.12516 0.10997 0.09564
0.82901
o.0826'7 0.07101
0.7 r 55 0.6981
0.06056 0.05126 0.04303 0.03579 0.02948 0.02400
0.6800 0.6610 0.@13 o.6207
0.01931 0.01531
0.5536 0.5295 0.5044 0.4783
0.0140 0.0120 0.010293 0.008769 0.00-t426 0.006249 0.005222 0.oo4332 0.003564 0.002907 0.002349 0.001878 0.001485
0.11
0.000081
0.00361
0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02
0.000051
o.00249 0.00165 0.00104 0.00062 0.00034 0.00016 0.00007 0.00002 0.00000 0.00000 0.
0.01 0.
0.90448 0.89679
o.0242 0.0212
0.12
l6
o.911'73
0.3456 0.3134 0.2833
o.o2'7 5
0.001159 0.000893 0.000677 0.000504 0.000368 0.000263 0.000183 0.000124
0.
o.92495 0.91854
0.000030 0.000017 0.000009
0.0000M 0.000002 0.000001
0.000000 0.000000 0.000000 0.
0.01196 0.00917 0.00689 0.00506
0.87088 0.86123 0.85105 0.84032 0.81710 0.804s9
0.79t4 0.7716 0.7632 0.7480 o.'7321
0.5992 o.57 69
o.4512 0.4231 0.3940 0.3639 0.3327 0.3003 0.2669 0.2323 0. 1966
o.159'1
0.1216 0.0823 0.0418 0.
214
Mechanical Design of Process Systems r"o=
OO SMALL END
r-= OD LARGE END
TRUNCATED CONE
that the cone-to-cylinder stresses computed by the equivalent circle method are very close in magnitude to those computed by more exact methods. Because of its close approximate answers and simplicity, the equivalent circle method is normally the method used for treating conical sections in towers. The method will only be outlined here, as others l22l have already derived it. Figure 4-33 shows how the sections of a truncated cone and a conical head are approximated by an equivalent circle, which is used to compute the section modulus and moment of inertia. These formulations are used in tower design and are demonstrated in the examples that
follow. Conical shells used in tower sections have a half anex anglecv ( 30degrees. Whenh. ( 0.10H, rhecon..an be approximated by considering two cylinders shown with dotted lines (Figure 4-34). In pracrice, stiffening rings must be used when required by the vessel code.
,."=[*&l
CONICAL HEAD
Figure 4-33. The equivalent radius for cones.
L t\/2
T'
TOWER SHELL DISCONTINUITIES AND CONICAL SECTIONS Most vessel codes do not discuss the analytical computation of tower shell discontinuity stresses, which are prevented by welding stiffening rings to the outside shell of conical sections. In addition, most codes do not consider discontinuity stresses on cylindrical shell sections. The ASME Section VIII Division I uses a safety factor of four to one to compensate for not computing these stresses.
Conical sections can be tieated quite simply by utilizing the equivalent circle technique. Bednar [22] shows
Figure 4-34. When h" ( 0.1 H, the cone can be approximated by considering the two cylinders shown with dotted lines.
The Engineering Mechanics of Pressure Vessels
EXAMPLE 4-l: WEAR PLATE REOUIREMENT ANALYSIS
o:
Vessel
material
: :
Q : 7,828.981 cA:0
5A-516-70 5.4.-36
Temp:300'F Design pressure
0
=
lb
\12
or = oo
:
:
8(1.750)
A
R-
l5oo t.750
=
-
or + op :
=k
0.857
o.u5
7,828.981
+
4(0.94r)[0.375
rad
+ L < 8R
14.00
-
1.s6[(21)(0.94)]0
-284.547
-
928.358
|,212.905 psi <
<
1.25 dr,rr
:
21,875
ring compressive stress in shell over saddle
_ [t# (, ,,1] [H#]
7,828.981
(0.941)[0.375
+
1.56[(2 1X0.941)]0rl
.I
: iilllt'.t :
5l
l2(0.05x7,828.98 1)(l.7s0) (10x0.941)r
80.0'
lr -
1,67i.50
os
1,728.00psi
:
865.678 psi
<
<
I I.990
19,000
psi
- cos(u4) +
=
sin
I
(l t4) cos (l14,
0.5 o,
Since the ring compressive stress and the circumferen-
tial
At Midspan
stress at the saddle are less than one half
of yield
stress and the allowable stress, respectively, wear plates
are not required.
From Equation 4-3
'
1,715.34t0r'
50.501 psi
: -!D
orr
:
8R
From Equation 4-1 at the saddle,
., = 10*13910)
oo
circumferential stress at horn of saddle
_ 1.396
l
+
=
r:lrso-91 =tzo' \21 t l5e I .r = __: l:: + 301 : 180
02
o7
671 psi 120"
=
37.845 psi
o2-r:
A horizontal vessel containing hot oil is to be completely analyzed using the Zick method to determine wear plate requirements (Figure 4-35). Saddle material
:
215
3(7,828.981X 10.0) ?r(21.0)11.0)
-
EXAMPLE 4-2: MEGHANIGAL DESIGN OF A PROCESS COLUMN
o 600]
A detailed mechanical design is required for the proin Figure 4-36. The design criteria
10'-o'
cess column shown are as follows:
I ol i-l c\t
*l
I
-l
Design temperature: - 150"F Design wind speed 100 mph Internal pressure at top head: 150 psig Internal pressure at boftom head: 162 psig Shell material: 304 SS
:
Skirt material: 436 External pressure requirement: None
PWHT: Yes
o-o Figure 4-35, Horizontal pressure vessel containing hot oil.
Radiograph: Full Ambient temperature
:
lO"F min, 100oF max
Wind distribution is to be computed from ASNI-A58.11982:
216
Mechanical Design of Process Systems
towER ANo
TNTEFATS
I
(Nor
ro
scAL€)
Ill;,
l
TTJBE
I ltt I rtt
r
I
r rrtl ltttr _!_rt-!-!
'..
VIBBATON ENSEMALE
-7
SHELL AND HEAT EXCHANGER
I
l:'
"oo -------+ t$
'roP
I
aEo
1.,
-'.. ,tt __ _.j--L___
___i-L__
____--L__
-------lr:l-
r*-------lli-I:
csruliiinny
,"r"*""
-T
|
I I
BOTIOMBEO
-ti
.__i1___
-Tl "-*.-,J:l
l*IU
l"l
F.-i-----+r N.RMAL LrourD
.."r.
I
ri
--l
-f
FI
I
+-
Figure 4-36. Tower analyses ensembles.
WINO
ENSEMBLE
The Engineering Mechanics of Pressure 9z
:
Kz
:2.58
0.00256 Kz (IV)'z;
V
:
2.58
Top portion of tower,
/r
s\'"
IZJ
for
z<
rs ft
+
Tower is in Exposure Category C, for which
a
:
7
217
Effective Cross-sectional Area (Figure 4-37)
= 100 mph
D" = 66.5 tn. + (12.75 + Kz
Vessels
.0, Ze
:
900,
D" =
12
:
in.
in. + (12.75 + 1l) in.
12)
12 in. pipe
12 in. pipe
plus insulation
plus insulation
127.00 in.
\-7-
ladders
0.005
and
platforms
.At 15 ft,
Bottom portion,
l1\''' = o.rot K,:2.58f \900/
D.
:
47.O il:'.
ForZ)15ft, K,'. :
2.58
/ 7
l:l
+
V=
I= az
I
in. +
:
12
in.
ft,
f:
:
0.01
107.50 in.
100 mph,
h=
104.292
0.981 Hz
/szzor\ c = 1""'-- I { l27.ool
and 5 of A58.1-1982,
\r04.2921
1.0
=
0.00256(0.801)( 1001
I 7
o, '" = 0.00256(2.58)1"
\D I
:
20.506 lb/fC,
z<
15
I7 66.048
fr
.(t+*)(ro75o) = 11s3s5
286
(100F
From A.58.1 Table A9,
\900/
:
11)
Structural damping coefficient
0.00256(0.801)(Iv)':
From Thbles
+
+ r2) in.
Gust Response Factor
\900/
:
(12.75
(12.'75
\0286
For 15 ft and under,
qz
+
1.00
- 0.5 Ih (10.5X0.981)1104.2921 r:_=#=lu.t4J (1.00X100) sv
\0.286
(eoo-1 . z > ts rt
f
tz'?erre1* u'r","*-rr*I.$ '*"u'o''on
ffJ Y Figure 4-37. Effective cross sectional area.
s:
1i'0
PtpE
6" THtcK INSULATION
214
Mechanical Design of Process Systems 1o4,292ft
ir rs.:os\
\ t'? /: 9: h 1o4.292
ffi:
o.oe5:c
I 18.305
:
_
+-
_>..
9.859
#----->r ooo"
I-
0.0055,
y=
D_
fly :
(10.743)(0.0055X0.145)
6.145
:
0.009
*--->.. o
s
oo.*,(fr-o|"'",0r,,. =
: l.l
For a tower with many attachments and connecting piping,
c-
0.6s
, [g!q * [(3 32x0 147)l?(l l)105 0.01 I { (0.002X9.85s).1
q--->E
(4-83)
1
G=
0.65
+
1.076
:
1.726
*+r-
30'oo
From Simiu[9],
\+-{)-->
9:9zG f00t
Figure 4-38 shows the wind pressure distribution q plotted along the tower length.
l5.oort
'|
+;
Figure 4-38. Wind force distribution (q) along tower is para bolic above 15 feet. Section wind force distributions are combined into a force vector located at the centroid of the wini
Centroid of a Spandrel Segment
section.
The centroid ofa parabolic segment is shown in Figure 4-39. Applying the general equation, Equation 4-117, to our case we obtain
. t^ \ i _ tn + Ql llaqn I ngn.tl ,.t 2(n + 2(}\ \dqn + nqn r/
.t
.r
(4-117)
From Figure 4-39 we obtain a general expression for the composlte area,
t7 -7 .\ Af - ::l-----:l--I {dqn + nqn r). lb/ft (n+q)
(4-118)
Solving for the wind resultant force acting through each centroid we obtain,
F:
AO"CI
Using this equation we compute the wind force distribution. From Figure 4-20, Cr = 0.6. Solving for sectior properties we have the following:
aa '" :66.048 Section
Z:
I7
\2t1
1.-l
\900/
A 104.292
tt
-
The Engineering Mechanics of Pressure
Vessels
)| ) l^l NINI
il:
$l-
il-
o
-l;l il-
I
st?l .l+l Nlcl
IN
ql
,_l-l Nt -,I
^,1 :l qo
N I
N
6 F
YI
I
1F
(l
I
r<
T-l '-l .el
gilrl
Lr-'
t:-o
Nir++
re
g^1
ihl
Ll rN
Jii
Q,ni+++ u,-
I
E (JO
|
=x":
N.
I.t
"l
^lN rf.f ^
r',.'NS
Ntd
ol
tN+
1l --t^
I
@
!L!
!L
>
tL>
(!
:l' :-^ ldl o* l. l
-___t91
€ - t: F[? 'iYrl
tl
:
N
6
,Yl.l
Y
dlB
q)
^l
tt
rr llld ! ilisl N' ll tql
'i! | -;-
o.l' nu' xl d;d
N
(G q
Rt
-----i:--
--J9
'l
.9 =N
oo
tN
lt
IN
\t-l
IN
:* ()+
i l'l Nl. rl-
ll
'N
219
220
Mechanical Design of Process Systems
/rr}4 rq?\0 --l 28o
l:: :
9z
66.048
q"
(l.726X3s.659)
9n-
(
t
:
\vwi / qR \0
q":48.852
:
6r.547
e"-r
286
l:;l
726t
Section D 35.659
166.048)
(12.75 )[(7X48.8s2)
+
(6.292)l(7)(6t.s47)
=
: (r.726)ffiul- (66.048):44.573
60.461
+
(2)(44.s73)l
(2)(60.461)l
2+7 610.739 385.735 lb/ft
r9r [r2rrzrror.5+zr r- r2x60.461)1,. .^.. 2t2 . A, [ {ix6tJ47) + {2x60r'61) l'" "'' 3. 151
o.
\o
(66.048)
(8.00x7)(60.461) ^_
:48 I
.
103
[
+
(2X59.007)l
(7x60.461)
+ +
(2
X59.007,,l {8.00} (2)(59.007)l
s l{zxzlt++.stz) + )(43.097)l (3.7s z: tlnl 0e4.sb + (2)@3.097 0)t44.s7, (2
)
t)
:
4.009 ft
1.881
ft
Section F
59 007
(43.50X7)(s9.007)
+
1
(7)(s9.007)
22.128 ft
(66.048)
4s.352
+
(2)(48.852)l
2,468.640 lb/ft
(2X7X59.007) + z: zl 32 [ +
=
(2X43.097)l
165.919
q.-, = (t.i26) (*#)""' (66.048) =
:
(66.048):43.097
s9.007
lb/ft
(2)(7)(60.461)
J2
+
=
Section C
=
x,r4.571)l
ft
286
\vw/
q"
6.430
{2
60.461
/ qn
:
+
Section E
, = 1l.726] l^il
-s
:
11211t11+r.tsz1
ft
Section B
q" =
o
,,., ,., nL 0@e8sz) nL a)@e8sz) + t2\44.s1rll"'''l
:
39.943
(2)(39.943)l
296 .713lblft (2)(48.8s2) (2X48.8s2) ]
,0, ,0,
eI(2)
nl 32 |
(7 ('7
)(43.o97) )|43.097)
+ (2X39. 943) + 12)(39.943)]n
oo,
The Engineering Mechanics of Pressure Vessels
Section J
Section G
q"
=
39.943 35.347
/ro
C"
oo\0
28o
| = (1.726) l-:::::l
(66.048)
\vlru/
^ :
z-
(3.00)ft?X39.943)
+
: 38.378
(2X38.378)l
9"_r
1.506
q(2"
-
Z" ,) =
(3s.347X15.0)
530.205 lb/ft
2
ft
z.so r,
Now solving for the section forces we have
38.378
:
(1.726)
: :
/r?
on\o
Section
(66.048)
+
=
36.63s
(2X36.635)l
e l2IlI38.3Z8rj i?I36.61s)l ,r nn, 321 (7x38.378) + (2)(36.635t'- "-'
I
(1.726)
/, <
^^\o
286
lj':Y:l \vUU/
(2.00)[(7)(36.63s) ^_
:
72.697
t66.048)
+
=
35.347
\
FB
=
Fc
:
FD
=
Fr- =
(481.103)
)
(3
ft
\ rl
/
(2.468.&0) {l?lq. ^
0l
\tzl
2,44e.4r7 tb
(6r0.73e)
=
{toLtol ,0.u, =
\12
n65.919r l'07
501
\12l
ro.ur
=
(ue- ) ,0 u, : \ 12 /
es6.ii3)
F6
=
(u8.786) {'ol=to) to.u,t \ Lz I
r," = (n3.e7z) (!Zi2t\ \
(s30.205)
,o
/'
I
\12
J
-
3,2E2.i22 rb
u,
31,,141.650 lb
I
Eel.8r5
r
rb
,5e5. r55 rb
=
638.475 lb
:
612.6oo rb
3e0.746 lb
Ito],to) ,0.u, =
,r.oo,
Fc
t5,675.864 lb
I
=
=
3.055.004 lb
=
(0.6)
FF
Fr
]
1
,0." :
{'t]^ool to.ut
\
lblft
32 32[
1.003
(385.7rs) ('']=oo) 12 /
Ft = (72.6si) I'ol=tol to.u, = r2
(2X35.347)]
- s[(2) (7 (36. 63 s) + (2) 5.347 ) Z=-l (7X36.635) + (2\(3s.347) :
":
ft
q":36.635
=
ArD"Cr
2s6
l:::-:::; \7wl
ll).972lblft
1.507
F= FA
=
:
q"_r
35.347
ll :
(3.00)t(7x38.378) ^_
-i
:
lb/ft
118.786
Section H
-
At
:
rle9.:]s{ c.oo, : 32e [r2rtrr32i+rt | e)e9.943) + {2x38.378)l '- --'
=
q"
9n_r
2,84e.852 lb
222
Mechanical Design of Process Systems
Solving for section moments we use the following ex-
1
presslon: n-
"OD 16 BWG TUBE
I
M"=M" t+(z^,-z^)DF,_, +
af\
F,z.
(4-8s)
M^
:
(2449.417)(3.151)
Ms
=
7,718, 113
Mc
:
39,560.960 + (5504.421X43.5) + (15,675.864)(22.128) = 625,g7g.rt
+
MD : ME
:
Mn
:
Mc
Mr
7,718.113 ft-lb
+ (2449.4r7)(8.oo) (3,055.004X4.009) : 39,560.960 ft-lb tt-tt
+ (2r,180.285)(12.75) (3,282.722)(6.430) : 917,035.328 ft-lb
625,878.792
+
Figure 4-40. The tube bundle is modeled in banks ofconcentric circles used to approximate the section moment of inertia. The tube bundle enhances the section stiffness.
9r7,035.328 + (24,463.007)(3.75) + (891.815)(1.881) : 1,010,449.109 ft-lb 1,010,,149.109
+
:
+
+
(25,354.822)(7 .00)
(1,s9s.155)(3.s2s)
1,193,555.784
Mu: Mr
:
+
:
I,193,555.784 ft-lb
(26,949.9'77)(3.OO)
(638.475X1.506)
:
+ (27,5 88.4s2)(3.00) + (612.600Xr.491) : 1,359,046.001 ft-lb
1,275,367.258
=
1,359,046.001
:
1,415,840.023
+ +
+
(28,201.052X2.00) (390.746X1.003) 1,415,840.023 ft-lb
+
For l-in. OD i6 BWG tube,
|,275,367 .258 tt-tb
:
(28,591.798)(15.0) (2,849 .8s2)(',7 .s0) 1,866,090.883 ft-lb
:
I : A: K: n :
:
0.0210 in.a
0.191 in.2
:
metal cross section metal area
number of tubes per circle number of circles
Thus, from the parallel-axis theorem the composite moment of inertia is
Section Moments of Inertia Section
,."
a-rl+-in.
" ffs+.sol, _ ile\"] 64 1\t2 I \12/J
Section
b-3/a in.
I:
t
: 0.756
DKIG + AL)
Values of
t
The shell and tube heat exchanger section moment of inertia is approximated by a set of concentric circles of tubes. The concentric circle pattern approximates that of the exchanger tube sheet. Using the parallel-axis theorem, we arrive at the section moment of inertia. Referring to Figure 4-40 we analyze the exchanger as follows:
I
are tabulated in Table 4-16.
For enclosing shell, :/a-in.
rta
I
"
64'1s+.zs)o
)-l = Lt' :
-
(54.00)41
t, -
23,676.070 in.'
rr4.i35.44r in.a + 23.676.070 in.' 138,411.511 in.a
or for the total cross-sectional area
Ib
:
6.675 fC
The Engineering Mechanics of pressure Vessels
-
Table 4-16 Values of I for Tube Bundle
16.364.299
t6,364.299
14.127 .503
30,491.802
12.104.531
; 10
;i#.uZr
17.00
2
14.50
210.250
89.000
0.191
0.021
l9l
o.021
0.
10.284.531
s2,880.927
8.574.543 7. r38.100 5.871.903
68,593.s70 74,465.473
86
r.765.174
6r,45s.470
.7s,230.641
85,937.106 88.197.856 89,860.696 91,063.953
9l,901.445 92,456.266 Jf,
t7
92,79t.181 92.980.407
18
93.074. 195
t9
t6
93.109.836 93.119.576 93.120.846
l0
2l
t55
Section
,
c-
t
I/z-in.
)ectlon
/s+ oo\*l - 64" [/ss.oo\[\ t2 / \12 /J
:
d-5/s-in.
64
0.917 fta
Section
r= :
e-
t
t/ro-in.
t
L[(r#| (:gl I
.013
ff
rL
_/+z.ool.l
1.1 10 fta
Section
t
l1:1.735.1,+1
I \12lJ
:
_/+:.oo\.1 ,: "[or4f l\ t2 I \t2lj
:
,=.[+:1!f 64 l\ 12
1.533 ft4
Section
t-rA-tn.
2t,6t4.595
r
g-r3/r6-in. t
ll43.62sl- _ - 64,r L\ t2 I \ t2 /J 142.001"1
:
1.208 fta
Referring to Figures 4-36 and 4_41 we calculate the of inertia as follows:
sectron moments Section h
,.r:(
26.193
2
+
21.812s
cos 6.934"
\t-
24. I80 in.
224
Mechanical Desisn of Process Svstems
Deflections
lso
o
Ia
ydla
+
! _ tb.292tt ltz.++s.+ngxo.zoztl "' (i.157 x lo") [I :
h.
$ lo
a"\
x
2.416
10-s
ft
(8.oot
.-
(2.787
[(e,oss.oo+)(a.oo)
[
10'9
8
(:2,449.4I7)(S.OO) --3-21 -
{Z,Zrr. r r:l1
reo=21.8125 in
:
rho=26.1925 in
x l0
3.088
5
ft
tto:29.1109 in 1o=
51.o in
Figure 4-41. The equivalent radii for the skirt sections.
. '
(43.50)'? I (15,675.864X43.5)
(6.402
10') [
(s,s04.421)(43.5)
+'32-)
: t /.- .-\+ | ,- ^.\q t.'' - o- | lr+6 rol - l4o dol l = 64[\12/ \12ll
(3 ,282
frr
+
/zs.rrr + zo.rs:\ r-* = t___t \ 2 cos 6.934' /
27.856 in.
(21 , 180.285)(
0.017
'' L'
/sr.oo +
\
2 cos
=
:s.rrr\
L\
i
\
iI
[tal
r. s
x r0) t
(7.00), (4.
7.846 fta
of each section's wind force, shear, bending
moment, and moment of inertia are summarized in Thble 4-17 for the entire tower.
:
razs,ttt.to4]
2l
rs)t:.zs) 8
(917,03s.328t
[(r,sqs.rssxz.oo) t-
635,10)L
(2s ,354.822)(7 .0O)
Values
+
0.002
6.934' /
j'" l/so.uor\t "" "1 | = ll"" '" 1 '1hs.ozo\*l 64 12 12
l2.75)
, (24,463.OO7)(3.75) -J-rl
j
5)
ft
(4230
"[/ss.zr,z\* /s+.oaz\tl 64 L\ 12 / \ 12 /l
.7
8
(3.'/r, Section
.722)(t2
('1
Section i
soo)l
0.055 ft
1
l.5i3
+ Q2lOo
0.006
ft
8
, (1,0r0,449.109t -2)
1l The Engineering Mechanics of Pressure Vessels
Table 4-17 Force, Shear, Bending Moment and Wind Summation of Section Moment of lnertia Fr (lb) 2.449.4t7
Section a
3,055.004 15,675.864
Mi
39,560.960
5.504.421
li (fta) 0.756
3.157
6.6'7 5
2.78'7
6.402 3.829 4.230
21. 180.285
625,878.'192
1.533
917.035.328
0.917
891.815
24.463.00'l 25,354.822 26.949.971
1,010,449. 109
1.013
27,588.452
1,193,555.784 1,275,367.258
1.110
638.475
28,20 r.052
28,591.798
3,282.',722
s
(ft{b) 7,118.113
Qi (lb) 2.449.417
612.600 390.746 2,849.852
3l,441.650
El (lb-ft'?)
t3.0t
= -',
0.001
(6.402
,
=
1.533
6.402
10'
1.415.840.023 1,866,090.883
2.54',7
x 1.064 x
7 .846
,
3.899
\
lOa)
[
"
orn:-l
3 .27
+
^ ^' ,,:
I (2.849.852)( 15.00) L
0.006 ft
8
I
+
?.718.I r3l I
14.2e2X43. s0) [ ( 1s,67s.864)(43. s)
0.027
15't
x
lOY) [
6
+
39,560.960]
ft
.792yr2.7s11(3 ,282 .122)(12 .'t s)
oJ29
(r,3s9,046.001t
. lo) [
(21 , 180.2
=
(28,59r.798)(r5.00)
:
7x8.00)
6
10 5ft
x
(6.402
=
x t0 a ft
(15.00), (J.276 l0'9
r
(5,504.421)(43.s)
ft
(28,201.052)(2.00)
2.626
(
, (r,27s,367.25U]| -)l
+'32ll
:
^
A'r:-l
8
12.001/ [(3e0.7abx2.00) 8 tr.oo+. ro9[
":
(2,,149.4
1.19J.555.7S4)l
[(612.oo](3.0u/
109
1,359,046.001
2
(27,s88.4s2X3.0)
0.001
{
10!)
loa
ft
13.oo1r
t-
,
lOto
I .208
(6.2e2)(8.00) [ (3,05s.004)(8.00)
3'l
10'q
t 4.635 ^ 5-045 x
(rJ8i ,, 109 t t26.s4s.s71
x x x x
o
85X12.75)
+
625.878 792
0.148 ft I
r70.542rr3.75,1{8q1.815)r3.?51
^ 't-
r+.::ot
, 1,415,840.023)l -21
_
(
r
tolL
24 .46 3 .001 )\ 3 .15
2
:
0.060 fr
.
, _ q tr,u:S.:28
I |
j
6
><
t}e 101r
1010
l0t'r
226
Mechanical Design
^ -_ -)6
r74.292n7.00) [{ t.5q5.155x7.00)
(4.6iai
ro1
Process Systems
t
Tower Section Stress Galculations
6
Section
(2s,354.822)(7.00)
+
:
"
ol
2
+
1 -,010,449.t09]I
t
a-ll+-in.
For tension on the windward side, using Equation 4?1
0.124 ft
/po\ / \4tl -
(8r.2s2)(3.00)[(638.4 75X3.00)
^1
Dt
(5!45 x rO
l-
(26 ,949 .977)(3 .0O)
:
-
6
* , "--'---"1 ,oa aaa ,ool
0.060 ft
:
(27,588.452)(3.0) 2
0.052
(87 .2s2)(2.oo)
(1.(064 )64
x
t0ro) t0ro)
l3s0.7 46)(2.o0) 6
|.
+l(28,591.798X2.00) + 1,359,046.001] 2 :
O.O23
w
0.423 kips
Di
54.0 in.,
rJ.276 < tolor
+
: rt ":
I
o
(2S,s91.798)(1s.oo)
2
+
\-,1 * \-,r L/" L/
ft + ir.
0.25 in.,
o=
8,218.43 psi tension on windward side
q=
7
!
161.009
-
42.57
,896.42 psi compression on leeward side
Internal pressure circumferential stress,
PD
2t
16,200
(
1s0.0)(54.0)
2(0.2sX1.0)
psi
<
18,800
=
o"
The circumferential stress governs in this section and is less than the allowable stress.
[t
b-
:/a-in.
t
r:o.orrs+.orl
, [ 16(54.75)(39.s60.960)(12)
-1
0.561
ft =
0.649
ft
T : -100'F,
54.50 in.
L(4)(0.37s) I
0.067 ft
0.088 '7 .787
=
t:
8,100
Section
I 1,4r5,840.023.j
D"
1.0,
o=
: -^ '" _ -
=
1
2(1.8t4) I - [tr(0lsxl08 d
'
(89.292x 15.00) [(2.849.8s2r 5.00)
+ Di,
[rrsO.Orrs+.orl I r6(54.50,{l2r{7.trA.rr:rl t {4x015) I = [.{015x t08J0)6J86.2t]
o^=
ft
E
150 psi,
ao., -'"1 ,aol ' ,-'-,ra'''"
ft
D,XDa
\
lzw\
\"
P
^ _ 184.2s2t(3.00r fr6l2. 60x3.00) -r8-(6J02^toq)L6 +
ron^na
\?r((D" -
]
=
[r{ 0J7s x 10850X5-9{3J63)l
_
[ :rrs.zor.oor I t.(0 3is,(t08
itl
The Engineering Mechanics of Pressure Vessels
5,400
+
550.16
-
237.30
5,712.86 psi tension
(150.0)(54.0)
:
< 18,800: Section
16(43.3?5)(1,010,,149. 109)(12) *[ -t r(0.688)(85.375X3,645.39r)
10.800 osi
zw,sor.sztt I - It"(0.o88x85.3?tl
o"
q
t
c-\lz-in.
l/re-in. f,
o=t-l [rrso.otr+z.or] [ {4x0.688) I
4,612.5 4 psi compression
2(0.375)(1.0)
e-l
Section
:
2,289.24
+
12,509.56
-
482.98
= 14,315.82 psi tension < 18,800 psi : o : - 10,703.30 psi compression
o Ir rso.olrs+.orl
0r = t-l
t
.
=
: o: o
r=
(4x0.s) I
I
rorss.oolrozs.s
sot os. ool (5.9a [-lr(0. (t
1
.
oo) I
lzot.tzz.oll
(lsq'Pl!4? oo) 2(0.688)
f-:/+-in.
Section
t"rcJ0l t0r)l
4,050.00
!
6,497 .53
-
10,106.884 psi tension
<
18,800
,
=
(150.0x54.0)
-
6.luuDSl
2(0.s0x1.0)
Section
d-s/s-in.
q: o:
t
o
o:t-l krso.ox+z.orl [ (4)(0.62s) I
*l -t
(L 6)
(43.25) (9 r7,03 s .328\ (12)
op
I
zt+:,+rs.oor I
4,578.488 psi
t
Iro(+s.soxr, ts:,555.7s4x12t I
I
"(0Jsxs550)(3,6562s0)
Izr+o.sst.sssl I
t"(oisx8s5o)l
2,100.00
+
13,533.81
l5,l67.61psi tension
-
<
466.199 18,800 psi
=
-11,900.01 psi compression
_
(1s0.00x42.00) _ 4,200.00 psi 2(O.75)
r(0.688)(8s.375)(3,&s.39r)
- t-l
:
krso.olt+z.orl [ (4)(0.75) I
-
440.@6
-2,888.176 psi compression
o^ = ::
'
'-
o"
78.isu'l2t]
Section g-t:71u-in.
g
lr(0.688t(85.375r1
2,520.00
!
11,320.361
13,369.777 psi tension
-
-
<
18.800
9,290.944 psi compression
(150'0x42'o) 2(O.62s)
=
o:1-l krso.otr+z.orl l(4)(0.813) I
470.584
5.o4o.oo osi
psi
:
o,
.
(r2) |,27 s,3 s.367 67 .258) .258)(t2 6(43. 625) (1,27 116(43.625)( 1.
=[
-
"(0-813X85525X3'667140
Izt+s.ozl.+ssr I t"(0-8t3l8s.6rtl
o,
228 q
= o: q:
Mechanical Design of process Systems 1
,937
.2'l
!
-
13,319.972
<
14,817.602 psi tension
-ll,822.342 psi
D": : D; : :
439 .64
18,800
psi
:
da
compression
All section stresses are less than the allowable stress of 18,800 psi. Thus, the tower thicknesses are acceptable.
OO of base plate
ID of
base
plate
98.00 in.
-rn2 - nll = '-o------1-
A.
First we determine the size and number of anchor bolts reouired.
Using an A- 193-87 high-strength bolt with an allowable stress of 40,000 psi per AISC and assuming a bolt circle of 107 in., the required bolt area, ,4.6, is
I
toz
*,. ,rrl "---) ^.
=
l.o I I ln-'
102
in. + 2(.2.375)
:
(
1.615 in.'?
.
<
W.
(4-.+
N
70,219.061 Ib
_
(12)(70,219.061)
+
1
1.s0)
l
63,815.727
n
63,8rs.721
2,22\.302
1.866.090.883X12)(l I L50) 2(3,059,323.380)
The concrete bearing strength criteria are met, so we ca. continue to the base plate design.
h
l2)(40,000)
p"
- D, _ lll.50 - 98.00 22 = 6.'75 : Base f, width = BP t =
1.680 in.2
21.947
(4-,11
: 379.340 + 28.'129 + 408.069 o. : 816.138 psi < Fb : 1.33(900) = I,197 psi
(4_1j
20,000 )
I
in. >
W
lo.
t2
=
2(6.j 5)
3.059.323.380
=
2,22t .302
-63,81s.727f
r( 106.75
lJOrr sDaclng
-
.302 in '
(8)(12X1,866,090.883X1 (.12)(22,036.250)
I
=
111.50
106.75 in.
The new required area becomes
[*tgg-
2(2.375)
o"
We select a lsls-in. d bolt of 8-thread series with a minimum root area of 1.680 in., Thus, using Figure 415, the new bolt circle becomes
BC
=
_
(
_
(12X40,000)
:
8MD,, N(Di + Dl)
_ '
(4-42)
l2){ 1.866.090.8S3)
+
/vl) " = iryl). \A.i iv). \A./ \2r.i
SKIRT AND BASE PLAIE DESIGN
[{4){
106.75
2221
4
fr4l " "",'- "' : I. = -/na 64
^,: [+-*]/*".
:
111.50 in.
18
in. minimum
Maximum bearing pressure on contact area:
=
,000 psi
n
oJo,
k
0.333
=
19
allowable working stress for steel, psi
The Engineering Mechanics of Pressure
:
:
1.588, C, = 2.376,2 = 0.431, of Equation 445 using Thsix iterations 0.782, and J ble 4-7, we obtain a value of k of 0. 186.
with k
-
c"
0.333,
0.186, 655.834 psi and o, = 26,850.892 psi The allowable stress in the base ring = 36,000 psi 3,000 psi The allowable shength in the concrete
o.
:
ti
- 0.845 ta -
:
r6s{ o,o, [zro.tg.]xtoo.zsr
o.1.,"y
:
769.139 psi
[
15116
in. thick
*(* irun'n n. \rDsr/
-n2
.
f. octmar lo5 nlfu\ : L l-l I o,ll I
0
0.901 in
4M
kt
-
,lJ
=
Calculating the minimum skirt-to-base-plate weld size we have from Equation 4-65
+ o.zsl 2(0. r83x 106.75r I
^
0.046
Make gusset plates
:
Using Equation 4-54 and solving for the maximum induced stress in the concrete,
229
Equation 4-64 becomes
tc =
k=
For
Vessels
(4-56)
s83rl rll02.00tr I
r2X r ,8oo,090.
t :
61.815 727 lrt102.00)
2,939.611
For wind or earthquake,
-
111.50
102.00
_,
?
i-
o*
2
: :
weld
BTHK
=
Make base
t
lqrlo " '""| -I v?6q = L 20.000 I fr
r
t4.75t l
t
15/8
[4{20.000)14.75
-
r
1.25I
1.33( 12,700X0.s5)
2.939.611 (2)(9290.0s)
size w
=
0.158
Anchor bolt torque is determined by Equation 4-66. For lubricated bolts with Fel-Pro C-5A,
in. thick
(b4,605.803x2.37s)
:
Use at least a 3/re-in. weld on each side of skirt.
1.613 in.
Solving for the compression ring thickness using Equation 4-63 we have
[
1.33 o.(0.55) 9,290.05 psi
I
: T: C
0.15
(0.15)(1.62s)(64,605.803)
:
15,747.664 in.-tb
or
^-^-
T:
1.625'1].j
1,313
ftlb
with torque wrench
Make compression ring :/+ in. thick
Checking the skirt thickness for reaction of the bolting ring against the skirt we have from Equation 4-39,
Using Equation 4-64 and Figure 4- l6 in calculating the compression ring thickness, we have
18.000
Fi
G*r"
-
{F,)tl
=
64,605.803
:
9.00 in.;
Grr
-
G* =
t-! ztE
,
1.500
4.25 in.
t
pp
1.76
/ \.. l--_5- I r' '
(4-19)
\m(GH)o"11/
r=
@-64)
t =
l. /o
[t_(70.2le.06rx2.3zsr t,
Q.672
q x
"00X
l'
/rozl' t'z /
'
':a'4? 'z0"000)l in. < r3lroin. skirt thickness at chair
Skirt thickness meets chair ring reaction cnterla. A sketch of the skirt and chair design is shown in Figure 4-42.
230
Mechanical Design of Process Systems NOTE:TOFOUE BOTTS 1313 tr-|bs WttH FEL-PRO C-sA USING TOROT'E
f 11td
^-$.-87
BoLls
Figure 4-42. The skirt detail.
