Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe

Mgchanica! Design of Process Systems Volume2 Shell-and-Tube Heat Exchangers Rotating Equipment Bins, Silos, Stacks

A.Keith Escoe

Gulf Publishing Company Book Division Houston, London, Paris, Tokyo

llctaniul

Design

of Pmctss Svsterns

\itme

2

SldLen*Tuh

Heat Exchangers

Roadng Equipnent r

o

Bins, Silos, Stacks

Copl right @ 1986 by Gulf Publishing Company, Houston, Texas. All righrs reserved. Printed in the United States of America. This b@k. or parts thereof, may not be reproduced in any form without p.rmission of the publisher.

Llbiary ol Congress Calaloging-in-Publicalion Data Escoe. A. Keith. \lechanical design of process systems. l-ocludes bibliographies and indexes. Piping and pressure vessels-v. 2. Shell-and-tube Conr€Drs: v. bear exchangers; rotating equipment; bins, silos, stacks.

l.

l-

Ch€mical

I- TirleTPI55.5.E83

plants

Design and construction.

1986

660.2

', 81

85-22005

O.ATant -562-9 (v 1) 6aaa (}ET2l)1-565-3 (v. 2)

lS€fl

iv

Contents

Foreword

........vii

by John J. McKetta

Preface

..........ix

Chapter 5 The Engineering Mechanics of Bins, Silos, and Stacks ........1 Silo and Bin Design, I Stack Design, 8 Vortex Shedding and Frequency Responsc. Ovaling. Helical Vortex Breaker Strakes.

Bin Stiffener Design. Vcssel Supports.

Example 5-2: High-Pressure Flare Stack Design, 20 Effective Diameters. Section Weights-Uncorroded weight. Required t Thickness. Anchor Bolt Design. Cantilever Vibration. Static Deflection. Dynamic Deflection. Anchor Bolt Torque. Design

Nozzle Loadings.

Pulsation Response Spectra Induced by Reciprocating Equipment, 62

Example 6-l: Horizontal Centrifugal Pump Sysrem Design, 65 Suction Line Pressure Drop. K-Values. Discharge Line Pressure Drop. The Effects of

Liquid Viscosity on Centritugal Pumps.

Summary.

Example 5-3: Stack Vortex Strake Design, 27 Example 5-4: Natural Frequency of Ovaling Ring Formula (Michell Formula), 28 Notation,29 References, 29

Example 6-2: Positive Displacement Pump Design,74 Suction Line Pressure Drop. K-Values. A word

About Priming.

Example 6-3: Centrifugal Compressor Selection, 79 Example 6-4: Installing a Compressor at Elevation, 34 Selecting the Reciprocating Compressor.

......31

Pumps, 31 Centrifugal Pumps. Hydraulic Requirements of Centrifugal Pumps. Positive Displacement Pumps. Pressure Protection for Positive Displacement Pumps.

Principles of Compression. Reversible Adiabatic (lsentropic) Compression. Polytropic Compression. Isothermal Compressron. Dimensionless Reference Numbers. Centrifugal Compressors. Reciprocating Compressors. \{ulriple Staging of Reciprocating Compressors. Cas Temperature for Reciprocating Compressors. Axial Flow Compressors. Specirying Compressor Flow Conditions. Mass Flow. Actual or lnlet Volumetric Flow. Standard Volumetric Flow. Properly Specifying Compressor Flow Conditions.

Piping Systems for Rotating Equipment, 60

Example 5-l: Granule Bin Design for Roofing Plant, 11

Chapter 6 Rotating Equipment

Compressors,43

Example 6-5: Naphtha Pump System Design, 86 Flow from Reservoir to Naphtha Storage Tank. Naphtha Pump Hydraulics. The Maximum Capacity Condition. Reevaluation of Reservoir Line.

Notation,9T References, 97

Chapter 7 The Mechanical Design of Shell-and-Tube Heat Exchangers ...... 99

Appendix A Partial Volumes and Pressure Vessel

Cafcufations

Fundamentals of Shell-and-Tube Heat

....,177

Partial Volume ofa Cylinder, 177 Partial Volume of a Hemispherical Head, 177 Partial Volumes of Spherically Dished Heads, 178 Partial Volumes of Elliptical Heads, 179 Partial Torispherical Heads, 181 Internal Pressure ASME Formulations with Outside Dimensions, 183 Internal Pressure ASME Formulations with Inside Dimensions, 184

Exchangers,99 Design Classifications of Heat Exchangers. Fixed Tubesheet Shell-and-Tube Heat Exchangers. U-Tube Shell-and-Tube Heat Exchangers. Floating Head Shell-and-Tube Heat Exchangers. General TEMA Exchanger Classes-R, C, and B. Basic Components of Shell-and-Tube Heat Exchangers. TEMA Formulations. ASME TUbe Joint Load Criteria.

Process Evaluation of Shell-and-Tirbe

Exchangers, 115 Tube Wall Temperature and Caloric Temperaturc. Overall Heat Transfer Coefficient. Fouling of Inside and Ourside Tube Surfaces. Tube Film Coefficients.

Appendix B National Wind Design Standards

Tube Vibrations, 139

.........

187

Criteria for Determining Wind Speed, 187 Wind Speed Relationships, 188 ANSI A58.1-1982 Wind Categories, 189

Plate-Fin Heat Exchangers, 147

Example 7-1: Regenerated Gas Exchanger Design, 148 Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Side Pressure Drop.

Example 7-2: Vibration Check for Regenerated Gas Exchanger, 153 Example 7-3: Chlorine Superheater Design, 154

Appendix G Properties ot Pipe

Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Sid€ Pressure Drop. TUbe Metal Temperature.

.

.

.....

193

Insulation Weight Factors, 200 Weights of Piping Materials, 201

Example 7-4: Asphalt Coating Mix Heater-A Non-Newtonian Fluid Application, 160 Tube-Side Film Coefficient. Shell-Side Film Coefficient. Shell-Side Pressure Drop.

Appendix D Conversion Factors

Example 7-5: Zero LMTD Exchanger, 165 Notation, 165 References, 166

Chapter 8 External Loadings on Shell Structures

....

.