Section Gentroids
Section c
Referring to Figure 4-21 we have the following:
ROO y.=;=4.00ft
Section a
Lz b(4a
-30
tot r.rt>
-
3(0.25)
ul"r"'", - o.rr) t : Lr =
s.857
in. =
0.488
=
2.50 + 4.00
6.50 ft
Section d
,F-l toio
:
0.488 ft
50
ft + :_: = z
2.988 fr
_ 2.00 : r.w tt lo= Z L: : 4.00 + 1.00 : Section e
'-2L.+
:
24oo 1.00
Section Section b
t,=+=2.5ort
5.00 ft
= +
:
12.00
:
13.00
ft
f
v :2'75 : -2 L5
l2.ooft
12.00
1.3?5
+
ft
1.375
:
13.375
ft
The Engineering Mechanics of Pressure Vessels
Ltt =
Section g
=
Ld
_
+ 4.00 :
1.3'75
5.375
Section
:
Section
,, _
:
4.875
'"2
ft
L13
+ l.'75 =
D".
2.625 ft
D3,
j
3HrDl
'mol
1.875
+ 3.50 :
5.375
ft
3.00
:
3.50
+
1.50
=
5.00 ft
- Di) r 8{D" -
D, ) ran a
- Di, = 43.25 - 42.00 = 1.25 D;. - Di : 1,870.563 - 1,',761.00 = t.\ cr = arctan lll : Ze.-scs'
= 43.625,D,.: 42.125, D". : r,903.r41, Di, = 1,774.516,
o=
arctan
/roz.oo
| \
-
+:.
ou
s\
2(240.00)
|
D,.
=
D;.
- Di :
1.500 in.
t28.62s
6.934
I
3(36)(128.62s) + 8(361(1.50) tan (6.93,1) 6[128.625 + 2(36X1.50) tan (6.934)]
D.,
106.563
\t2l
3(12X106.563) + 8(I\2(1.25) tan (26.565) 6[106.563 + 2(12)(1.25) tan (26.56s)]
:
ft
Section o
l.75oft
0.875
8.00
Section n
i
t, '2 :350: La
:
Lr:
4.00 + 0.875
:
2
v,=17s=0.875ft "2
:
1.875
7.00
ft
Section h
Li
+
Section m
8oo:4.ooft
i," = '"2
6.125
231
:
18.556 in.
= 1.546 ft Lr,r = 1.50 + 1.546 = 3.046 ft y.
6.247 rn. Section p
t =
0.521 ft
=
Lq
1.750
+
(1.0
-
0.521)
:
2.229 ft
Section k
D.,
:
52.381 in., D1
50.756 in., D".
DZ"
=
2,743.'t9s,
2,s'76.r97,
D3.
j'^
) ?S '1-'
:
I
=
2
6.125 fr
: Dl. :
=
0.521
+ 6.125 =
3(204X167.598)
Section I
"2
3.75
= l.X/l tf
6.646
ft
Di.
=
- Di = 167.598 in.
6[167.s98
Lro
-
+
+ 8(2}4)r(t.625) tan (6.934) 2(204)(r.62s) tan (6.934)]
: I13.044 in. yp : 9,420 tt L,. : (3.00 1.546) + 9.420 : Lro : 17.00 - 9.420 : 7.580 ft
10.874
ft
1.625
Mechanical Design of Process Systems
2.625' 4.a75 5.375'. r3.375' 13.00'
.. 9 q ;iI qS p
.9 9 9 | i q H E ! $ R 3 H: H € s;^x^x^^x^^^;^;xx .'
l
P
:.
N
Figure 4-43, The vibration ensemble of lumped masses.
Vortex.lnduced Vibration Referring to Figure 4-43 we have the following:
M.:0 Mb: (0.423)(2.95 8) : 1.251 *o-t M" : 1.251 + (1.814)(6.50) : 13.042 kip-ft Ma : 13.042 + (15.201X5.00) : 89.047 kp-ft M" : 89.047 + (16.192X13.00) : 299.543kip-ft Mr : 299.538 + (29.004)(13.375) = 687.472 ktp-ft Mc : 687.46'7 + (30.813Xs.375) : 853.091 kip-ft Mh : 853.086 + (35.084X4.875) = 1,024.126 kip-ft Mi - |,024.r2r + (36.016)(2.625) = 1,118.668 kip-ft Ivl = 1,118.663 + (37.s32)(2.229) : r,202.322 ktp-ft M,. = ,2o2 .322 + (37 .913)(6 .646) : | ,454 .292 ktp-tt Mt : |,454.292 + (43.171)(800) = 1,799.660 kip-ft M. : 1,799.660 + (4s.028)(5.375) = 2,M1.685 kip-ft M" : 2,041.685 + (47.662)(s.o0) = 2,279.995 Y,tp-ft M. : 2,2'79.995 + (50.684)(3,046) : 2,434.379 kip-ft MF = 2,434.379 + (s 1.937X10. 874) : 2,999. r42 kip-ft Ms^, = 2,999.142 + (63.816)('7.58) : 3,482.867 kip-ft 1
M' (30 ,
{, - = E.I,
:
4.320
x
x
x
lOe
&=
x
x
ro-5
:
1.038
x
10
687 ,472
l0)(0.756)
10)(6.675)
er+;ffi1j3,,
10)(1.533)
8s3,091
,4
= t't _ A
!" '
?)
-
lft"t,
"
r Sll' - 1.288 '
1.O24.t26
r Jx) = 1.546 l'118 668 : 1.689 r
(4.32
x
|
14.32
l0e)(1.533)
4
10-4
to
'
lo
'
.202.322
.lo"ltt.gtot
'
I L
r,, -
(4.32
\4.32
_14?|v|^4
f'7q9'660 4.tt2 t x 10,X1 .013) -
ro
"
204l'685 -4.258xlo1 ^ l0')(1.1l0)
:
3.830
x
10-7
!,,. '
=
4.523
x
l0-1
-
=
r.345
x
1o
, r,<
-
5
x
(4.32
\blf€
13,042
(4.32
4.523
tO")tb/in.,(t44tin.b/ft,
1,251
(4.32
* : 6r?ffir,rral :
r
(4J2
1_70 00<
169 x l0 /' 10\1108) - -' '
2,434,379
(4.32
v
l0)( 1.s32)
--r.u78xl0a
4
The Engineering Mechanics of Pressure Vessels
2'99q'l42 = r,- = (4.12 \ I0'X7.011)
q.902
r. . (4.121482'q67 /
l.l5o
10)(7.01l)
''
,.
ro
,
Io
a
Sr: =
\rl
x l0
)(2.958)
:
2
S:=
t(3.83
2.?15
x l0 ) + (4.523 x x
10
,
+
3.678)( r0-4)
(3.678
x
10
1+
(3.046)
9.902
=
1.226
x l0 r
x l0 ) (10.874)
2
:
(9.902
:
8.111
x
10-'
x l0 5 + 1.150 x
10 r)
(7.58)
(6.s0)
x
10
1
6
x l0
[(4.523
Sro
?)l
10
(,1.369
2.538
x l0 '
5.665
_ 2.t57 ,, l0
2
Sr+
/. + l,l,\ , ^ = 18,*t Li J, l-l (3.83
t4.258 + 4.369x10 "r(5.00)
s,,
?)
+
(1.345
a =q+\-q:s+,1
x l0-)] (s.00)
j=n
2
3.476
x
Ss:
: 5"') -
3.814
9.966
x
x
10
10
t + (1.038 x
l0-4)l
2
(1.288
+
1.546)(10-1
L689)(10
e.625)
:
4.246
x
3.506
x r0 I
r,.
x
P,. :
:
(1 689
+ L457Xl0r) e.2zg) =
Sr
r
s,, =
10-) (6.646)
9!\?9(8.00) (4 112
+ t258xl0
)
-
x l0 I
s,
3.671)(
2
l0
6.908
+
+
\
=
(1.546
)
b.2sr
(4.875)
:
(1.457
(13.375)
a
- !?88110'-,5325,
011
a
A: =
)] (r3.00)
10
s8
Sro =
: 8.111 x l0 8.111 xl0-4+2.538xl0r:3.349xl0 l 4.575 x l0-r $ : 3.349 x l0 3 + 1.226 x l0 Ir = At : 4.575 x l0-r + 2.15'7 x 10 : 6.?32 x 10 r As : 6.'732x l0 3 + 2.249 x l0 3 = 8.981 x 10 l Ao = 8.981 x l0-3 + 3.113 x l0-r : 1.209 x l0 r 1.704 x 10 3 = 1.379 x 10-2 N : 1.209 x 10 2+ 2+3.506 x 10-1 : 1.414 x 10 l As : 1.379 x 10 As = 1.414 x 10-2 + 4.246 x l0-1 : 1.457 x 10 r r No : |.45'7 x 10 2 + 6.908 x 10 a = 1.526 x 10 r Arr : 1.526 x 10-2 + 6.251 x 10-1 : 1.589 x 10 Arz : 1.589 x 10 '? + 9.966 x l0 a - 1.688 x l0 Ar: = 1.688 x l0 2 + 3.814 x 10 a = 1.'726 x 10 N+: 1.726 x l0-22 + 3.476 x l0-56 :: 1.730 x l0-' 1.730 x 10': Ars : 1.730 x 10 + 2.115 x l0 Aro = 1.730 x 10 2+5.665 x 10 r = 1.730 x 10'?
Ar
x l0 4
t(4.523
,-1
5
x l0-) + (4.523 x
[(1.345
:
10
:
: (s.37s)
:
1.704
3.113
r0-l
10 r
/\ p'\21 lA'+ =
x
1.o
8.111
t,,\.349
r :
)(7.58)
x
10
x
l0-2
1
( .262
l
lr-,
: (ry,
x ro l
z.z4g
A'.
1.207
x10r x l0
r
:
3.s74
"
ro
,
+ 3.349
x
10
+ 4.575
x
l0 1 (3.046)
t ,
(
I
10.874)
234
Mechanical Design of Process Systems
Pr.:( 4.575 x l0-3 :
x
2.827 6.7
P,r:( =
4.223
v
.428
x
,
l0-r +
,
_d
x
10
(8.00)
x l0-
lO-'z
P":(
1.414
x
l0-z +
1.457
x
10-
(2.229)
T 10
2
.457 X 10, + 1.526 'r.4
,
x
1.915 1.526
x l0
(2.62s)
10-2
xl0, x l0
7.593
+ 1.589
,
x
l0 -i
)
x
Pr:( /r.osa x =
P":( : P,:( :
1.730
8.650
: tt5 : : pro : : pB : :
730
5.117
x
l0-2 + 1.730
,
x
10
_n
-) (6.s0)
x l0-, x
10-, + 1.730
,
x l0-
(2.958)
x l0 ']
x l0 3 ft : y(16) : 0.037 in. x 10-3 + 2.262 x t0-2 x 10-2 ft : Y(15) : 9.39t n. x 10'? + 1.207 x I0 x l0-2 ft : V(t4y = 9.45, .r. 3.'176 x l0-2 + 2.827 x l0-2 6.603 x 16-z 1 : y(13) : 0..792 in. az = 6.603 x 10'? + 4.223 x 10 : 1.083 x l0-rfr : y(12) : 1.399 1r. p11 : 1.083 x l0-r + 8.428 x 10 ' : 1.925 x 10 ! ft : y(11) : 2.310 in. p.6 : 1.925 x l0-r + 9.281 x l0-2 : 2.854 x 10 ' ft : y(10) : 3.425 'n. : 2.854 x 10-r + 3.200 x l0-2 : 3.174 x 10-' ft : y(9) : 3.809 in. = 3.174 x l0-r + 3.915 x l0 : 3.565 x 10-'ft: y(8) : 4.278 in. : 3.565 x l0-r + 7.593 x 10 , : 4.324 x 10 I ft : y(7) : 5.189 in. : 4.324 x 10-r + 8.807 x l0-2 : 5.205 x 10-r ft = y(6) : 6.246 tn. : 5.205 x 10-r + 2.283 x 10 ' : 7.488 x l0-r ft : Y(5) : 8.986 in. : 7.488 x lO-t + 2.246 x 10 | : 9.734 x l0 rft: y(4) = 11.681 in. : 9.734 x 10-r + 8.650 x 10-2 F3 : 1.060 x l0-'ft : y(3) : 12.720 in. : 1.060 + 1.125 x l0 : r.r72 ft : y(2) : 14.064 ir'. , Pl : 1.172 + 5.117 x l0 : r.224ft: y(1) : 14.683 in. p16
3.074 3.074 2.569 2.569 3.776
2
(5.37s)
2
I
ro t +
,
1.726 x. 10 -,\
(r3.37 s)
)
|
|.726 x. t0
2.246
5)
10-'
x l0
2.283
(.4.87
2
1.589 x l0 ' + 1.688 x l0P.:l '\ , 8.807
(6.646)
1.125
r
15 175I
J
L730
2
x
:
1.209
l0-1 + 1.414
9.281
Pr:(
10
:
=
:
x
t0-3 + 8.981
1Q-2
P'r=( 1.379 x
3.2( .200
Pr:( :
,
:8
Pr:(
(s.00)
l0-z
8.981 .v
P'':(
10-
10-2
x
32
x
+ 6.732
,
2
+ 1.730
,
x
l0-1
x
10-, + 1.730
> l0-2
t
x
10
_n
) ,\ l0-
(
13.00)
(s.00)
Section weights and displacements for computing the tower's period of vibration are listed in Table 4-18. The first period of vibration, T, is determined as follows:
,=r"\E leDwv
(4-98)
--__-4 -
The Engineering Mechanics of Pressure Vessels
Table 4-18 Tower Vibration Def lections Dellection
w (lb)
(in.)
y
Section
(in.lb)
wy
14.683
423
6.2 r0.909
14.064 12.720
1,391
t9 ,563 .024 170,282.640 I1,575.871
13,387 9l I
11.681
e
5.
4.278 1,516
3.425
1
5
381
,774.444
s )sR
12,145.980
.300
1.857
2.414.100
0.792 0.453 0.308 0.037
2.634 )s?
2.086.128 1.368.966 385.924
20,493
439.523
3.O22
|
t] .056.797 2r ,994.85',/ 4,469 .368
| ,304.925
2.310 1
70,5'73.64r
rr4,999.754
22,162.219 3,98'7 .096
4.271
3.809
t35,217 .749
I,034,545.887
fi,299.0r4
1,809
189
91.194.771 5,134.3'70 2,165,995. r 81 2'7
t15,128.632
12.812
8.986 6.246
Wy' (lb-in.'?)
28,057.214 3,138.330 1,652.213 62Q.142
l 18.865 16.262
D*, = 3l6,t2s:ss
:
(386.4)(386,129.39s)
f : l/T :
Hz =
0.976
0.981
Hz
The second critical wind velocity, V2, is 1.024 sec/cycle
:
104.292
:
34.764
3
54.00
+
1.00
t2
:
ft
-
d
T
4.583
1.024
ft
sec
:
6.25
Vr
F,
10.375 mph
:
65.163 mph
: 0.00086(0.6x60)(4.583)(104.292)(10.37 r, = 1,592.930 lb
if we have a problem with vortex-induced vibrations, we must compare the force amplitude of 1,592.93 lb against the corresponding maximum wind force amplitude for the same region (either top l/r or r/+ of tower-in this case, the top r/:). Using Figure 4-39 we have the following: To determine
34.764
ft, from
1M.292 tt-34.764
above
ft :
69.528
n. = al 716x15 659)
se:
cycle
fi
=
L:
(3.40)(4.s83) ft
3.40 d
Yz
From Equation 4-94a and Table 4-13 we have the initial assumed value
Considering the upper third of the tower as being the effective length for vortex shedding the first critical wind velocity is as follows: T_
D*r,:3.g64,78s.40.
o"
,=
9" r
:
/60 srr\o 1l.726)
61 547 lb/trl 286
l"-^^"^-"I
\900/
54.808 lb/ft2
ft
(66.048)
Mechanical Design of Process Systems
_
+ (2+7)
(34.7 64)l(7)(6r.
F=
t2087.559r
s47)
/r rr nn\ l'-;;""1 \ rz I
(2)(54.8o8)l
(0.6)
= l?
:2,087.559
Finally, if the Reynolds number is greater than approxa vibration analysis is not required, because in these regions the vortices break-up. In our case.
.
imately 350,000,
)55 000 rhNn"
_
or
F*,0
:
13,256 lbr
Since F*;"6
)
>
1,608.56
F,iu.",ion,
lbr
:
where
DcVp
D. :
F"
0.071
the wind stresses are greater
1.285
lhan those at resonance vibrarion, so no further vi6ration analysis is required. If the vibration amplitude force had been greater than
the maximum wind force, further investigation would have been required. Dynamic stresses ar the-crirical wind velocity can be approximated by taking the ratio of the vibration force amplitude, F", to the maximum wind force amplitude, F1,, and multiplying this ratio by the bending stress term in Equation 4-29. The pressure stress, which is a primary stress, and the weight load stress in tension are unaffected. Shear is not considered in the equation because it is almost always negligible. Defining the ratio of vibration force amplitude to the maximum wind force amplitude as R. Equirion 4-29 be-
effective wind diameter at top r/: or r/+ o: tower : 127.0 in. critical wind velocity = 15.292 ft/sec
N"" :
lb./fc
x l0 5lb-/ft-sec
/rzzoo\ rh "f fi tts.292t /n\ lj:i--:, l:' lrO.Orr,) l " I \ Lz \sec/
11-
(1.285
x
:
894,215
1o-1 ;lb. It-sec
Since N*" : 894,215 > 350,000, a vibration analvsis is not required since we are outside rhe range of vortex formatron. Vortex formation has been observed at NRe > 3.5 x 106, but wind velocities encountered would not cause Reynolds numbers that high.
comes
oD:
t(?J--[**"un#.J .l 2w \
In determining wind loadings in this example we used the formulation to compute wind forces:
= \",rO. + where
Equivalent Diameter Approach versus
ANS|-A58.t-1982
oo oD
DD7
= dynamic stress, psi < static allowable stress
Staley and Graven [15] state rhar when dynamic stresses are combined with axial compressive stress. the result can be compared to the allowabie sutic srress. The same is generally true for tension, but one must be cognizant of discontinuity stresses at the locations or irregilar changes of geometry, such as welds. The latter can be
avoided by using stiffening rings. Certainly a more accurate and detailed analysis, such as the octahedral shear stress theory of yield, can be used, but such a detailed analysis can be avoided in most tower designs. A detailed fatigue analysis is mandatory in many aipplicarions and should always be used in case of doubt. Weaver [24] discovered in wind-tunnel tests that vortex sheddins cannot prebently be analyzed as a response spectra beiause
of its random nature and unpredictable motion.
This greatly complicates the study of vortex excitation by use of finite element methods, but efforts are being made.
p:
q.CC,A,
(4-81
in which Ae is
r
computed using the total width of the tower, insulation, ladders, platforms, and attached piping as an equivalent or effective diameter of a cylinber. called the effective or equivalent cylinder. This iquivalent cylinder represents the total wind area. Suih an analysis is called a quasi-analysis, because it is not exact. The equivalent cylinder concept used for conical sections is similar when compared to the exact analysis of a cone. The ANSI-AS8.1-1982 uses a more refined and equally complex analysis to determine the wind loadings. The relationship used for wind force is as follows:
F:
q7G2CrA61
where G2
:
Acr
=
416
:
+ qzcciArr
gust response factor for cladding and compo, nents calculated at heisht Z area of insulation tclaJdingt of tower. and al. external attachments such as platforms. lad ders. and piping rhat resist wind area of the tower shell itself that resists winc
The Engineering Mechanics of Pressure Vessels
The term G7 is given in Table 8 of ANSI-A5S.1-1982 rhat is determined by the following expressions:
Gz
-L1
:
0.65
:-
2.35 (D")os (z/3o1tt"
+
=
1,500
q - 4.5.22:
1,200
For category B, 0.010,
For category C,
D" = 0.005,
a :7.0,2e:
9OQ
For category D,
:
D.
0.003,q
:
10.0,
ze =
700
G2, which is used for cladding and components, varies with height and is a parabolic distribution. The term G is used with the tower shell and only is constant along the height of the tower. Comparing the two methods we set Equation 4-81
equal to the comparable expression given by ANSIA58.1-1982.
F
-
q/GC,A,
-
q7G7C,A,
r
qrCc,e,
We now define the following variables:
Acr
. Arr
Ar
Ar
average value of G7 across the height of the
above more credible. After applying the real numbers for several cases, it is seen that the equivalent diameter method using the
D" = 0.025,o:3.0,2e
:
=
tower.
Also, rarely is y as great as 0.5, making the inequality
3.65 Tz
For category A,
D.
where G21u"ry
ANSI-A58.1-1982 gust factor for flexible structures, G, is more conservative than the ANSI method of using the two gust response factors G2 and G. Thus, being more conservative than ANSI A58.1 1982, one meets the minimum requirements ofthe standard, as it is stated in the title, "minimum design loads for buildings and other structures." Certainly, using the formula for lattice structures, Equation 4-83, is a conservative approach. For designing a tower without a computer software package, the equivalent diameter method is recommended. In such a design, one is faced with numerous calculations, which leads to a greater possibility of error. Also, the use of two gust factors with one varying in height adds considerable complexity to the problem. When using a high-speed electronic computer the use of two gust factors would be a very good method to use, although cumbersome to verify. Certainly, some could argue that with less conservatism a cheaper vessel is produced. Such a consideration must be analyzed in each separate circumstance. For some, the additional manhours may offset the economics of the vessel or time may be the ruling criterion.
EXAMPLE 4.3: SEISMIC ANALYSIS OF A VERTICAL TOWER A client has a vertical tower that is to be moved from a Dlant in Jackass Flats. Nevada to a location northeast of Los Angeles, California. The vessel must be analyzed for seismic zone 4 to determine if it can be moved. This result is to be compared to a wind analysis for an 80-mph wind.
from which
qzcCA:q2C,A1(xQ.+yG)
G-xGzayG G1t -y; > xc'
Now, for many, if not almost all cases,
c>G, This is certainly true as one moves up the tower in computing Gz. It can be safely said that
G
)
Gau,er
Seismic Analysis
V=
ZIKCSW
(4- 106)
For zone 4,2 : t,I = 1, K : 2.0, W : 15,571 lb Since the tower is not of uniform thickness, equation 4-108 cannot be used. Either the Rayleigh equation (Equation 4-97) or a modified form of the Rayleigh Equation, the Mitchell Equation (Equation 4-112), can only be used. For illustration purposes the Mitchell Equation will be applied and then compared to the more accurate Rayleigh method.
238
Mechanical Design of Process Systems
Using values in Table 4-15 we determine the values to be used in Equation 4-112. Connecting piping exerts a concentrated load o12.7 kips at the support point midway in Secrion @-@. using the values in Table 4-15 we construct Table 4-19,
n:
Ee(,f,)'.a,
\2
:
:
:
3,484.0 lb
36
+ Fr =
(0.15)(3,484.0)
:
0.15V s22.60
From Equation 4-115 we obtain
0.673 sec/cycle
Ft) -YYhY
:
13.484
-
D*'*" i=
522.60)
w)hv
515,380
I
Using the more accurate Rayleigh method, Equation 4-97 , the value of T is
:
:
F- : (V -
u00/
T
(1)(1X2.0X0.078X1.434X1s,571)
Using Equation 4-114 to find F,, we have the following:
Fr
Using Table 4-18 we have 111
v: h72 D2
A = !twa" + *Btt;
where
Solving for V we have
:
0.0057 wr,hy
0.734 sec/cycle
in which the Mitchell Equation is in 8.3 % error (which is
quite normal). For application ofthe Rayleigh Equation see Examples
4-2 and,4-4.
Now, we must solve for the bending moments induced by the seismic forces. First we find the base shear using Equation 4-106. To accomplish this we have the followrng:
1""'r
(r.i" -
l:125 l.U
=
Flexibility facror
1.t25
< t.5... K -
= C: -]= 15(l1tr':
W)h). F,- and V, we solve for the seismic moments using Eouation 4-116:
MM,
-
M3 : Ma : M5 : M6 = M7 : Ms :
2.0
O.OZA
The characteristic site period, T,, is determined by soils consultant to fall within the following range:
To solve this equation we must set up the table shown
in Thble 4-20. After determining the values for W, h",
: : Mrr : M,
M16 a
M12:
Vxi Ly_r
+
Fx Ci
Dt
: 2.770 2.'770 : 8.138 10.908 9.s88 20.496 3.810 24.306 16.72o 4r.026 : 9.240 50.266 : 25.sm 75.766 : 103.966 : 13r.624 : rs7.304 : 166.828
(0.30)(5.083) + (0.49)Q.s42) (0.49)(7.50) + (1.19X3.75) (1.68)(5.417) + (0.18X2.708) = (1.86X2.00) + (0.09x1.00) = (1.95X8.00) + (0.28)(4.00) = (2.23X4.00) + (0.16)(2.00) (2.39X10.00) + (0.32)(s.00) (2.71X10.00) + (0.22X5.00) 28.200 (2.93)(9.083) + (0.23)(4.542) 27.658 (3.16)(8.00) + (0.10X4.00) 25.680 (3.26)(2.917) + (0.01)(1.458) 9.524
0.5
T
O ?14
_l s - ;;u.)u =
will
use the lower value
1.468
> 1.0 in which Equation 4-tl3b
applies. Thus, we have
S
:
: s: S
1.2
+ 0.6 El
\TJ-
1.2 +0.6(1.468) 1.434
of 0.5. Now,
0..
El' \TJ
-
0.3(1.468f
The wind moment for an 80-mph wind was calculated ro be 106,716 ft-lb. Since 166,828 ft-lb > 106,716 ft-lb seismic phenomena govern. The skirt and base plate analysis is identical for seismic and wind analyses. Just as in Example 4-2, the seis-
mic forces and moments are used instead of the wind forces and moments. In the case of this tower a thicker base plate was welded on, the number of gusset plates were doubled, and anchor bolts of a high strength alloy were used to meet the seismic criteria. In an earthquake zone other than zero, a comparison of seismic to wind should always be made.
t -
The Engineering Mechanics of Pressure Vessels
Table 4-19 Numeric Integraiion ol Period ot Vibralion, T sec/cycle
whv kipsfft
Aa 1
.00
1.506
o.567
0.878
5.840
0.820
0.939 0.329
0.100 o."t45
0.067
0.1r7
0.543
0.607
0.265
0.552
0. 168
o.278
0.125
0.097
0.161
0.r24
0. 161
o.414
0.3t2
0.998
0.998
0.997
0.997
0.986
0.986
0.973
0.973
x l0
0.904 0.021
0.006
1
0.763 0.0649
0.002 0.504
0.1175
0.0001
0.160
0.040
9.541
0.0080
0.020
0.504 0.0004
x
0.0015
0.016
0,0004
1.234
0.0010
o.763 0.007
0. 151
1.000
0.035
0.007
0.285
1.000
0.904 0.037
0.276
1.000
0.010
0.0,14
0.155
1.000
0.033
0.610
0.t42
1.000
u0i
o.219 0.045
0.079
1.000
l9l'to"
0.054
0.597 0.923
E
WAB/H
2.103
0.091
2.'7
WAa +
P
H
0.160
0.0412
0.380 0.000
A:0.,140
B:0.261
10-6
5
240
Mechanical Design of Process Systems
Table 4-20
Wind Load Distribution x"'o-ri. Lzt
w\-r kips
ztttp
+
\:
+
+ +
+
+ +
63.2
0.542
l. l9
56.7
30.73
0. 18
0.284
53.0
15.05
0.09
1.0
48.0
48.00
0.28
0.645
42.0
27 .09
0.16
1.613
15.0
56.46
0.32
1.550
25.0
38.75
0.22
$
2.581
15.5
40.01
0.23
€
2.493
'7
.45
0.10
1.109
1.5
l .66
0.01
207
.':
->s,* i +2s.k1.0'
-l
/: --> rsr
..:
'+
G
$
+ @
-+
+
3.289
Fx
.86
-\3
+
w,h, ffi
!r 72
o 5l
v,
*,1-u
0.49
2.770
2.770
1.68
8.138
10.908
1.86
9.588
20.496
1.95
3.810
24.306
2.23
16.720
41.026
2.39
9.240
41.026
1
2s.500
15.766
2.93
28.200
103.966
3.16
27
.658
131.624
3.26
25.680
157.304
9.524
166.828
2.7
15.571
.O
17
5
15.38
3.270
3.27
*,oTi
The Engineering Mechanics of Pressure
=
EXAMPLE 4-4: VIBRATION ANALYSIS FOR TOWER WITH LARGE VORTEX-INDUCED DISPLACEMENTS
D.
A phone call from a plant manager reveals that an existing tower needs to be analyzed for wind vibrations. The tower was designed, built and installed overseas and is vibrating so badly all the natives drove off the plant site in fear of the tower falling over. The tower with the appropriate wind load distribution is shown in Figure 4-44. The tower is divided into wind zones at 30 ft,40 ft, and 75 ft and according to shell diameter and thickless. The variation of wind zones based
D"
Zone 1-Sections 7. 8. and 9
D"
:
in. + 2 (4) in.] + [6.625 in. + 2(3.5) in.] [2.375 in. + 2(3.0) in.] + [4.5 in. + 2(3) in.]
D" = 40.00 + D"
:
72.5
in.
13.625
:
+
6.042
4.521
ft
: D. :
in. + 2(4.5) in.] + [3.50 in, + 2(4) in.]
[24.50 33.50
in. + 11.50 in.
D" = 45.00 in.
=
3.75 ft
Zone 7-Section I D.
:
in. + 2(4.5) in.l + [6.625 in. + 2(5) in.] + 2(4.5) in.] + [6.625 in. + 2(5) in.]
136.625
+
[3.50 in.
in. + 16.625 in.
D"
=
46.625
D.
=
104.875
in.
:
8.740
+
12.50
in. + 16.625 in.
ft
Moments of Inertia
[32
+
in. =
8.375
+
10.50
r:#(D".-Di) \ :
ft
:
Zone 2-Section 6
De:[32in.+8in.] + 14.5 in. I : 4.042 ft
2(2)
in.l
48.5 in.
-
hl36.62s)4
(36.000)41
=
5,876.389 in.a
0.283 fta
Transition Piece-Section 2
Referring to Figure 4-45, Zone 3-Section
5" :
5
[25.25 in. + 2(2.5) in.] + [3.5 in. + 2(3.5) in.]
D"
=
30.25
in. + 9.50 in.
D"
:
50.25
in. = 4.l88ft
*
+
[4.5 in.
+
2(2.5) in.]
10.50 in.
Zone 4-Section 4
D" : D" :
2.521
+
D"
:
125.25
=
30.25 in.
req
+
2(3.5) in.]
in. + 9.50 in.
*
10.50 in.
18.375
+
12.375
2 cos 26.565' 17.
190
+
=
D.q
34.380 in
r, = #(34.380)4 -
(33.630)11
:
0.279 fta
:
5791.250 in.a
-
e4.00)11
:
r,400.ri2
\ = L64Kz4.i5)o -
(24.00)11
=
2,133.181 in.a
\ : :
3
in. + 2(4.5) in.l + [4.5 in. + 2(2.5) in.] +
[3.5 in. 34.25
2(2.5) in.
ft
Zone 5-Section
9" =
,"r:(
Iz 25.25 in.
241
Zone 6-Section 2
on the shell diameter and thickoess is necessary since the
tower's section moment of inertia will vary. To begin the analysis we start with defining the effective diameter of each section as illustrated in Figure 445. Thus we have the following:
54.25
Vessels
-
1,
Kz4.sq4
0.068
in.a
fc
0.103 fta
Mechanical Design of Process Systems
* ";
".".
'
%: *,*
l\' '"*
T(
Figure 4-44. Tower wind ensemble.
The Engineering Mechanics of Pressure
ry'essels
Wind Moment Calculations Sections
M2
:
I
and 2
es8.4zs)
(#.
tr.r) * o,uno.rrrr(U)
+ 4,450
Mz: Mz : Figure
445. Tfalsition
piece of section 2 of Figarc
444.
lL,99O.762 + 18,158.661 34'599.423 ft-lb
=
(788.425)(15.2W
+ M: M:
: 1g- [(25.ooy - (24.00)41 : :
0.139
0,177
-
@4.oof1
:
3,667.316 in.a
tr
: =
17.00)
+
17.0O)
+
Q,690.r72)(6.75
+ 4,450 + (1,453.50)
25,394.381
+
63,891.585
+
ht\
tt
4,450
+
12,354.75
106,090.716 ft-lb
Section 3 and 4
lvl4
fll
u.= fir
2,888.744 in.a
4,450.00
Sections 2 and 3
M3
I.
+
=
(788.425)(32.209
+
10.00) + 10.00)
+
(2,690.172)Q3.75
+
(1,453.s0X10.00)
rroi
+ Q21.5s2\lrl
+ (268.541(+)
Section 7
Referring to Figure 446
_ ," -'* =- lrs.as + n.azs\ :14.174in. ,
\-ffi/
+
D.e
y
:
b: I8
28.348 in.
f,11zt.z+ty4
: =
-
2,704.843 in.a
= #rc2.00)4 =
r,
=
0.565
:
0.130
fll
=
r1,i1r.wzin.a
- eo.6zr4l :
8,2e2.684n.a
-
(30.00F1
fll
fftfrz.oof 0.2t00
(27.72141
ff
Figure 4-46, Section 7 of Figure 4-44.
Mechanical Design of Process Systems
Mt:33,278.631 + 90,793.305 + + 3,607 .76 + 402.821
=
Mq
147 ,067
4,450
+
14,535.00
Sections 7 and 8
M8
.517 ft-lb
:
+8) + (2,690.172X68.833 + 8) + 4,4s0 + (1,453.50X35.083 + 8) + (721.552)(30.083 + 8) + (268 .547)(26.583 + 8) + (349.41 l)(21.083 + 8) + (39.328Xr7.583 + 8) + (522.662)(4.542 + 8)
(788.425X67.292
Sections 4 and 5
:
M5
+ B.O) + (2,690.172)(43.7 s + (1,453.50x10 + 8.0) (721.552)(5 + 8)
(788.425X42.2o9
+ +
8.0) + 4,450
+
(268.547x1.5
-
8)
-
(J4s.41)
l:l
+ Mr =
\21
+
:
M:
M5
=
lll \zl
(3e.328)
Ma
39,586.031 + 139,216.401 + 4,450 + 26,163.00 + 9,380.176 + 2,551.197 + 1,397.&4 + 19.664
=
:
Me
:
+
/^\
-, Ms
:
:
+
45,893.431
+
160,737.'177
+ 4,450
+ 37,79r.00 + t5,152.592 + 4,699.573 + 4,192.932 + 334.288 + 2,090.648
M6
=
:
Mz
M7
:
+ +
:
{3e.328X8.s
53,054.695
+
2t,706.449 691.504
+ 2.gt.l,) + ,Zt+.OOr(2.717\
\z
I
=
401.003
413,166.837 ft-lb
Wind Deflections
(788.425Xs8.209 + 9.083) + (2,690.r'12)(59.75 + 9.083) + 4,450 + (1,453.50)(26.0 + 9.083) + (721.552)(2r + 9.083) + (268.547)(17.5 + 9.083) + (349.411X12 + 9.083)
-
Ms
17s4.042\A
ft-lb
2'7Q,892.241
Sections 6 and 7
M?
ftib
61,661.931 + 214,541.217 + 4,450 + 66,861.00 + 29,583.632 + 10,070.513 + 11,181.152 + 1,120.848 + 8,079.832 + 5,215.709
\21
Mo
390,632.690
5.292 + 2.9 17) + Q,690.r72)(.1 6.833 + ).:917) + 4,450 + (1,453.50)(43.083 + 2.9t7) + (721.5s2x38.083 + 2.9t7) + Q68.547)(34.583 + 2.9t7) + (349.41r)(29.083 + 2.917) + (39.328)(25.583 + 2.917) + (522.662)(r2.sQ + 2.917)
lll
rs22.662t
59,362.095 + 206,693.985 + 4,450 + 62,621.t41 + 27,478.86s + 9,287.16r + 10,161.920 + 1,006.128 + 6,555.227 + 3,016.168
Q 88.425)(7
222,7&.113 ft-Ib
(788.425)(50.209 + 8.0) + (2,690.172)(5r.75 + 8.0) + 4,450 + (1,453.50)(18.0 + 8.0) + (72r.5s2)(13 + 8) + (268.547X9.5 + 8) + (349.411)(4 + 8) + (39.328X0.5 + 8)
/n\
l:l \zl
Sections 8 and 9
Section 5 and 6
M6
17s4.042t
+
332,94'1 .484
r 9.083) + rszz.ooz, (9 983) \z I
185,172.609
+
7,138.785
2,373.669
ft-lb
+ 4,450 + 50,993.141 + 7,366.632
1B),
'
t4.176
: !z
_
x
0.00113
[r:.+ZS.:SZtr
t0"x0.28J)
+
8
2
)
0.04081
ft
ft (17)'
(4.r76
[
r:) , +,+sOl
\
l0)(0.068)
(r,4s3.5_0)(17.0)
821
(10F
l{2,+tt.serot
t3
.o)
+34,s2s.42]:
l1+,vzz.ost11ro1 Y:: Ar?6t-To"xorort :
E The Engineering Mechanics of Pressure
(99o.o99xro) _
*,
ff
(sf
(4J?6
x
8
(8f
_
001658
.