Alphabetical Conversion Factors, 226 Synchronous Speeds, 233 Temperature Conversion, 234 Altitude and Atmospheric Pressures, 235 Pressure Conversion Chart, 236

169

Lifting Lug Design, 170 Example 8-1: Lifting Lug Design and Location, 170 Notation, 175 References, 176

vl

.....225

t'oreword

chanics and the engineering mechanics of piping (Volume 1). 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 (Volume 2), 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

In this two-volume work on Mechanical Design of

A. K. Escoe has performed a monumental service for mechanical design engineers and chemical process engineers alike. The information is Process Systems,

presented in such a manner that even the neophyte engineer can grasp its full value. The author 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 extensiv e worked examples throvghout 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 process, and the author has treated this with proper respect in two excellent chapters on fluid me-

for students. I recommend these volumes highly for each design engineer's professional library.

Joe C.

vtl

John J. McKexa, Ph.D. , PE. of Chemical Engineering Universitv of kxas, Austin

Waher Professor

Dedication

To the memory of my beloved parents, Aub-ri:y

tt.

Es-

coe and Odessa Davies Escoe; and to the dedicated enei-

neer, Dr. Judith Arlene Resnik, U.S. astronaut aboid the ill-fated space shuttle Challenger (Flight 51-L).

v||l

Preface to Volume 2

of any accepted standard or code that may govern. It is 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 and the TEMA standard for shell-and-tube heat exchangers. The intent is not to be heavily prejudiced toward any standard, but to discuss the issue-engineering. If one feels that a certain stan-

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 processing and pharmaceuticals, power generation (including cogenera-

tion), ship building, and 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.

dard or code should be mentioned. olease remember that lhere are olhe15 who may be using different standards and it is impossible to discuss all of them.

While practicality is probably its key asset, this second volume contains a unique collection of valuable information, such as a practical approach to bin and silo design as well as practical methods of controlling wind vibrations of stacks using vortex strakes; new information on nozzle loadings on compressors and turbines; comprehensive discussions and examples on sizing pumps and compressors for various process applications; expanded tube count tables for shell-andtube heat exchangers; a practical approach to design against tube bundle vibration; and a comparative synopsis of the various national wind codes. Topics included in the text are considered to be those typically encountered in engineering practice. For reasons of time and space the dynamic analyses of seismic response spectra and an extensive discussion on pulsation response spectra in piping induced by acoustic pulsation are not discussed. However, a short discussion is given on pulsation response spectra induced by acoustic pulsations. Single-phase flow is much more common in mechanical systems than two-phase flow, so because of time and space two-phase flow is not discussed. This book is not intended to be a substitute or a replacement of any accepted code or slandard. The reader is strongly encouraged to consult and be knowledgeable

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 expenence.

Junior or senior undergraduate engineering students 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-

cal textbook for junior-, senior-, or graduate-level courses in the mechanical, civil, or chemical engineering

fields. The book can also be used to supplement an introductory level textbook. The French philosopher Voltaire once said, "Common sense is not very common," and unfortunately, this is somelimes 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 Iearned from books alone. It is one ofthis book's soals to

tx

unite these three elements of "book learning," common 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; other engineering faculty

members at the University of Texas at Austin for their comments; Albert T. Taube, P.E., who was so kind to

offer helpful and useful comments while reviewing Chapter 6; and John D. Guenther, P.E., for his helpfirl critique of Chapter 7. 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 possible.

A. Keith Escoe, P.E.

The Engineering Mechanics of Bins, Silos, and Stacks

The engineering mechanics of bins and silos differ from the mechanics of oressure vessels because solids behave differently from liquids and gases, both in storage and in flow conditions. The mechanics of stacks are almost identical to those of towers, but are somewhat simpler. An engineer has more fiexibility and approaches for solving vortex shedding around stacks than around towers, because stacks rarely have as many attached structures.

4.

Dead storage-residual build-up of solids caused by the inability to exit bin. Segregation-a heterogenous solid of varying specific gravity in which the lighter particles exit the bin first, leaving behind the heavier particles. Degradation-the chemical change of solids caused by remaining in storge too long. Spoilage, caking, and oxidation are some examples.

5. 6.

Solids behave differently from gases or liquids because they can transfer shear stresses without movement,

SILO AND BIN DESIGN The mechanics of solid flow theory is a fairly complicated subject. The proper design of silos and bins is more than meets the untrained eye, and involves every aspect of engineering mechanics. This chapter only " sketches" methods of approaching this complex phenomenon, and refers the interested reader to literature on

this specialty. The field of solids handling has been augmented the past twenty years by two researchers-Jenike and Johanson [1]. The methods presented in this chapter are largely influenced by their work. Bins and silos appear to be very simple devices, but what goes on inside is not so simple. To design an efficient bin the design engineer must understand why solids in bins do not flow (Figure 5-1):

1. Development of a rathole or stable arch that ceases flow. 2. Erratic flow-transient arches form within the solid resulting in variance of the bulk density such that flow becomes unstable. 3. Fiushing-the fluidization and flushing of powders creates erratic flow.

and because of their cohesive strength, they can retain their shape under load. The shear stress transferred between the solid and the channel walls is a function of the normal pressure, w. The relationship between the two is as follows: 1t -

tdttrg

where

{' : p:

S

-- w

(5-l)

kinematic angle of friction between the solid and the bin wall coefficient of friction between the bulk solid and the bin wall

Typical values of @' are given in Table 5-1 for various solids and bin materials. This table can be used in applications where the bulk solid properties are not known (as is commonly the case). The value of @'is required by the methods presented to be a constant value so that using the table will produce a conservative design. There are two flow conditions that can occur-mass flow and funnel flow. Mass flow is a flow Dattern in which all the material in the hopper or bin is ln motion

flow occurs along the bin walls. Funnel flow is a flow pattern in which the material flows primarily in the center resion of the bin. and the

Mechanical Design of Process Systems

NO

NO

FLOW

FLOW

FUNNEL FLOW

:\

):^.-,r. .. 1:' ,i :fr,f;:,,*::',.d r'"

RATHOLE OR

li"li:'.;:,.,i

PIPE

OEAO STORAGE

Lqilii I

I I

-l

t.-. t,;

t.|..:

ARCH OR DOME

Funnel Flow Charactedstics

1. Material

segrEgates and ratholes may be formed.

2. Flow may be erratic. 3. Low headroom. 4. Powders willflush.

Figure 5-1A. Problems of flow of solids.

Table 5-1

Properties of the Materiats Used in the Stacking-Out Bins

[11

9r

Hopper Material Iron ore

Rec.

39 33 39 33 63 47 63 47 46 40 46 40

*

concentrate

(H2O, 1.5%) Iron ore (H2O, r0.0%)

Cir.*+ Rec.

Cir.

Dolomite-

Rec.

Michigan

(H2O,4.2%)

Cir.

Dolomite-

Rec.

(Moller) (H2O,8.2Va)

Cir.

+ Rectangular opening, 4

*+ Circular openinq,

4

ft

by 2.5

diam.

ft.

55

lo

55

39

tb/tt3 23

190

23 25

190

141

tbfil2 585

T,

fi

sec

calculated, lb/sec

1.25

5.50

5.7

16,7N

467

1.25

343

4.65 1.50

5.7 9.5

18,200

0.97

8,450

25 25

l4l

395

r.05

t0s

1.50

286

v.f

9,250

1.14

3.20

8.1

8,150

25 1A

105 100

229 263

t.t4

2.80

1.05

t .70

8.1 11.9

6,220

26

100

2r0

1.05

1.60

11.9

6,660

8,600

The Engineering Mechanics of Bins. Silos and Stacks

arch lhickness, T

Figure 5-2. Formatjon of an arch. FR€E SIJifACE

srREss

{q)

sTiEss

(L)

sti€ss t laLl) CALCUIATEO S-IRESS

Mass flow characteristics

I

1. Material segregation problems are minimized 2. Fine Dowders deaerate 3. Material flows unilormly 4. Smooth steep hopper

IALL

)

Figure 5-18. Ideal flow of solids-mass flow.

Figure 5-3. Stress distributions along hopper wall [1].

The strength of the solid material is the criterion for flow behavior in bins. Failure conditions ofthe solid oarticles can result in arching. no flow. piping (a hole formed in the solid formation), or limited flow Figure

per wall. When the hopper angle is less than 30', the limits of radial stresses will occur in conical hoppers, as shown in Figure 5-4. Even though the hopper opening is large enough to prevent arching, mass flow piping will occur. The critical diameter at which the pipe is unstable is given by the followine:

5-2 illustrates an arch formed by a solid in a hopper. The failure of the arch will occur when the major compressive stress, R equals the unconfined yield strength, fc. lii) prevent arching, the critical dimension, B, ofthe hopper opemng must De

_flJ>

'

7(1 where

+

m: m:

?

:

m)

D>

4\+ ^l

(5-3)

(5-2)

0 for slot opening of width B 1 for circular opening of diameter B bulk density of the solid, lb/ft3

The calculated stress and radial stresses are shown in Figure 5-3. When the stresses induced between the solid particles and the hopper wall are not compatible with radial stress, a flow pattern will not develop along the hop-

Figure 5-5 shows a plot ofthe piping factor, O, against the angle of internal friction, f. The limiting relations for arching and piping in Equations 5-2 and 5-3 are functions of the material yield strength, f". This parameter can be determined empirically only if the consolidating pressure ol for steady flow is known. This pressure is denoted bv or

:

IBQ

(54)

Mechanical Desisn of Process Svstems

z.^ E

= -to

Figure 5-4. The criteria for flow when 0' < 30".

o(1

where Q =

d: o=

+

sin 6)

2sin0

mass

(s-5)

angle of hopper slope computed stress function along the wall

Combining Equations 5-2 and 5-5 we obtain

1> t"

(r +

where o1lf"

-)e :

(s-6)

flow factor of solid

The critical flow factor for arching in channels represented by

n:

: (?J".-*,

(ff)

is

'e_

(1

+

m)Q

(s-'t)

F

o z

Figures 5-6-5-9 show the values of ff for straightwalled converging bins with various material properties and wall slopes. These factors are presented as straight lines in the f" vs. o1 graph in Figure 5-10. The consolidating pr€SSUre 01 that the flowing solid particles exert in a vertical cylindrical channel is

ot =

D"yG

I

30 30

40

50

60

70

ANGLE OF Ii{TERNAL FRICTON IDEGREESI,Q

Figure 5-5. Piping factor, iD, versus angle of internal friction, (5-8)

6.

The Engineering Mechanics of Bins, Silos and Stacks

EFFECIIVE AI{GLE OF Ti|cNOfl

2O3.6070 IOEGf,EESI,

E.rECrrE

6

Figure 5-6. Wall friction angle, @', versus effective angle of friction,6.

^*GLE

OF FitcT|Ox roEci€Est,6

Figure 5-7. Wall friction angle, friction,0.

{',

versus effective angle

d',


5

6ro

EFFECTTVE AXCTE

Figure 5-8. Wall friction angle,

friction,6.

d',


of

Of FFICTION,6

Figure 5-9. Wall friction angle, friction, d.


of the flow of solid particles. This pressure is reduced internally somewhat because as the solid particles de-

I

scend through the hopper, a vacuum in the void between particles develops and produces a negative gauge pressure. As the particles approach the outlet, atmospheric pressure is obtained. While the wall pressure is maximum at the bin-hopper tangent line in mass flow, it is only a fraction of a hydrostatic pressure for a liquid head equivalent to the height ofthe solid in the bin. Thus, designing solid bins for hydrostatic loads results in overdesign of the bins. As a guideline, the maximum hoop pressure at the bin-hopper tangent point is about seven times that of the pressure of the solid induced by gravity. That is,

t(,

= lrl E

(',I

F

CR

ot JI

lrJ >l

ITICAL

STREI{GTH

RoP(e$i{L

I

o trj

.

lrl

<= ori

l! = -o ()

F .I' -t! taE ()C

z,

--------)coNsoLroaTr G PRESSURE,

=

l6

P*:7{'y)*{H)ft

q

Figure 5-10. Critical values of or and f". Line A represents strength properties and Line B the constant flow factor [1].

where G is a function of the effective angle of friction, 6, and the internal angle of friction, {. This consolidating pressure, o1, provides the strength of the material that forms the pipe in the bin. Combining Equation 5-3 with 5-8 we have

(+) \r./

"

where "y

H

: :

(5- 10)

bulk density of the solid, lb/ft3 height that solid is stored in bin,

Table 5-2

Critical Hopper Dimensions tor Material With Flow Properties Shown in Figure 5-12 [11 Critical width ot a slot opening

o*o

.,,,:(,1)",.""=o*o

ft

lor arching, ft

(5-e)