-'6 -
3
t+'t.OOt.SZ]
*'
2 l-= 0.00989 ri
(56.50X9.083) ft6.833.596)(9.081)
x t0\0260)t
14.176
+
(572 730x9 083)
6l
(71.583X8)
3
(4.176
+
8
(4.176
x
Zzz.lo+.tnl
*'
2
=
82j
-
18
(7s4.042)(8)
821 +
-" -
821 l7)
(13.5)(
*
6
(1'453 50)(17)
6l
0.00507
ft
=
0.00201 ft
z
ro.rnn.or]:
0.05519
ft
(30.50Xr0) ft+.erz.owxror \4.176 x 10"x0.103)[ 2
'
, +
-
,4.
(990'0?9x
6l
t0)
106.090.721
:
(40.50)(8) [rs.lzz. rvolr x to\rn t rorl Z
0.07709 rr r
17,6,
-, --- 6
{388.738x8)
'
+
, ,, +, l+/,uo ".1.s2l =
I
Lz
0-09071 rt
)
3.58r(2.g t67 [rS. rOO.:OStrZ.l rOrr x to"1o,+ogt 2 tuo 1+, 17
: total deflection at top of vessel : \LtA, 2y, + \: 0.743 ft : 8.910 in. at top for static gust wind
Referring to Figure 4-47 , we determine
[tf.+la.sertr t r r
*
10)(0.565)
I
39!.632.69]
looxol68)t
(4.176-,.
0.143 ft
* 121!!!)t2!tfr)+ J90.632.691 = 0.05r74 ft 6)
ft
0.012
a r
:
332,s47.481
t274.u2\2.st667,
+
't
:
(2.gt667tt [rt. roo.:os x z.r reor I t+.tzo x ronxo,+oott :
-
=
ft2,+oo.rz r'11r;
6l
+270,8s2.24rf
[tr.+oo. rzox t' - ,aJ6 v 1g\05sr[ .l
x
+(7s4'y2)(8) + n2,s4i.481:
-'* -
(8),
+
2io.8s2.z41f
0.0r I 15 ri
)-
10)(0.260)
(572.730)(9.033)
+
+
2
ko,:ro.s:+Xs)
Af?6 x ro)(oJ??)-t t522.66UG)
245
622.662t8t+ 222.764.1131 r, 'T ".. ,., . "l = 0.t3055 rt
fr
ks,szz.rso)(s)
t06x0x9)t
(388,738)(8)
+
106,090.721 _.-l:
Vessels
0.09560 fr
(48.s0x8) ft6.310.934)(8) (4.176 x t0')(0.177)[ 2
:0 M, : (4.71)(6.961) : 32.786 kip-ft Mz : 32.786 + (4.823)(8.789) : 75.u5 kip-ft M4 : 75.175 + (7.533X13.25) : 174.987 kip-ft Ms = L'74.987 + (10.013X9.00) : 265.104 kip-ft M6 : 265.104 + (12.023)(8.00) = 361.288 kip-ft Mi : 361.288 + (14.253X8.862) : 487.598 kip-ft Mr : 487.598 + (ri.693)(8.221) : 633.032 kip-ft Ms : 633.032 + (21.233)(5.458) : 748.922 l
T:M/I Mt T, '' = tz -
32'786 0.279
:
rv.5t2.54
246
Mechanical Design of Process Systems T^
:M.:
T4
:Mo:
T6
M'=
-q-
4,987 _ 1,698,902.91
265,104 _ |,907 ,223.02 0.139
I5
:Mu= I6
T-
17
0.103
r4
=
75,t75 _ I,105,514.71 0.068
I3
:Mr: 11
361,288
_
o.t77
487598 _ 0.130
2
,041 ,r7
5
.14
3,7 50,7 53.85
---->4.71k T8
:Mt= :M,: Ie
=M'o= Ie
Tro s.
--r.2.71k Sro
------€)
=
_
|
_
1,872,305.00
0.565
Is
-------e
633,032
'748,922 0.400
,r20 ,4r0 .62
782,@ n /An - 1,956,660.00
M dx/I
_
(1,956,660.00
+
1,872,305.00)
(1.458)
:2,791,315.49
----------->2 .48x
(1,872,305.00 2.01k
+
t,r20,410.62)
2
------e
8,167 ,120.93
->
^"2
(1.120.410.62
+
3.750.753.85) \'-_:___:__________________:__________rv,,,r
2,23k
(5.458)
-> -------€
^ ^^"
:20,022,921.55 S7
_
(.3,75O,7s3.8s
+
2,041,175.r4)
+
1,90',1
(8.862)
344k
-----e
: ,5
-->
Sr:
-----l3.54K
(s) (;\
Figwe 4-47. Tower vibration ensemble.
S5
_
15
(2,O41,175.14
,793 ,592 .64
(1 ,907 ,223
.02
+ 2
:
,223.O2) (8.00)
2 15
' \-"/ ----------> 1.91x
664 017
16,227,566.69
| ,698 ,902 .9r) (9.00)
t The Engineering Mechanics of Pressure
Sr:
1,105,514.71)
2 18
$=
+
(1,698,902.91
(13.25)
. _ lE_----_-2-
,579 ,266 .73
+
(1,105,514.71
lr7,512.54)
2
(8.789)
^ rt
(117,512.54\ a
=
172,393,524.9
=
--------------T-
Po:
6.961\
+ s6.&5.39:.32)
(30.981.357.97
Ps: 1M1
dx)/!
2,791,315.49
+
P4
+
(56,645,395.32
72,438,9U .96)
2
_
:
10,958,436.42 30,98r,357 .97
+
30,981,357 .97
+
25,ffi4,037.35
+
15,793,592.&
+
16,227 ,566.69
+
18,579,266.73
20,022,921.55
P::
(8.00)
(88,666,554.65
88,666,554.65)
+
107.245,821.4)
z 1
,297
-
(to7,245,821.4
+
1
t2,620,4t4.7)
2
Pz=
(112,620,414.7
+
113,029,417.1)
2 785,374,239.6
88,666,554.65
88,666,554.65
: 2,034,868.99 w : 2,034,868.99 + 37,523,072.96 ttto
rc7,245,82t.4
tu,245,821.4 +
5,37 4,593.25
=
112,620,414.7
lL2,620,414.7
+
ps
409,002.40
rt3,o29,4r7.r
pt
2,O34,868.99
lt4 458)
14
39,557 ,941 .95
39,557,941.95 211,951,466.9
+
172,393,524.9
=
: :
211,951,466.9
+
388,274,143.9
@0,225,61O.8
ffi0,225,610.8 |,116,563,144
+
516,337,533.2
|,116,563,144
+
724,974,941.7
+
1,297,919,492
: t'.s : :
,_^. ---:---------:- | l -4)x) Pro: 2.79t.315.49.-
,U2 .96
:
t4 =
)u
Q,79r,3r5.49 + 10,958,436.42)
,,..., lr5'zJ)
,919,492
72,438,987.96 72,438,987 .96
+
(8.789)
966,202,r7 5.0
56,&5,395,32
56,&5,395.32
(72,438,987 .96
8,t67,120.93
10,958,436.42
37 ,523
$.862)
724,974,941.7
2,791,315.49
o=(*,
$.22t)
516,337 ,533.2
Q9,002.40
e, = Ds, =
30,98r,357.9't)
:388,274,143.9
5,374,593.25
Sz:
+
(10,958,436.42
ry'essels
=
:
1,841,538,086 1,841,538,086
3,139,457,578
= 3,139,457,578 + 966,202,175.0 = 4,1O5,659,753
(6.961)
248 p2
: :
Mechanical Design of process Systems
4,105,659,753
+
785,374,239.6
t:0]1'868 (4.32 x l0r)
li :4.it0x
aft =
4,891,033,993
r,,:
'
l44Ei
Yz:
4,891,033,993 144(30 x t05
The tower section weights and displacements are combined in Thble 4-21 to determine the period of vibration of the tower.
4,105,659
,7
53
(43' x tOt 3,1,39,457 ,578
(4.32
t5 -
x
l0e)
: l.lJ n = lj-)v
:
0.950
:
I,841,538,086
1bt =
-..T
11.405 in.
3.40 d
0.727
ft =
8.721 in.
0.426
ft :
5.1 15 in.
L= 16";-=re.24tt
. = (,+*) $740) +(,uaA.,r',
0.258
ft :
3.102 in.
fy
:
:
0.139
ft :
1.667 in.
V,
: fvD S
0.049
ft :
0.589 in.
@tt]ott
J9-
First critical wind velocity, V,
ln.
":z1 |,1t6,563,r44 : 600,225,610.8
2rr,951,466.9
$8 16
39,557 ,94r.95
w2t16
0.006in.
q6
(43' x iort
Y8:
ft :
r0
:
= ,.,,,
From Equation 4-101, at resonance vortex shedding frequency
:
to 91)(7.1221
U.l
:
:
natural frequency
34.540a Sec
23.550 mph
Considering the top portion (Section 1) we have
:
0.009
ft
v-
= 0.1l0 in.
(o
eT(lfa)
u.z
=
423s
L sec
=
2E.eo mph
Table 4-21
Values for Determining Tower's Period of Vibration Detlectlon 1_!:-! 13.59
w 4.7 r0
869.880.95 14.711.26 064.06
1 54n
64.008.90 1.289.33 23.63t .20 .60 6.231 .00 3.724.10 2,029.60 389.40
1.9i0
19.10
0.19
8.72
710
5.r2
2,480
l0
2,010
1.67
2,230 3.444
3.
0.59 0.11 0.01
Dtr : First Period of Vibration, T
ILwy' i 11. t82.441.8r) r = z,r \/etrwv = zr 1/(386.4X114,020.23, = J tou
t
1.03 sec/cycle
of=
O.9j Hz
114,02s.23
65.01 l.7 t
19.316.10 6.219.25 1.197 .46
Dwy, =
r,182.443.81
The Engineering Mechanics of Pressure Vessels
Since the field measurements indicated an air velocity at resonance to be 30 mph and a stack deflection of 13 inches, this analysis agrees with empirical results. From the calculations for the first critical wind velocity, it appears that the larger diameter of Section t has a larger influence on this deflection. For this reason we use the top I/+ of the tower rather than the top 1/:. Now,
Y1
:
6.25;
Vr
:
(6.25)(28.90)
:
180.63 mph
A tower that has been fabricated and installed in the field is beyond design changes. Unlike stacks (see Chapter 5), vortex strakes are difficult to install on many towers and impossible on others. Shortening the tower height is impractical, since the tower's internals are necessary (unlike a stack). Consequently, the only resolution is to mount guy wires to the tower's upper section (normally 2/3 the height). Except for special applications, guy wires are to be avoided in practice. They use a lot of space and plant maintenance people sometimes must temporarily remove one or two to gain access to an area for equipment installation or some other reason. Problems then may arise in keeping the tower from falling over during this temporary time interval, remembering to reconnect the guy wire(s), and making sure the wires are properly tensioned once they are reconnected. Despite these disadvantages, guy wires were essential in this application. EXAMPLE 4.5r SADDLE PLATE ANALYSTS OF A HORIZONTAL VESSEL
2
=
r\36)\'l
expansion of the vessel, so only uniform compression is considered in evaluating the saddles. Even though a Zick analysis indicates that the vessel is grossly overstressed, the saddle in Figure 4-48 is to be evaluated. To analyze the saddle plate, refer to Figure 4-48 c. Each section of the saddle plate, A-B, B-C, C-D, is considered separately. Each section supports a portion of the vessel weight indicated by the dotted lines. Sections A-B and C-D support equal weights. Section
x
:
A-B
4.27
and
ft :
C-D
51.24 in.,
_ o,12r'lst.zq _
2 |
=
15l.2ar1l
l(361 j
259.52 gal in one head
From Equation A-1 in Appendix A the partial volume of liquid in the cylindrical portion is calculated.
.,
(72)2(150)(l2t
2
lott+0.+St ^ --l
L 180
:
9,351 ,647 .46 in.3
=
40,483.32 gal
Total fluid volume above Section
Y:
4O,483.32 gaI
:
+
I
A-B
2(259.52) gal
5,481.22 ft3
=
Ri
:
6.0
ft = i2rn.
is
4t,002.36 gal
The total fluid weight is then
Wres :
Wrco
=
t5-48t.22t fr' tOZ.qt Ib,
rr
.+r
478,839.22 tb
Metal Weight Above Each Section, A-B and C-D For outside surlace on h.ud, thuiur" V, ir,. tt'i.k,
:
.25 )(7 2 .5
), _
"
-
62,434.25 in.3
The inside volume in the head was determined in computing the fluid volume as being 59,948.76 in3. The metal volume in one head is then
VM
:
62,434.25 in.3
-
59,948.76 in.3
:
2,485.49 in.l
For two heads,
Yu =
2(2,485.49)
:
4,970.98 jn.3
The metal volume in the cylinder portion above Section A-B is determined as follows:
For outside surface,
From Appendix A, Equation A-8, the fluid volume in A-B is as follows:
vessel above Section
)z
59.948.76 trl.3
2r\36
A proposed horizontal vessel design shown in Figure 448 is fully loaded with corn syrup used by a confectionery manufacturing plant in Fayetteville, Arkansas. The corn syrup has a specific gravity of .y = 1.4 un6 . ut 90"F. The thickness of the head and shell is t/z in. since the corn syrup is at 90'F, there is practically no thermal
2
_
(72.5)2050)(12) 2
=
l""l;';"' - o'r]
9,512,090.41 in.l
250
Mechanical Desisn of Process Svstems
It
I50
TAN/TAN
T
lrot I
lI
T
i\
A,
f.i.,--" i"['i"'
i-8 wi=3 46
tttl
tl
ABCD
Figure 4-48. Horizontal vessel containing corn syrup.
The inside volume was determined in computing the fluid volume as being 9,351,647.46 in3. The metal volume in the cylinder is then
V:
9,512,090.41 in.3 160,442.95 ir.3
:
-
9,351,647.46 in.3
The total metal volume above Section
vM
-
4,970.98 in.r
+
160,442.95 in.3
A-B
:
lcl
rr AB -
vvcD -
Section
B-C
525,651.36 lb
is
165,413.93 in.3
r : {#["
r- -
.lb, =
rn.J
46,8t2.14 lb
Combining with fluid weight the total weight,
W
: :
46,812.14 lb + 478,839 .22 lb 525,651.36 lb
For each saddle,
lb
:
t#l :
135,483 43
in3
For total volume,
v = 2(135,483.43) : 1r65.413.93) in.J (0.283)
262,825.68
Q
Similarly to Section A-B, for the head, the liquid volume is determined from Equation A-7 in Appendix A.
The metal weight is
wy =
:
270,966.86 in.3 for one head
For both heads,
v:
2(270,966.86)
:
54r,933.73 in.3
Liquid volume for cylinder portion is
v : :
r(72)'?(r50)(r2) in.3 10,611,534.46 in.3
-
2(9,351,647.46) in.3
{ The Engineering Mechanics of Pressure
The total liquid volume above Section
Vr :
10,611,534.46 in.3 11,153,468.19 in.3
=
+
B{
vru
is
Ws =
For outside surface on a single head, usin€ Equation
:
A-7
- r(7?.s\2[rt * - tr#J :
=
137,097.43 in.3
-
135,483.43 in.3
=
1,614'35 in.3
For two heads,
:
3228.72 in.3
:
487,258.58 in.3
B-C
is
lb
.^
-^^-. (487.258.58)in.i (0.2833)
ft3
137,894.18 lb
in.3
w,- _ (11.151,198.I?)in.r | rn.3
(62.4)
,723
: =
E
(1.4)ftj
563,869.78 lb
The total weight above Section
Wr
Vr,,r
+
251
The total liquid volume above Section B-C is
B7,oe7.7e
The inside volume was determined from calculating the liquid volume as being 135,483.43 in.3 Thus the metal volume for a single head is
Yu
484,029.86 in.3
The total metal weight above Section
541,933.73 in.3
Metal Volume Above Section B-C
u
:
rGssels
137,894.18
lb +
B-C
is
lb
:
563,869.78
701,763.96 lb
For each saddle,
2(1,614.36)n.3
:
3,228.72 in.3
Wrc:Q:
701,763.96 lb
:
350,881.98 lb
The metal volume for the cylindrical portion is determined using Equation A-l and the total volume ofa cylinder as follows: (72)z(r50X12)
rQz.0)2(15O't02')
V:
Saddle Plate Buckllng Analysls The critical buckling stress for a plate is determined from Equation 4-17a.
19,963,181.93 in.3 for inside volume
(4-r7a)
For outside volume,
_
r(72.5)?(150)(12)
*f0a6.'12"\
V=
(72.5)2(rs0)(r2)
where
2
=
:
:
+ 2hG
-
1)
(12)(3.46X0.s) + 2(0.sxls
= 0.59
-
-
1)l
in.
19,963,181.93 in.3
For both sides of centerline in Figure 448 c,
Yu =
ldi ts
(12x3.46X0.50)
20,205,196.86 in.3
20,205,196.86 in.3 242,O14.93 in.3
=
h = 0'50 in'
I
- 0.551I
The metal volume is Vr,a
h
2Q42,014.93)in.3 484,029.86 in.3
Combining both the cylindrlcal and head metal weights we have
AIso,
: Kt. h = (1.28X0.5) = 0.64 in. (use.0.597 in.) b.
(+1s)
Adding more length to web plate will net. increase the local buckling strength for pure compression. The same also holds for bending and shear. Substituting the value of b, above into Equation 4-17a ws have
252
Mechanical Design of Process Systems
vc,_ -,-____ x- 106) :4.980.860psi ,,1, _ 1l l(3.46x l2 )1,
Horizontal Reactlon Force on Saddle
(1.28)r, (29
From Equation 4-19 the horizontal reaction is
\ e/\ 0.s I
Substituting this value into Equation 4-18 we determine the buckling load for compressive loading as follows:
Fs
:
n(A, +
FB
:
(4)[7.5 + 2(0.597)(0.5)
2be
Since 161,321.4
tJo. lb <
:
z-
- B * sin B cos p
(4-18)
:
262,825.7
-:)
'r -f = no"
=
161,321.389 lb
o=
(rso
lb <
^ v:
2(262.825.68)
we must use more stiffening plates t/z-in. saddle plate. Now
FB."
F:Q
350,881.98 lb
if
we are to use a
351,000 lb
+
350.881.98
z
:
:
438,266.67 lb
8s,294.56 lb
The effective area resisting this force is
From Equation 4-18 we have 351,000
:
n[7.5
+
^"
2(0.597X0.5)]o".
= (,u),. =
(9
(o 5o)
:
12 ss 1n,
This results in a stress of 351,000
8s,294.56 tb: _ ^-^ ^_ /'uJ6 60 PSr o= tzttg irtl
n
The effective plate width normal to the web plate axis is
d"
:
where
di (0.25
:
0.91\'?)
\ = (l)[9" \w,/ \o*i ^
w"
+
Referring to Table 4-6, the allowable stress for A-36 is 0.60 o, : 22,000 psi. Since 7,058.86 psi < 22,000 osi. the saddle is sufficient for the horizontal reaction.
=
1{OTATION
(u*;)(':'-'*f':
(3.46)(12)(0.25
+
0.91 (0.41)'?)
:
oo' 16.74
dimension from saddle centerline to tansent head (Figure 4-2) ft, in. effective area of concrete, ft2
1n.
b
n=
10.392(
l2)
=
16.74
7.449 -use E stiffeners
BP
BPW C
o^, -8= FB
=
:
l5l'ooo
:
43.875.0 osi
(8)[7.5 + 2(0.597X0.s)](43,875.0) 2,842,W7.0 lb
Since 2,&42,047
sufficient.
lb > >
351,000 lb, eight stiffeners are
CA:
c.:
cs=
of
plate width (Equation 4-15) in. bearing pressure, psi base plate thickness, in. constant for bolt torque (Equation 4-66), dimensionless; friction coefficient (Equation 489) dimensionless; structure period response factor (Equation 4-106) dimensionless corrosion allowance, in.
critical damping factor (Equation 4-90), dimensionless
compressive strength of concrete (Thble 4-7), psi
The Engineering Mechanics of Pressure
D= Dr : D. : D,
=
E:
F=
F; : f. :
f, : Gr : Gg
=
G* : H:
I:
I" =
K: k: K' = Kz : L:
L" =
M:
m: Mc : Mr : N: P
Pu
: :
R: Ri : & : r: Q:
diameter (Equation 4-27), in.; dynamic magni fication factor (Equation 4-9 1), dimensionless
effective wind diameter (Figure 4-22), in. outside diametet in. inside diameter. in. welding joint efficiency (Table 4-2), dimensionless: modulus of elasticity. psi wind force (Equation 4-94) bold uplift force (Equation 4-39), lbr natural frequency of a ring (Equation 4-100), Hz vortex shedding frequency Equation 4-101, Hz dynamic gust response factor, dimensionless gusset plate height (Equations 4-39 and 4-63), ln. gusset plate width (Equation 4-63), in. depth of vessel head (Figure 4-2), in. moment of inertia (Equation 4-24), in1 ;occupancy importance factor (Equation 4-106), dimensionless
qF
:
g:o
: :
S
T=
: t6q : t8 : tr, : ( : vo : vr : Tr
=
W=
coefficient of buckling for shear (Equation 415 and Figure 4-3), dimensionless dimensionless parameter for concrete (Thble 4-
xO =
of effective area of
7) plate buckling coefficient (Equation 4-15), dimensionless
velocity pressure coefficient (Thble.4-9 and Equation 4-78) length of a horizontal vessel from seam to seam (Figure 4-2), ft, in. effective column length (Equation 4-19), in. bending moment, in.lb, ft-lb bolt spacing (Equation 4-39), in. compressive bending moment in the shell of a horizontal vessel (Figure 4-2), tt-lb tensional bending moment in the shell of a horizontal vessel (Figure 4-2), ft-lb number of anchor bolts (Equation 440), dimensionless
buckling load for compressive loading (Equation 4-18), lb6; probability of exceeding wind design speed during n years (Thble 4-11) and Appendix A), dimensionless annual probability of wind speed exceeding a given magnitude-see (Appendix A), dimensionless mean radius of shell (Figure 4-2), ft, in. inside vessel radius (Equation 4-13), in. outside vessel radius (Equation 4-73), in. inside radius of vessel (Figure 4-2), ft
reaction at saddle (wl2),
lbl
253
velocity pressure of wind on structures (Equation q-i6), rcJf( basic wind pressure at 30 ft, lbrift'? Strouhal number used (Equation 4-102), dimensionless; structure size factor (Equation 482)
bolt torque as defined (Equation 4-66), in.-lb exposure facior for wind (Thble 4-11), dimensionless
compression plate thickness (Equation 4-63), in. gusset plate thickness, in. head thickness (Equation 4-7), in. shell thickness (Equation 4-1), in. theoretical ovaling velocity (Equation 4-102), mph or ft/sec first critical wind velocity (Equation 4-94), mph
v30
con-
moment of inertia crete, in1
Vessels
x.t
:
y= Z:
Z=
basic wind speed at thirty feet used as design wind speed (Equation 4-75), mph vessel weight (Equation 4-40), lbr static deflection of a spring acted upon by a force (Equation 4-90). in. displacement as a function of time (Equation 490), in. total lateral displacement of tower (Equation 4-88, Figure 4-21), in., ft elevation or height above a reference point, such as the ground (Equation 4-74), ft reference height in which basic wind speed is considered (30 ft or 10 m), ft
Greek Symbols
a : ir -
(tr 1180)(012
B=
-
+ B/20) (Equation 4-6), de-
grees
A= 6; = d
:
(180 012), degrees (?./180x5di 12 30), degrees lateral translational deflection oftower, (Equation 4-88 and Figure 4-26), in. angle of contact of saddle with shell (Figure 41), degrees, radians; rotational displacement
t
of tower (Figure 4-26), degrees (t/bxE/ocil used in Equation 4-18, dimension-
\ = less p : radius of gyration : (I/Af 6 = general term for stress, psi o" : allowable stress values (Table 4-3) psi d. : allowable stress induced on concrete (Equation .5
ogp
=
4-40), psi; general tern for compressive stress (Equation 4-16), psi critical stress in a flat plate defined in Equa-
tion 4-15, psi
Mechanical Design of Process Systems
: oE oP
o. ow oy
: : : : :
z=
elastic buckling stress (Equation 4-16), psi; 28-day ultimate compressive strength of concrete (Thble 4-7), psi stress due to weight, lbr pressure stress induced by either internal or external pressure, psi; longitudinal stress in Equation 4-67 , psi tensile stress in steel, psi stress induced by wind or earthquake response spectra, psi minimum yield stress for a ductile material, psi Poisson ratio for a given material, dimension-
Building Officials, Unlform Building Code, Whittier, California, 1982. 11. American National Standards Institute, Inc., "ANSI A58.1-Minimum Design Loads for Buildings and Other Structures- 1982," New York. 12. Kuethe, A. M. and Schetzer, J. D., Foundations of Aerodynamics, John Wiley and Sons, New York,
less
15. Staley, C. M. and Graven, G. G., The Static and Dynamic Wind Design of Steel Stacks, ASME 72Pet-30, New York. 16. Vierck, R. K., Vibration Analysis, Harper and Row, New York, 1979. 17 . Paz, M., Structural Dynamics, Van Nostrand Rheinhold Co. New York, 1980. 18. Australian Standard 1170, Part 2-1983 SAA Loading Code, Part 2-Wind Forces, p. 55. 19. Timoshenko, S., Young, D. H., Weaver, W., Vibration Problems In Engineering, John Wiley and Sons, New York, 1974. 20. Higdon, A., Olsen, E. H., Stiles, W B., Weese, J. A., and Riley, W. F., Mechanics of Materials, John Wiley and Sons, New York, 1976. 21. Mitchell, Warren W., "Determination of the Period of Vibration of MultiDiameter Columns by the Method Used on Rayleigh's Principle," an unpublished work prepared for the Engineering Department of the Standard Oil Company of California. San Francisco, California, 1962. 22. Bedna\ H. H., Pressure Vessel Design Handbook, Van Nostrand Rheinhold Co.. New York. 1981. 23. Boardman, H. C.. "Stresses at Junction ofCone and Cylinder in Thnks With Cone Bottoms or Ends," Pressure Vessel and Piping Design, coTlected, papers, ASME, N.Y., 1960. 24. Weaver, William, Jr., "Wind-Induced Vibrations in Antenna Members," American Society of Civil Engineers, Paper No.3336, Yol. 127, Part 1, N.Y.. N.Y., 1962.
d:
10. International Conference of
1959.
13. Blevins, R. D., Flow-Induced Vibration, Van Nostrand Rheinhold Co., New York, 1977. 14. Macdonald, A. J., Wind Inading on Buildings, Applied Science Publishers, Ltd., London, England, 1980.
concrete bearing parameter (Equation 4-20), dimensionless
REFERENCES
l.
ASME Boiler and Pressure Vessel Code, Section VIII Division I , American Society of Mechanical Engineers, New York. 2. Zick, L. P., "Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports," Welding Research Journal Stpplement, 1971. 3. Brownell, L. E. and Young, E. H., Process Equipment Design, John Wiley and Sons, New York, 1959.
4. U.S. Steel,
Steel Design Manual, U.S. Steel, Pittsburgh, Pennsylvania, 1981. 5. American Institute of Steel Construction, Manual of Steel Construction, Eighth Edition, AISC, Chicago,
Illinois.
6.
1980.
5., Theory of Plates and Shells, McGraw-Hill Book Co., New York, 1959. 7. Bickford, J. H., An Introduction to the Design and Behavior of Bohed Joints, Marcel Dekker, Inc., New York, 1981. 8. Faires, Y. M., Design of Machine Elements, The Macmillan Co.. New York. 1962. 9. Simiu, E. and Scanlan, R. H., Wind Effects on Stuctures, John Wiley and Sons, New York, 1978. Timoshenko,
'
Appendix A
Partial Volumes and Pressure Vessel Calculations
PARTIAL VOLUiIE OF A CYLINDER
v"'
RiL
:
: R: L
|to' _ ,inol 2 \180' rl
panial volume
shown (A-l)
In snaoeo regron
length of cylinder
J- __
inside radius of cylinder
Examplg lFigure
-/.\
_
--x^L?-q -ait ' I
A.tl
For a cylinder with 144-in. ID find the partial volume of a fluid head of 60 in., if L : 100 ft:
|= w.+r (721!zoo) v,' : 2 ["tlggrsri r80 - sin (160.81")l [
Yp
:
Figure
Sketch for calculating partial volume of a cylin-
I
7,707 ,650.2 in.3
:
33,366.5 gal
PARTIAL VOLUIIE OF A HEIIISPHERICAL HEAD rry':(3Ri -D) ,,rP _- -------------
r(3sft3(50)
-
l00l
:
64,140.85 in.3
:
277.7 ga|
(A-2)
J
V. =
A.l.
der.
Example
partial volume shown in shaded region
For horizontal volume in Figure A-2b find partial volume for a head with Rr 50 in. and y 35 in.'
:
Example For vertical volume in Figure A-2a find partial volume 50 in. and y = 35 in.:
for a head with Ri
277 .7
:
255
=
138.85 gal
:
256
Mechanical Design of Process Systems
Example-Spherically Dished Horizontal
(a)
Head
A spherically dished head with a 114-in. @ OD is spun from l-in. plate. Determine the partial volume of l0 in. of liquid. From vessel head manufacturer's catalog we determine the following: IDD
:
^
ll4 -
K, =
Figure A-2. Partial volume of vertical hemispherical (8) Partial volume of horizonral hemispherical head.
16.786 in. (Figure A-5), 2(1.0)
z
-=-:
a:
159.43"
L:
108
:
p
:
193
1n.
)O.U ln.
2.78
- 16.786:91.2r
in.
head.
-_r--T
-lY' ll I lv tl
I
ln, I
t?
PARTIAL VOLUMES OF SPHERICALLY DISHED HEADS
--.-{-}
--
-
Horlzontal Head The partial volume of a horizontal head (Figure A-3) is
v="lJGt:lT-{p-v-F
ryl
(A-l)
Figure A-3. Partial volume of spherically dished horizontal neaqs.
Vertical Head The partial volume of a vertical head (Figure A-4) is
-. v:
?rv(3x2
--:--:----------
+
v2)
-
v)
6
(A-4)
or
,,
rry2(3o 3
(A-5)
Figure A-4. Partial volume heads.
of spherically dished
vertical
n Appendix A: Pressure ry'essel Formulations
Yi
= 6.786"
Figure A-5.
r=\:.,O/l-
1..,fi082
(91.21)(562
V
:
38,893.21 in.3
--61s6-,P
-
-
6.7862)
=
168.37 gal
J(lo-s:
-
5FF
Example- Spherically Dished Vertical Head For the same head above, determine the partial volume
of a head of liquid of 9 in.
x
:
55.456 in.
:
u_r(9)[3(55.a56f+g'z]
14,874 in.3
:
64.4 gal End View of Horizontal Head
PABTIAL VOLUTES OF ELLIPTICAL HEADS The exact partial volume of (Figure 4-6) is as follows:
a
Flgure A-6. Partial volume of horizontal elliptical
horizontal elliptical head
u = (I93)'-(Rl - n1i
(4-6)
6RI
Vertlcal Elliptical Heads Volume of top portion @ of Figure A-7 is
oR't[" t'I v^: - 2 r - 3GDD),1
(A-7)
Volume of bottom portion .
.
v^=
2r(tDD)R''? rRl ' ' -
_______:
Ilv
2 l'
O
is
uj
I
3(IDD)'?j
(A-8)
Figure A.7. Partial volume of vertical elliptical head.
258
Mechanical Design of Process Systems
Horizontal Head Exampte
A
Find the partial volume of a 2:1 (Ri/IDD = 2) elliptical head that is 108-in. OD. The level of the liquid ii 35 in.. and the head is spun from l-in. plate.
vertical head
IDD:
108
-
2(1.0)
:
26.50 in.
From Equation ,4-6 and Figure A-8 we have the follow_
IDD
rng:
-X
.,t :
a r-6R v{K,' - yi.f
(IDD)
a:138.80":2.42 v_ V:
(19.0)12.42t
.,?r
6(53)
s _ / rEtrl
B horizontal head
17,512.94 in.3
:
75.81 gal
Vertical Head Example For some head above, determine the partial volume for vertical head with 19 in. of liquid. Using Equation A-g we have the following: a
v
:
2r(lDD)R,2
6
_ "n, [, 2I''
,, - 2rQ6.50)(53.U2
-
V= V
:
_ y,, I 3(rDD4
c vertical knuckle region
-z-'lteo-
zrt53.0) [
77,951.81 in.3
-
1310.75 in.3
76,641.06 in.3
=
331.78 gal
H=IDO-KR
D horizontal knuckle region
Figure A-8.
Figure A-9. Partial volumes of torispherical heads: (A) vertical, (B) horizontal, (C) vertical knuckle region, (D) horizontal knuckle resion.
Appendix A: Pressure vessel Formulations
PARTIAL VOLUilES OF TORISPHERICAL HEADS Figule
For Figures A-9 and A-10,
: : p:
Vr : knuckle volume Vo : dish volume KR : knuckle radius
y IDD
4F10.
height of liquid inside depth of dish inside dish radius
For vertical heads (Figure A-9c) the knuckle-cylinder partial volume is
v-: ?
4rM2
+
(A-e)
ri2)
The partial volume of the dish region of a vertical head is
.,vD _
?ry(3x2
-
+
y2)
(A-10)
6-
The total partial volume in a vertical head is ?rY(3x'z + Y'z) oH v": '" + 12) " + ' 6'"(r^2 + 4ru2 6
(A-11)
wherey:IDD-KR Horizontal Todspherical Hcad$ Partial Volume of Dish
O
(Figure A-l
l)
Vo:o {F:1tr - vG, - R-5 _ L(&, - yf )
(A-12)
Volume of Knuck-Cylinder Region @ (Figure A-12)
vo = *FI9 + Rr
-
KR)
*
(*,
-
K*)'l
end view of dish volume
Figure A-11. Sketch for example partial volume calculation of horizontal torispherical head.
(A- 13)
The total partial volume for a horizontal torispherical head is as follows: V1
: V6+
V6
- \GI:TF - L(&'? 2 *
"[#
+ Gi
wherel: p _ IDD
-
KR)
+ (&
-
KR),]
yf)
(A-14)
Figure A-12.
260
Mechanical Design of Process Systems
Horlzontal Head Example
A
102-in. @ OD flanged and dished (torispherical)
head made to ASME specifications (KR ) 0.60p and KR > 3th, tr, = head thickness) is spun from l-in. plate. The head is horizontal and the liquid level is 35-in. determine the partial volume. From the vessel head manufacturer's catalog and Figure A-12 we determine the following:
p= R,
96 in., KR
too
=
=z
:
6.125 in.. IDD
:
:
R,
llR trl 5l = '-- - 2.=-" -', = 67.50 in.;
132 in.,
KR = 3 in.,IDD = 20.283 in.
- (31 -
H2lo5
:
66.446 in.
50in., L = 96.0 - 17.562 = 78.4J8 in. For kluckle-cylinder region,
(78.438)(50'
(5o.oo
14.091.,14
-
-
+
uOai-
tcl
3
,
15')
6.12s)
in.r =
-
r,,
/.) < r1, 14(6.125) T JT
(50.00
-
138-in.
6.125f1 )
147.59 ga.
d OD F&D (flanged
=
Rr in.
:61.50;ri
Ri
=
-
KR
:
67.50
-
3.00
67.50 + 64.50 rm=-=ob.ul
f
Vertical Head Example A
:
x = 67.50
vr = Q.532) vaq6t--rsry
Vr =
p
17.562 in.