The value of ff is plotted against 6 and { in Figure )-l l. Figure 5-12 shows flow properties of a typical bulk solid, which are quite useful in problem solutions. Thble 5-2 lists critical hopper dimensions for the material with flow properties given in Figure 5-12. Once the problems of arching and piping are solved and the bin is designed to handle the solid mixture, the next step is to examine flow pressures induced by solid particle flow. As mentioned previously, solid particles suspended in vertical storage bins do not behave linearly, such as liquids. To a much greater extent than liquids, solids manifest shear forces between particles and on bin walls. Figure 5-13 shows typical pressure distributions for mass flow and funnel flow, and illustrates how in mass flow the pressure is maximum at the bin-hopper junction poilt. The geometric discontinuity causes an increase in flow pressure because of change in momentum

Type Flat bottom or nonmass flow

Freshly stored

Stored for 24 hr

bins

0.2

1.0

Stainless lined hopper

0*

o.4

0,*

0.6

(d, = 30", 6"= 21.t Mild steel hopper

(0'

:3o" a' :3s")

Critical diameter of a circular opening for arching, ft

Flat bottom or nonmass flow Stainless lined conical hopper

0*

2.0 0.9

Mild steel conical hopper (0' : 15", d' : 35')

0.4* *

2.O**

0.4

bins

(0'

:

1s",0' :27")

Critical dimensions

5.6

bins

7.7

+

Dictated only by porticle size or dynamic conditions. +* mese ralues are the same as the flat botrom bin values because the

6' = 35" is too rough to proride of the cone when 0' : 15"

steel conical hopper when

walls

mid

flor"'along the


The internal pressure in Equation 5-10 can be inby the use of pneumatic air supplied to the bin. In the case of bins where funnel flow exists or for small bins with cohesive solids, supplying forced air through ducts in the bin is desirable to prevent the formation of arches and pipes within the solid itself. To compensate for the additional internal pressure, Equation 5-9 be-

crease.d

60

comes e,

z E

P.,":77H+Pu;

t40

where

P";.:

(s-1r )

air pressure, psig

=

o

The use of pneumatic air in bins is often desirable and

o-z

in the situations where air cannot be used because of chemical interaction with the solids in a closed svstem. nitrogen is commonly used.

40

50

60

ANGLE OF FRICTION (OEGREES),6

Figure 5-11. Critical flow factor for piping.

Hlso (!

6'

? 3

1oo

Figure 5.12. Typical bulk solid flow properties used to determine critical dimensions for piping and arching.

coNsoltDAT|NG

PRESSUAE,

q, Lb/Fr2

Mechanical Desisn of Process Svstems q,

PSI +

0 Psl bin

fu _

FUNNEL FLOW

bin haf

tu -

F

I

Figure 5-13. (A) Pressure distribution for solid flow is maximum at cylinder-cone intersection primarily because of discontinuity stresses; @) The relationship between mass flow and funnel flow for conical sections. The angle of kinematic friction, d', is a function of the coefficient of friction between the solid and bin material and the compression the solid is subjected to in storage.

In stacks, lining is often used where high temperatures

STACK DESIGN The analyses of stacks subjected to wind and seismic response spectra are identical to those methods used for process towers discussed in Chapter 4. The differences

in the two types of equipment are twofold: (1) stacks have different values for logarithmic decrement and dynamic magnification factor, and (2) the solution to problems induced by vortex shedding are different. Both of these factors are a result of stacks having simpler geometrres.

The simpler geometry of the stack works for

and

against the engineer. The positive aspect comes as a result of the methods used to break vortex shedding-vortex breakers are much easier and more practical to install on stacks than on process towers. The negative aspect of

stacks is that they do not have connected piping and structures to break up vortices and to damp wind-induced vibrations. Thus, we will focus our discussion on those aspects of wind design that are peculiar to stacks, remembering that the fundamental basis of design is the same for stacks and towers.

Vorter Sheddlng and Frequency Response As explained in Chapter 4, only the fundamental mode of vibration is considered for process towers and stacks. Consequently, the Rayleigh method is applied to obtain the vibration characteristics of the stack.

are encountered and carbon structural steel is the stack material. Lining must be used for temperatures in excess of 800 " F because of the danger of carbon precipitation in the steel. To avoid this and not use lining, one must use hot-rolled, high-strength low-alloy steels that have good elevated-temperature properties. Such steels are not generally pressure vessel quality and require heat treatment, such as the Cr-Mo steels described in ASTM specifications A-387 and A-542. These low-alloy steels are of structural quality, contain 0.75-1.257o chromium, and are cheaper than pressure-vessel-quality alloys. When common carbon structural steel is to be used with lining, the effect of gunite lining must be considered with the mass and stiffness to accurately determine the fundamental frequency of the stack. An approximate value of the modulus elasticity of gunite is 1.3 x 10opsi. The effect of lining in a stack must also be considered with the flexibility of the base. Table 5-3 is a list of conservative values of the logarithmic decrement and dynamic magnification factors for various soil conditions for lined and unlined stacks. For explanation and use of these values the reader is referred to Chapter 4.

Ovaling When slender stacks, i.e., rings in which the thickness is small in comparison to the radius, are subjected to vortex shedding caused by air currents, the elastic strain en-

The Engineering Mechanics of Bins, Silos and

ergy of the cylinder is distributed in such a manner as to induce flexural and torsional modes of vibration. The ring is subjected to the following modes:

1. Extensional (axial elongation and contraction about the ring's own axis).

2. Torsional (twisting of the ring about its own axis). 3. In-plane flexural (inextensional vibrations in the 4.

plane of the ring). Out-of-plane flexural (inextensional displacements in the plane of the ring).

The flexural modes are generally the only modes of practical significance since the fundamental natural frequencies of the torsional and extensional modes are much greater than the fundamental natural frequencies of the flexural modes. Figure 5- l4 shows these various modes.