From Equation A-14 we have
+
The head is vertical and the liquid level is 18-in. Determine the partial volume. From the vessel head manufacturer's catalog we determine the following:
and dished) head nor made to ASME specifications is spun from 1llz-in. plate.
h
=
120.283
-
(3.0
+ 15.0)l :2.283 in.
" -l-'' l(67.50), + vv = -() o )9,11
*
4(66.0)2
z(17.283)[3(64.500)'?
+
+
(17.283)'?]
6
Yv = 31,247.726 in.r + 115,645.832 Vv = 146,893.558 in.r
(64.5011
:
635.903 gal
in.3
:
64.50
Appendix
A:
Pressure Vessel Formulations
INTERNAL PBESSURE ASIIE FORIIULATIOI{S
wtrH ouTsrDE DlllENslol{s
Cylindrical Shell Longitudinal Joint
i=
D_ oEt '-R-O3t
PR oE + 0.4P
Circumferential Joint
'-
PB"
^
2'E + 1AP
2:l
t=
2oEl Ro
-
1.4t
ElliDsoidal Head
^
PDo
2oE + 1-BP
2oEl - 1.8r
D.
Sphere and Hemispherical Head
t=
o_
PRo
2oEl
2dE + O-8P
ASME Flanged and Dished Head when UR = 16qh
_ 0.885P1 '-;E+o-sP
|
When
.
qEt
^
PLM
2oE+P(M-0.2)
UB <
0.885L
-
0.8t
161b
2oEt ^' ML-(M -0.2)
Conical Section PDo r= - 2 cos o(oE + 0.4P)
^Y=-
2SEl cos a - 0.8t cos c
Do
Mechanical Design of Process Systems
INTERI|IAL PRESSURE ASME FORMULATIONS WITH INSIDE DIMENSIONS
Cylindrical Shell Longiludinal Joint
t=
PRi oE
-
0.6P
I'ti
+ u.bt
Circumferential Joint
t=
1-\ ilt-----Ti
-'------t
PRi
' -F;- o.4t
2oE + O.4P
2:1 Ellipsoidal Head
^ l'-
2oEl Or
+ 0.2t
Sohere and Hemisoherical Head
^
2oEl R + 0.2t
ASME Flanged and Dished Head when UR = 16E3 sE
-
0.1P
0.885L +
l-_, FOR VALUES OF
M
SEE SUPPLEMENT
When UR
t=
<
16?e
'-"' 2oE
-
0.lt
^
O.2P
2oEt LM + 0.2t
Conical Section
t=
PDi
2 cos d(oE
-
0.6P)
o_ ^
2oEt cos a Di
+ I.2t cos a
a Appendix A: Pressure Vessel Formulations
263
Supplement for ASME Formulations cylindrical shell, when the wall thickness exceeds one half the inside radius or P > 0.385dE, the lormulas in ASME Code ADDendix 1-2 shall be used. For hemispherical hsads without a straight flange, the efficiency of ihe head-to-shell joinl is to be used if it is less than the efficiency oI lhe seams in the head.
1. For a
For elliDsoidal heads, where the ralio ol lhe major axis is other than 2:1, reler to ASME Code Appendix 1-4(c). 4. To use the lormulations tor a conical section in the table, the half apex angle, €r, shall not exceed 30". lf d > 30o, then a special analysis is required per ASME Code Appendix 1-5(e).
For an ASME flanged and dished head (torispherical head) Ur< 1643 the lollowing values ol M shall be used:
when
Values ot Factor M M
1.00 1 .00
Ur
7.OO
M
1.41
UT
1.25 1.03 7.50 1.44
1.50 1.06 8.00 1.46
1.75
2.00
.08
.10 9.00 1.50
1
8.50 1.48
1
. The maximum allowed ratio: L-t=
M=
1
/ fL\ oit.!;/
2.25 1.13 9.50 1.52
D. When Ur
2.50 1.15 10.0 1.54
>
2.75 1.17 10.5
3.00 1 .18 11.0
3.25 1.20
3.50 1.22
1.5
'12.0
t.co
'1.58
1.60
1.62
1
4.00
4.50
5.00
1.25 13.0 1.65
1.2a 14.0 1.69
1.31
1.72
5.50 1.34 16.0 1.75
6.00
't.36
6.50 1.39
164s 1.77
16?3 (non-ASME Code construction), the values of M may be calculated by
i
I
I
xrl
-@
Appendix B
National Wind Design Standards
One of the most widely accepted international standards
A standard is a collection of current practices, past experiences, and research knowledge. Standards that are developed by consensus groups (e.g., ASTM, ANSI), trade associations (e.g., AISC, ACI), or government groups (e.g., HUD, CPSC) carry more authority than other standards because they reflect wider ranges of materials. The ANSI A58.1-1982 is a collection of information that is considered to be the state-of-the-art in the design of buildings and other structures. Local and regional building codes adopt portions of the ANSI standard for their own use. These local and regional codes are developed to represent the needs and interests of their respective areas and are written in legal language to be incorporated into state and local laws. Because these building codes are regional or local in scope, they often do not include everything in the ANSI standard, which is national in perspective. For this reason, one must be certain that a local code written for one area is applicable to the site being considered. The ANSI standard does not have as much authority as the ASME vessel codes, and, unfortunately, does not have a referral committee or group to officially interpret
is the Australian Standard 1170. Part 2-1983. SAA Loading Code Part 2-Wind Forces. The Australian Standard I 170 is more applicable to the process industries because in it are shape factors for geometries that are more common in that industry, e.g., circular shapes. However, before applying the shape factors of the Australian standard to the ANSI or any other national standard, one must be very careful to correctly convert the factors. This is because the codes have different basis upon which these factors are deiermined, and a direct application of other parameters is not possi ble. This is discussed later after we discuss the basis for the various standards. CRITERIA FOR DETERMINING WIND SPEED Wind is caused by differential heating of air masses by the sun. These masses of air at approximately one mile above the ground circulate air around their centers of pressure. At this altitude, the velocity and direction of the wind is almost entirely determined by macro-scale forces caused by large scale weather systems. Below this gradient height, the wind is modified by surface roughness, which reduces its velocity and changes its direction and turbulence. A secondary criterion, except for extreme wind conditions, is the temperature gradient, which affects the vertical mobility of turbulent eddies and therefore influences the surface velocity and the gradient height. Therefore, the exact nature of the surface wind at any point depends, first, on the general weather situation, which determines the gradient wind and the temperature gradient, and, second, on the surrounding topography and ground roughness which, together with
the document. Therefore, one must make decisions based on past experience and accepted methods of design. The ANSI standard (Paragraph 6.6, p. 16) states that in determining the value for the gust response factor a rational analysis can be used. A note below the-paragraph states that one such procedure for determining the gust response factor is in the standard's appendix. The note at the top ofthe appendix (p. 52) states clearly that it is not a part of the ANSI 458.1 mirninum design standard. What all this implies is that one may follow the guide of the ANSI standard's appendix or use another rational analysis, which includes another wind standard. Thus, one caz use another standard for design purposes.
265
266
Mechanical Design of Process Systems
the temperature gradient, modify the gradient wind to the surface wind. Wind motion is further complicated by the rotation of the earth, which induces additional forces that cause the air moving across the earth's surface to be subjected to a fbrce at right angles to the wind velocity vector. These additional forces are known as Coriolis forces. Each country has adopted its own standard for measuring wind velocity. The U.S. National Weather Service and U.S. codes use the fastest-mile wind sDeed. which is defined as the average speed ofone mile of air passing an anemometer. Thus, a fastest-mile wind speed of 120 mph means that a "mile" of wind passed the anemometer during a 30-second period. Other nations, namely Australia and Great Britain, use the two-second gust speed. This is based on the worst 2-second mean as measured by a cup anemometer. The mean gust speeds are recorded over a period of time such that a mean recurrence interval is determined. The mean recurrence interval is the reciprocal of the probability of exceeding a wind speed of a given magnitude at a particular location in one year. The risk, or probability, R, that the design wind speed will be equaled or surpassed at least once in the life of the tower is given by the expression
R:l-(l-P,)" where P, : annual probability of exceedance (reciprocal of the mean recurrence interval) n : life of the tower or stack The risk that a given wind speed of specified magnitude will be equaled or exceeded increases with the period of time that the tower is exposed to the wind. Values
of risk of exceeding design wind speed for a designated annual probability and a given design life ofthe structure are shown in Table B-1. For example, if the design wind speed for a tower is based on an annual probability of 0.02 (mean recurrence interval of 50 years) and the projected tower life is 25 years, there is a 0.40 probability that the design wind
Table B-1 Probability of Exceeding Wind Design Speed
Pr = 1-(1 -
Annual Probability
5
0.10 0.05 0.01
0.005
l0
15
will be exceeded during the life of the structure. The United States and Australian wind codes use the 50speed
year recurrence interval. The instrument for measuring the wind in the United States, Great Britain, and Australia is the cup-generator anemometer shown in Figure B-1. This device is operated by the wind striking the cups, which drive a small permanent alternator. The indicator, which incorporates a rectifier, is simply a voltmeter calibrated in miles per hour. In most recent cup-generator models the generator output is used to activate a pen-chart recorder which provides a record of continuous wind soeed.
WIND SPEED RELATIONSHIPS As stated previously, another method can be substituted for the appendix in ANSI A58. l. What this means is that another code could be used instead of the appendix. To do this one must be careful to utilize the correct conversion factors between standards. To accomplish this we refer to Figure B-2. For a 100-mph fastest mile wind speed in ANSI 458.1 we wish to determine the equivalent fastest mile wind speed for a 2-second gust using either the Australian or British code. From Figure B-2 we read from the ordinate 1.54 fior 2 sec. Knowins that one mile ol wind moving at 100 mph will pass thi anemometer in 36 sec, we read 36 sec on the curve and arrive at V,/V3666 = 1.30. Thus, the equivalent fastest mile wind speed is
Po)*
/r
Design Lile of Structure in N Years
PAI
Figure B-1. Cup generator anemometer.
25 50
100
0.410 0.651 0.794 0.928 0.995 0.999 0.050 0.226 0.40t 0.537 0.'723 0.923 0.994 0.010 0.049 0.096 0.140 0.222 0.395 0.634 0.005 0.025 0.049 0.072 o.tt8 0.222 0.394
sa\
V - t;:^lrl00) \1.30i
mph
:
tt8.4
mph
0. 100
for a 2-sec gust. For I l0 mph, the values becomes
V:
(1.18)(ll0) mph
:
129.8 mph
a Appendix B: National Wind Design Standards
Figure B-2, Ratio of probable maximum wind speed averaged over t seconds to hourly mean speed.
Thus, the 1.18 factor would have to be used in the 2-sec gust code if that code were to be substituted for Appen-
dix A of ANSI A58.1-1982. Similarly, the Canadian code we must convert to obtain an equivalent fastest mile wind speed from the mean hourly. The mean hourly implies that the wind moves an average of 100 mph across the anemometer in a period of 3,600 sec. Reading Figure B-2 we have V'/Vru* = 1.6. Thus
lj:
ozor
which yields an equivalent velocity of 76.9 mph. With the Canadian code one must use 0.769 in use of shape constants and the various other parameters when using with ANSI A58.1. A comparison of the major wind codes is given in Thbles B-Z, B-3, B-4, and B-5.
ANS| A58.r-1982 WIND CATEGORIES In the ANSI A58.1-1982 there are four wind categories-A, B, C, and D. The categories are described as follows:
Category A-A very restricted category in which the wind speed is drastically reduced. Most petrochemical and power facilities do not fall within this category. The wind force is reduced because the structure is considered to be among many tall structures. One example would be a ten-story building in downtown Manhattan, New York, where the taller buildings would block the stronger air currents. Category B-A classification that encompasses some tall structures, but not enough to block the majority of wind gusts. An example of this category would be a tower in the midst of a large petrochemical facility where there were other towers that would block some of the wind force. A forest surrounding a tower is another example. Category C-The most common classification for petrochemical applications. This category is open terraln where the tower would receive full impact from the wind with minimum ground resistance to the wind. An example of this category would be an open field or an alrDort. Category D-A classification for wind moving over water. A beachhead, in which there is flat beach up to a row of buildings would be in Category D. Miami beach, from the ocean front up to the facade of hotels, is a good example. Behind the hotel fronts would be Category C. Another example of this classification would be a tall vertical vessel on an offshore structure.
Mechanical Design of Process Systems
Table B-2 Malor U.S. and Foreign Building Codes and Standards Used in Wind Design
Standard
Edition
Code or Australian Standard I 170, Part 2-Wind Forces
1983
British Code of Basic
1972
Data for Design of Buildings
(cP3) Wind Loading Handbook (commentary on CP3) National Building Code ofcanada (NRCC No. 17303)
1974
Organization
Address
Standards Association
Standards House
of Australia
80 Arthur Street/North Sydney,
British Standards Institution Building Research Establishment
N.S.W. Australia British Standards Institution 2 Park Street
London, WIA 285, England Building Research Station Garston, Watford, WD2 7JR, England National Research Council of
1980
National Research Council of Canada
The Supplement to the National Building Code of Canada (NRCC 17724) ANSI A58.1,1982
1980
National Research
Ottawa, Ontario K1A OR6
Council of Canada
Canada
1982
American National Standards Institute
Uniform Building Code
1982
Standard Building Code
1982
International Conference of Building Officials Southern Building Code
1430 Broadway New York, New York 10018 5360 South Workman Mill Road
with
Congress International
Canada
Whittier, California 90601 900 Montclair Road Birmingham, Alabama 35213
1983 rev.
Basic Building Code
1984
Building Officials and Code Administrators International, Inc.
17926 South Halsted Street Homewood, Illinois 60430
Table B-3 Reference Wind Speed
Feference Averaging time
Australian 1983)
(SAA,
British (BSl, 1982)
Canadian (NRCC,
2-3
2-second
Mean hourly
second
gust speed Equivalent reference
wind speed to fastest
mile 100 mph
118.4
1980)
United States (ANS|, 19s2) Fastest mile
gust speed
I18.4
76.9
100
'l'*"1iil Appendix B: National Wind Design Standards
Table B-4 Parameters Used in the Maior National Standards
Australian
British
Canadian
Wind Speed l,ocal terrain Height variation Ref. speed
4
4
Terrain roughness
Yes Yes
2-sec gusts Tbbles in
appendix includes figures Gusts Magnitude Spatial correlation Gust frequency
Gust speed Reduction for large area Dynamic consideration
for h/b
>
5
is straight-forward.
4 None Yes Fastest mile
Thbles, includes figures
Figures and tables in
Thbles, figures and notes
Yes
commentaries
factor factor
Gust speed None
Gust effect Gust effect
Dynamic consideration not included
Dynamic consideration
for h/b > 4 in. or for
This standard is consid- Overall a very good code, its weakest part ered by many the best is the lack of dynamic for use in the process industries. Figures and tables are easy to read. The standard actually provides the user with equations to cutves. The analysis procedure
3
None Mean hourly
h> Analysis procedure
1982)
Yes Yes 2-sec gusts
Wind Pressure Pressure coefficients
United Siates
,1
Parametel
consideration
.
400
Gust response factor Area averaging Dynamic consideration
for h/b
>
5
ft
An excellent wind Although the appendix is technically not constandard. The analysis procedure sidered a part of the is straight-forward standard, it contains figures difficult to read, and the docunamely Figure 6. For ments-code and many structures the supplement contain tables and fig- data extend beyond the ures easy to read. limits of the curves in Figures 6 and 7. In the method in the appendix, one must assume an initial natural frequency, resulting in an iterative process. This method is extremely difficult in designing petrochemical towers without the use of a computer.
270
Mechanical Desisn of Process Svstems
Table B-5
Limitalions of Codes and Standards Code or Standard
Australian Standard I 170, Part 2- 1983 National Building Code of Canada
(NRCC,
Statement of Limitation "Minimum Design Loads
Location Title
on Structures"
"...EssentiallyaSet of Minimum Regulations . . ."
Guide to the Use of the Code
1980)
British CP3
United States
ANSI A58.I
Uniform Building Code Basic Building
Code (BOCA, 1984) Standard Building Code, 1982 (SBCCI, t982)
". . . Does Not Apply to Buildings. . . That Areof Unusual Shape or Location For Which Special Investigations May Be Necessary . . ." "Minimum Design Loads . . ." "Specific Guidelines Are Given For. . . Wind Tunnel Investigations . .. For Buildings. .. Having
Section 1 (Scope)
Title Paragraph 6. I
IrregularShapes..." "The purpose . . . is to provide minimumstandards..."
Section 102
"The Basic Minimum Wind Speeds
Section 912.1
Are Shown in Figure 912.1 . . ." "The Purpose of This Code is to
Provide Minimum Requirements . . ." "The Building Official May Require Evidence to Support the Design Pressures Used in the Design of Structures Not Included in This Section."
Preface
Article 1205.2(a)
Appendix C
Properties of Pipe
272
Mechanical Design ol Process Systems
PROPERTIES OF PIPE Th6
tollowilg tormulqs dre used in lh€ computorior of th6 volues
i
Tlr€ lsEilic ste6ls rnay be sbout 5% les!, dDd the crEte.itic stdin_ legs sleels qbout 27o greate! thon the values shown in tbiE tqble which ore bcsed ort weigbts lor cdrboIt steel.
,bo\|'n in lhe toble:
t weighl
ot pipe per toor (pouDds)
weight ol lPcler p€r foot (pou!ds) squqre leet ou&id€ ludoco per loot squorc leet inside surlace F€r loot inside drea (squdre hches) dred o{ rnetcd (squore irches) moment ol
10.6802(D-0
= : =
ir6rtia (inches.)
saction moduluB (inches3)
=
lodius oI gyrqtion (i!ches)
=
* achedule numben
0.340sd, 0.2518D
0,785(Dr-d?)
Stordord weight pipe qnd schedule rlo qte the scrae in oll sizss lhrough lo-isdr; lrom lz-ilch thtough 24-irch, stqndard {eight pip6 has d croll thicloess oI %-ircb.
0.049r(D.-d)
Extro BtroDg woight pipe ond schedule
0.26r0d 0.785d,
gO dla the sdEe in oll sires lhrough 8-i[ch, llom 8-inch thlough 24-trch. ertrd strong weight
A^E o'
0.0982(D.-ci.)
pipe bos a wall thicloess oI ){-incb.
D
Double €nr(l 3troDg weight pip6 bss no c-orrespodding schedule auEbe!,
0.25t/D,'D,+--
An = oted of Eetql (square i4ches)
d D R, t nordnol
piF .ize
achedule
ou|lide
b
in % 0.405
% 0.540
I0s 40
srd
80
xs
40s 80s
40
srd
40s
80
xs.
80s
l0s
% 0.840
40
;;;
80
xs
40 80
;;
xs
i.050
s0
xs
80
I.66'0
80 160
in.
in"
0.01s 0.068 0,0s5
0.307
0.06s 0.088 0.119
inside metdl rq. rn
0.269
0.0740 0.0568
0.2I5
0.036{
0.410 0.364
0.1320
0.302
0.0716
0.065 0.065
0.7I0
0.0st
0.493 0-423
sq.
in
0.0548 0.0720 0.092s
Bq
li
sq
tt
stoight outaid6 inlide F!Il, surtdce, aurldce, Ib* po! tl Per lt 0.r06 0.106 0.106
0.0804 0.0705 0.0563
0.186 0.215 0.315
Feiqht o[ wcter
moD€ttl
aoction
rardiur
OI
psr It.
inertic,
Eodulu&
lior|,
gyrc-
iE 0.0321
0.0m88
0.0216 0.0157
0.00108
0.330 0.425
o,0512
0.00279
0.0451
0.00331
0J35
0.0310
0.538 0.423 0.568 0.739
0.I716
0.1853 0.1765 0.1628 0.1433
0.538 0.571
0.t220
1.304
0.127t
0.00437 0.0052s 0.00600
0.llt6
0.003?8
0.01032 0.01230 0.0139s
0.1694 0.1528 0.1547
0.01197 0.00585 0.00730 0.00862
0.0285 0.01737 0.02160 0.02s54
0.2750 0.2169 0.2090 0.199r
0.171
0.0120
0.0285
0.27S0
0.1547 0.1316 0.1013 0.0740 0.0216
0.0I431 0.0r710
0.m4I
0-2892 0.2613
0.02125
0.0407 0.0178 0.0s27 0.0s77 0.046? 0.0s66 0.0706 0.08s3 0.1004 0.1104
0.3{9
0.443 0.428 o.121 0.107 0.387
0.00t22
0.1215
o.t427
0.2173
0.t77 0.r77 0,t77
0.3959 0.357 0.304 0.2340 0.1706 0.0499
0.1583 0,1974 0.2503 0.320 0.383 0.504
0.220 o.220 0.220 0.220 0.220 0.220
0.0660
1.714
0.20u
0,684 0.857
o.2a82
0.2t57
l.r3l
0.2301
0.2961
1.937
0.r875 0.1284
0,434
0.1d79
0.1913 0.1607 0.1137
1.414
0.614
o.275 0-275 o.275 0.275 0.275 0,215
0.2409 0.2314
0-7 42
0.655 0.614 0.s33 0-132
2.441
0.0641
0.02451 0.02970 0.03?0 0.0448 0.os27 0.0s79
1.185
1.t03
0.3{4
0.868
0.915
1.401
0.0500 0.0757
0.133
I.049
o,37 4
0.087{
0.s57
0.86{ 0.t19
1.679
0.179
0.3{4
2.t72
0.31t
0.1056
0.250 0.358
0.815
0.522
0,413 0.494 0.639 0.836
0.478 0.409
0,0760
1.097
0.310 0.2872 o,2746 0.2520
1.076
o.2261 0.1221
0.t2s2
0.28r8
0.213{ 0.r570
2.444
0.599
0.344 o.314
0.1329 0.1606 0.1900
0.140s
0.2t37
0.36t
0.06s
1.530
1.839
0.326
0.{01
0.1038
0.1250
0.55{
0.109
t.142
1.633
u.531
1.107 1.805
0.797
r0s
0.434 0.434
0.7tl
0.r60s
0.1934
40s 80s
0.140
1.380
1.496
0.669
0.434
0.361
0.618
0.1s48
0.335 0.304 0.2345
2.273 2.991 3.765
40s 80s
r0s 40s 80s
0.126
0.674 0.822 0.sd6
0.294
0,252
0.06s
0.920 0.884 0-821
0.083
10s 80s
0.113 0.154 0.218 0.308
*ts r0s
0.545
0.065 0.083 0.10s 0.147 0.187
l0s
rt4 1.900
dioEr-
0.12{6 0.16t0
l0s
40s 80s
l';
i!3ide
thick.
0.1859
xxs
40
wcll
0-220
t60
r%
836.19 6tdiDle3s steel pipe schedule uuEbols
0.1582
10s 40
c: ANSI
woll thichress dosiglqtio!
0.396 0.2333 0.1910 0.1405
xxs
I
836.10 steel pip€ DoDilrol
0.111
160
J.3t5
b: ANSI
pip€ woU thickness (inches)
st€el pipe schedule Dub.b€rs
0.1073 0.0955 0.0794
n(s
;;;
o: ANSI836.10
0.141
160
10
inside didoeter (incb€s) outside diqrn€ter (incheB) radius ol gFcrion {iiche3)
0.0970 0.1250 0.1574
ss % 0.675
= = = =
+
0.065 0.109
0.710
0.466
0.1041
0-2321 0.333 0.435 0.570 0.718
0.111
0.344 0.344
0.r91
l27A
1.283
0.250 0.382
1.160
r,057
0.88r 1.I07
0.{34 0.43{
0.896
0.631
1,534
0.434
0.065 0.109
t.770
2.161
0-375
0-497
1,682
2.222
0.613
0.497
0.1295 0.1106
0.378
0.463 0.440
0,851
r.0€8
3.659
5.2t1 1.274 2.08s
0.1011
0.0827 0.0609
0.2661
0.02010
0-022t3
0.ll5r
0.2505 0.2402
0.2rs2 0.343 0.334 0.321
0.304
0.28{0
o.24t8
0.2316 0.2913
0.{58 o.2r32
0.2839
0.342
0.341
0.411
0.5s0 0.540 0.s24 0.506 0.472
1.067
0.ts80
0.962
0.2469
0.1663 0.2599
0.649 0.634
*Couftesr of ITT Gtinncll.
F Appendix C: Properties of Pipe
PROPERTIES OI' PIPE (Continued) noainail prpe !ir( outride diotreter
.chedule
trcll
!uEber'
tbicL-
b
iE"
{0 80
rh
40s
xs
80s
160
xxs
J.900
;; ;; 2.3r5
i|r.
80 160
xs
40s 80s
xx!; ''''.
...'
;; :.. 2% 2.875
80
xs
l0s 40s 80s
ta: )0(s
;i d; 3
80
3.500
160
xs
l0s 10s 80s
xxs
-' 5S 3y2
*Un
40 80
;;
xs
r0s 40s 80s
xt(s tGs
4.5N
;;
s;;
80
XS
40s 80s
t20 t60
5S
;; -:. 80
xs
10s
4os 80s
t20 r60
,ots -
Bq.
i|r.
2,036
1.500
t-761
0.28r
1.338 1.100
0.8s0 0.600
0.065 0.109 0.154 0.218 0.343 0,436 0.552 0.587
2.215
0.083 0.120 0,203 0.276 0,375 0.552 0.6?5 0.800
2.709
2-ts7 2,087 1.939 1.689
r.503
metcl qted,
1.6r0
1.406
0.s50 0.567 0.283 3.96 3.65 3:36 2.953 2.240
1.251
t.774 t-229
1.001
0.187
aq.
i|l.
lt
sq
lt
outride inaid€ surtdce, BUttdc€, per It Frft
w6ight per It,
lbt
0.7ss r.068 1.429
0.{97
0.421
2.718
0.497
3.63r
1.885
0.49? 0.197 0.497
0.393 0.350 0.288 o.223 0.157
2-287 2.551
o.472
0.{97
0.979
9.029
0.769 0.533
I.163 1.3I2 1.442
0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916
0.873 0.8s3 0.803 0.759 0.687 0.602 0.537 0.471
t-017 t-o47 t-041 t.047
1.00{ 0.98{
3.47 4.57 12.51
1.047
0.929 0.881 0.716
1.152
l.l78
1.135
0.6t10
2.49S
0.710 0.988
0.4s4 0.687
0.988 0.975
2.076
1.530
L064
0.9d,
1.837
1.925
1.339 1.637 1.s98
15.860
0.792
t7.729
0.554
2.353 2.872 3.0890 3.2250
0.924 0.894
13.70
1.535 1.087
2.1490 2.2430
0.8140 0.7860
3.03 4.33 7.58
3.78
1.301
o,144
1.208
3.6r
ta22
1.011
1.195
3.02
t.124
1.164
3.90 5.03
18.58
1.80t
5.99
2t.487
1.431
24.Os?
t.103
6.5010 6.8530
2-228 2.876 3,43 3.7150 3.9160
r.136
14.32
3.20 2,864 2-348
5.0r
1.960
0.980
4.81 4.28 3.85 2.530
2.756 4.79 6.28 9.8480
1.378
1.385 L.312
2.351
t.337
3.t4
1.307
4.92d0
1.2100
6.{0
2.8u
1.249
1.562
6.17 5.800
3.96 5.8500 7.23
1.162
1.549
2.600.0
1.5250
2.175 3,531
3.334 3.260 3.068 2.900 2.62A 2.300 2.050
4.73 8.35 7.39
0.891
0.083 0.120 o.226 0.318 0.636
3.834
0.083 0.120 0.188
4.334
14.75
{.260
14.2S
4.t24
13.35?
2.547
1.178 1.178
4.826 3.826
t2-73
3.-17
1.178
1.054
10.?9
I1,50
{.{l
1.178
r.002
l{.98
t.178
0237 0.337 0.437 0.500
2.680 3.68 6.721
10.33
0.674 0.800 0.925
3.s00 3.438 3.152 2.900 2.650
0.109 0.134 0.258 0.375 0.500 0.625 0.7s0 0.875 1.000
5,345 5.295 5.047 4.813 4.563 4.313 4.063 3.813 3.563
5.793 7.661 I0.01
10.25
9.ll 22.450
l.ll5 1.082
8.560
2r.360
4.98 4.48 4.160
12.71t0
22.51
4.O2
13.21
Lr0
1.178
0.949 0.916 0.900 0.825
9.294
t.178
0.75S
27.51 31.613
t0.384
].l78
0.694
1.868
1.t56
1.399
2.245 4.30
l.{s6
1.386
1.455
1.321
t1.82
6.lI
1.156
t.260
7.95 9.70
1.456
1.195
14.61
Ll29
t2s7
t1.34
1.456 1.456
I1.413
12.880
1.4s6 1.456
0.998 0.933
9.62r 9.24 7.80 6.602 5.513 22.11 22,02
20.0r 18.t9 16,35
6.283 6.62
l{.328
1.178 1.178
1.064
0.r81
r.2140 1.2740
0.083 0.120 0.216 0.300 0.437 0.600 o;125 0.850
9.89 8.89 5.845
0.s19 0.5200 0.4980
1.5130
5.2t2
3.548 3.364 2.728
1.104
0.623 0.605
0.341
10.882 12.385
t,276
1,463
0.756 0-729 0.703
0.971
0.451 0.399 0.334
r.021
0.817 0,802
7.141
t.275
ll.l0
0.581
0.73t
1.825
3.t60
0.508 0.598 0,6470 0.6670
0.868
2.464
7.073
0.483 0.568 0.6140 0.6340
0.666
t.525
1.800
0.326
0.{12
1.280
1.771
4.21
0.310
0.39r
5.O22
2.t25
3.17
in.r
0.2652 0.120 0.s61
2.251 2.915 4.03 4.663
5.42 4.15 3.299 2.543
UoE
inJ
0.499
0.709 0.690 0.646 0.60s
2.228 3.02
9l.rc_
lus,
0.3t5
0.75s 0.753 0.753 0.753 0.753 0.753 0.753 0.753
t.274
modu-
1.7I6
0.128
t.701
0.882 0.765 0.608 0-112 0.218 0.123
ol inertiq,
1.582 1.455
o.622
0.508 o.442 0.393 0.328 0-262
ol wlter p€! lt,
1.604
3.641
2.190 2.656
0.541
!adiu!
weiEhl
2.638 3.553
3.I99
r.075 t.417
0.588 0.565
4.859 6.408 7.710 8.678
o.622 o.822 o,622 0.822 o.822 o,622 0.622
0.116
1.039
2.469 2.323
6q
4,75 4.24 3.55
0.531
)c;
i!!ide
0.145 0.200 0.400 0,525 0.650
l0s
inside dicnroler, in-
3.21
0.64d0
0.84{
1.091 1.o17 1.0140
0.9840
1.510
t.477
9.61
1.445
16.6610
35,318
2.864 2.391
5.18 s.6760 5.90 6.79 7.1050
17.7130
7.8720
1,3380 1.3060
?,77
9,73 9.53
6.95 8.43
2.498 3.03
r.929 t.920
I5.17
5.{5
20-74 27,01 32.98 38.55
t.89
20.68
7.09
25.74 30.0
1.43 9.25
1.878 1.839 1.799
10.80
!.760
{3.8I0
4.9S1
36.6450
t'|.'134
1.232
39.11l0
18.96
r5.29
l-1250 1.416
t.371
!2.10
s-82
13.1750 14.0610
1.6860
t.6s20
Mechanical Design of Process Systems
274
PROPERTIES OF PIPE (Conti:rued) pipe size
wqll
irgide
ihick-
diam-
in, 5S
0.109
t0s
schedule
lt
weight weight per It. per lt,
inertiq,
lu5,
radiu3 sYrotion.
in.'
in.1
in.
sq. rn.
sq, ia.
6.407 6.3s7
32.2 31.7
2.231 2-733
1.734
t.677
5.37
r3.98
1I.85
3.58
2.304
0.134
t.734
1.664
9.29
13.74
14.40
4.35
0.2IS
6.187
30.r00
4.4I0
t.734
1.620
15.020
r3.I00
22.6600
6.8400
r0.280
6.06s
28.89
1.734
1.588
t8.s7
l2.sI
28.t4
0.432
5.76I
26.O7
5.58 8.40
2.295 2.2700 2.245
I.734
24.5',1
I1.29
0.562
5.501
23.77
10.70
t.734
I.508 L440
36.39
10.30
40.5 49.6
0.7t 8
5.189
21.t 5
r3.33
1.734
1.358
45.30
0.864 1.000
4.897
18.83
15.64
1.134
r.2s2
4.825
17.662
t.134
l.2l I
60.076
1.125
4.37S
18.192 r5.025
I9.429
t.'t34
1.145
66.084
0.109
8.407
2.916
s.9l
24.07
26.45
8.32S
2.180
13.40
23.59
35.4
0.219
8.187 8.125
22.38
22.900 22.48
5t.3200
0.2s0
2.150 2.127
1s.640
20
2.258 2.258 2.258 2.25a
2.201
0.148
55.5 54.5 52.630 51.8
30
0.211
8.07t
51.2
2.2s8
2.t13
24.70
22.t8
0.322
7.981 7.813
2.089 2.045
35.64
7.625
45.7
2.258 2.258 2.258
28.55
0.406 0.500
50.0 47.9
7.26 8.40
1.996
43.39
100
0.593
7.439
50.87
0.7I8 0.8I2
7.189
I.882 L833
60.63
0.906 1.000
6.813
2.258 2.258 2.258 2.258 2.258
1.948
r20
43.5 40.6
t.784
1.125
2.2s8
5S
0.134
to.482
86.3
4.52
2.815
I0s
0.16s
10.420
85.3
5.49
2.815
0.219
10.312
'1.24
2.815
20
0.250
10.250
83.52 82.5
8.26
30
0.307
10.136
80.7
sld
80 120
40s 80s
160
xxs
l0s 8 8.625
sq
in.
40
6.625
lt
metcl
b
6
Bq
inside
40
std
;;
60 80
I
t40
8.625
r60
xs
80s
10.020
0.500
10.750
80
0.593
9.750 s.564
I00
0.718
9.314
2.195
14.s8
2.153
5S.0
17.81
2.104
66.3
20.0s
2.060
72.1190 76.5970
21.1120
2.0200
23.1244
L98s0
6.13
3.01
a.2l
3.00
2,S53
21.69 20.79
88.8
20.58
2.938 2.909
19.80
I0s.7
24.52
2.879
t8.84
12t.4
28.t4
2.847
17.60
140.6
32.6
2.847
74.69
16.69 15.80
I53.8 I65.9
35.7 38.5
2.777 2.748
I.734
81.437
14.9{5
177.1320
41.0740
2.',1t90
1.669
90.I1{
I3.838
190.6210
44.2020
2.6810
r5.
63.7
11.8S
3.75
3.74
2.815
2.744 2.724 2.10 2.683
I0.07
2.815
3.71 3.69
78.9
ll.sl
2.8r5
4.7
16.10
2.815
7L8
I8.92
I0.48 t2.76 14.96
t1.84
ls.s3 23.942 26.494
0.36S
9.16 8.17 1.284 6.SI7
8.50 t2.23
2.562
34.454
80s
lb
14.69 16.81
31.903
4;;
lbt
63.4 72.5
6.375
xs
lt
2.9700
6.625
std
per
13.3S
2t.97
60
lt
of
-7
6.58
36.5
40
pe!
inside
11.9000
7.00I
l0
t20
3.94
5.800
outside
7
57
ts
37.4
18.70
36.9
24.63
100.46
28.04
36.2 35.8
I4.30 I8.69
Ir3.7
2l.r6
2.654
34.24
3S.0
137.5
40.48
34.I
160.8
54.74
32.3
2t2.0
39.4
2.815
2.623 2.553 2.504
64.33
3l.l
45.6
22.63
2.815
2.438
76.93
29.5
244.9 288.2
324
60.3
333.46
82.O4
3.72
29.90
53.2
3.60 3.56 3.52 3.50
0.843
9.064
64.5
26.24
2.815
2.373
89.20
0.875
9.000
63.62
27.!4
2.815
2.36
92.28
2e.0 27.6
t40
1.000
8.750
60.1
30.6
2.815
.04.13
26.1
160
l.I2s
8.500
34.0
2.815
u5.65
?4.3
8.250
37.31
2.815
424.t7
79.65
1.500
7.75D
43.57
2.8I5
2.03
t48.I9
24.6 23.2 20.5
399
L2s0
56.7 53.45 47.15
2.191 2.225 2.18
478.59
89.04
0.I56
12.438
t2t.4
19.20
4.45
I2.390 t2.2s0 t2.090
120.6
22.93
t.44
u7.9
6.17 7.t I 9.84
3.34
0.180 0.250 0.330
114.8
12.88
0.375
12.000
I
l3.l
0.406
I1.938
III.9
;i 30
10s
;,; 4;;
40
3.43 3.39
20.99 24.20 3s.38 43.7'l
s2.7 52-2
t22.2 I40.5
30.r
4.42
{9.7
39.0
4.3S
3.14 3.13
49.56
49.0
r91.9 248.5 219.3
43.8
4.38
53.S3
48.S
300
47.1
4.37 4.33
3.34
3.24
3.34
3.21
3.t1
14.s8
3.34 3.34
15.74
3.34
0.500
I1.750
I00.4
19.24
3.34
3.08
65.42
47.0
362
0.562
11.626
2r.52
3.34
3.04
73.16
46.0
401
62.8
4.3r
0.687
I1.376
106.2 101.6
26-O4
3.34
2.978
88.51
44.0
475
74.5
0.7s0
I1.250
99.40
28.27
3.34
2.94
96.2
43.r
510.7
80.1
0.843
11.064
96.1
31.5
2.897
07.20
41.6
562
88.r
0.875
11.000
32.64
2.AA
10.3
4t.l
s78.S
90.7
120
t.000
10.750
25.49
3S.3
642
100.7
1-t7
140
1.125
10.500
39.68
37.5
701
109.9
L250
I0.250 10.t26
95.00 90.8 86.6 82.50 80.5
3.34 3.34
4.21 4.25 4.22
53.6
35.8
75s.S
60.27
34.9
781
4.13 4.09 1.01
t2
;;
)2.750
80 100
80s
126.82
68.4
r.312
36.9
3.34
4I.l
3.34
45.16
3.34
2.414 2.749 2.68
47.1
3.34
2.651
r22.6
Appendix C: Properties of Pipe
275
PROPERTIES OF PIPE (Continued) noEit'al pipo rirc
.chedule
outside
|tumb€r'
didr!€ter
ilride
tbicL-
diqra-
itr.
b
i|r
wqll
t0s
l4
;;
14.@o
40
13.6S8
t47.20
13.624
145.80
0.210
13.580 13.562
|rretol aq.
in
per
lt
216.2
3.55 3.53
32.2
225-l
32.2
3.67
255.4
36.5
3.S2
4t.2
285.2
3.50 3.48 3.41 3.44
45.68
344.3
40;I 4{.9 t9.2
429
61.2
13.3I2
t39.20
14.16
3.87
13.250
137.9
16.05
0,{37
13.r25
r35.3
18.62 19.94
3.67 3.67
12.500
t00 I20
0.937
12.t28
1.093
ll.8r4
109.6
38.5 44.3
140
1.250
rr.500
103.s
50.1
160
1.406
11.188
98.3
3.67
3.42
3.67 3.67
3.40
72.09
3.35
84.91
3.34
8S.28
3,61 3.67 3.57 3.67 3.67
3.27 3.17
108,13
4.10 4,09 4.06 4.03 3.99
28
3.93
82.17 107.50
26.25
0.165
15.670
192.90
a,2L
4.19
15.624
19r.70
9.3{
4.ls
0.250
r5.500 r5.376
188.7
12.37 15.38
4.19 4.19
15.250
185.7 182,6
18.4I
{.I9
15.000
116.7
24.35
14.688
169.4
31.6 40.1
4.19 4.19
0.375 0.500
16.0@
2.929
189.12
42.6
70.3
9I.S
72.1
{.I9
3.35
24S.ll
4.7
L
4.63
136.46
lt5?
144.6
r64.83
66,1
r365
170,6
10.52
4.71
{.61
17,500
210-S
r3.94
4.71
4.58
20
0.312
17.376
237.1
11,34
17r50
233-7
20.76
l8
30
0.3?5 0.437
t7.126
24.t|
0.500
17.00
230.4 227.0
27.49
r8.o00
40
0.562
r6,876
223.7
30,8
1.?l 1.?l
60
0.750
15.500
213.8
{0.6
1.71
80
0.937
16.126
204.2
50.2
100
l.ls6
15.688
193.3
61.2
4.71
4.tI
207.96
120
1.37S
15.250
71.8
4.7
|
3.99
244.t4
140
1.562
14.876
182.6 173.8
80.7
4.71
3.89
214.23
150
1,781
r4.438
t53.7
90.7
4.7
|
3.78
308.51
0.r88
1s.634
302.40
5.14
I9.564
5.24
0.250
19.500
15.5r
5.24
1s.250
300.60 298.6 291.0
11.70 13.55
s.24
0.218
23.r2
5.24
0.500
r9.000
283.S
30.6
5.24
0.593 0.812
r8.8I4
278.0
r8.376
265.2
0.875
18.250
80
1.03r
17.s38
252-7
100
1.281
17.438
238.8
36.2 48.9 52,8 61.4 75.3
5.12 5.I I 5.04 4,97 4.93
20
20.000
30 40
60
;; xs
5.24
4.8r
5.24 s.24 5.24
1.78 4.70 4.57
292
73.4 69.7
t7.624
20
32.2
732
0.188 0.2s0
i;
4,48
5S.2
129.0
10s
159.6
562
245.20 243.90
4.55 4.52 4.48 4.45 4.42 4.32 4.22
l{6.8
48,0
t7,670
i;
I32.8
473
12.814
l0s
930
384
58.5
4;13
tt27 l0l7
117.8
80.5 79.1
6458
4.88 1.57 4.57 4.86 4.85 4.91 4.83 4.82 4.80 1.79 4-74 4.74 4.69 4.63 4.58 4,53
825
81.8
0.165
9.24
98.2
52.36
223.64
144.5
13.126
80.3 84.1
42.05
192,29
13.564
1.437
589 687
69.1
257
3.44
r.218
140
156.8 484
83.5 83.0
3.55
120
4.I9
s3.3
32
4.19
152.5
55.3
t70.22
4,19
160.9
r3.938
s8.7 s8.0 57.5
3.09
135.3
r4,3t4
1.031
314
59.7
3.01
4.19
0.843
60.9 50.3
50.0 47.5 45.0
48.5 s6.6 65.7
80
62.1
130.73 150.67
3.85 3.75 3.65
r00
160
36.71
50.2 54.57 63.37 67.8
0.188 0.312
{.90 62.8
0.375
0.750
ia.
30.9
0.344
80
Uon
inJ
3.55
3.67
12.750
lu&
in.
3.67
t3.42
0.625
inerlid,
lb
tbt
2't.8 30.9
140.5
24,98
pe! ll,
perlt
194.6
l2.ll
0.593
auddc6, !'er IL
63.1
141.80
2t.21
aeclion !adiu! modu- qryr6-
27.7
13.438
134.00
ol
weisht
23.O
10.80
t32,7 r29.0 t27.1 t22.7
lreight
3.57
143.1
13,062
rq It iagide
3.S8
13.S00
13.000 12,814
40
lurlcc€,
144.80 111.50
0.469
30
outgide
3.67
0.s00
io
tt
sq
8.16 9.10 9.48
0.312
;;
l6
in
0.r88
0.250 0.281
20
aq,
0,156
0.219
l0
i!-
idside
933
l5s6
194.5
I760
220.0
5.18 s.13 s.37 5.30 5.24 5.12
1894
236,1
I06.2
368
40.8
6.31
105.7
4t7
47.39 59.03
104.3
6.30 6.28
102.8
549 678
46.4 61.0
70.59
101.2
807
89.6
6.23
82.06 93.45
99.9
93I
I03.4
6.2r
s8,4
1053
117.0
104.?5
97.0 92.7 88.5 83.7 79.2 75.3 71.0
tt72
130.2 168.3
1834
203.8
2180
242.2
2499
217.6
6.10 6.04 5.97 5.90
27sO
306
5.84
3020
336
5,77
40
13t,0
574
46
130.2
52.73
t29.5
78.50
126,0
t04.I3
31
138.r7 170.75
r22.91 r66.40
6.2S
s't.4
7.00
56,3
6.99
757
75.7
6.98
lll4
n t.4
6.94
t22.8 t20.4
1457
I45.7
6.90
1704
170.4
lls.0
225.?
178.73
1t3.4
22s? 2405
208,87
109.{
2772
t03,4
3320
240.9 277.2 332
6.79
276
Mechanical Desisn of Process Svstems
PROPERTIES OF PIPE (Continued) notlrindl pip6 .iz€
schedule
woll
idrids
thick-
di(rm-
i!L
b
rn. 20 20.000
22.000
weight
po!It, sutldce, 6urlcce, tbf per lt perlt
16.500
227.0 213.8
100.3
5.24 s-24
4.45 1-32
296.37 341.10
160
1.968
I6.064
202-',l
Iu.5
5,24
4.21
37S.01
0.188 0.218
2L.824
367.3
12.88
5.76
2I.564
365.2
5.76
0.250
21.500
363.1
t4.92 17.t8
5.?6
0.375
2r.250
354.7
25.48
0.500
346.4 338.2 330.1
50.07
0.875
21.000 20.?s0 20.500 20.250
322.1
58.07
80
1.125
19.750
100
I.375 I.625
19.2s0
306.4 231.0
73.78 89.09
18.750
276.1
104.02
1.87s
I8.250
261.6
1t8.55 I32.68
5.76
5.75
4.65
t0s
20
io
30
xs
0.625 0.7s0
;;
47.2
44
170
l{3.1
197
r39.6
25r
132.8
303
t26.2
4.91
354
u9.6
4.78
403 451
113.3
4ll
41.4
406
6.28 5.28
s0.3 54.8 16.29
22.250 22.064
388.6
I.218
21.564
365
100
1.531
r08.I
l.8I?
20.938 20.316
344
t20 t40
328
126.3
6.28 6.28
19.876
3t0
r42.1
8.28
159.4
6.28
160
10
srd 20
xs
26.000
0.2s0
25.500
0.3I2
25.376
0.37s 0.500
40.06
6.81 6.81 6.81
5.48 5.33 5.20 5.06
7.56
zs1 -2
?.52
295.0
7.17
4029
366.3
475S
432.6
7,33 7.31
6054
550.3 602,1
7.23 7.15 1.07
493.S
t07.2
109.6
8.40
161.9
8.35
125.49
180.1 178.1
1943 2550
2r2.5
8.31
2840
237.0
t78.2 t74.3 t72.4
3140
281.4
8.29 4.21
3420
245.2
8.2S
37I0
309
8-22
r88.9
lt52
96.0 3s4.7
8.41
140.80
t56.03
vt.r? 186.2{ s5 216
42S6
8.18
388
Lt5
158.3
4650 5670
473
8.07
1{9,3
6850
57I
7.96
141.4
7830 8630 9460
719 788
7.r9
221.1
I646
126.6
9.10
2t9.2
20?6
r59.7
9,08 9.06 9.02
238.11
165.8
296.36 367.40 429.39 483.13 5{1.94
134.5
t27.O
7.87
I03 r36
217.1
2418
I90.6
2t2.8
3259
7.70
0.625
24.750
481.1
49.S2
l6s
208.6
40I3
471.4
59.49
6.8I 6.8t
6.48
24.500
6.4I
202
204.4
4744
0.875
461.9
69.07
6.81
6.35
235
54S8
4I9.9
452.4
78.54
6.81
6.28
6149
4?3.0
443.0
8?.91
6.81
6.22
267 299
200.2 I96.1
l25
24.250 24.000 23.750
192,1
6813
524,1
8.80
0.250
27.500
21.80
1,20
74
257.3 255,0 252.6 244.0 243.4 238.9 234.4 230.0 225.6
2098
t49.8
9.8r
296.3 293.7
2',1.376
0.375 0.500
583.2 572.6
32.54 13.20
7.33
xs
27.250 27.400 26.7S0
562.0
s3.75
7.33
7.07 7.00
183
26.500 26.250
64.21
7.33
6.94
2ta
54I.2
0.625 0.750
7.t7
27.t4
530.S
Ll25
26.000 25.750
520.8
94.98
0.250
29.500
683.4
23.37
7.85
0.3I2
25.316 29.250 29.000
617.8
29.19
srd
0.375
xs
0.500 0.625
z8.'ts0
92
lll
253
74.56 84.82
0.875 1.000
l0s
7.63
l3l6
0.3I2
l0
6,48
183.8
6.68 6.64 6.61 6.54
6.41
188.0
srd 30
30
490.9
6.28
459
63.41 94.62
594.0 588.6
l0
20
25.000
30.I9
6.28
5.83 5.78
6.S6
0.750
L000
30.000
I9.S5 25.18
25.250
s10.7 505.8 500.7
6.28
376 422
250.7 308.7 364.9
l
20
19.314
63.54 70.0 47.2
6.28 6.28 6.28
0.875 0.968
2.062 2.343
t77.5 2t4.2
1953
6.02 5.99 5.96 5.92 5.89
382
135.4
2400 2429 3245
6.28
60 80
1490
146.6
6.09
24.000
l0l0
150.2
6.28
23.564
7.10
157.4
143
27.83
::
1,71
80.4 91.8
l15
6.28
402
69.7
88S
s.43 5.37 5.30 5.17 5.04
18.65
398 436.1
766
158.2
5_50
434 425 415
0.750 0.218
t59.1
5.76
247.4
tior
3760 4220 4590
5.76
5.76 5.76 5.76 5.76
gytq-
92.6 87.S
98.3
4t.97
17,750
0.687
in.
33.77
23.500 23.250 23.000 22.876 22.750 22.628 22.500
io
ia..
I53.7
0.250 0.500 0.562
lb
87
l0
0.375
tcdiut
pe! ll,
Ino|'lent aection ol noduin€rti(r, lus,
5.76
2.t25 srd
rroight
5.65 5.63 5.56
I40 r60
0.62s
30
in
sq lt ir16ide
17.000
30
28.000
aq
It
outside
1.750
20
2A
sq in.
6q
1.500
120
28
met(ll
r20 I40
i; 22
idaide
672.0
34.90
7.85 7.85
650.5 649.2
46.34
7.85
57.68
7.8s
6.8t 6.7r
288 323
7.72 7.69
79 9
251.2
7.59 7.53
r58
286.2 281.3
99
8.98 8.93 8.89 8.85
260r
185.8
9.79
3105
221.e 291.8 359.8 426.0
9,7',1
{90.3
9.60
552.8 613.6
9.55 9.51
258S
172.3
3201
213.4
10.52 10.50
3823
2S4.8
t0.48
335.5
10.43
4t4.2
10.39
408S
5038 5964 7740 s590
62I3
9,72 9.68 9.61
Appendix C: Properties of Pipe
277
PROPERTIES OF PIPE (Continued) nomincl schedule
pipe si:e outside
diamelet, b 40
woll
inside
lhick-
didtn-
neat, ilr.
sq. in,
rrlelal Bq.
in.
sq It
sq It
oulside sultcce.
inside
per ft
per
637.9
68.92
620.?
80.06
1.000
28.s00 28.2s0 28.000
6I5.7
9t.l
1.t25
27
50
604.7
t02.05
7.85
0.250
31.500
779.2
24.9s
8.38
o.312
3r.376
7'13,2
31.02
8.38
rio
0.375
3t.250
766.9
31,2s
XS
31.000 30.750
754;1
49.48
742.5
61.59
736.6
0.875
30.624 30.s00 30.2s0
1.000
30
0.750 0.875
30.000
l0
32
30
0.s00 0.62s
32.000
10
0.688
20
inside
.',t
7.85 7.85
It
weight per Il,
lbf
weight modu-
gYra-
per ft
inertid,
Iug,
tb
in.'
in.3
tion, in.
7.44
234
r
49t.4
10.34
272
276.6 27 t.B
137
7.3S
8494
566.2
10.30
7.33
3t0
267.O
63S.4
10.25
347
262.2
9591 10653
t0.2
r0.22
8.25
85
337.8
3l4
t
196.3
8.21
106
335.2
3891
243.2
tt.22 u.20
8.38
8.18
Lll
t2'l
332.5
4656
168
327.2
6l{0
291.0 383.8
I
8.38
8.38
8.0s
209
321.9
7578
473.6
8.38
230
319.0
518.6
I LoS I1.07
250
8298 8990
561.9
11.05
l
73.63
8.38
85.52
8.38
7.92
291
3t6.7 3l1.6
t8372
648.2
I
30.000
706.8
97.38
8.38
7.85
331
306.4
n680
730.0
10.95
LI25
29.750
694.7
8.38
7.ts
371
301.3
1302s
814.0
10.92
0.2s0
33.500 33.376
881.2
26.50
8.S0
4.77
90
382.0
371s
22t.9
11.93
0.312
s74.9
32.99
8.90
8.74
tt2
379.3
4680
275.3
I
srd
0.375
33.2s0
867.8
39.61
8.S0
8.70
135
3',18,2
s597
329.2
II.89
XS
8.64
l?s
370.8
7385
434.4
I1.85
223 245
365.0
9124
I1.80 I1.78
359.5
10829
s36.7 587.8 637.0
354.1
l2s0l
735.4
tt.12
348.6
141t4
830.2
343.2
15719
924.1
I
4491
109.0
0.500
33.000
855.3
52.62
LS0
30
0.625
32.750
65.53
8.90
34.000
40
0.688
32.624
841.9 835.9
72.O0
8.90
8.54
0.7s0
32.500
82S.3
78.34
8.51
0.875
32.2s0
8r6.4
91.0t
8.90 8.S0
8.44
1.000
32.000
804.2
103.67
8.S0
8.38
310 353
I.I25
31.7s0
79r.3
116.13
8.90
8.31
395
0.250
35.500
98S.7
28.1r
9.42
9.29
96
429.1
0.312
35.376
9-42 9-42
ll9
426.1
35.250 35.000
34.S5 42.01
s.26
0.37S 0.500
s82.9 975.8
9.23
143
423.1
9.42
9.16
I90
30
0.625
34.750
9-42
s.l0
236
4I
40
0.750
34.500
934.7
83.01
9.42
9.03
0.875
34.250
96.50
1.000
109.96
9.42 9.42
8.97 8.90
Ll25
34.000 33.750
920.5 907.9 894.2
123.I9
9.42
36.000
20
l.l8 l.l4
718.3
34
2D
I
730.5
10
l0
't
8.02 7.98
0.750
20
rddius ol
;,; xs
962.1 948,3
69.50
9992
l.0I
l.9l
r 1.76
I.63
249.S
12.64
309.1
t2.62
6684
370.2
12.59
4t1.1
8785
l.l
t0a72
48S.I 604.0
t2.51
282 324
405.3
I2898 I4903
716.5
12.16
399.4
82',1.9
12.42
374
393.6
I685I
s36.2
12.38
8.89
419
387.9
r8763
1042.4
t2.34
586.4 s79.3 s72.3
7t26
339.3
I4.73
to627
506.1
14.71
14037
565.{
17373
14.67 14.62 14.s0
12.55
0.250
41.500
1352.6
32.82
l12
0.375
41.250
r336.3
49.08
10.99 10.s9
I0.86
srd
10.80
xs
0.500
41.000
1320.2
65.I8
10.99
I0.73
167 222
40.7s0 40.500 40.000 33.500
1304.1
81.28
t0.99
10.67
1288.2
97.23
r0.99
20589
10.99
544.8
27080
1289.5
53t.2 5I7.S
33233
1582.5
t4.41
1194.5
10.3{ t0.21
544
39.000
r28.81 I60.03 I90.S5
330 438
558.4
I256.6 r22S-3
10.60 10.47
668.4 827.3 985.2
3918I
1865.7
t4.33
42
30
0.6?5
42.000
40
0.750
I.000 1.250 1.500
10.s9 10.99
649
14.59
278
Mechanical Desien of Process Svstems
INSI'LATION WEIGI{T FACTORS
To determine the seight per foot of any piping insulation, use the pipe size and nominal insulation thickness to find the insulation l'eight factor F in the chart shorvn belorv. Then multiply F by the density of the insulation in pounds per cubic foot.
Nominal Insulation Thickness
Nominal Pipe Size
I
Erample. For 4" pipe rvith 4" nominal thickness insulation, F : .77. It the insulation density is 12 pounds per cubic foot, then the insulation rveight b .77 x 12 : 9.24lb/tt.
1%"
2rA"
3%"
lt/i
.057 .051 .066
.10
r% 2
.080
.r4
2%
.091
.19
.58
.r0
.36 .34
.46
3
.23
.41
.54
.30
.39
.cr
.66 .63
.34 .38
.45
.58 .64 .80 .93
3%
.16
.24
6 8
.34
10
.43
.59
t2
.50
.68 .70
.66
.88
1.07
l.l I
.74
.90 1.01
.87
\.\2
.96 1.13
1.23
1.50
l4 18
20 24
.30 .38
.29 ,29
.21
4
.70 .83
.40 .39 .48 .47
.31
.11
4"
4%"
5%"
.59
.70 .68
.83 .81
.97 1.10
.96
.88
t.04
.97
r.13
1.17 1.32
1.36
1.20 1.34 1.56
1.24
1.7
|.37
1.64
1.92
1.79
2.09 2.44
2.10
1.75 1.99
1.52 1.3.{ 1.49
t.44
6"
2.51
2.24 2.34 2.58 2.82
2.50 2.62 2.88 3.14
2.73 3.16
3.06 3.54
3.40 3.92
1.99 1.81 2.01
4
2.O7
2.29
2.40 2.80
LOAD CARRYING CAPACITIES OF THREADED HOT ROLLED STEEL ROD CONFORMING TO ASTM A.36 Nominal Rod Diameter, in. Root Area of Thread, sq, in. Max. Safe Load, lbs. at Rod Temp. of 650"F
lz .068
%
,126 .202
v4
.302 .419
1
1
1r/e
.693
.889
r% 1.293
1.7
2
2y4
44 2.300 3.023
21/2
2y4
3.?19
4.619
3
3r/q
5.621 6.724
3'h 7.918
610 1130 1810 21L0 3??0 4960 6230 8000 11630 15700 20700 21200 33500 41580 50580 60480 ?1280
Appendix C: Properties of
l"
WEIGHTS OF PIPING MATERIALS
Pipe
279
prpe r.sr3' o.D.
A /\ w {l\ u-r'
z i.
?
z
E-I 4/ a^
B
t_J-----,
\]J Temperature Range
z
'F
tr{agnesia
Calcium
F Combina-
z
tion
FiberSodium
ffi
z ,t
&
Njs
{|s.:ssr 7 F
z.(
T} '-11
4l
N /9N
type is ueight in weight is veight factor for Boldface
pounds. Lightface t]'pe benerth insulation.
Instrlation thicknesses and weights are based on average conditions and do not constitute
a
recommendation
for
specific
thicknesses oI materials. Insulation Neights are based on 85/6 magnesia and hvdrous calcium silic&te et 1l lbs,i cubic foot. The listed thicknesses and Neights of
combination covering are the
sums of ihe inner layer of diatomacecus earth at 2l lbs/cubic
foot and the outer layer at 11 lbs,/cubic
foot. Insulotion rveights include allorvcnces for wire, cemerrt, canvas, bands and paint, but not special surface finishes. -
To find the weight of covering
on flanges, valves or fittings,
multiply the \veight frctor by the
@ tr\ qJ +€
Fsc
* 16 lb cu. ft. density.
uoight.pcr foot of covering nsed on slrarght prpe.
Vf,tve \veights 3re rpproximate. When possible, obtain
Neights from the nranufacturer. Cast iron valve $eights are for flangcd end valves; steel $eighLs for welding end velves.
AII
flanged
fitting,
fl&nged
valve and fllnge $'eights include the DroDorlion.l \leieht of bolts
or siudi to make up all joiots,
280
Mechanical De:ign
l/a"
z
of
Process Systems
wen r.660, o.D.
WEIGHTS OF PIPING MATERIALS
f'^
F
t+,!
z
HJ
3 F
-4L. E:::t ttl
n_Lt
{- i--r
\LJ Tenrpcraturc Range "F
! ! o z
Ma,gnesia
Nom. Thick.,In.
Calcium Silicate
uon
FiberSodium
Boldface type
ffi
is s'eight in
pounds. Lightface type benerth
weight
is weight factor
Jor
insulation.
I effi
Insulation thicknesses and weights are based on average
fs-is$
of ma,terials- Insulation weights are based on 85% magnesia and hydrous calcium
z
! T:lii--qF
.-al
z
/A 4 ,N
7
/>
conditions and do not constitute
a
recommendation
for
specinc
thicknesses
silicate &t 11 lbs/cubic foot. The listed ihicknesses and i{eights of combination covering are the 6ums of the inner layer ol diatomaceous earth at 21 lbs/cubic
foot and ihe outer laycr at 11
lbs/cubic foot.
Insulstion weights include alIowances for wire, cement, csnvas, bands end peint, but not speeial surface finishes, -
To find the weight of covering
1.<3
@ l[' +€
)
rc
on flanges, valves or fittings,
multiply the weightfactor by the werghl per loot ol coverrng used on strargnt prpe.
Valve weights are approximate. lVhen possible, obtain
$'eights from the manufacturer. Cast iron velve weiqhts arc for flanged end valves; sGel weights for weldins end valves.
.All flanged fitting,
flanged
valve and flange weights include the Drooortionrl weiqht of bolts or si,udi: to make up all joinl,s. * 16 lb cu. ft. density.
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS Schedule No. Wall Designation L Lic
A
kness-In.
Pipe-Lbs/Ft lVater-Lbs/Ft
fl.2
IJJ
n z^"{"u E E
L.R. 90' Elbow
40
80
srd.
XS
.145
.200
.28r
.400
3.63
4.86
6.41
.88
,77
.61
.41
.E
1.1
1.{
1.8
.8 .2
1
3.1
3.7
.6
.6
r-i\ (, F!-+
Tee
.6
e
Lateral
1.3
.7
Lt_!
Reducer
\IJ
c"p
.3
Sodium
.84
1.35
2-52
3.47
3.47
3.47
4.52
4.52
4.SZ
Nom. Thick.,In.
2)i
214
2%
3
3
3
Lbs/Ft
4.20
4.20
4.20
5.6t
5-62
5.62
\om. Thick., In. Lbs/Ft Raiing
Screwed or
I
1
1.07
1.07
d}.'.=N!
Blind
.'11 ,tJ
t44\ lF -ll
1.07
r%
lr/4
2
2
2rz
2%
3
3
1.E5
1.85
3.50
3.50
4.76
4,16
6.16
6.16
Boldface
tlpe is rfeight
Cast Iron 125
250
3.5
7
Steel 150
3C0
400
600
8
9
9
9 E
7 1.5
9
t7
* k33
Flanged Bonneb Clobe or Angle
Gxte
Irlanged Bonnet Check
J<[J
Itressure SeaI
FSO
Pressurc Seal
Rorrret-Crie Bonnet-Globe
16 lb cu. ft. density.
2500
l9
19
3l
t2 9
t2 9
9
1.5
10
19
l9
34
1.5
1.5
1.5
l9
l9
3l
t0
l9
1.5
1.5
23
26
3.8
3.9
l1
19
3.5
20
30
5.6
6.8
30
is
rveight' iactor lor
3l
Insub.tion ihickncsses
*eights arc based on
and
average
conditioris and do not constitute
D recommendation for specific of m$terials. lnsulation Neights are bcsed oD 8570 thicknesses
rd sscights cights of listed thiclinesscs cn(l ing are the combin.tion covering sums of t,he inner lrver of dirlbsr'cubic cubic tomaceous earth at 2l lbs: lD,J'er 5n 5t :cr lD,l'er fooi and the outcr
39 70
5.8
6
70
t25
.1.5
40
ivcight
3,?il*'11 ll'9"lxli:l:","'.*'"is,3 46
23
3.4
in
oounds. Lichttace hDc bencath -
insul:rtion.
13
L.R. 90' Elbow
Tee
1500
1.5
S.R. 90" nlbow
45" Elborv
900 1.5
10
1=
3uu
2
Slip-On
flanged l3onnet
'
.84
3
\Yelding Neck
e,\ z tc
r%
3
Lap Joini
/
1
3
ss]s
,a I
1
2%
psr
:ffi
t00-1c9 200-299 300-309 400-499 500-599 600-699 700-799 300-s99 c00-3c9 1000-1009 1100-1200
2%
Prc-rsure
sffi$
.7
.3
2r/6
Lbs/Ft
Fiber-
t
2
\om. Thick., In.
z
1.2
t
.5
Temperature Range 'tr'
Combina-
xxs
5.4
(----1--l
N
160
.6
1.3
.6 .2
2
Ywn
.3 .2
/.,e^
l/2"
281
.6
S.R. 90' Elbow
L.R. 45' Elbow
{_O
r.eoo" o.D.
Pipe
45
170 5
ll0
4D
42
1.9
42
11 lbs/cul)ic foot.
bs includc alInsulltion weights
ccment. ctnlo$lnccs for 'iviro, ccmenl. rint, but not vcs, bllncls {Lnd plint, hcs. sulf.rce linishcs. strccial -
lt of covcring To find the rvcight fittitrgs, on tlonlles, vxlvcs or fittiogs,
fr, tor bv the multipll; tlic wciFht frctor uscd \\cighi t)cr foot of covcring :ovcring'uscd
on stftLisht lliDc.
Vxlvc-
:rlrptori\\(iihts rrc arc apptori-obtlin
siblc, obtoin matc, Whcn Dossiblc, irnufarcturcr. rvoights from thi mtnufacturcr.
'eights rre for Cast iron vtlve weights lllnged cnd vrlves; stccl \eights for rveldine cnd valvcs.
flanged ;ing, flanged .\ll flriised fitting,
.ights include includc valve rnd 1|rngc ivcights l)olts cight of ol l)olts the l,rorntlion l N(iglrt :rll ioints. up:rll or sluds to m.tku up ioints,
242
Mechanical Design of Process Systems
2"
ptpn
zs. B, o.D.
IVEIGHTS OF PIPING MATERIALS
!r
u'N
z
u,r'
Ih
d-J.-t
-r--r-\ z
/> fin
{_L_!
Temperature Range oF
z
Magnesia
Calcium
F
5 Combinatron
z
FiberSodium
Boldface tyDe
Nr$ z
+fi$ N*s cr.i-s
z
/A, /a) ,-61
is
weisht in
pounds, Lighifbce type bdneath
weigit.
b weight factor
lnsutailon.
for
Insulation thicknesses and weights are based on average conclrtrons and do not constitute & recommendation for
soecific
thicknesses of materials. I_nsulaiioo veights are based on 85/o magnesia and hydrous calcium silicate at 11 lbs/cubic foot. The listed thicknesses and weishts of combination coverinc are the sums of the inner laler of diatomsceous earth at 2l lbs/cubic
foot and the outer layer at
,N
z
/D IN' '{I
1.
@ rfl [],._/
+
1l lbs/cubic foot.
, Insulaiion weights include allowances Iol wlre, cemen!, can-
vas, bands and oaint. but not special surface finishes. To 6nd the weieht of coverinc
on flanses. valvds or fittinssi multiply tlie weight factor by tIe weight.per foot of covering used on-slr&lghl prpe.
valve wergnF are approxlmate. When possible, obtain
weights from th; msnuiacturer. Cast i.on valve weights are for flanged end valves: sGel weiehts for ielding end vaives.
All
nsnsed fittios.
flanced
valve and flange weigF* inclide the prcportional weight of bolts or 6tuds to make up all joints, ' 16 lb cu. It. density.
fr Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
2.87s"
o.D.
Pipe
2/2"
283
Ywn
A w {T\ u-r'
7 F
z
E'
-l
F--1 -/.>\
'
/-A q-!_, \]J Temperature Range "F
z
Magnesia Calcium
f
Combinatron
o
z
FiberSodium
ffi z
weight
insulation.
Insulation Lhicknesses
$q1$
a
recommendation
for
specific
thicknesses oI materiels- Insulation weights ere based on 85/6 magnesio and hvdrous calcium silicate at ll lbs/cubic foot. The listed thicknesses end rveights of combination covering are the sums of the inner laver of diatomaceous eerth at 21 lbs/cubic
N .-al
T.A
A
foot and the outer b,yer at
a-4
1l lbs/cubic foot.
,N
Insulation weiqhts include al-
L4
z
and
weights are based on average
conditions and do not constitute
Nl-s$
z
type is s'eight in is weight factor for
Boldface
pounds. Lightface type beneath
for rvird, cement, canvas, bonds and peint, but not lowances
special surf&ce linishes, -
To find the weighi of covering
on flanges, valves or fittings,
.|-{ 'l
multiply the ileight factor by the weight per foot of covering used on straight pipe. Valve 1Aeights are approxi-
@ flr)
mate. Whe[ possible, obtain
weights fron the manufscturer. Cast iron velve weiqhts sre for flanged end valves; sGeI *eights for welding end valves. All flanged fitting, flanged valve ond fiange iveights include the proportional \ieight of bolts
+
t4
+ 16
lb cu.
lt.
o! studs to make up &ll joints,
density.
284
Mechanical Design
3"
of
Procesr Systems
WEIGHTS OF I'IPING N{ATERIALS
B.boo' o.D.
"t"" Schedule No.
40
EO
Wall Dcsignation Tlrick ness-In .
std.
xs
.216
.300
.438
.600
Pipe-Lbs/Ft
7.54
10.25
14.32
\1'xter-Lbs/Ft
3.20
2.86
2.35
t8.56 l.E0
4.6
6.1 .8
8.4
lo.7
.8
.8
.8
4.4
5.4
W
L.R. 90' Elbow
|4 {I/
S.R.90'Elbow
.5
.5
L.R. 45' Elbow
.3
.3
zr\{it E : {1\ r.'.'g
.8
Lsteral
1.8
(-r__)
Rcducer
.3
\JJ
cup
.5
rl F4q
?
Calcir.rm
Y Silicete z
FiberSodium
?
qF{i.llqn
2 E
l^a /'11
B,N u /9N .:
< E BJ
ti]
ll---J
{-
,k€ j
r\J
+
rc
.z
3.7 .5
.5
.5
100,14r 200-:0c 300-3c9 100-lm 500-599 600-699 700-7s9 800-80s 900-g?9 1000-1099 1100-r200 2
2
2%
3
3
3
t-25
2.08
3.01
3.01
4.07
5.24
s.24
5.24
\ont.'.t'hick., IIL
2\
3
3
3
3%
3%
II-1i Ft
5.07
6.94
6.94
6.94
9.17
9.17
I
LLs Ft
\om. TLick., In. Ll's, Ft
ot
1
I
1
1rz
1.61
1.61
1.61
2.74
250
9
17
300
9
t7
tl 1.5
19 1.5
9
l,ap Joint
l0
l9
l0
20
26
46
32
S.R- 90' Elbow
3.9
4
3.9
30
50
40
63
L.R. 90' Elbow
4.3
4.3
4.3
4.3
41
2E
46
45" Elbow
67
Tee
5.9
6
Flanged Bonnet
66 7
Gate
53
Globe or Angle
7.2
Flanged Bonnet Check
7.2
2
3
3
3%
3%
3.9E
3.9E
6.99
6.99
8.99
8.99
600
20
20
900
1.5
1.5
1.5
1.5
38 1.5
19
l9
36
1.5
1.5
24 1.5
24
1500
2500
6l
102
6l
ll3
1.5
1.5
60 1.5
99 1.5
r05
38
6l
1.5
1.5
67
98
4.1
4.3
r50 4.6
3.8
3.9
E1
102
l5l
23E
5.9
6
6.2
70
125
t55
260
1.8
5
95
t55
495 440
4.9
5.n
Pressure Seal
208
235
Bonnet- Cate
3
Pressure Seal
r35
Bonnet-Globc
70 +.4
.onditions and do not constitute nstttule sPecific a recommendetion for specific Insulethicknesses of materials. Insula>n 85% 857a tjon Neights are based on macnesia and hvdrous calcium rot. The "ili;r. 't l1 lhs/crrhin foot ights of o listed thicknesses and $eights
the rre th cornbination covering are diasums of the inncr layer of dit )s/cubic tomrceous earth at 21 lbs/cubi 11 lbs,lcubic foot.
al Insulation rveights includel rL-
for \rire, cenrent, crn no ves,.blnds and Irrrirrtr buL not
lorvences
fittings, on flanges, valves or fitting: )r bv b\ the th multiply the Neight factor
t50
60
Insulation thicknesses and average weighis are based on ave.age
410 5.5
4.8
100
$eieht is weight fachor for
strccrcl surlace nnlsnes. -
r20
46
u'eight in
6.9
1.8
4.3
is
tvcr at a Ioot and the outer laJcr
135 4
60
Boldface iype
pounds. Lightface type bene3th
insul&tion.