Stacks

9

These relationships were formulated by the great pioneers Michell and Love during the nineteenth century. The reader is referred to Example 5-4 for further clarifi-

cation of units. In practical stack design, because vortices form alternately on either side of the stack, the flexural frequency (ovaling frequency) given in Equation 5-13 is taken to be twice that of the vortex shedding frequency. The vortex shedding frequency is given by Equation 4-101 as

-'D 0.2v

(4-l0l)

Now since f

,,

:2f,

we solve for

V

and obtain

60f,D

(s-14)

The flexural modes, in-plane and out-of-plane, are used in determining the resonance frequency of the stack caused by ovaling. Since out-of-plane flexural vibrations

in which

are coupled to torsional vibrations, it is the out-of-plane frequency used ro describe the vibration of the siack; however, the natural frequencies of the flexure modes in and out of the plane of the ring vary only slightly for circular cross sections. The natural frequency of the ring is

critical wind velocity in which ovaling occurs. Both the vortex shedding and flexural frequencies should be evaluated at each elevation if ovaling rings are to be used. Norrnally, rhe upper third of the stack is all that is required to be investigated, based on various wind

siven

as

, -_ I I Etn2(n2 - l), lo5 " t tpAr6t+ I + /t

(s-12)

The lowest flexural mode exists when n tion 5-12 reduces to

"

:

2 and Eoua-

4.4O9t E

(5-

f'

l3)

s:

the Strouhal number (is equal to 0.2 for a wide range of Reynolds numbers). The value of V. is the

tunnel tests. Now we come to the most practical aspect of stack design-how to alleviate flexural excitation. This can be done in two ways-ovaling rings or vortex strakes. Ovaling rings are used to increase the mass distributed along the tower to dampen flexural vibrations. When the flexural frequency equals twice the vortex shedding frequency, i.e., if the design wind speed range includes the critical wind velocity, V", stiffeners are added at those sections where f = 2f. The section modulus ofthe stiff-

eners is given by

s

-

(7

where V"

:

: o, :

l): j-r

H,

i, t n=2

Figure 5-14. Stack mode shapes.

(s-15)

,"r"0 velocity (Equation 5-14), fpm

D = "rnr"u, internal stack

!l \

n=l

x l0 )v:DrH,

investigation,

diameter at elevation under

ft

stiffening ring spacing, ft allowable tensile stress of stack material.

DSi

Ovaling rings provide a redistribution of the mass of the stack, resulting in localized stiffening that tends to offset flexural frequency modes. This is particularly desirable with stacks of several diameters. However, with stacks of constant or tapering cross section the use of vortex strakes is becoming increasingly popular.

10


Helical Vortex B?eaker Strakes

a stack. The helix angle,

{,

should fall into the following

range:

For critical wind velocities less than 35 mph, dynamic stresses should be investigated. One optimum solution

for such stresses in stacks has been found in wind tunnel tests and in practice to be helical vortex strakes. The application of helical vortex strakes to vertical cylindrical towers has shown remarkable results. The strakes' function is to break up vortices such that flexural frequency modes are quickly dampened. It is significant to note that adding the strakes increases drag and thus wind loading. These strakes are shown in Figure )-l). To minimize the flow-induced drag and optimize the vortex-breaking effect, the strake height, W(ft), should be in the following range:

D:

There are always three strakes per stack to counter the of vortices on either side of the stack. Strakes can be fabricated from a flat piece of metal, normally 3/ro-in. or 5 mm thick. Each strake is divided up into a certain number of strips, usually five to twenty

alternate formation

segments, depending on the length of the stack. The overall length of the individual strakes that is divided up is determined by (5-16)

S:[(?rD)2+L2]oj

where D = OD of stack, ft L height of tower portion straked (V: of total stack

0.09D
54'
:

height),

OD of stack, ft

Figure 5-15 shows a helix generated on a cylinder by taking a template z'D long by L high and wrapping it around a cylinder. The length, L, of the helix is the top l/3 of the stack. Wind tunnel tests have shown that vortex breaking devices are most effective on the upper third of

The number

ft

"S"

is divided into individual strips that

are cut from a larger piece of plate shown in Figure 5-16. The strips must be cut to a radius of curvatue, r, that is determined as follows:

+8

a2a2

(5-17)

aa2

.

D-

wherea: --, lt z

,L

0.090s W<0.1D

d= 54o

Helix angle

2rw

:

number of revolutions around stack cylinder made by

helical strake (usually

:

1)

An alternative formula, developed by Dr. Frank Morgan, and two to three percent in error of Equation 5-17, IS

XW

(s-18)

1-)\ \rhefe A

T L

I

|-,D Figure 5-15. Cylindrical strake helix geometry.

S,

interior arc Iensth of helix

= _ : ------:--------: S" exterior arc length of helix

(5-le)

The value Si is determined by using the outside diameter of the stack in Equation 5-15, and S" is obtained by using D * 2W in place of D in the same equation. For the most accurate results, Equation 5-16 should be used, as it is the exact radius of curvature of a helix projected on a cylinder [3].


Strips are laid out, as shown in Figure 5-16, with an inner radius of curvature determined bv Eouation 5-17 and outer radius of curvature of r : r + W. it is desired that the helix be perpendicular to the centerline of the cylinder along the entire length of the helical strake shown in Figure 5-15. To obtain this each metal strip is placed in a rig shown in Figure 5-17. The rig is composed of two clamps, each 45' from the plane perpendicular to the table, or 90" offset from each othe;. O;ce the metal strip is clamped-in, a hot torch is run up and down the length of the metal strip hot-forming it to the shape formed by the clamps. The strip should not be heated any longer than necessary to hot-form. The metal strips should be the same material as the stack. The effectiveness ofthe system is not impaired by a gap of 0.005D between the helical strake and cylinder. This method leads to ease and quickness in fabricating helical vortex strakes.

EXAMPLE 5.1: GRANULE BtN DEStcN FOR ROOFING PLANT

Figure 5-16. Strake fabrication detail.

1t

As seen in Figure 5-13b, the minimum hopper angle for mass flow is

0 :37.74'1" From Figure 5-4,

6'

From Figure 5-5,

:

l0

=

0, which implies that we will not

have piping forrning in the bin

6=70' For a circular opening, m =

1

s'(l + sin 6)

^

(5-5)

zslnd

From Figure 5-6,

ff

:

1.6

ff=(l+m)Q Q: or

Twelve granule bins are to be designed to provide granules for the manufacture of roofing shingles of Example 3-6. Each bin is to contain 10.02 tons of sranules. yielding 120.24 lons rolal capacity for all twe'ive bins. The client desires to use an existins steel frame that limits the bin to a rectangular shapJwith an off-centered opening as shown in Figure 5-18. From this figure we consider the first criterion in bin design-to satisfu flow conditions such that the granules wili move.