93
I
t2l
tr'langed Bonnet
400
3%
2
60
3.6 39
3%
Steel 150 1.5
Welding Neck
Blind
1tz
t-cst lron 125
Slip-On
N-i.s
4.7
.3
.3
1k
Screwed
ils
3.7
.8
r-Fn
s{
.8
14.8 .8
1
\orn. Thllk., In.
psr
O
.3
12.2
.1.8
Pressurc Rating
rffi
.3
l9
'li nrpcrrlur. ncngc'F Magnesia
xxs
7.4 Tce
3
1C0
coverinl To hnd the Neight of covefnlg
rng usei usect welghl per loot ol coverlng on straight pipe.
spproxi Valve weights are approxrobtair mate. When possible, obtain
acturef. weights from the ma,nufacturer. fo Ls are for Cist ilon valve weiehts weight flansed end valves; steet. weights for weldine end valves.
All flrnged 6tting,
180
3
flange. flanged
includ valve and llanse rleiqhtss include bolt of bolts the proportionlel \r eight.of Il joints. or studs to mirl(e uP all Jorntt
* 16 tb cu, ft. densitY,
pipe
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS Schedule No.
Wall Dasignation Thickness-In. Pip€-Lbs //Ft Water-Lbs / Ft
fr? ut {J-/
z^, F [/) El#
: {l\ 3 /)\
/.-N Irt
srlLcate
)mbina-
tit 6 z
.636
t2.51
22.8s
4.28
3.85
2,53
6.4
8.7
.9
l5.4
.9
.9
.6
4.4 9.9
Tee
t2.6
20
.9
.9
.9
Lateral
1.8
1.4
26 3.1
Reduce!
"
'F
Efsfs$ O ,'4
2td E-q
BN O /. 3\
<.: E Ptn
1"<3
HKP fqJ
+
l€
.3
2.t
2.a
.6
.6
.3 .6 1100-1200
2
2%
2ti
3
3
3%
314
3%
3.71
4.EE
4.88
6.39
6.39
7.80
7.80
7.80
Nom. Thick., In.
2%
3
3
316
3%
3%
Lbs/Ft
6.49
E.7l
r0.6
r0.6
10-6
2
2
3
3
3%
3%
5.07
5.07
E.66
8.66
r0.62
10.62
Lbsi/Ft
Pressure Rating psr Screwed
Slip-On
or
1%
1
r.E3
Lbs/Ft
NIM
6.9
.a
r00-199 200-209 300-399 400-499 500-599 600-699 700-799 800-899 900-999 1000-1099
Nom. Thick., In.
Sodium
itS
.6
L.R. 45' Elbov
Fiber-
3S4
ewr.
4.3
S.R. 90' Elbow
Nom. Thick., In.
,ffi
3/2"
xxs
9.tr
L.R. 90' Elbow
Temperature Range
:
EO
XS .318
cuP
agnesta
40
srd.
4.ooo'o.D.
1.83
1
1
r%
z.4l
2-41
3.65
250
150
300
13
2l
13
21
13
Elbor
Tee
Flanged Bonnct Gste Flanged Bonnet Globe or Angle
Pressure Serl
Bonnet-Globe
* 16 lb cu. ft. density.
900
r600
15
2l 25
40
26 1.5
54 4.4
3l
5l
39
86
70
6
8.2
6
a2
t43
90
7.1 74
137
7.7 125
7.7
\aeight fcctor for
recommendation
for
specific
thicknesses of rnetcriu,ls. I_nsrrhtion lveights are b:rscd on 8b7,
35
m:rgnesir and hvdrous lrlcium silicsle rt I I Ibs'cul,ic foot. The listcd thickncsses :rnrl \.eiqhts of combination coveriDg ar:e the sums of the inner hier of diatomil(eous e.Lrth at,21 lbs/cubic
Ioot and thc outer lll,!.er at 11 lbs:cubic foot.
75
Insulltion $eights inclutle al,Iowances ioa wlre, cement, can-
3.9 54
is
is *eighi in t)pe benecth
condlt)ons xn.l Jo noI constiiute
a
26 1.5
4.3
62 4.4
Boldface _tvpe
Pounds. Llghtf:rce
Insulation thicknesses and \eights are lssFd on averagc
82
4.L 4.4
2500
lvelglrt. 32
49
7.3
Bonnet-Gate
600
1.5
Fhnged Bonnet Pressure Seal
23
|
msul& on.
l4
8.R.90'Elbow L.R. 90" Elbow
400
1.5
14
8.7
Ste"l-_-
t25
Lap Joint Blind
1X
Cast Iron
Welding Neck
45"
28.tt
vas, blncls &nd Dcint, but, not
t33
spcciu.l surface fi nishes.
6.4 155
180
360
4.8
5
5t0
160
ma,te. When possible. obtlin
t2s
t40 | 295 2.5 | :.8
To firrd ihe $eigl,t of covering fiftincs. multit,lj thc $eight f"(bor l,v thc wuight per foot ol cov|jrinlj'usc(l on straiqht DiDe. Vxlvc \,eigl,ts rrc epprori-
on llrnges, vxlves or
rveights from
3E0
3
th_e mtnuiacturer. ( ust iron v{Llvc Neiq}rts arc lor flangtd entl velvesistaci leishts Ior rveldirrg end vdves.
,\ll fluhged fit tins, fllrnsc,l vxlve xnd flxnge rrcigl'rs inclu,le thc proporlional weight of bolts
or studs to mcke up:rll joints.
286
Mechanical Design of Process Systems
4" prcn 4.500' o.D.
1YEIGHTS OF PIPING MATERIALS
\\ attr-l-bs/I t
f'2 !x tr2 o
z F
z
{,\
t-i .t
{i\
HI e-
\IJ 'l'cmtx,miurr lLrngc'Ir
z
o F
I z
Ilagnesia Celcium
Coml)inl- Nom.'l'hick., In.
iion
FiberSodium
Boldface type is rveight in pounds. Lightf:lce tl'pe benextlr
$'eight
is weight lactor lor
insulation.
l Stits
Insulation thicknesses end weights are based on average conditions and do not constitutc
a
recommendation
fol
thicknesses of materials.
spccific
Insull-
tion weights are based on 85t;
z F
7
/''ll
/A
,N />
magnesia and hydrous calcium silicate &t 11 ibs/cubic foot. The listed thicknesses and \\'eights of combination covering are the sums of ihe inner layer of dia-
et 2l lbs,/cubic foot and the oute! la\.cr at tomaceous earth 11
lbs/cubic foot. Insulation weighL includc al-
lowances Ior uire, cement, can-
vas, bands and paint, but not special surface finishes. -
To find the weight of covering
F{3
@ +€ ,lr1
rc
on flanges, valves or fittings, multiply the we;ght frctor by thc Neight per foot of covering uscd on straight, pipe.
Valve wcights arc approrii-
mcte. When possiblc, obtrin
lveights from thc manuf&cturer. Cast iron valve lvcights &rc for flanged end valves; stecl \cights for lelding cnd valves. All fleriged fittins, flanged valve rnd flange rvcights inciude the proportional rveight ol bolts or studs to make up all joiDts.
" 16 lb cu. ft. densitv.
C Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
5.563"
O.D.
Pipe
5"
287
PtPe
(-!j z F
z
w fl-\
15.6
|
r7 .7
4'e.
B
,-'1-l
c_i_) a-1--r
Tcmperature Range
z
'F
FiberSodium
F Combina-
z
tion
Magnesia
Calcium
z
BolJfrce type is rreight in pounds. l,ighbf.lce tYpe beneeth
ffir$
$'eight
s{lrs
lreights
lnsulation thicknesses
/r4
listcd thicknesses and \'eights of combination covering are the sums of the inner layer of diatomoceous earth at 2l lbs/cubic
,N
1l lbs/cubic {oot.
/11
Ioot and thc outcr l&r-er at
/>
Insulotion l eights include al-
lorvances
special surfrrcc {inishes.
t{
To find the rveight of covering
on llanges, volvcs or fittings,
multitt]'thc wcight f$ctor by thc \reight pcr foot of covoring used on straight pipe.
@ 0
Vdve rveights arc
Flanged Bonnet Check
++3
rc lt
cu.
for {ire, cement, can-
vas, bands and p&int, but not
ll' IH 'll
* 16
and
of m&teri3ls. Insuhtion weights :rre based on 85% magnesia and hvdrous calcium silicate at 11 lbs/cubic foot. The
z
J
rre
thicknesses
Els:i-:5$
z ti
for
besed on everage conditions and do not constitute recommendotion a for specific
$sj-N$
F
is weight lactor
insul.rtion.
ft.
opproxi-
mate. When possible, obtain
weights from the manuflcturer. Cast iton valve rveights are for flonged end valves; steel rleights for welding end valvesAll flangetl Iitting, flrnged vslvc and flange weights include
the proportional weight of bolts
or studs to rnake up all joints. density.
288
Mechanical Design of Process Systems
6" ,t n
6.625. o.D.
WEIGHTS OF PIPING X{ATERIALS
gJ-f z
{n {1\ E:cl a-1J
z
E_=_=r
' !._!____,
\t/
Tcmpcraturc llange 'F Ma,gnesia
liom. Thick., In.
2 Calcium o F D
z
Combinltion
tr'iberSodium
Boldface
4q-x$ z
sfil$ dN-s {Jss;s
#4l
,41
z
=
z
,N
/9s
weight in
Insulation thicknesses and weights are based on average conditions and do not constitute
a
recommendation
for
foot and the outer layer at 11 lbs/cubic foot.
Insulation $eights include al-
for rriie, cement,
lowances
lt'
sDecial surface finishes. -
'{t
@
ir)
+
ffi
specific
thicknesses of matedals. Insulation weights &re based on 85% magnesia and hvdrous calcium s;liAte at 1l lbs/cubic foot. The listed thicknesses and weights of combina,tion covering are the sums of the inner layer of diatomaceous ea,rth at 21 lbs/cubic
Eq-A
t{3 3
iype is
beneath tr.pe oounds. Liehtface ' q eight is - weight iactor for insulation.
can-
vas, bands snd paint, but not To find the $eight of covering
on ffanges, valves or
6ttings, eight frctor b-\' the !\eight per foot of covering used on straight pipe. Valve $eights are {rppror mate. When possible, obtain weights from the manufecturer. Cast iron valve weights are for flenged end valves; steel weights
multipit
the
u
for selding end valves.
All
ffanged titting, flanged
vclve and flenge Neights in.lude thc DroDortronal wcight of bolts
or studi to mrke
ut rll
joints.
* 16 lb cu. ft. densitJ'.
il Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
8.625. O.D.
PiP.
8"
249
"r",
A
e,
T,Jr'
z F F
z
,
uJ
{T\ r';J
lA
/t\ rFr
\iJ Temperature Range
z
'F
1r00-1200
Magnesia Calcium
F Combina-
2 tron
FiberSodium
2
ffi
ireiglrt.
s{tlts
Insulation thicknesses and rlcights cre brsed on rveruge
$s
is
!N z F
z
Roldfrce tlpe is $eight in tvoe beneath trounds. L;qhtfcce '
A rA A /> €ela
;s
\rcight
iacLor lor
conditions cn.I do not corstitute
a
recommendation
for
specific
of materills- Insulation \reights cre based on 85lo magnesia and hydrous cslcium siiicate at 1l lbs/cubic foot. The listed thicknesses and leights of combination covering are the sums of the inner loyer of diatomaceous eadh at 21 lbs/cubic loot snd the outer lol er at thicknesses
1l lbs/cubic foot.
Insulation rveights include allowances for uire, cement, canvas,.b!.nds ond paint, but not sDectal surlace nnrsh€s. -
To find the weisht of coverins
1-{3
t4s^
+
on flanges, vrlvis or fittings,
multiply the \aeightf&ctor by the \Yeight.per foot of covering used on strarqn! prDe,
Yalve rvciIhts cre appro\imcte. l\rhcn possible, obtxin
\leights from th6 manuflcturer. Cast ilon valve iveights ore for flanged end
vrlves;stecl \\'eights
for \\elding enLl valves.
All
flanged
fittine,
flanged
vslve and flongc Neights jnclude the proportionlrl lveight of bolts or studs to make up all joints.
290
Mechanical Design of Process Systcms
10t'prpe
\VIJIGIITS OT PIPING I{ATDRI,\i,S
,o.zso"
\\-rtcr-Lbs
'
l'
i
IA (,
z k
//\ w {i\
.l
4'd',
E.-I !-l_, t,t! Trmprrx6url 11''ra. "P N'Iagnesia
z Calcium
Combina-
\om. Thick., In.
uon
Fiber-
\om.
TlLn k., I rr.
Sodium
ffi A,/TmA z qIS I l\S
N-ls ry--rp z F
,--ll
Boldfcce
type is neight in
is
$eight, Jsctor for
pounds. Lightfece t) pc benertll
$cight.
lnsut& on. We)ding Neck
Insulrt,ion thicknesscs and iveights arc based on avenge
conditions and do not constitute
a
rccommendrtion
for
specific
thicknesses of matcdcls. Insul:rtion \ieiqhts are bascd oir E59. magnesii and hldrous calciuni silicate at 1l lbs/cubic foot. The listed thicknesses and $eights of combination covering are the sums of the inner laler of diatomeceous earth at 21 lbs/cubic
foot and the outer laver z
/> tP ql
s,t
11 lbs/cubic foot.
Insulation \Yeishts include alfor rdr;, cement, cenvas, bands and paint, but not lowonces
special surlace frnishes,
To find the wejsht of coverine
J-<3
@
'l
ll.J
++l
rc
on flonges, valvds or
6ttings] bt the Neight per foot of covering used on strsight pipc.
multipll
the neight f:rctor
|alve \rcishts ore luorori-;l)trirr
matc. \\'hcn- possil)le,
\r0iqhls from thc n)rnufscturcr. Crrst iron rrlvc $cights rfe for 13rngcd t'nrl \.l|lvcsi stccl Neights fot l-clding end vrlves. -\11 flrngcd fitting, fllnged vslve and flcngc $eig)r1s inrlude thc propottionul \eight of bolts or studs to rn.rke up all joints.
* 16 lb cu. ft. densitl..
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS Schedule No.
20
30
40
Wall Designation
{?
4
nuj
7fh F:-
60
std.
rz.75o" r00
80
o.D.
12"
I20
140
160
Thickness-In.
.250
.330
.406
.500
.562
.687
.843
1.000
Pipe-Lbs/Ft
1.125
1.312
33.36
43.E
49.6
53.5
65.4
73.2
Wster-Lbs/Ft
r25.5
r39.7
5l.t0
8E.5 1t07.2
160.3
49.7
49.0
48.5
47 .0
46.0
4,r.0
39.3
37 .5
34.9
lr9
L.R. 90' Elbow
I
I
4r.6
t57
s
)
80
104
2 60
L.R. 45" Elbow
7a
IEl
1.3
Lateral Reducer
Crp Temperature Range 'tr'
{-iryTiu
1.3
r32
167
180
273
5.4
5.4
33
44 .7
94
30
38
t9
360
1%
1%
2
2tz
Lbs/Ft
6.04
6.04
E.13
10,5
Silicate
{ 7
uomotna- Nom. Thick., In.
z
tion
Sodiuo
Nom. Thick.,In.
Bs$
!stu Nls
Screwed or
Slip-On
EA z&4
dflq 1.{3
*@
j
rqJ
{={t
ts0
'
16 lb cu.
ft.
5.22
3
3%
4
12,7
15.1
t7.9
250 7L
t.5
150
137
S.R. 90' Elbow
L.R. 90' Elbow 45" Elbow
Flaneed Bonnet
Flanged BoDnet Check Pressure Seal
Bonnet-Gate Pressure Seal
Bonnet-GIobe den6rty,
164
163
2t2
1.5
1.5
164
t87
1.5
4
4%
4%
26.7
26-7
3r.l
31.1
2%
2%
14.20
14.20
1500
2500
E20
l6u
434
843
1.5
433
341
265
453 5.2
345 5
509
669
E15
485
624 6.2
375
6.2
6.2
235
3E3
4.3
4.3
403
684
687
6.2
4.3
4.5
513
754 7.8
943
1015 5
1420
4
1410
r200 9.5.
7r0
674 9.4
I160 9.5
560
8.3
a.g
32.&
BoJdface t1'pe pounds. Lightfaco
Insulrtion thickncsses and base
902
1573
& Iccommendatio4 fot
928
1474
1775
conditions and do not constitule
11 lbsTcubic foot.
I rr24 4.7 | 4.8 136 t
Insuhtion rvcights includc al,to\l'anccs lor $lrc, ccncnt, canv:rs, hanrls lrnd Drint, but not
8.7
9.3
2155 7
2770
4650 8
1410
2600 8
3370 8
2560
45t5
6
7
spccial surface firishes. To lin,l bhc ur'rglrt of coveling on flxrgcs, vrlvcs or fittirrae. mult;l'h tl,c \reiglrt i,, tul l,\.the \\(iAht l)cr foot ol coverirrg uscd on strrlalrt DrDc.
Vrtr
1975 5.5
suecific
tliicknesses of materirls. Iirsul:rtion Neighis are l,rsrd on E5% mrgncsiu and hrdrous calcium silicxte at lL lbs/'cubic loot. The listed thickncsscs and Ncishts of combinrtion covering aie the sums of thc inner loier of dirrtomlceous ctrth at 21 lbs/cubic
foot and thc outer la\'er at
?0s
7.2
is rvciqht in
tlpe bencxth \reigl,f. js reight frctor for
neights are
5
720
32,&
r.5
6.2
4.3
9.4
80E
475 1.5
5
ldsulallon.
6.2
469
l29a
|
1.5 |
4
1919 1.5
l59E
414
24.@
900
261
20.4
4
388 1.5
209
20.4
3%
| | | 272 | 1.5 I 286 |
11E
17.9
2t.9
600
177
4%
3
26r 1.5
96
7.a
Globi or Angle
400
l1()
1.5 88
Tee
Flanqed BonDet
300
4%
17.7
r%
1%
r
Cast lron
Lap Joint
o
lA
lrl
1%
Welding Neck
s\"ssF ,-{t 2Ld ,. Al
1%
Lbs/Ft Prcssure Rating psr
|
3
Lbs/Ft
Fiber-
"
r00-199 200-299 300-399 400-499 500-599 600-699 700-7s9 800-899 900-999 1000-1099 1100-1200
Nom. Tbick.,In.
Y
prpx
375
3
S.R. 90" Elbow
291
XS
7
- J,l '
Pipe
e
rrcights
rtc
errnloriobt:rin
m:*c. \1'herr possil'le,
r'cights from the m:rnuilrcturcr.
Crlst iron vtlye wciqlrts &rc lor flangctl end v0lves: stccl \eichts Jor rrcltiine cnd vclves. -
.\lt
flerrgcd fitting, fl:rnged
vnlvc rn4 lixfigc \rcigirts include thc proportionrl Ncight lcight of bolts or studs to make mrkc up rrn all rll joints. ininlq
292
Mechanical Design of Process Systems
ptnE
14"
14" o.D.
1VEIGHTS 0F PIPING IIATERIALS
{? z |.
z
fh
{t}
EJJ
t -=;t
/-\
\t/ Temnr.r:1turc Rrngc
'F
Nlaguesia
2 Calcium F
Conlbina-
z
Nom.
Thick.,In.
tlon
Fibe!Sodium
ffi z
6{rls ds]s Elsisp
z |.
I
/A ,-11 // ,\
t&
tlpe is rrcight in $eight is \eight f.rctor tor Boldlacc
pouncls. Lightface tl'pe bencalh
insulation.
Insulation lhicknesscs
$eights arc besed on
and average
conditions and do not constitute recommendalion for spccilic
a
thicknesses of materials. Insulation tieights al.e based on E5fi magnesia and hvdrous ralcium silicate at 11 lbs/cubic foot. The
listed thicknesses and rveights of combination covering are thc sums of the inner laver of dia-
tomaceous e:rrth xt 2l lbs/cubic foot and the outer lal er et 11 lbs,/cubic foot.
lnsulaiion weights include al-
lorvances
Ior uire, cement,
can-
D' .{
vas, bands and paini,, bui not
+.{
on flanges, valves or fittings,
@ r)
+
rc
special surfece finishcs.
To find the $eight of covering
multipl]
the \\'ejght facior by the lYeight pcr foot oI covering used on straight, pipe.
Valve rveights are approri-
mete. When possible, obtain
scigbts from tha manufrcturer. CasL ilon valve Neights are for flanged end vrlvcs; steel *eights
tor rYelding end valvcs.
All
flanged frttiDg,
flanged
vrlve end frcnge $rights include the proportionri \rcighi of holts or studs to meke up all joints.
*
16 lb cu.
ft.
density
I Appendix C: Properries oi
ro'o.o.
WEIGHTS OF PIPING MATERIALS
Pipe
16t'
2gl
prpt
G
n
L!_r'
t4
z
f>\
F
L4J
{l\
z
e4'4 B
r't\ !+i
f--.+--l Temperature liange
'F
1100-1200
Xlagnesia Calcium Silicate
! i
j
6 z
Cornbina-
tion
Sodium
z
Se
Bo i.lce t\.pe is rveielrt in ttpe benesth rferqht is \\eislrt frctor fof
s{-N
Insulation thicknesses and ireights .Ire bascd on avcrrge conditions and clo not consiir.u[e
Nis s\sf z |.
d
A ,N
z
1
pounJs. Lightfi, e
lnsul<on.
a
recommendrtion
for
succitic
thicknesses of materiais. Iirsul:r-
tion \\'eights are brsed on 859% magnesil and hydrous cllciui silicate rt ll lbs/cuLic [oot. 'Ihe
Iisted thicknesses and seights of
combrlctlon covering ace the sums of the inner laier qI dia-
tomsceous eorth at 2l lbs/cubic foot and the outer layer at 11 lbs/cubic foot.
_ Insuiation
weights include allovances Ior wirc, cem€nt, can-
!!!q
vas,.bands and-' pxint, but not
specrat surlace hnlshes. To_
1"<3 E
t
@ fi1
+
l4
'
16 lb cu.
ft. density.
find Lhe weight of covering fittines.
on llxngcs, vnlves or multipl] t|e
weight flctor bl the werght.pcr foot uf covcriDg uscd on strxrqht DlDe, Valve rri-iel,ts al,rrroxi-
^re 0l,tcin m.Ltc. \\'hcn I'ossil)le, weights from
th_e
manui:rciuror-
vrlve $cishts cre for flangcd cud valvesi stiel $eiehts for rvelding end v:rlves. Cast iroD
AII flrngcd fitting,
frxnged
vclve and flxngc ncights i clude the proportionrl weight of bolts or studs to make up all joints.
294
Mechanical Design of Process Systems
18"
prpo
18" o.D.
WEIGI{TS OT' PIPING MATDRIALS
{.!-r' z F F
z B
f>\
a-+-!
{T\ -t\"
I-5:I
&\ \JJ
'fonrl)erllturc
lhrlac'Ir
Magnesia
2 Calcium o F f
z
Combin.r- .\oro. Thi, k.,ln. tron
FiberSodium
z
Soldface i,r'pc
ffi stfN$
Insul&tion thicknesses and Fcights arc bascd on average
Nls
c
r7 ,N 4!44
D',
benecth
for
insulation.
7
z
tlpc
tcigl,t is scight factor
qN F
is rrcight in
pounds. Ligbtl.rce
.S
B--rl
conditions and do not constitute
lecommcnd:ltion
IU
+
rc
specific
foot and the outer laycr at 11 ibs/cubic foot,
Insulqtion $'cights include al,]O$an(:os 1or \\-rre, cemcni, canves,.1'ends and- pflint, but not Slrcr-li1l sUl I3CC IlnlSnCS.
To find the rvcight of covering
on flrngr-s, valvcs or fittings, multitilj
@
for
thickncsscs of mstcriols- Insulstion $eights &re b:rsed on 85% rnagnesia and h)'drous calcium silicate at 11 lbs/cubic foot. The listed thickncsses and rveights of combinction covcling arc the sums oI the inner layer of diatom&ceous clLrth at 21 lbs/cubic
the $ c;glrt fxctor by the
Neight t)cr foot of covering used on.sirlrigLt pipe,
v srvc \{crgn[s crc apl)roxlmate. \Vhen possiblc, obtain
\\cights from the manuf&cturer. Cast ilon velve \Yeights &re for flanged end valves; stecl weights u clding end valvbs. fl:rnged fitting, flanged
for
All
valve and fiange \\riHhts include the proportion:rl \cight of bolts or studs to make up all joints. * 16 lb cu. ft. deDsity.
Appendix C: Properties of
WEIGTITS OF PIPING ]TATURI,\LS
zo"
Pipe
20"
o.D.
295
ptpp.
Pipe-Lbs/ I t $ atcr-l,bs,,lft
z
z
to
f\ w {l\
L=I
F4'1 f-l LJ-!
Tempcrriurc llrnge "F
z
1100-r200
Magnesis,
Calcium Combina-
z
!ton
FiberSodium
Roldfrce tvpe is \\'cight in
z
pounrls. Liglrtfrce t) po bcnerth
4dJ$
\\ciglrt. is Neiglrt flctor for
$fu
$cights rrc b.rscd on avcrrqe
Insulrtion
curditions rLnd do not roD-qtituie l reconrmt'ntlrtiori for. spccific thickncssrs ol nlrtolirls. Iirsula-
Njis
tion rveights ruc brscrL on 55.,1 rn:rgncsio :rnd hldrous rllrium
qlss,rs
silicllte rrt 1l lbs ruhit foot. The listc(l tl\i(,lincsscs r!n(l rvcislrts of
,-8.
z
/Ai
comlrinotidl covoring rio the sums of the irrner l:uer of rlirtornsceous crrth rlt 21 lbs (ul)ic
A
Ioot .rnd thc outcr la|er rt 11
,N
z
thit knesses rnd
ll)s'(ul)i0 foot.
hsu|rtion Noights irv.ludc r1lorvlrnccs for ivir{], (cmont. (1!n-
le-{
vrs, brnds url
prLint, but, not su frlco {inishos. To liud tho \\ c;ght of covcring ,rrr l1lLrrg' s, vrl!(s or fittirrgs,
sp(,(
ill
rnLrltitlt tlrt $eielrt hrrtor l,r thc
@ flr\
Flanged Bonnet Globe or Angle
n1'ights from thc nlxnulllcturcr. OlL\t, irorr vxlvc NoigLts urc for
fllugctl cnrl v:rlvcs; stccl Neights for lel
+<{ '
rc
16 Ib cu.
ft.
leig[i lrcl foot JI coverirrA uscd orr stlLlight l)il)c. |itlvu $1 i{lrts rlc rr)r,ro\i-ol,trin nrxto. \\'lrrn possil,lc,
-\ll fitngcrl Iitting,
ilrrngcd
vlllve &n(l llllngc ryci'alrts il)(ludc thc prol)ortionrl \ycight of l)olts or studs to mrke up ull joir)ts. deDsity.
296
Mechanical Design of Process Systems
24" ptpB \\'rll
24, o.D.
\YItIGIII'S OF PIPING IIATEITL\LS
Dcsigrr,rtiou
f,.d
1,!J
z
t-
z
{G
t\
w
{i} 1_'*,.1 14'1
/i\ -t Lr----t i--t
\*t"J 'I-cnDer:lturc llcngc "F
z
9
Magnesia,
Norn. TLick., In.
Calcium Conrbine-
z
tiolr
FiberSodium
ffi z j
+r[1$
N+S l:N /14 ,N
z
/> .{ l,, D---S
ffi 3
@ fi1
J-
rc
Boldfrre
is weight in
,t\pe tJpe benexth pounos, Lrgnlttce lleight.
is $eight factor
Insulation thicknesses
for and
\reights are based on average
conditions &nd do not constituie
a
recommendction for specific of msterials. Insuletion $cights are b.rsed on 857, magncsia and hydrous calcium silicste rt 1l lbs/cubic foot. The listed thicknesses and \eiqhts of combination covering are the sums of the inner laver of diatomaceous certh at 2l lbs/cubic thicknesscs
foot and the outer laver at
ll lbs/cubic foot. Insulation *eights include al,loNMces 1ot wlre, cement, canvas, bands and paint, but not
speciel surface finishes. To find the geieht of coverins on Banges, vrlvis or 6ttinss] muJtipll the rreight factor by the \aeiglrt.lrrr foot ol covering used on sLrsrght DlDe. \'Rlvt $ciehts rre annroxi-obtain mxtc. \\'hen- possiblc,
\'eights from thi manuflcturer. Cast iron valve \icights :rre for frengcd end v:rlvcs, steeJ *eights
lor \reldrng end vslves. A)l flerrged tittins, 63nsed
vxlve ar)d {lrngc seights include thc proporiiunxl \reight of bolts or sLuds to mekc up all ioints. * 16 lb cu. ft. deDity.
I Appendix C: Properties of
W!]I(;I]TS OF PIPING MATERIALS
za"
o.o
pipe E7
26tt
prpt
fif u-r'
7 F
h
IL4J
{l}
E=:l F
-4\"
,TI ri\ r-r--r
u/
Temperature Range
'F
llagnesi.r Celcirrm = irrltcate o F A
3
tion
;r:r::::: FiberSodium
Boldface tvDe is weisht in pounds. Lighiface typ"e beneath weight is weight factor
ffi$
ror lnsulalron.
Insulation thicknesses and weights are based on average conditions and do not consaitute a recommendation for specific thicknesses of materials. Insulation weights ale based on 85% masnesia and hydrous calcium siiicate at 11 lbs/cubic foot. The listed thicknesses and weights of combination covering are the sums of the inner later of diatomaceous ealth it 21 lbs/cubic
S{''l$ N-l-s d\slN|] /'41
z 3
z
t4
foot and the outer laver at i1 lbs/cubic foot. Insulation weiphts include allowances for w_ire, cement,
,N />
aglg
B,s Ht
canvas, bands and paint. but not special surface finishes. To find the weiqht of cover-
F<]
tings, multiply the weight fac-
ing on flanges, valves or fittor by the weight per foot of
@ lll')
covering used on straiqht Dipe. Valve weishts are aoorbiimate. When- possible. bbtain
weights from manufacturerCast iron valve weights are for flanged end valves: steel
+
weights forweldinqendvalyes. All flanged fittlng, flanged
valve and flange welghts include.the prolo.rtiohal weight oI oorls or studs to make uD
FqJ *
16 lb cu.
ft.
densit\-.
all joints.
298
Mechanical Design of Process Systems
28"
prpn
28" o.D.
WEIGHTS OF PIPING MATERIALS
ff &?
f^ w
F
z
{i\ E::I
F
-4\. t-t-! f---Fr
\iJ
Temperature Range "F trIxgnesia
Cclcium Combina!ron Fiber Sodium
ffi
&
Nis
EN
A
#
z F F
,N /9N
z
D',
F-Jl'il
l"<3
@ m
ll
+
rc
16
li
cu. ft. density.
Boldface type is weight in pounds. Lishtface tvDe beneath weigii is weighi'factor
rot lnsulatron. Insulation thicknesses
and
weights are based on average conolllons and do not constltute a recommendation for specific thicknesses of mate-
rials. Insulation weiphts are
based on 8570 masnesia and hydrous calcium silicat4 at 11 lbs/cubic foot. The listed thicknesses and weishts of combination coverind are the sums of the inner lafer of diatomaceous earth at 21 lbs/cubic
foot and the outer laver at 11 lbs/cubic foot, Insulation weiehts include allowances for wlre, cement, canvas, bands and paint. -6nishes.but hot special surface To find the weisht of covei-
ing on flanges, v-alves or fittings, multiply the weight factor by the weight per foot of
covering used.on straight pipe. v arve welghts are approxtmat€. When possible, obtain
weights from manufacturer, Cast iron valve weishts are for flanged ehd valves; steel
weightsforweldingend valves. All flansed fittins. flansed valve and-flanse wiiehts "include.the propo-!tional- wei ght ol Dolts or studs to make ur)
all joints,
if, Appendix C: Properties of
\ 'EIC I ITS ()F'PIPIN'; IIIATFIRTALS
Bo'o.D.
Pipre Ag
30"
"rpe
45
u-r'
ii
z
!
z
lj:I
{i\
i .4\"
\tJ -!----l
Temperature Range
'F
\Iagnesia Calcium
FiberSodirrm
ffi z
sf,J$
Nl$ {f.,-::r:q}
z
4l
F
,\ 7
B,s
i;>t
u> / \
ltl
.ll,
@t e$-+ * 16 lb cu. ft. density.
Boldface ti,pe is weight in pounds. Lightface type beneath w€ight is weight factor IOr lnsulailon.
Insulation thicknesses and weights are based on average conditions and do not constitute a recommendation for specific thicknesses of matelials. Insulation vreights are
based on 85i. maqn-sia and hydrous calcium siticate at 11 lbs/cubic foot. The listed thicknesses and weights of combi-
nation covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic foot and the outer layer. at 1l lbs/cubic foot-
Insulation weights include allorvances for w-ire, cement, canvas, bands and paint, but not special surface ffnishes. To find the weight of covering on flanges, valves or fittings, multiply the weight factor by the weight per foot of
covering used.on straight pipe. v alve werEhts are approxr-
mate. When possible,;btain weights from manufacturer. Cast iron valve weights are for flanged end valves; steel weights for weldingend valves. All flanged 6tting, flanged
valve anO nanqe werghts rn-
clude,the proportionai- wei ght oI, oolEs or studs !o make up alI Joln!s.
300
Mechanical Design of process Systems
32"
prcn
82, o.D.
WEIGHTS OF PIPING MATERIALS
{!-r'
I i)
z F
{l\
2
L-Li
b
E:-:t
f,t\ ri\
\tJ Temperature Range
.F
Magnesia Calcium Z Siliccte
l
UOmOrna-
5 tion
Fib€rSodium
Boldface type is weight in pounds, Lightface type beneath weight is weight factof
ffi
for insulation. Insulation thicknesses
$fu fs],m
rials. Insulation weights are based on 85% magnesia and
qJt.rrr.:qs
hydrous calcium silicat€ at
/.4
nation covering are the sums of the inner lay€r of diatoma-
d
F tr
at 21 lbs/cubic foot and the oute! layer at ceous earth
11 lbs/cubic foot.
A
Insulation weights include
Fdl
allowances for wire, cement, canvas, bands and paint, but not special surface finishes, To find the weight of covering on flanges, valves or fittings, multiply the weight factor by the weighi per foot of
D
mate. When possible, obtain weights from manufacturer. Cast iron valve weights are for flanEed end valves; steel
9.4
z
D' .f B_{i
covering used on straight pipe. Valve weiEhts are approxi-
@
+
weights forweldingendvalves, All flanged -fi tting, flanged varve ano nange werEhts lnclude the proDortional weisht of bolts o; stjuds to make-up
rc
'
11
lbs/cubic foot. The listed thicknesses and weights of combi-
AI
z
and
weights are based on average conditions and do not constitute a recommendation fo! specifrc thicknesses of hate-
16
lt
cu.
ft.
density.
all joints.
!r Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
84'o.D.
Pipe
34"
3Ol
prpt
A
TJ-/
z F tr
z F
b {T\
//\" E_=_=iI
"t\ \IJ Temperature Range "F Magnesia Calcium
FiberSodium
Boldface type is weight in pounds. Lightface type beneath weight is weight factor
ffi 2 3
for insulation. Insulation thicknesses
stits
rials. Insulation weights are based on 85% magnesia and
Sql-s$
hydrous calcium silicat€ at
N t
nation coverine_ are the sums
/AJ
of the inner laier of diatomaceous earth ai 21 lbs/cubic foot and the outer layer at 11 lbs/cubic foot.