Stacks

:

1=

: o1 : B

=).

=

(s-7)

0.80

7BQ 90 lb/ft3

0.667 ft (90)(0.667)(0.80)

:

43.6, tbrtU

From Figure 5-12,

f"

:

s0 lb/fC

Figure 5-17. Clamping each strip on 45 degree offsets and hot forming with torch obtains desired geometry.


12

l--j*---l E

,.T ;l

t;;lr\l tl

\

1 /\

I

Figure 5-18. Granule bin silo.

:

In this problem, a 12.625 ft and b = 4.00 pressure at the bottom of the plate is

Thus, the critical arching dimension is

B=

r(l

f{o ' + m)

Since 0.278 the bin

-' (90X2)

:0.278

(5-2)

ft

ft < 0.667 ft = 8 in. archins will not form

sure distribution exerted on the bin walls is taken to be a simple hydrostatic load. The bin walls are fixed on three ends and free on the top edge. The solution for the maxi-

mum stress is given by uno F :

orPb at x = 0, z :

a b

0

:

t

:

4.000 12.625

*r :0.030 Vz

=

0.032

The maximum stress occurs at the bottom side at

z:0

(5-21)

:

12.625

ft:

plate thickness, in.

x=

0 and

/<.)n\

151.50 in.

For 5.4-516 Gr. 55,

o4

:

13,700 psi. Solving for t in

Equation 5-20 we have

r: /v,pu'\o' l__-l

reaction force exerted on the plate edge normal to the plate surface, lb/in. load per unit area, psi

p,r

(5-20)

where Vr, V2, 01, and 02 are in Figure 5-19

P

z,ur

_ _ vrPb2

*1!o' unoF orPbatx +a.z b = = = = ' ifu > borz:0.4bif a'( b :

(n.6zs)ttffi :

From Figure 5-19 we obtain the following:

b

F

eo*

The

in

After flow criteria have been met, we proceed to the structural design of the bin. The allowable stress used in the case of bin design is the ASME allowable, since the granule weight forms a pressure distribution, thus making the bin walls pressurized components. For simplicity and ease in calculations, the solid pres-

: v{bt

:

P

ft.

1:l

ko.o:o)(z.ssr)

I

.\ tn'

r:,eoo

(rsr.sofin.'lo,

--lb-

| I

:0.627 in.


The stress at mid-plane is

"" z

,

:

b a

t2

:

,

12.625 4.O

At x = 0, z :b = 12.625 ft

4.734 psi

_ lro.orzlr+.rl+rr rs r. sor'lo ' = 0.502 in.

Selecting SA-516 Gr. 70,

.

Deflections of bin plate"

v,Pb2

0.4b, P

_ [ro.o:otr

z.

13

oat:

ae1)fl51.50),lo

I

(0.00020)(7.891) ',Jb- 1+t.oy in.,

Dlb

ln.

17,500 5

-- 0.557 in. at bottom edge

_lto.ozzx+.tt+xrsr.sor,lo' _= 0.446 in.

ar

z = 5.050 fr

D

:

flexural rigidity of plate

Et3

12(1

-

v'?)

o 16

I

Figure 5-19. Rectangular flat plate solutions.

14 D


(30.0

>

12(1

106x0.562)r

-

0.311

:48:

.b49.25J

in which,

w :7.4565

x

10-o in.

Bin Stilfener Design To reduce bin plate thickness, stiffeners can be used with thinner plate. A thinner bin plate makes fabrication simpler because a thinner plate is easier to weld and is cheaper.

With stiffeners, each enclosed area is analyzed as a flat plate with three edges fixed and one edge simply

-b = Atx = u,z t

supported. The stress in the plate is given by the following:

(0.004x7.891)(48.0), w_

ob

Ph2 = 't,'l:-:

and

^Ph2 : *,5o'

and F

t-

481 ,649.253

w=

1.4913

x

Itr

l0-1 in.

For a e/ro-in. plate deflections are negligible and no stiffeners are required for this plate thickness.

"

F-

QrPb at

x = 0. z = 0

-

02Pb ur

*

: tJ. z'0.4b

\5-22)

(5-23)

where V1, V2, 01, and 02 are shown in Figure 5-20

.09 .o8 .o7

.05

.o4

Figure 5-20. Rectangular flat plate solutions.


: P: t: F

reaction force exerted on the plate edge normal to the plate surface, lb/in. load per unit area, psi plate thickness, in.

rhI

P = 90--l f 2.625

fcl

:

:8.0 ft, a/b :

0.50. From Figure 5-20 we obtain Vr = 0.064. Thus, from Equation 5-22 we have

_ :_ o.",

(0.064x 7.891)(96)2

_

11

r

(0140 = JJ.009.228 psi > al)owable Consider b : 4.0 ft, a/b = 1.0. From Figure 5-20 we have i{'' : 0.192 and from Equation 5-22, o^, : 24,756.921 psi > allowable :

Similarly, considering b o-"-

:

11,475.865 psi

<

2.0 ft,

:

17,364.2?9 psi

- 3.5O)

-(rq)

4.036 psi

allowable

=

<

5-21 hold, using Figure 5-18. By iteration we obtain

: 6.458 ft, P - 4.036 psi, a/b = 0.619, Vr :0.091 o^":15,643 psi o 17,500 psi

b

and

Since the maximum stress is less than the allowable for the top portion, no third stiffener is required.

First Stiffener Design a = 4 ft-o in.: b

:

2 ft-8

in. a/b:#:t.roo

17,500 psi

ofb :

By a process of iteration we obtain a value in., in which

o^,

(2.667

The top portion ofthe bin is now a plate with three sides fixed and the top edge free. Thus, Equations 5-20 and

First Stiffener Consider b

-

15

/'-TR

2

ft

lt Pt

8

| |

I I

l.

tco

fi l' ,H1

17,500 psi allowable

/r )ll \q--7891 psi |

Thus, we place the first stiffener 2 ft 8 in. above the bottom seam, 'Yr

= 0.383

v

ffi UV

u,

Second Stiffener

At 2 ft 8 in. the maximum pressure exerted on the bin wall is

rh P - e0;

/ rf': 2.62s - 2.667\ ft ln;-l

Consider b = 4.0 ft. a/b

:

\

=

1.0 in which Vr

6.224 psi

:

0.192 from

Figure 5-19. Thus, o-",

='o'n',)lu:?.',!'08)2 (0. 141)

:

I STIFFENER

19.s26.e psi

>

R

:

.yrpb

:

(.383)(7.891X32.0)

:96.712lbhn.

:

w

17.500 psi

By a process of iteration we arrive at b = 3 which o-"" : 17,502 psi

ft I in. in

Third Stiffener At the new elevation, 6.167 ft above the bottom seam, we obtain the maximum pressure exerted on the wall.

With plate pushing uniformly on stiffener, the latter will be analyzed as a fixed end beam with uniform loading.

96.712 lb/in

16


w/

w:

:

(96.712X48)

(4'92

-

M-^.

M -

^-; W=wf 24

M.*:

4,642.18 tb

181x48 0) 24

:

=

9.284.36r in.-rb

, _- (8,532.384) in.Jb (0.54) in. _ ., ".,, ,l?soo rbfinj

773.697 ft-Ib

rtun

I

For design purposes select a design stress of o

:

0.37 in.a

t/+-in. thick,

(9,284.361) inlb(.49)

in.

:

17,000 lb/in.'? .zr

:0.39

=

P

-'yD

From data provided by the client, P = 400 lb/ft'z tion point. Using a factor of 7 we have

0.268 in.a

at

junc-

P = 7(a00) = 2,800 lb/ft2

in.a

Therefore, 3-in. x 2-in.

x t/+-in. 4 is sufficient

Stiffener at Junction Point ot Bin Hoop Force

x2-h. a

o

17,000 psi.

I:M"g

I of

:

Therefore, Ztlz-in. x 2-in.

With a factor of safety of 2. This would give a yield stress of 34,000 psi, which is conservative.

Select a 3-in.

x z-in. x tl4-in. 4

Select a 2rl2-in.

I

'

'ol Rs1?.3E4in.-rb A-","". =

'266 '1921(48

I:M"q

Mc

,

@

><

tla-in.

4

is sufficient

P

:

2,800

rb/rt

(r-lq)

=

re.zt44 psi

UseP = 20 psi For bottom plate,

a:4

ft-0 in.:

: 0'383 R : (0.383X20.0X32.0)

b:2

ft-8 in., a/b = 1.500

rr

= 245. r20 lbl in.

w, w = (245.t20X48.0) M.*: =-: 1.+ Second Stiffener Design

M _ ( I 1.765.760X48) : A_.-'--

P = 6.224 psi

a:

4ft-}in.;b

:

3 tt-6

By linear interpolation, 1t

R: pr-". =

in.;

a/b

=!:3.5 :

4

slj.520 injb

t.t+l

88.879 lb/in.

{: w = (88.879) lb/in.(4E.0) rn. :

11.765.760 Ib

Select a 3rl2

in. x 3 in. x tla in. 4

:9.349

(0.340)(6.224) lbl\n.2(42.0) in.

w

1"t

=

,266 .192

lb

I.in :

(23,531.520X0.79)

_

1.094 in.a

17,000

I = 1.3 in.a for section

Therefore, 3rlz-in. x 3-in. long side facing bin

x r/+-in. r is sufficient with


Bottom Portion of Bin

0. | 825(6.31 3X50.928)'

-

Bottom portion of bin will be approximated with four tdangular plates welded together, as shown in Figure 5-18.

'-'----'''

(0.438)2

Therefore, use 716 in.

f,

for bottom plates

Bending Stress in Bottom Portion

*ll11 ->l Ptt

I

ll-tl ll --'l' Y

Pr = 7.891 lb/in.2

pz

:

e0 lb/n3(16.50

ft)

:

J

[-]q144

10.313 psi

--tt t La-

t-ll It-

At an angle ot90o-0:37.7474, P:

10.313 sin

37

.747" = 6.313 psi

CROSS SECTION CUT AT MIDPLANE OF TEIANGLE

By linear interpolation, B' :9.3659

o:412 o=

It; -il rJ

1$

-_tt

=o.rszs

0.1825Pa'z

,,

qan

,

P = 6.313 psi on triangular plate

m.l8r5x6.rl3x5o.%y

- \l

17.s00

= u.4rJ rn. A

with

t:3/E in.,

,'" -_

0.1825(6.113)(50.928),

(0it5,-

:

21249.532 38,000

:

:

-

area of triangte

= Ia'20'lro.z*> =

\21

: 1,497 .589 in.2 = F : (6.3 13) lb/in.,(I,497.589) in.2 : at3 : (4.244)(12)13 : 16.916 in. M, : F(a/3) : 160,495.84 in.-lb

s?? nci YJ' -= ,t '''-",4q -J-

:

38,000 psi

55.92% of minimum yield

Mc % yield,

:

with rhe

in.

21249.532 70,000

f,

,

:

t0.40

ftj

ot A

For SA-516 Gr. 70, minimum yield % yreld

From previous information,

= l/,JWPSl

30.36% of ultimate yield

I thJ r/{O Otl\3 r:-=-:[,007.49Er l,/. Iz

9,454.279 lb

17


18

,^ 50.928 atJ:_=lD.y/orn.

For three horizontal plates,

3

(

160,495.84)(16.976).

o"u

(1r,007.498X

:

(r2.62s itx8.0 rt1 = '2

17,500 psi

1!30-1f

- z,3ts.22JIb

or for three plates,

,_

'

-

(160.495.84) in.-lb (16.976r (r 1,00?/98xr?J00)

Therefore, tlrc

in.

t_

in.

_ .,.,,,, i"rlb/i"r - " "'-'

m.

wt :

6,945.669 lb

is sufficient.

i:\\:-j

Vessel Supports Consider all trusses as pin connected.