AI
F
/14
z
A
Insulation weights include
allowances
+.{
covering used on straight pipe. Valve weights are approxi-
mata. When possible, obtain weights from manufacturer. Cast iron valve weights are for flanged end valves; steel
weights lor weldingend valves. All flanged fitting, flanged
+
rc ft.
cement,
tor by the weight per foot of
@ a
16 lb cu.
for u'ire,
canvas, bands and paint, but not special surface finishes. To find the weight of covering on flanges, valves or frttings, multiply the weight fac-
|i'a
r
11
lbs/cubic foot. The listed thicknesses and weiehts of combi-
.-al
z
and
weights are based on average conditions and do not constitute a recommendation for specific thicknesses of mate-
valve and flange weights include,the proportional weight oI Dolrs or stucts to make uD
all joints.
deDsity.
302
Mechanical Design of Process Systems
36tt
prpo
s6, o.D.
WEIGHTS OF PIPING MATERIALS
Water-Lbs/Ft
f.;
F
tr
L.R.90' Elbow
{t/ /\ I tt {} dJ
; 44" L_r-!
\tJ Temperature Range "F
Ilrgnesir z
Crlcilrm.
F
J Com !ton z
FiberSodirm
ffi
IOr lnsulatron_ Insulation thicknesses and
6{-,l$
tute a
N*S $:T,\1I
.4 /.4 F
Boldface type is weight in pounds. Lightface type beneath weight is weight factor
/.--tl
,\ z
ll' 'rl F--+l
.,r,eights are based on average
conditions and do not constirecommendation for specific thicknesses of mate-
rials. Insulation weights are based on 85% rnagnisia and
hyd.ous calcium silicate at 11 ibs/cubic foot.The listed thicknesses and weights of combination covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic foot and the outer layer at 11 lbslcubic foot,
Insulation weights include for wire, cement,
allowances
canvas, bands and paint, but not special surface finishes. To find the weight of covet-
Fd3
ing on flanges, valves or fittings, multiply the weight factor by the weight per foot of
fi^l
mate. When possible, obtain weights from manufacturer. Cast iron valve weiqhts are
F{]
+
coveri ng used.on straight pipe. v arve wergnrs are approxl-
for flanged end valveis;
steel
weights forweldingend valves. All flanged fitting, flanged valve ano nange werghts rnclude the proportional weieht of. bolts oi siuds to make'up
all lolnls.
304
Mechanical Design of Process Systems
Alphabetical Conversion Factors TO CONVERT
I
NTO
MULTIPLY 8Y
A
Abcoulomb
Statcoulombs Sq. chajn (Gunters)
2.998 x l0'o
t0
Rods
Acre
Square links (Gunters) Hectaae or
sq. hectometer sq feet sq meters sq mrles sq yards cu feet ga ons
acres acres acres acre-feet
acre'feet amperes/sq amperes/5q amperes/sq ampetes/sq amperes/sq amperes/sq
cm cm In. rn.
meter
mete.
ampere,hours arnpere-hours ampere-turns
ampere-turns/cm ampere-turns/cm ampere-turns/cm ampere.turns/in. ampere-turns/ In,
ampere-lurns/tn, ampere-turns/metet ampere-turns/meter ampete-tufns/metel Angstrom unit Angstrom unit Angstrom unit
amps/sq amps/sq amps/sq amps/sq amps/sq
In.
meter
cfi
meter cm anps/sq in.
coutonbs faradays grlberts amp-turns/ In.
amp{urns/meter Salberts/cm
amp-turns/cm amp-turns/meter grlberts/cm
amp/Iurns/cm amp{urns/in. gilberts/cm tncn Meter Micron or {Mu)
160
ates ares
Astronomical Unit Atmospheres atmospneres atmospheres atmospheres atmospheres almospheres almospheres atmospheres
acreS
Btu/min
.4047 43,560.0
Btu/man
Btu/sq ft/min
4,O47. 1.562 x
l0 '
4,840, 43,560.0 3.259 x 6.452
105
l0l
0.1550
Ton/sq. inch cms of mercury ft of water (at 4"C) in. of mercury (at 0.C) xgs/ sq cm
kgs/sq meter Pounds/sq in.
tons/sq ft
10.
6.452 x 10 3,500.0 0.03731 1.257
barrels (ojl) oars
bars Dars
bars bars
Batyl
Eolt {US Cloth) BTU
cu, Inches quarts (dry)
ga
Centigrade centigrams
t.257 0.3937
Centiliter Centiliter Centiliter
39.37
0.4950 0.01
centiliters
o.0244 0.o1257
3937 x 10-' I x l0-r'
1x 10-.
.0247
|
100.0 1.495 x
10
.007348 76.O
33.90
Liter-Atmosphere
8tu 8tu
ergs
Btu
gram-caiones hofsepower-hrs
loot-lbs
btu Btu
joules
8tu
krlogram,calories xrogram-rheters krlowatt-hrs foot-pounds/sec
Btu Btu Btu
/hr
105.0
ons
Meters
0.9869 1.020 x 10. 2,089, 14.50 1.000 10.409 1.0550 x 10'o 77a.3 3.931 x 1,054.8
10 |
o.2162
centimeters centimetels centimeteFdynes centimeteFdynes centimeter-dynes centimeter-grams
centimeterc/sec centimeters/sec centimeters/sec centimeterc/sec centimeters/sec centimeters/sec centimeterc/sec/sec centimeters/sec/sec centimeters/sec/sec centimeters/sec/sec Chain Chain Chains (surveyors' or Gunter's)
circular mils circular mils Circumference
circular mils
o.2520 r07.5 2,928 x
centimeters centimeters
centrmeter-gfams centjmeters of mercury centrmeters of mercury centimeters of mercury centimeters of rnercury centimeters of mercury centameters/s?c
7056.
106
centrmeters
centimetergrams
29.92 1.0333 10,332. 14.70 1.058
atmospheres oynes/sq cm kgs/sq meter
centimeters centimetels
centameters
119,60
42.O
Calories, gram (mean) Candle/sq. cm
Candle/sq. inch centares (centiares)
2.540
gallons (oil)
pounds/sq ft pounds/sq in. Dyne/sq. cm.
bushels bushels bushels bushels bushels bushels bushels
Sran-cal/sec
horsepoweahrs
watts toot-lbs/sec hoasepower
kilowatts watts
watts/sq in. Cubic Cm. cu
ft
cu in. cu meters liters pecks
pints (dry) quarts (dry)
Cords
lO-.
MULTIPLY BY 0.0700 3.929 x 10-. 0.2931 12.96 0.02356
0.01757 17.57
o.t22l
1.818 x 10 1.2445
2,t50.4 0.03524 35.24
4.0 64.0 32.0
.
100.0
B
Barrels (U.S., dry) Earrels (U,S., dry) Barrels (U.S., liquid)
Bucket (Br. dry)
ll{T0
1,550.0
o.02471
sq meters Kilometers
Btu/hr Btu/hr Btu/hr Btu/min
8tu/min
lx1O5
Acre (US) sq. yards
TO COI{VERT
Cord feet Coulomb coulombs
8.T.U. (mean) Lambeds Lamberts sq meters Fahrenheit grams
ounce ftuid (US) Cubic inch drams
liters feet inches kilometers meters
miles millimeters m ils yards
cm-8rans meter-kgs Pound-feet
cfi-dynes
meter-kgs
pound{eet atmospneres feet of water kgs/sq meter
pounds/sq ft
Pounds/sq in.
teet/min leet/sec kilometels/hr knots
meters/min m
iles/hr
fiiles/min feet/sec/sec
kms/hrlsec meters/sec/sec
miles/hrlsec Inches meters
3.9685 x 1.0
(C'x9/5)+32 0.01 .3382
.6103 2.705
0.0r
10-'
3.281 x
0.3937 10-
5
0.01
6,214 x LO-r 10.0
l-094 x 10-I 1.020 x l0-' 1.020 x 10-. 7.376 x 10 | 980.7 10 -5
l0-5
7.233 x
0.01316 0.4461 136.0
0.1934 1.1969 0.03281 0.036
0.1943 o.02237 3.728 x 10-. 0.03281
0.036 0.01
o.02237 792.0O
20.12
yards sq cms sq mils Radians sq inches
22.OO
cord feet cu. feet
8
Statcoulombs laradays
10-:
3.142 .4470
5.057 x 0.7854
l0-.
7.854 x
10-'
2.998 x 10 1.036 x 10-!
L Appendix D: Conversion Factors
305
(Continued). Alphabetical Conversion Factors
INTO
TO CONVERT coulomb9/sq cm coulombs/sq cm coulombs/sq in. coulombs/sq in. coulombs/sq meter coulombs/sq meter cubic centimeters cubic centimete6 cubac centimeters cubic centimeteas cubic centimeters cubic centimeters cubic centimeters cubic cent;meters cubic leet cubic feet
cubic feet cubic leet cubic cubic cubic cubic cubic
teet feet feet feet feet
cubic feet/min cubic teet/min cubic teet/min cubic feet/min cubic feet/sec cubic feet/sec
cubic inches cubic inches cubic inches cubic inches cublc inches cubic inches cubic inches cubic inches cubic inches cubic meters cuDrc meters cubic meters cubic meters cubic meters cubic rneterc cubac meters cubac meters cuorc meters cubic yards
cuFic yards cuorc yatos cubic yards cuDrc yards
cubic yards/min cubic yards/min cubic yards/min
coulombs/sq coulombs/sq coulombs/sq coulombs/sq coulofibs/sq coulombs/sq
in. meter cm meter crh in.
cu feet cu Incnes
cu mete6 cu yards gallons (U. S. liq.)
liters pints (U.S. tiq.) quats (U.S. liq.) bushels (dry) cu cms cu inches cu meters cu yards gallons (u.S. liq.)
liters pints (U.S. liq.)
quarts (U.S. liq.)
cu cns/sec gallons/sec liters/sec pounds of water/min million gals/day Sallons/min cu cms cu feet cu metets cu yards gallons
lite.s mal-feet pints {U.S. tiq.) quarts tU.S. liq.) bushels (dry)
cu cms cu feet cu inches cu yards eallons (U.S. liq.) laters
pints (U.S. liq.) quarts (U.S. liq.) cu cms cu feet cu inches cu meters Sallons (U.S. ljq.)
liters pints (U.S. liq.)
quarts (U.S. ljq.)
cubic ftlsec gallon5/sec lrters/sec
MUI.TIPLY BY
101
0.1550
10-.
6.452 x 10-' 3.531 x 10 5 0.06102 10-6 1.308 x 10-. 2.642 x 10-. 0.001 2.113 x 10-l 1.057 x 10-' 0.8036
-24320.O |,728.O 0.02832 0.03704 7.44052
2432 59.84 29.92
472.0
olams drams drams Dyne/cm
radians/sec revolutions/min revolutions/sec
Dyne/sq. cm. dynes
0.01745 0.1667 2.778 x LO . 10.0
liters
10.0
metets
10.0
ounces {avoidupois}
0.r371429
ounces (troy)
0.125
cubic cfi. grafis
Inch of lVercury at 0'C Inch of Water at 4'C grams
oynes dynes
joules/cm joules/meter (newtons)
dynes dynes
kilograms poun0a t5
pounds
cfi
MULTIPLY BY
gGms
Erglsq. millimete.
oyne/sq. cm. Dyne/sq. cm.
oynes/sq
0.4720
INTO
grains ounces
dynes
o.1247
oars
1.7718 27.3437 0.0625 .01
9.869 x 10-' 5 2.953 x . 4.015 x 1.020 x 10-r
l0 l0 l0-' l0-
5
1.020 x 10-. 7.233 x 10-, 2.248 x lO 6 10_6
62.43 0.646317 448.831 5.787 x l0-. 1.639 x 10-s 2.I43 x 10-5 4.329 x t0-3 0.01639 1,061 x 105 0.03463
o.ot132 28.38 106
35.31 61,023.0 1.308 264.2
Etl Erl
Em, Pica erg5 erg5 ergs ergs
ergs ergs
r,000.0 2,113.0 105
days
decrgrams
seconds grams
deciliters
Irers
oecrmeters degrees (angte) degrees (angte) degrees (angle)
meterS
0.1 0.1 0.1
qua0ranr5
0.01r1t
1.650 x 1.0-r. 86,400.0
0.01745 3,600.0
Btu dyne-centrmeters
foofpounds gram.cmS
horsepower-hrs loules kg-calories kg-meters
kilowatlhrs watt'houts
kg-calories/min kilowatts
o.7646 202.O
Gram
.4233 cm/sec
horsepo\der
46,656.0
Dalton
45
ft-lbs/sec
27.O
764.6 1,615.9 807.9 0.45 3.367 12.7 4
-
114,30
Btu/min ft-lbs/min
r,057. 7.646 x
um. tncnes tncn um, Dyne
ergs
0
raclrans Seconos
CONVERT degrees/sec degrees/sec degrees/sec dekagrafis dekaliters dekameters Drams (apothecaries' or troy) Drams (apothecaries' or troy) Drams (U.S., fluid or apoth.) TO
farads Faraday/sec faradays faradays Fathom fathoms
mrcrofarads Ampere (absolute) ampere-hours
leet
centimeters
{eet feet feet feet feet
krlometers meters mrles (naut,) miles (stat.)
teet feet of water feet of water feet of water
armospneres rn, of mercury
coulombS Nleter
feet
millimeters m ils kgs/sq cm
1.000 9.480 x 10-r' 1.0 7.367 x 10-i 0.2389 x 10-' 1.020 x 10-: 3.7250 x 10-la 10 r 2.389 x l0 -rr 1.020 x 10 |
O.2J78x IO tt
0.2778 x 10 -'o 5,688 x 10 ' 4.427 x lO-6 7.3756 x l0-l 1.341 x l0-ro 1.433 x 10 -, 10- r0
106
9.6500 x lcr. 26.80 9.649 x lcr. 1.828804 6.0 30.48 3.048 x l0-r 0.3048 1.645 x 10-. 1.894 x 10 . 304.8 1.2 x I Cl. 0.02950 0.8826
0.03048
306
Mechanical Design of Process Systems
(Continued). Alphabetical Conversion Factors TO CONVERT feet of water feet of water feet of water
leet/nin
I
r'lT0
kgs/sq meter pounds/sq ft
poLrnds/sq in.
cms/sec feet/sec
feet/min teet/min
MULTIPLY BY 304.8 62.43 0.4335
knot5
0.01667 0.01829 0.3048 0.01136 30.48 1.097 0.5921
meters/min
14.29
miles/hr miles/min
0.6818 0.01136 30.48
kms/hr
feet/ rn in feet/ rnin
meters/min
feet/sec feet/sec teet/sec feet/sec feet/sec leet/sec
cms/sec
leet/sec/sec
cms/sec/sec
feet/sec/sec feet/sec/sec feet/sec/sec feet/ 100 feet
kms/hrlsec
1.097
meters/sec/sec
0.3048 0.6818
Foot
-
miles/hr kms/hr
candle
miles/hrlsec per cent graoe Lumen/sq. meter Btu
foofpounds
ergs
foot-pounds
gram-calories np-nrs joules
foofpounds foot.pounds foot-pounds
foo!pounds foot'pounds/ min foot-pounds/ min
Kg-ca{ones
kg-meters kilovr'att-hrs
Btu/min foot-pounds/sec
toot-pounds/min
toofpounds/min
kg-calories/ min
foot-pounds/man
kilowatts
foot-pounds/sec foot.pounds/sec foot-pounds/sec {oot-pounds/sec foot-pounds/sec
8tu/hr
Furlongs
furlongs turlongs
in
gallons/min gallons / m in gausses gausses gausses gausses
gilberts
gilberts/cm gilberts/cm gilberts/cm Gills (Britash)
gills gills
kilowatts miles (U.S.) feet
gallons (U.S.) gallons of water /m
horsepower kg'calories/man rods
gallons Sallons Salrons gallons Sallons gallons gallons (liq. Br. Imp.) gallons
Btu/min
cu cms cu feet cu inches cu meters cu yards
liters gallons (U.S. !iq.) gallons (lmp.) pounds oJ water cu ft/sec
liters/sec cu ftlhr lines/sq in. weoers/sq cm webers/sq in. webers/sq meter ampere-turns
amp-turns/cm
amp{urns/jn amp{urns/meter cubrc cm. liters pints (liq.)
Grade
Radian
G€ins
drams (avoirdupois)
g.ains grains grains grains
0.5080
Srarns
dynes grains
grams grams Srams Srams
r.286 x 10 l
grarns/cm grams/cu cm grams/cu cm grams/cu cm
107
grams/ liter
l0 '
Srams/
3.24 x 10-. 0.1383 3.766 x 10 , 1.286 x 10 ! 0.01667 3.030 x 10 -' 3,24 x 10 . 2.260 x lO- 5 o.o7717 1.818 x 10-' 0.01945 r.356 x 10-' 0.125 40.0 660.0
3,785.0
0.1337 231.0 3.785 x 10-' 4.951 x 10-1 3.785 1.20095 0.83267 8.3453 2.228 x lO- I
0.06308 8.0208
6.452 10 | 6.452 x
grains (avdp) grams ounces {avdp) pennyweight (troy)
Srams Srams Srarns
10.764
1.356 x 0.3238 5.050 x
{troy) (troy) (troy) (troy) grains/l.J.S. gal Srains/U.S. gal graans/ lmp. gal grams grams
1.0
10-l
10-. 0.7958
0.7958 2.021 79.58
t4?.07 0.1183 0.25
.0t571 0.035s7143
INTO
TO CONVERT
liter
grams/ liter
grarns/liter
parts/million pounds/million gal
parts/million
MULTIPLY gY 1.0
0.06480 2.0833 x 10-1
0.04167 17.118 142.86
14.286
980.7 15.43 joules/cm 9.807 x 10-! joules/rneter (newtons) 9.807 x 10-r kilograms 0.001 milligrams 1,000. ounces (avdp) o.03527 ouhces (troy) 0.03215 poundals 0.07093 pounds 2.205 x 10-r pounds/inch 5.600 x 10-l pounds/cu ft 62.43 pounds/cu in 0.03613 pounds/mil-foot 3.405 x 10-' graans/gal 58.417 pounds/ gal 8.345 pounds/cu ft 0.062427 parts/mallaon 1,000.0
grams/sq cm gram'calofle5 Sram-catofles gram-calories gram-catofle5 gram-calones
pounds/sq tt
2.0481
8tu
3.9683 x 4.1868 x
gram-calo es gmm-calories/sec
watt-hrs
ergS
foot-pounds horsepower-hrs
3.0880 1.5596 x 1.1630 x 1.1630 x
kilowatt-hrs
Btu/hr
10-!
l0'
10 .
l0-. l0-3
t4.2a6
9.297 x 10 . 980.7 9.807 x l0-! 2.343 x 10-r
gram-centimeters gram-centimeters gram-centimeters gram-centimeters gram-centimeters
joules kg-cal kg-meters
Hand
Cm.
necrares hectares hectograms
sq feet grams
1,076 x 10' 100.0
hectoliters
liters
r00.0
hectometers hectowatts hennes Hogsheads {British) Hogsheads (U.S.) Hogsheads (U.S.) horsepower
meters watts
Btu ergs
l0
-5
H
ho15epower
horsepower horsepower (metric) (542.5 ft lb/sec) horsepower (550 ft lb/sec) horsepower horsepower horsepower horsepower (boiler) horsepower {boiler) norsepower-nrs norsepower-nts norsepower-nrs horsepower-hrs norsepower-hrs
10.16 2.47
mrllihenries cubic ft. cubic ft.
100.0 100.0 1,000.0 10.114
8.42184
Sallons (U,S.)
Bt!/min
foot'lbs/ min foot-lbs/sec
4?.44 33,000. 550.0
0.9863
horsepower (550 ft lb/sec) horsepower (metric) (542.5 ft lb/sec)
1.014
kg-calories/min kilowatts watts
Bt!/hr
kilowatts Btu ergs
loot-lbs gram-calories
joules
|
10.68 0.7 457 7
45.7
33.479 9.803
2,547. 2.6845 x 10r' 1.98 x 1Cl' 641,190. 2,684 x 10.
1|
Appendix D: Conversion
Factors T7
(Continued). Alphabetical Conversion Factors i,ULTIPLY BY
t1{T0
TO CONVERT horsepower-hls horsepowet-nls horsepower-hrs hours houls Hund.edvreiShts (long) Hundredweights (long) Hundredwei ghts (short) Hundredweights (short) Hundredweights (short) Hundredweights (short)
kg.calories kg-meters
inches inches inches inches inches inches
centimeters
641.1 2.737 x LA o.7457 4.167 x 10-t 5.952 x 10-t 112 0.05 1600 100 0.0453592
kilowatt-hrs days
pounds tons (long) ounces (avoirdupois) pounds
tons (metric) tons (long)
miles millimeters mtls
anches of mercury
inches inches inches inches inches inches inches inches inches inches inches
ol mercury of of of of
mercury mercury mercury mercury of water (at 4'C) ot wate. (at 4'C) of water (at 4'C) of water (at 4'C) oI water (at 4'C) of water (at 4'C) lnternational Ampere International Volt
lnternational volt lnternational volt
almospneres inches of mercury Kgs/sq cm
ounces/sq In. pounds/sq ft pounds/sq in. Ampere (absolute) Volts (absolute) Joules (absolute) JOUIeS
JOules
joules joules joules joules ioules iouies/cm joules/cm joules/cm
2.540 x 10-1 0.5781
joules/'cm
joules/cm
1.0003 1-593 x 109.554 x 10'
10-'
107
l0-'
2,778 x lO-' 1.020 x 10. 10t 100.0 723.3 22,44
K kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms
kjlograms/cu meter kilograms/cu meter kilog.ams/cu meter kilograms/cu meter kilograms/meter KaloSram/sq. cm, kilograms/sq cm kilograms/sq cm
kilometers kilometers kilometers
5.204 0.03613 .9998
0.7376 2.389 x 0.1020
meter meter
kilolines kiloliters kilometers kilometers kilometers kilometers
o.4912 2.458 x 10 I 0.07355
9.480 x
meter
kilogram-calories kilogram-calories kalogram meters kiiogram meters kilogram meters kilogram meters kilogram meters kilogram meters
2.778 x lo-1 0.03342 1.133 0.03453 345.3 70.73
)
Btu ergs foot-pounds kg-calories kg-meters watGhrs grams dynes joules/meter(newtons) poundals pounds
heter
kilogram.calories
10-r 10-,
I,000.0
pounds/sq ft pounds/sq in.
inches of
meter rneter mm kilogram-calories kilogram-calories kilogram-calories kilogram-calories
2.540
yards atmospneres feet of water kgs/sq cm kgs/sq meter
kilograms/sq cm kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq
I
2.540 x 1.578 x 25.40
INTO
kalograms/sq cm kilograms/sq cm
0.0446429
meters
TO CONVERT
dynes 980,665. grams 1,000.0 joules/cm 0.09807 joules/meter(newtons) 9.8Q7 poundals 70.93 pounds 2,205 9.842 x 10-l tons (long) tons (short) 1.102 x !0 ' grams/cu cm 0.001 pounds/cu ft 0.06243 pounds/cu in. 3.613 x l0-' pounds/mil-foot 3.405 x l0-'o pounds/ft 0.6720 980,665 Dynes 0.9678 atmospheres 32.81 leet of water
"
kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr/sec kilometerc/hr/sec kilometers/hrlsec kilometers/hr/sec kilowatts kilowatts kilowatts kilowatts kilowatts kilowatts kilowatt'hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs knots t(hots
xnols knots
MULTIPLY 8Y
mercury 24.96 ft 2,048. in. 14.22 atmospheres 9.678 x l0-' bars 98.07 x 10 ' feet ot water 3.281 t 10 2.896 x 10-1 inches of mercury pounds/sq ft 0.2048 pounds/sq in. 1.422 x 10 t kgs/sq meter lcl' Btu 3.968 foot-pounds 3,088. hp-hrs 1.560 x l0 I joules 4,185. kg-meters 426.9 kiiojoules 4.186 kilowatt-hrs 1.163 x 10-' Btu 9.294 x l0 I ergs 9.804 x 10t foot-pounds 7,233 joules 9.804 kg-calories 2.342 x 1O-' kilowatt.hrs 2,723 x lO'. maxwells 1,000.0 liters 1,000.0 centimeters lot feet 3,281, inches 3.937 x 1Cl. meters 1,000.0 miles 0,62f 4 millimeters lO yards 1,094. cms/sec 27.74 feet/min 54.68 feet/sec 0.9113 knots 0.5396 merets/ fltn lt.t / miles/hr 0.6214 cms/ sec/ sec zl,Ia ft/sec/sec 0.9113 meters/sec/sec 0.2718 mifes/hrlsec 0.6214 Btu/min 55.92 foot-lbs/min 4,426 x W foot-lbs/sec 737.6 horsepower 1.341 kg-calo.ies/min 14.34 watts 1,000,0 Btu 3,413. ergs 3.600 x 10rt footlbs 2.655 x 106 gram-calories 859,850. horsepower-hrs 1.341 joules 3.6 x lcl. kg-calories 860.5 kg-meters 3.671 x lot pounds/sq pounds/sq
1
pounds of water evaporated from and
at212'F. 3.53 tuon62'to272'F. 22.75 teet/hr 6,080. kilometers/hr 1.8532 1.0 nautical miles/hr statute miles/hr 1.151 pounds of water raised
308
Mechanical Design of Process Systems
(Continued). Alphabetical Conversion Factors TO CONVERT
INTO
knots
Yards
KNOIS
feet/sec
MULTIPLY
lhl
8Y
2,027.
microhms m
1.689
Ljght year lines/sq cm lines/sq an. lines/sq in. lanes/sq in. lines/sq in. links {engineer's)
webers/sq in.
liters lrters
pints {U.S. liq.)
lrterS
Iiters liters liters Ite15
liters
liters/min liters/rhin
lumens/sq ft
quarts (U.S. cu ftlsec
laq.)
gals/sec
Lumen/sq. ft.
foot-candles Spherical candle power Watt Lumon/sq. meter
lur
foot'candles
Lumen Lumen
0.1550
miles miles miles miles miles
1.550 x 10-r
males
3.0 5.9 x l.0r:
9.46091 x 101! 1.0
8aus5e5 Sausses
webers/sq meter tncnes Inches bushels (U.S, dry) cu cm cu feet cu inches cu meters cu yards gallons (U.S. liq.)
links (surveyor's) liters
l0-l
1,550 x
10-'
12.O
7.92 0.02838 1,000.0 0.03531
6r.02 0.001 1.308 x
l0-!
o.2642 1.057 5.886 x 10-' 4.403 x r0 ' 1.0
.079s8 .001496 10.76
kilolines
megohms
rneters meters meters meters meters meters meters meters meters
centimeters feet
meters/min mbterc/min meters/min
cms/sec
meters/man meters/man
meters/min melers/sec
fieters/sec
tnches kilometers miles {naut.} miles (stat.)
millimeters yards varas
10r'
1oi 100.0 3.281 0.001 5.396 x 6.214 x
0.05458 0.06 0.03238 0.03728 196.8 3.281 3.6 0.06
knots males/hr feet / min
me(ers/5ec
miles/ hr
melers/sec meters/sec/sec meters/sec/sec meters/sec/sec met€rs/sec/sec
miles/min cms/sec/sec ft/sec /sec
meteFkilograms
cmdynes
kms/hrlsec miles/hr/sec cm-8lams pound-feet farads Srams meEonms
10-' 10-'
1.094 1.179
teet/sec kms/hr
(statute) (statute) (statute) (statute)
miles/hr miles/hr miles/hr miles/hr miles/hr miles/hr m iles/hr miles/hr miles/hr/sec miles/hr/sec rniles/hrlsec m
meteas
miles (statute) yaros
centimeters feet Inches kilometerc
metels males (naut.)
yaros
feet/sec
kms/hrlsec meters/sec/sec cms/5ec teet/sec kms/min knots /rn in
miles/hr cu inches
nilligrams/liter
parts/million
kilograms meters gra ins Srams
millihenries
henraes
millilite|s
liters centimeters leet
tls
miner's inches
Minims (British)
Manims (U.S,,
inches kilometers me(ers m
fluid)
(angles) (angles) (angles) {angles) myr;agrams mytrameters mynawattS
r,609. 0.8684 1,760. 44.70 88. 1.467
rles
rls yards cu ttlsec
26.42 44.70 1.467 1.609
0.4470 2,642. 88. 1.609
0.8684 60.0 9.425 x 1,000.
10-.
1x 10-t 0.01543236 0.001 1.0 0.001 0.001 0.1
3.281 x
10-t
0.03937
l0-.
0.001 6.214 x
10-'
1.094 x
10-!
m
centimeters feet IncneS
mils
10
r.509
0.8584
miles/min
mils
6.336 x
l.609
c|hs/sec/sec feet/sec/sec
millimeterc millimeters millimeters millimeters millirneters million Sals/day m ils
l0'
o.o26a2
rfieters/min
millimete6
l.l.516 2,027. 1,609 x
kms/min knots
in
1,853.
kms/ht
mil-feet milliers Millim;crons Milligrams milligrams
rTr
1CP
6,080.27
kilometers
teet/min
males/hr/sec niles/ min miles/
feet
cms/sec
lnils
0.03728 100.0 2.237 9.807 x
{statute)
millimeters millimeters
r,000.0
3.28r
meters/sec meters/sec
mrcrotarad micrograms mtcronms
l0-.
teet/min
feet/sec kilometers/hr kilometers/min
meterkilograms meterkilograms
0.001 1C|'
mrcrohms ohms
miles miles miles miles miles
miles/min miles/min miles/min
0.0929
M
megarnes megohns
meters
(naut.) (naut,) (naut.) (naut.) (statute) (statute)
MULTIPLY BY
10-. 10-. 1x 10-.
liters
miles (naut.)
miles (approx.) Miles Kilometers
INTO
ohms
icroliteIs
Microns
L
league Light year
TO CONVERT
kilometers yaros cu ft/min cuDtc cm. cubtc cm.
minutes minutes minutes minutes
deSrees
nepers Newton
decibels
quaorants radians seconds kilograms kalometers kilo,,ratts
1.54723
2.540 x 10-' 8.333 x 10-! 0.001 2.540 x 10-3
2.778x 1O-, 1.f,
0.059192 0.061612 0.01667 1.852 x 2.909 x 60.0 10.0 10.0 10.0
10-.
l0-r
105 N
l0-. Dynes
1x105
309
Appendix D: Conlersion Factors
(Continued). Alphabetical Conversion Factors MULTIPLY
TO CONVERT
BY
0 OHlvl (lnternational) ohms ohms ounces ounces ounces ounces ounces ounces ounceS
ounces ounces ounces ounces ounces ounces ounces
(fluid) (fluid)
(troy) (troy) {troy) (troy) (troy) Ounce/sq. inch
ounces/sq rn.
OHIVI (absolute)
megohms
mrcrohms drams grains grams pounds ounces (troy) tons (long) tons (metricJ cu inches
liters grains grams ounces (avdp.) pennyweights (troy) pounds (troy)
0ynes/sq. cm. pounds/sq in.
1.0005
10-, 10. 16.0
2a349527 0.0625 0.9115 2.790 x l0-5 2.835 x 10 5 1.805 o.02957
parts/mill,on
Miles Kilometers grains/U.S. gal grains/lmp. gal
parts/million
pounds/million gal
Pecks (British) Pecks (Britash) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) pennyweights {troy} pennyweights {troy) pennyweights (troy) pennyweights {troy) pints (dry) pints (liq.) pints (liq.)
cubic inches
parts/million
pints (liq.) pints (liq.) pints (liq,) pints (liq.) pints (liq.) pints (liq.) Planck's quanturn
rotse Pounds (avoirdupois) poundats p0unoals pounoars pounoats poundats pounoars pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds (troy) pounds (troy)
liters
graans
ounces (troy) grams pounds (troy)
4309 0.0625
19 x 10u 3.084 x 10rr
0.0584 0.07016 8.345 554.6 9.091901
8.809582 8 24.O
cu mererS cu yards ga||ons
liters quarts (liq.)
-
second Gram/cm. sec. Erg
ounces (troy) dynes grams
joules/cm joules/meter (newtons) kilograms pounds drams dynes
grains grams
joules/cm joules/meter (newtons) krlograms ounces ounces {troy) pounoars pounds (t.oy) tons (short) grarns grams
INTO
ounces {avdp.) ounces (troy) pennyweights {troy) pounds (avdp.) tons {long) tons (metric) tons (shoft) cu feet cu Inches ga
Ions
cu ltlsec cm-dynes cm-grams meter-kgs
ft tt
ft
grams/cu cm kgs/cu meter poun0s/cu rn,
ft
pounds/mil{oot
an.
gms/c(1 cm
in. in. in.
kgs/cu meter pounds/cu ft
pounds/ in.
pounds/mil-foot pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq rn. pounds/sq in. pounds/sq in. pounos/sq In. pounds/sq in.
pounds/mil{oot kgs/meter gms/cm gms/cu cm almospneres feet of water inches of mercury kgs/sq rneter pounds/sq in. atmospheres
MULTIPLY 8Y
12.0 240.0 0.a22457 3.6735 x 10-r
3.7324x 1o-'
4.1143 x 10 0.01602 27.64 0.1 198 2.670 x 10-r 1.356 x 10' 13,825.
'
0.1383 0.01602
t6.02 5.787 x 5.455 x 2.768 x 1,724. 9.425 x 1.488
10-'
10-'
l0' 10
6
178.6
2.306 x 1Cr6 4.725 x lO-' 0.01602 0.01414
4.882 6.944 x
10-!
0.06804 2.307 2.036
inches ot mercury kgs/sq meter
703.1
pounds/sq ft
144.0
0.05
o
4.1667 x 10-r
cu rnches cu cms. cu feet cu inches
(troy) (troy) (troy) (troy) (troy) (troy) (troy) pounds of water pounds of water pounds of water pounds of water/man pound-feet
pounds pounds pounds pounds pounds pounds pounds
pounds/cu pounds/cu pounds/cu pounds/cu pounds/cu pounds/cu pounds/cu pounds/cu pounds/ft
31.103481 1.09714 20.0 0.08333
bushels cubic inches
liters quarts (dry)
CONVERT
pound{eet
480.0
P Parsec Patsec
TO
413.2 0.01671 24.47 4.732 x 10-' 6.189 x 10-' 0.125
o.4732 0.5 6.624 x 10-11 1.00 14.5833
t3,826. 14.10 1.383 x 10-1 0.1383 0.01410 0.03108 44.4823 x 7,000.
lcl'
quadrants (angle) quadrants {angle) quadrants (angle) quadrants (angle) quarts (dry) quarts (1,q.) quarts (liq.) quarts (laq.) quarts (liq.) quarts (liq.) quarts (liq.) quarts (liq.)
deg/ees
.ad ians
degrees
radtans radians radians
mrnutes quaoran(5 seconds
90.0 5,400.0
minutes rad ra ns
1.57I
seconds
cu Inches cu cms cu feet
cu rnches cu rneters cu yards
8aIons liters
radians/sec radians/sec radians/sec radians/sec/sec
revol!tions/min
0.4536 16.0 14.5833
rao rans / sec/ sec
radians/sec/sec
revs/sec /sec
32.t7
revoru!ons
4.448
1.21528 0.0005
5,760. 373.24177
9.464 x 1.238 x o.25 0.9463
l0-.
10-!
R
revolutions/sec revs/min/rnin revs/min/sec
0.04448
3.24 x 105 67.20 946.4 0.03342
revolutions tevolr.rtions
revolutions/min revolut,ons/min revolutions/min
quadranls radtans oegrees/ sec
€dians/sec tevs/sec
3,438.
0.6366 2.063 x 9.549 0.1592 573.0 9.549
0.1592 360.0 4.0
6.2a3 6.0 0.1047 0.01667
105
310
Mechanical Design of Process Systems
(Continued). Alphabeticel Conversion Factors IO
CONVERT
revolutions/rhin/min revolutions/min/min a€volutions/min/min revolut'ons/sec revolutrons/sec revolutions/sec revolutions/sec/sec revolutions/sec/sec revolutions/sec/sec KOO
INTO
radians/sec/sec revs/min/sec revs/sec/sec oegrees/ sec
radians/sec revs/mrn radians/sec /sec
revs/min/min revs/min/sec Chain (Gunters)
Rod I\reters Rods (Surveyors' meas-) yaros
feet
rcds
MULTIPLY BY 1.745 x 0.01667
l0
l
2.778x lO-. 360.0 6.283 60.0 3,600.0 60.0
TO CONVERT square square square square square square square square square
mils
6.452 x
mrls yards yaros yards yards yards yards yards
sq
Pounds
sq feet sq inches
sq inches sq meters
feet
square square square square square
mles
sq millimeters sq yards
meteas
sq rncnes sq mrles sq millimeters sq yards acres sq feet sq xms sq meterc sq yards
square rniles square miles
millimeters millimeters millimeters millimeters mils
10
rr
l0-. \o-' l0!
144.0
circular mils
square miles
0.1550
929.O
Incnes Inches Inches Inches Inches Incnes kilometers kilometers kilometers kilometers kiiometers kilometers kilometers meters meters metets meters meters
1.973 x 10r 1.076 x l0-r
5q crhs
5q
square square square square square square square square square 5quare square square square square square square square square square square
20
circular mils
sq merers
sq cms
sq feet sq millimeters sq mrls acres sq cms sq ft sq Inches
sq millimeters
temperature
absolute temperature ('C)
1.0
temperature ("c) + 17.78 temperature
temperature ('F)
1.8
absolute tenperatlre ("F)
1.0
temperature (" F)
temperature ('C)
0.09290 3.587 x 10-r 9.290 x rd 0.1111 1.273 x 106 6.452 6.944 x 10-! 645.2 106
7,716 x 247.1
('F) +460
tons tons tons tons tons tons tons tons tons tons tons tons tons tons
(long) (long) (long)
-32
(metric) (metric) (short) (short) (short) (short) (short) (short) (short)
(short)/sq tt (sho.t)/sq ft tons of water/24 hrs tons ol water/24 hrs tons of water/24 hrs
Volt/ inch Volt (absolute)
sq feet
circular mils sq cms sq {eet
sq Inches
circular mils
kilograms pounds tons (short) kilograms pounds kilograms ounces ounces (troy) pounds pounds {troy) tons (long) tons (metric) kgs/sq meter pounds/sq in. pounds of water/hr
gallons/min cu ft/ hr
watts
foot-lbs/min
907.1848 32,000. 29,156.66 2,000. 2,430.56 o.a92a7
0.9078 9,765. 2,000. 0.16643 1.3349
10
'
106 106
1,973.
1.076 x l0-r 1.550 x 10-l 1.273
3.4r29 0.05688 107.
44.27
fooflbs/sec
0.7374
norsepower horsepower (rnetric)
1.341 x 1.360 x 10-! 0.01.433
Watts (Abs.) Watts (Abs.)
kg-calories/min kilowatts B.T.U. (mean)/min. joules/sec.
watt-hours
Btu
watfhours
erSs
watt-hours watt-hours watt-hours watt-hours watt.hours watt-hours
foofpounds
106
2.590
0.0I
Btu/hr 8tu/min ergs/sec
10.76 1,550. 3.861 x l0-' 10. 1.196 640.0 27.88 x 106 2.590 x 3.098 x
2,205.
w
10.76 x 106 1.550 x l0'
l0
1.120 1,000.
.39370 .003336
Statvolts
1otr
0.3861 1.196 x 2.471 x
1,016.
2,240.
I0 '
106
sq miles sq yards acres sq cms
0.8361
3224 x 1O-, 8.361x 10'
sq males
T
2.778 x 10-. 0.01667 3.087 x 10-. 4.848 x 10-6 14.59 32.17
0.0001 3.861 x 100.0 1.196 x 2.296 x 1.833 x
sq mrles sq millimeters sq yards actes
2.066 x 10-a 8,361. 9.0
cfis
16.5
Steradians
ci.cular mils
10-'
5,029
grains minutes quadrants radrans Kilogram
10 -6
sq inches actes
('c) +213
Scruples seconds (angle) seconds (angle) seconds (angle) seconds (angle) Slug Slug Sphere square centimeters square centimeters square centimeters square centtmeters square centimeters square cenrmelers square centameters square feet square feet square feet square feet square feet
MULTIPLY 8Y
INTO
watts
Watt (lnternational) webers webers
Eram-caloneS norsepower-has
kilogram-calories kilogram-meters kalowatt-hrs Watt (absolute) maxwells
kilolines
l0-'
0.001
0.056884 1
3.413 3,60 x l0ro 2,656.
859.85 1.341 x
0.8605 0.001 1.0002
lo
l0'
l0-1
I Factors
Appendix D: Conlersion Synchronous Speeds Synd'ronout Spced
:
Frsoucncy
x
120
N;;|T;G;TREOUENCY
FNEOUENCY
2
60
.ycl.
50
cy.lo
50 Gyclo
50.y.ls
3600
3000
1500
12
't71.1
112.9
lg00
t 500
750
11
r
63.6
136.4
1200
|
000
500
15
t
56.5
t
30.1
8
900
750
375
18
t50
t2s
t0
720
600
300
50
141
t20
l2
600
500
250
l1
514.3
128.6
214.3
t6
450
375
t8
400
20
360
2l
30
r
38.5
rr5.4
51
|
33.3
lll.t
187.5
56
t
2s.6
t07.t
166 -7
5S
121.1
103
300
150
60
t20
100
272.7
136.4
62
l
l6.l
96.8
300
250
t25
61
1r2.5
93.7
276.9
230.8
It5,4
66
|
09. I
90.9
257 .1
211.3
|
07.1
68
t
05.9
88.2
210
200
100
70
r02.9
85.7
72
100
83.3
225
93
-7
.5
176.5
71
97 .3
8l,l
200
166.7
76
91.7
78.9
38
189.5
t57.9
92.3
76.9
,t0
180
t50
90
75
31
2
35
.8
Courtesy Inge$oll-Rand Co.
78.9 80
311
312
Mechanical Design of Process Systems
Temperature Conversion NOIA Thc c.ntlr .olsm'| of .'rmbcrt in boldl.ce r.ter3 to the tempe.ot'rre i. degree3, €irher Cenriorodc or fohre.heir, which ii i! dcti..d ro convcrt into th. othe. .col.. lf .o.v.dine from Fohrenh.it ro Ce.ligrode degreei, lhe equivolen. tempe.oture will be found in rhe tefr coiumn, whit€ if Gonve.ri^s trom d.er.er Cenligrodc to desrc$ Fohrenhi.t, th. on.wer wi be found in thc cotumn on rhe righr. Cenligrod.
-273.t7 -268 -267 -257 -25l -216 -210 -231
C.ntisrode
-159.f
-20.6
-,150
-212 -207 -20 |
-196 -190
-16.7
-ato
-16.
-184 -179 -173
-r69 -r68 -162 -157
-l5l
-t1.t
-360 -350
-260 -250 -240
-t10
-220
-r31
-2to
-129
-200 -190
-tol -96 -90 -81 -79 -73.3 -67.8 -62.2 -59,a
-t!0
-r70
-10.6 -10.0
-9.1
459.1
-151 -136
r00
-90 30
-lt
-70
-15.6 -12.8 -10.0
-5t
-{5 -{0
12.8 r
3.3
39.2
l3 .9
4r.0 t2.g
!
11.6 46.1
9
14.2
-361 -316
t0
50 .0
t2
53.6
tl
5.7
-310
t27.1 t29.2
l3l
60.0
.0
62
15.0 15.6 r
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113.6 115.4
6.l
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18.3 18.9 19.4 20.0
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62.6 61.1 66.2 68.0 69.8
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forhulot ol thc right moy olro be urcd conyerling Centi!.odc or tohrcnh€ir inlo the orhcr i.ole.,
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563 572 590
171
320 330 340
192.2 194.0 195.8 197.6
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350
t82 t88
360 370
680 698
716 731
608
626 611
40
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|
99.4
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201 .2
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105.8
147.6 | 09.1
203.0 201.8
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95 95
390 400
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770
216
420 430
806
39
a3 44 45
35.6 36. I
113.0
15 47
1 1
a9 50
5t
Des,ee3 c€.r.. .c =
206.6 208.1 210.2 212.0
221
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230
213 219 251 260
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Dcaree! Kelvin,
92.
ln.2
=
Courtesy Ingersoll-Rand Co.
82 .1 81 .2
34 35 37
371
98 .9
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95.0
329 338 317
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0.6
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281 293
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266 275
55 55
73.1 75.2
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80.6 .7
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821
812 860
878 896 914
932
Appendix D: Conrersion
Altitude and Atmospheric Pressures
Ke/'q Hs Abr. -5000
77 75 73
-1526
25 21 23
,{500
-t373
-1000 -3500 -3000
-1068
-9r5
70
21
-2500
-763 6t0
58 66 61
20
6l
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2000
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0
500
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t9
l8 l7
59 57
t1
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t500
158
2000
6t0
2500
763
3000 3500
915
4000 ,1500
t2.t6 .78
I I
22.23 2l .39
632.s 609.3 586.7 561.6 513.3
.860
3
21.90 23.99
12.23
3S
,91
.828 .797 .767
10.50
.738
20.58
522.7
t0.10
r6.89
.7to
A29 .0
13.76 .12 8.903
319.5 226.1
8.29 6.76 5.46 1.37
.060
't79 .3
3.17
111 .2
2.73
_9
3050
1O,67i
66
18
37 .9
61,o20
720,O00
240.000 260,000
1t .7 45.5 19.3
67,122 73,221 79,326
2S0.000
53.1
85,128
300,000
56.9
91,530
,{00,000 500.000 600,000 800,000 1,000,000
75.9
122,010 152,550
l,{
r52 189
-11
-70 -70
-57 -55 62
52
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-59 -16
_26
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12/11 18,8t 6 51,918
28
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68.9
2.135 1.325 18.273 |
51.2
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8.36
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5 .917-7
2./16-7 1.284-' 5.816-r
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2.523 ' 9.955-. 3.513-r
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1,600.000
30,{
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312
5!9,r80
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610,200
L 2-r'
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10
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224 266
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87
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| ---l-r 83,060 - |I 211,080 -305,100 --
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1,200,000
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12,2O1
200,000
I
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22.8 26.6 30.4 31.2
91.8
9
23
610? 7628 9153
120,000 1,{0,000 160,000 180,000
.960
611.1
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2A,108 27,159 30,510 36,612
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|
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17.1
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15.2
719.6 706.5
7 5
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60,000 70,000 80,000 90,000 t00,000
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2136
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35,000 40,000 45,000 50,000 55,000
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889.0 871.3 859.5 845. t
52
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17.18 17.19
35.00 31.12 33.84 33.27
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5000
10,000 15,000
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PSIA
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Hg Ab3.
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ot
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Facrors
313
Mechanical Design ol Procesr Sysrems E
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Index
concrete modulus of elasticity of, 186 concrete and steel, relative strength of, 186 gusset plates, 188* 189
ACI bearing strengths, 180 American Institute of Steel Construction. See AISC. Anchor bolts analysis, preloaded bolt, 184, 186 bolt area, required, 184 bolt loads, allowable, 187 bolt load, minimum required, 184 bolt spacing, 186 common types of, 190 large bolts, undesirability of, 184 loading force, distribution of, 186 loadings induced on, 184 lubricant, 190 philosophy, design, 184 size and number, 228 stress in, 184, 186 tension on gross area, 187 torque, anchor bolt, 189-190, 229 ASME Piping Codes ASME 831.1, 48 ASME 831.3, 48 ASME B3I.4, 48 ASME B3I.5, 48 .ASME 831.8,48 ASME Section IlI, 48. Also see Pressure vessels. for piping, 48 for pressure vessels, 48 ASME Section VIII, Division II for piping, 48 Aspect ratio, 85
k-factor, offset, 188 steel, modulus of elasticity, 187 steel-concrete moduli ratio, 186 tension on gross area, 187 torque, anchor bolt, 189-190, 229 Bernoulli equation, 2 Bingham, 6-7 Boundary conditions for saddle plate design, 178 Buckling coefficients for saddle plate design, 175-178 Centroid, section,212 Circumferential stress, moment, 170 Codes, vessel differences in, 159 foreign, 159 Cold-spring,49 Colebrook equation, 4. Also see Friction factors. Compressible flow adiabatic
flow, 2
compressibility effects, 24 introduction to, l-2, 24 isothermal flow 1 modulus, bulk compressibility, 24 non-steady flow, 24 sound, velocity of, 24 steady flow, 24 Concrete mixes for baseplate design, 186-187 Concrete modulus of elasticity, 186 Conical sections, 199, 224
Baseplate design, 186-189 anchor bolt size range, 186 bearing pressure on, 189 concrete foundation for, 186 concrete mixes, 186, 187
Cost-plus contractor, 183
Creep,49 Critical damping factor, 202, 2O4 Critical pressure, 83 315
316
Mechanical Design of Process Systems
Critical temperature, 83 Critical wind velocity, 236
Heads
Damping coefficient, 2OZ 2M
thickness of, 160 Heat transfer
Deflections, windt 199-2Ol , 242 Degree of freedom, 201 Discontinuity, 236
Drag, 195,203 Ductile materials, 50, 52 Dynamic magnification factor, 201-204 Dynamic response, 200
EJMA. Sze Expansion joints, bellows. Electrical tracing, 103 Equivalent length, 2 Expansion joints
bellows, corrugated, 77 gimbal joint, 79 hinged joint, 78-79 inJine pressure balanced, 79 multi-ply, 80 pipe span, allowable, 78 pressure thrust, 78-79 single ply, 80 standards of the Expansion Joint Manufacturers Association (EJMA), 80 stiffness, rotational, 78 stiffness, translational, 78 tie rods, 78-79 reasons for, 78 universal joint, pressure-balanced, 78 Fanning equation, 3
Fluid Mechanics, piping. See Hydraulics. Fourier number, l5l Friction factors, 4 Colebrook equation, 4 laminar flow, 4 Moody friction factors, 4 Prandtl solution, 5
turbulent flow, 4 von Karman solution,
5
Gimbal joint, 79 Grashof number, 132, 134, 153 Gusset plates, 188-189 Gust (wind) effects, 194-196, 236-237 Guy wires, 249
-*T co'\J 'rv foot of, 2 pressure, I
Head
5oo
r{ 'll"i, '
static, I velocity. See Velocity head.
manufacture
of,
160
control mass, 115, 131 control volume, 115, 13l electrical tracing, 103 Fourier number, 151 Grashof number, 132, 134, 153 in jacketed pipe, I 12- I l5 LMTD (log mean) chart for, 114 definition of, I 14 Nusselt number, 132, 134, 153 in pipe shoes, 135- 136 application of, 156 heat balance for, 136 temperature distribution
in,
136
in pipe supports, 133 in piping temperature distribution in, 134 typical applications of, 133- 134 Prandtl number, 112, 139-140 in process systems, 103 in residual systems applications of, 132 deflections, thermal, 134-135 overall heat transfer coefficient, 134 tubular tracers. See Tracing. in vessel skirts application of, 152- 154 coefficients of, 132 convection, significance of, 133 free convection, 133 rate
of,
133
temperature, distribution oI, 132- 133 Heat transfer design example, 148-150 static analysis, i48- 150 transient analysis, 150- 152 Heisler's chart, l5l Hesse formula, 82
Horizontal pressure vessels saddle bearing plate design, 180 ACI bearing strengths, 180 bearing plate thickness, 180 factor of safety for, 180 saddle plate buckling analysis, 251 252 saddle plates
application of , 249 -252 boundary conditions for, 178 buckling coefficients for, 175- 178 design
of,
174- 179
effective area, 174, 178
l:;:.. effective width, 113, 178, l'79 horizontal reaction, 119, 252 stiffener plates, I74, 179 STTESS
criterion for residual, 178 elastic buckling, 179 inelastic buckling, 179 U.S. Steel design method, 174-179 web plates, 174 wear plate requirements, 215 Zick analysis, 166, 215 bending moment diagram, 167 constant, circumferential bending moment, 170 introduction to, 166 saddle supports, location, criteria for, 172 shear stress, 171
yield-pseudoplastic, 6 7 piping, reasonable velocities in, 25 problem formulation, 24 two-K method, 8,21 viscosity,24-26 Incompressible flow. See Hydraulics. Internal pressure, 159- 160 Jacketed pipe
annulus, hydraulic radius for, 112 applications of, l12-115, 139 140 details of, 104-106, I 12-l l3 expansion joints for, 105- 106 heat transfer, I 12- I l5 coefficient, film, I l2
coefficient, overall, 112
shell
stiffened by head, 171 unstiffened, saddles away from head, 17l
stiffening rings, 172, 174
rates of, I 12- 115 pressure drop in, I l5- I 17
rules of thumb for, 103
allowable compressive, 166 circumferential compressive, l7 I circumferential at horn of saddle, 17l
versus traced pipe, 103- 106 Joints. expansion. See Expansion joints. Laminar flow, 4. Also see Friction factors. Lumped-mass approach, 204-205
head used as a stiffener, 171
Lump-sum contractor, 183
STTESS
"Hot-spring," 49 Hydraulic radius, definition of, 2i
Maximum allowable working pressure, 160 Mitchell equation , 210, 212 Moments equations
tabulated values, 24
Hydraulics basic equations, I Bernoulli equation, 2
modified form of,
3
compressible flow adiabatic flow, 2
compressibility effects, 24 introduction to, l-2, 24 isothermal flow, I modulus, bulk compressibility, 24 non-steady flow, 24 sound, velocity of, 24 steady flow, 24
incompressible flow, 1 non-Newtonian fluids
Bingham,6-7 introduction to, 5-7 Metzer and Reed, 7 pseudoplastic, 6-7 rheological constants, 8
rheopectic,6-7 thixotropic, 6 7 time-dependent, 6-7 time-independent, 6-7 viscoelastic, 6-7
for, 198 of inertia, for tube bundle, 222-223 wind-induced, 198 Moody friction factors. See Friction factors. Myklestad method, 200-201 Non-Newtonian fluids. See Hydraulics. Nusselt number, 132, 134,153
Ovaling, 205, 208 Pipe loops, 59-68 Pipe lug supports , 70-12, 98-99 Pipe materials ductile materials, 50, 52 non-ductile materials, 50 plastic deformation, 50 52 stress-strain curves, 50-51 Pipe shoes, heat transfer in, 135-136 Pipe supports, heat transfer in, 133 Piping codes. See ASME. Piping expansion joints. See Expansion joints. Piping mechanics anchor, pipe, definition, 58
API,47
318
Mechanical Design of Process Systems
equipment nozzle loads, 94
stiffness beam element, 54
extraneous piping loads
"cold spring" for, 80 vibration applications for, 100- 101 natural frequency of beam elements, 86 vortex shedding, 83,87 resonance,83 Reynolds number, 195, 200, 2Ol, 236 Strouhal number, 84-85
vortex force, 83 vortex streets, 83 flexibility (compliance) matrix, 53 flexibility method, 59-68, 8l advantages of, 53, 68 application of, 95-98 "hot-spring," 49 nozzle flexibility factors, angle of twist, 70 circumferential, 70 longitudinal, T0 Oak Ridge Phase 3 Report, 70 rotation deformation of, 70 rotational spring rate, 70 pipe loops, 59-68 pipe lug supports , 70-72, 98-99 pipe restraints moment restraints (MRS), 5'7 -59, rotational 58, 68 translational,58,68 pipe roughness, 5
Prandtl number,
77
, 88-94
prpe stress
circumferential bending/membrane, 7l "cold-spring," 49 creep,49 "hot-spring," 49 internal pressure, circumferential stress, 49 longitudinal stress, 49 pipe weight, bending stress, 49 pressure, 72 prestressed piping, 80 primary stress, 49-50, 72 range, allowable, 42 residual stress, 5l secondary stress, 49-52, 72
self-spring,49 "shakedown," 52 thermal expansion, 49 torsional or shear stress, 49 self-spring,49 shear flow, 58-59 spring supports, 72, 75, 76 guided load column, 72 jamming of, 77
concrete,69 matrix,53-54 method,8l advantages,53,68 applications of, 88-94 piping elements, 55-56, 69 translational, 54 Pipe Stress. See Piping mechanrcs. Piping systems adiabatic process, 83 API 520 Pafi 2, 82 ASME 31.I, 82 critical pressure, 83 critical pressure ratio, 83 critical temperature, 83 Hesse formula, 82 impulse-momentum principle, as applied to a pipe elbow, 8l nozzle correction factor, 82 nozzle discharge coefficient, 82 nozzles,83
ll2,
139-140
Pressure vessels ASME Section VIII Division components, 159- 160
I,
160
design, philosophy of, 159 external pressure, 160 heads, 160 horizontal saddle bearing plate design, 180 saddle plate buckling analysis, 251-252 saddle plate design, 174- 179 application of , 249-252 boundary conditions for, 178 buckling coefficients for, 175- 178 effective area, 174, 178 effective width, 173, 178, 179
horizontal rcaction, 179, 252 stiffener plates, 174, 179 stress, criterion for residual, 178 stress, elastic buckling, 179 stress, inelastic buckling, 179 U.S. Steel design method, 174-179 wear plate requirements, 215 web plates, 174 Zick analysis, 166, Zl5 bending moment diagram, 167 compressive B-factor, 174 constant, circumferential bending moment, 170 head used as stiffener, 171 saddle support location, 172
b"l- ! moments equations
shear stress in head/shell, 171 shell
stiffened by head, l7l unstiffened, saddles away from head,
for, 198 of inertia, for tube bundle, 222-t3
171
stiffening rings, 172, 174 stress, allowable compressive, 166 stress, circumferential con.rpressive, 171 stress, location of, 168- 169 tangential shear, 167- 171 wear plates, 171- 172 internal pressure component thickness, 159 maximum allowable working pressure, 160 quality of welds, 159 upset conditions, 160 vertical anchor bolts analysis, preloaded bolt, 184, 186 bolt area, required, 184 bolt loads, allowable, 187 bolt load, minimum required, 184 bolt spacing, 186 common types of, 190 large bolts, undesirability of, 184 loading force, distribution of, 186 loadings induced on, 184 lubricant, 190 philosophy, design, 184 size and number, 228 stress in, 184, 186 tension on gross area, 187 torque, anchor bolt, 189-190, 229 ANSr-1982,215 baseplate design, 186- 189 anchor bolt size range. 186 bearing pressure on, 189 concrete foundation for, 186 concrete mixes, 186, 187 concrete modulus of elasticity of, 186 concrete and steel, relative strength of, 186 . gusset plates, 188- 189 k-factor, offset, 188 steel, modulus of elasticity, 187 steel-concrete moduli ratio, 186 stress, compressive, on concrete, 188 thickness, baseplate, 188 centroid, section,212 combined loads on, 181 compression plate, 189 cone, truncated, equivalent radius for, 214 conical head, equivalent radius for,214 conical sections, equivalent radii for,224 earthquake, See Seismic design. loads, wind and seismic, 190-191
pressure sections, centroids vectors, section force, 198
of,
198
wind-induced, 198 wind pressure, distribution of, 198 section properties of, 181 seismic analysis of, loads, combined, 190-l9l seismic design baseplate design, 238
coefficients, Mitchell, 210, 213 coefficients, structure type, 210 criteria, quasi-static, 210 criteria,238 Mitchell equation, 2lO, 2lZ compared to Rayleigh equation, 237 -238 occupancy importance factor, 210 period
characteristic site, 238 numeric integration of vibration, 238-239 of tower, 210, 2lZ Rayleigh equation, 212 compared to Mitchell equation, 237 238 seismic zone factor/map, 210-211 site structure interaction factor, 210, 212 equation for, 212 shear forces earthquake force, total, 212 lateral force, equation for, 212
vertical distribution of, 212 seismic moments, equation for, 212 skirt design, 238 structural period response factor, 210
Uniform Building Code, 209 210 self-supporting, 180 skirts controlling criteria for, 184 design of, 183, 185 cost-plus contractor, 183 Iump-sum contractor, 183 stress equation, 183 supports, 183, 185
thichess, 183- 184 stress, bending, 181 combined loading,
181
compressive B factor,
l9l
compressive, leeward side, discontinuity, 236 elements
in,
182
tensile, windward side, l8l vacuum, 183 towers centroids, section, 230-231
181
319
32O
Mechanical Design of Process Systems
definition of, 181 equivalent circle method, 214 section moment of inertia, 241-243 skirt and baseplate destgn, 228-229 anchor bolts, 228 anchor bolt torque, 229 compression ring thickness, 229 skirt thickness, 229 weld size, minimum for skirt-to-base plate, 229
skirt detail, 230 stress, discontinuity
criteria foq 2 14 for conical sections, 214 stresses, wind section, 226-228 transition piece, 241, 243-244 vibration ensemble, 216 of lumped masses, 232, 246 wind deflections modes of, 199 schematic diagram of, 201 superposition, method of, 199 wind ensemble, 242
vibration, wind-induced angular natural undamped frequency, 205 applications of, 232-236, 241-249 area-moment method, 205-207 conjugate beam. See Area moment. controlling length, 203 critical damping factor, 202, ZO4 critical wind velocity, 208-209 , 236, 248,249 total wind force, 209 Zorilla criteria, 209 damping coefficient, 203 damping ratio, 202-203 degree of freedom, single, 201 differential equations for, 201-2OZ dynamic magnification factor, 201-202, 2O3,
2M dynamic response, 200 example of, 232-236 first period of, 204
force amplitude, 235 force amplitude, dynamic, 200 forced vibration theory, 200 frequency
natural,248 ratio,202 vortex shedding, 208, 248 guy wires, disadvantages of, 249 Holzer procedure, 200 lock-in effect, 200 logarithmic decrement, ZO3-204 lumped mass approach, 204-205
mode shapes, 200 Myklestad method, 200, 201
ovaling,205 natural frequency of, 205 vibration due to, 208 wind velocity, resonance, 208 period of vibration, 234-235, 248 phase angle, 202 Rayleigh equation, ZOO, 201, 204, 205 resonance,236 Reynolds number, 195, 20O,201,236 soil types, 204 stresses, dynamic, 236 tower fluid forces on, 203 model for, 201-202 moment disrribution in, 205 stiffness, 205 vibration ensemble, 209 of lumped masses, 232 vibration, first peak amplitude, 200 vortex shedding, 199 vortex strakes, 249 wind tunnel tests, 236 wind analysis of, loads, combined, 190-191 wind design speed ASA 58.1-1955, 194 ANSI-A58.1-1972, 192 basic wind pressure, 192 effective velocity pressure, 192 gust response factor, dynamic, 192 ANSI A58. 1- 1982, 196, 236-237 effective velocity pressure, 192 gust response factor, 192 importance coefficient, 192 velocity pressure coefficient, 192 wind speed, variation of, 192 wind tunnel tests, 192 centroid of spandrel segment, for wind section, 218 coefficient, drag, 195 structural damping, 217 conical sections, 199 constant exposure category, 195 cross-sectional area, effective, 217 cylinder, pressure fields around, 196 equivalent diameter method, 236-237 vs. ANSI-A58. 1- 1982, 236-237 exposure lactor. 196 fatigue failure, 198 flexible structures, defined, 197 gust duration, 196 vs. gust diameter, 197 gust frontal area, 196
ii l:r.=
gust response, dynamic, 194 gust response factor, 195, 196,217,236-231 gust size, 196 isopleths, 192- 193
Kutta-Joukowski theorem, 195 loading analysis, quasi-static, 196
logarithmic law, 192 parabolic area, centroid of, 219 parabolic function, 194 peak values, types of, 196 power law, 192 probability of exceeding. 196 response spectra, 198 return period, 192 similarity parameters, 195 structure size factor, 196, 197 surface roughness, 195 tower
application of , 249 -252 boundary conditions for, 178 buckling coefficients for, 175- 178
effective area, 174, 178 effective width, 173, 178, 179 horizontal react\on, 179, 252 stiffener plates, 174, 119 stress, criterion for residual, 178 stress, (in-) elastic buckling, 179 U.S. Steel design method, 174-179 wear plate requirements, 215 web plates, 174
of, 198 fluid force exerted on, 194-195 gust velocity vs. structural response, 197
.
natural frequency of, 197 wind area section properties, 219 wind force distribution, 218 wind distribution parabolic, 194, 218-219 triangular, 194 wind load applications of, 215-231, 241-245 equivalent static, 195 mean, 195 weld size, skirt-to-base plate, 189 welding, joint efficiencies for, 161-165,172 Zick analysis, 166, 215 bending moment diagram, 167 compressive B-factor, 174 constant, circumferential bending moment, 170 head used as stiffener, l7l saddle support location, 172 shear stress in head/shell, 171 shell
stiffened by head, 171 unstiffened, saddles away from head, 171
stiffening rings, 172, 174 stress, allowable compressive, 166 stress, circumferential compressive, stress, location of, 168- 169 tangential shear, 167- 171 wear plates, 171- 172
30,32 41. 1,19-l{l"t. l-!:. 145,147 non-Newtonian fluids. See Hydraulics. Non-Newtonian fluids. Strouhal coefficient vs., 85 vortex shedding, for, 83-85 Newtonian fluids, 21,
Saddle plate design, 174- 179
cross-sectional area
171
Seismic design baseplate design, 238
coefficients, Mitchell, 210, 213 coefficients, structure tYPe, 210 criteria, quasi-static, 210 compared to wind, 238 Mitchell equation , 210, 212 compared to Rayleigh equation, 231-238 moments, equation for, 212 occupancy importance factor, 210 period, characteristic site, 238 period, vibration numeric integration of, 238 239 tower,210,212 Rayleigh equation, 212 compared to Mitchell equation, 231-238 seismic zone factor/map, 210, 2ll shear forces earthquake force, total, 212 lateral force, equation for, 212
vertical distribution of, 212 site structure interaction factor, 210, 212 equation for, 212 skirt design, 238 structural period response factor, 210 Uniform Building Code, 209-210 Skirts, 185 controlling criteria for, 184 cost-plus contractor, 183 design
in, 132-135 in piping, 154- 155 Reynolds number, 195, 2OO, 2Ol, 236 drag coefficient vs., 203 Residual systems, heat transfer
r
of,
183
lump-sum contractor, 183 stress equation, 183 supports, 185 thickness, 183- 184
322
Mechanical Design of process Systems
Strouhal number, 84 Reynolds number vs., 85 vibration, vortex shedding, 84-85, 200, 20g Supports, 72,75,76. Also see p\ping mechanics.
heat transfer, rules of, 107 modes of heat transfer, 107
Thermal design. See Heat transfer tie rods, 78-79 Towers
definition of, l8l equivalent circle method, 214 section moment of inertia, 241-243 skirt and baseplate design, 228-229 anchor bolts, 228 anchor bolt torqte, 229 compression ring thickness, 229 skirt thickness, 229 weld size, minimum for skirt{o-base plate, 229 skirt detail, 230 stress, discontinuity criteria for, 214 for conical sections, 214 stresses, wind section, 226-228 transition piece, 241, 243t244 vibration ensemble, 216 of lumped masses, 232, 246 wind deflections of modes of, 199 schematic diagram of, 201
of,
film coefficients for, 143 of, 115 applications of, 130, 140- 148 film coefficient, vessel-side, 147 use
heat duty of, jacketed heads, 146 heat transfer coefficients, reasonable values of, 130
transient, I l5 criteria for, 115 importance of, 130 internal baffle plates, heat duty of, 144 jacketed walls, heat transfer film coefficient, 145 jackets, types of, 115, l28,13l non-Newtonians, use of, 146 plate channels, equivalent velocity of, 147 reasons
for,
Turbulent f|ow,
115 4
- Also see Friction factors.
Velocity head
introduction,3,8 method,3 two-K method, 8, 21 values of, 9-20, 21, 22-23, 30-32
199
wind ensemble, 242 Tracing
Vessels. See Pressure vessels.
of pipes applications
of vessels and equipment agrtators
centroids, section, 230-231
superposition, method
outside film coefficient, 107 overall heat transfer coefficient, 107 procedure for design, 107
of,
136- 139 condensate return for, I l0 condensate load, determining, 1l I
guidelines for, 110-l spargers, 1l I
ll
separation keys, I l1 typical layout, 111 water hammer, 11 I hot oil, application of, 137-139 steam, application of, 136-137 versus jacketed pipe, 103- 106 with heat transfer cement, 106, 109- I 10 advantages, 106
procedure for, 109
film coefficient, natural convection, 108 heat balance for, I l0 heat transfer rates of, I l0 without heat transfer cement, 106-109 advantages of, 106 disadvantages of, 106
equivalent insulation thickness, 107 heat balance
fog
107
109
Vibration, wind-induced angular natural umdamped frequency, 205 applications of , 232-236, 241 -249 area-moment method, 205-207 conjugate beam. See Area moment. controlling length, 203 critical damping factor, 202, 204 critical wind velocity, 208-209 , 236, Z4g-249 total wind force, 209 Zorilla criteria, 209 damping coefficient, 203 damping ratio, ZO2-203 degree of freedom. single. 201 differential equations for, 201,202 dynamic magnification factor, 201 -202, 203, ZO4 dynamic response, 200 example of, 232-236 first period of, 204 force amplitude, 235 force amplitude, dynamic, 200 forced vibration theory, 200 frequency
natural,248
,!i
lri:r ftIio, 202
vortex shedding, 2O8' 248 wires, disadvantages of' 249 -suyi{olzer procedure, 200 lock-in effect, 200 losarithmic decrement, 203 -204 lumfed mass aPProach, 204-205 mode shapes, 200 Myklestad method, 200, 201 ovaling,205 natuial frequencY of. 205 vibration due to, 208 wind velocitY, resonance, 208 period of vibration, 234-235, 248 ohase angle, 202 ilayleigh-equarion. 200. 201. 204 ' 205 resonance,236 Reynolds number, 195, 200, 2O1' 236 soil types, 204 stresses, dYnamic, 236 tower fluid forces on, 203 model for, 201-202 moment distribution in, 205 equations for, 205 stiffness,205 vibration ensemble, 209 of lumped masses, 232 vibration, first peak amplitude' 200 vortex shedding, 83-87' 199 vortex strakes, 249 wind tunnel tests, 236 Viscosity, 24-25 von Karman solution, 5 Vortex shedding,83-87 aspect ratio, 85 cylinders,83 damping vs. amPlitude, 87 guidelines for, 85 mode shaPes, 85 reduced damPing, 85
Weld sizes recommended values, for Plates, 71
skirt to baseplate, 189 Welding, joint efficiencies for, 161-165, 172 Wind design sPeed ASA 58.1-1955, 194 ANSI A58.1-1972 basic wind Pressure, 192 effective velocitY Pressure, 192 qust response iactor. dynamic. 192 ANsl A58. l-1982, t96, 236-231 effective velocitY Pressure, 192
sust response factor. 192
irpottun." coefficient.
192
velocitv pressure coefficient, 192
wind speid, variation of' 192 wind tunnel tests, 192 : i -r centroid of spandrel segment, for wind section' coefficient, drag, 195 structural damPing, 217 conical sections, 199 constant exposure category, 195 cross-sectional area, effective, 217 cvlinder, pressure fields around, 196 equivaleni diameter method, 236-237 vs. ANSI-A58.1- 1982, 236-231 exposure factor, 196 fatigue failure, 198 fle;ble structures, defined, 197 gust duration, 196 vs. gust diameter, 197 gust frontal area, 196 iurt t.rpon.., dYnamic. 194 iurt ,.tpont" factor. 195. 1c0.217.236-237 gust size, 196 isopleths, 192- 193 Kuna-Joukowski Theorem. 195 loading analysis, quasi-static, 196 losarithmic law, 192 paiabolic area, centroid of, 219 parabolic function, 194 peak values, tYPes of, 196 power law, 192 probability of exceeding, 196 iesponse sPectra, 198
return period, 192 similarity parameters, 195 structure size factor, 196' 197 surface roughness, 195 tower cross-sectional area
of,
198
fluid force exerted on, 194-195 gust velocity vs. structural response' 197 iatural frequencY of,
197
wind area section Properties, 219 wind force distribution, 218 wind distribution parabolic, 194, 2t8-219 triangular, 194 wind load applications of, 215-231, 241-245 equivalent static, 195 mean, 195
Yield,
159
octahedral shear stress theory, 236
324
Mechanical Design of Process Systems
Zick analysis, 166, 215 bending moment diagram, 167 compressive B-factot 174 constant, circumferential bending moment, 170 head used as stiffener, l7l saddle support location, 172 shear stress in head/shell, 171 shell
stiffened bv head.
l7l
unstiffened, saddles away from head, 171 stiffening ings, 172, 174 stress, allowable compressive, 166 stress, circumferential compressive, 171 stress, location of, 168- 169 tangential shear, 167- 171 wear plates, l7l-172