Side Truss

For simplicity and to keep things conservative, let us analyze the internal plate to determine if we need any supports on inside of structure.

weighr of internal load

w

rblfr

t:

3/8

: (t20.24) lz'z+o v\ 'on'I ,on / :

269,337 .60 tb

End Truss

For two outside plates,

in.;

wt :

(12.625)(8.0)(0.375)(1,14)(.283)

wto'.r

:

:

1,543.482 Ib

3,086.964 lb

For two side plates,

Wtt"d

ftXt)

:

(1s 1.s0)(192)(0.s63)

wt:

:

=

6,173.9r,

tO

For each bin,

16,362.0 in.3

ro*r

2(3,086.964)

Under Bins-4 Triangular Plates

Weight of steel (Wt): (12.625 ftx16.0

:

A

0.283 lb/in.3 (16,362.0)(0.283)

:

4,630.446 tb

/a qor \ - 4 l- '"'l A.244\tt44\

wt of

\21

each

bin

-

=

5.990.355 in.1 of metal

(5.990.355)(.283)

=

1.695.270 lb

The Engineering Mechanics of Bins. Silos and Number of Bins

:

as continuous beams in the longitudinal and lateral direc-

:

13,562.164 lb

Empty weight of structure

: :

=

Wt of granules Total

wt loaded

w

-

:

wL: lzsss.+rglli [+.olrt :

so,g73.ozo ro

lt:

:

4

4.0 ft

RA

:

: Ro :

911,210.313 lb/in.

rur Y, w . (9 .210.313r lb E in. : 174,952,380.1 lb (174952'380 1)(192)

8"

:

0.393 wt

=

RB: Ll43 wf:

303'739 771 .. 75.934.r93 lb/rt 4.0

Rc

Considering the plate in Figure 5-18,

M-

FoR EACH spAN

303,'736.7711b

Total number of internal plates Total length

tions.

4,630.446 lb + 6,945.669 lb + 3,086.964 lb + 6,173.928 lb + 13,562.164 tb 34 ,399 .r7 | Ib

269,337 .60

:

19

The frame structure shown in Fieure 5-18 is analvzed

8

Therefore, Wtrorur

Sacks

1. 143(30,373

.676)

=

11,936.3tt

,O

= 34,117.rt b

:

0.928(30,373.676)

:

wf:

1.143(30,373.676)

:34,717.rt

0.928 wf 1.143

0.393(30,373.676)

28,186.77t tb rO

Solr ing for reacrion\ in lateral plate

92.1 ,n.

FOR EACH SPAN WL= 30.373.676 lb

= 4 rqx x\7 r)l,n

-rh

Therefore, bin must have internal supports under botaom.

Number of vertical supports

=9=R: =

Number of ioint suDDorts

F

tol 716 ?71 : --"' _-:j____: : IJ

303

33,748.530 tb

: 9 tl

20,249.118 lb

'73-6'771 9

v.* : V-* :

0.607(30,373.676) tb 18,436.821 lb

RB

=;6 (10.373.676X2) = 37,967.0q5

Ra

= ft. =

lb

11,390.129 lb

Design each support column for 37,967.095Ib srde saructure

=

38,000 lb

The bin structural detail is shown in Figure 5-21.

20


BIN JUNCTURE DEIAIL

STIFFENER DETAIL

Figuie 5-21. Bin struclural frame detail.

EXAIIPLE 5-2: HIGH.PBESSURE FLARE STACK DESIGN

Add 12 in. for platforms and 12 in. for ladders.

A high-pressure flare stack shown in Figure 5-22 is to be designed and construcred to the following specificatrons: Base diameter

:

l0 ft

Height from bottom of steel base to tip of flare stack

ft

Gas pressure in stack = 2 psig Gas temperature = 100oF Design wind velocity = 100 mph Maximum gas flow rate 300 MMscfd

Earthquake design

:

:

World Mercali 6-7

Effectlve Diameters

:

200

Add 4-2-in. d lines.

2-in. g dia. line

D

:

(3.375X4)

D"^"".,

: DB : Dc : De

: :

+

2.3'75

in.-Add

:

=

2(12)

42

+

37.50

:

79.50 in.

90

+

37.50

=

127.50 in.

120

+

t/z

13.50 in.

13.50

37.50

:

37.50 in.

157.50 in.

in. insulation

The Engineering Mechanics of Bins, Silos and Stack

Height

(fD

Wind Pressure P, (rb/ftr)

w = B x De x

Wind Load Pz

(5,270.98X110.5

26

: to6)(!f)tz6):20415

30-40

33

: ro.olffit:3):25e.88

40-74

38

: toor(lle)o

74-76.5

44

: too(l#J(44):34650

'16.5-125

44

:

0-30

125

48

:

28o.so

= t0.6tl'-'""1t48t = \ 12 /

306.00

159-t74

r:

so\

: ro.orfifJt+t):

48

866.25

+ 2.5) +

x

(90.0

+

(13,604.25)(24.2s

+ 2.5) +

(2,862.0)

(10,404.0)(65.5

+

2.5)

+ 2.5)

:2ee.2s

,0.u,(]?Za)r*) /r

159

Moment

lb/tt

reo.8o 51 PSF

174-200

:

51

202.'73

48

Wind Load

159 PSF

Moment

s.270.98

(s,270.98)(13.0 + l5 .0) + (2, 862.00) 2,862.00

llrl \21

44 PSF

169,052.44 ft-lb

(5,270.98)(28.0 + 34-0)

+-

(')

!

__!

86rn) 38 PSF

r0,404.00

x

(7.5

+

34.0) + (1 o,404 .0) I34.01

\)

I

622,44r. 76 ft-lb (5,270.98)(62.0

+ 48.5) +

,rO-l 30_

_t

-l ;1.

33 PSF

(2,862.0) 26 PSr

t3,6U.25

x

(41.5

+

+ 48.s) + (10,404.0x17.0 +

(13.604.25)

48.5)

/an s\ | -'l = 1.851.388.35

\2l

fr-lb

Figure 5-22. High-pressure flare stack; unless otherwise indicated, all dimensions in feet, design wind speed 100 mph.

:

22


Wind Load

For Section D (5,270.98)(113.0

+

+

34.0)

(2,862.0)

x (92.5 + 34.0) + (10,404.0X68.0 + 34.0)

+

x

.25

+

34.0)

+

x

(126.50

+

(r3 ,6O4.2s)(60.7

x

(35.25

+

10.0)

I

+

(2,862.0) 102.0

+

+ r0.0)

/,,r.0\

+

30.0)

+

(13,6M.25)(70.7

x (45.25 + 30.0) + (10,174.5)(27.0 + 30.0) 30.0)

+

:

s,

r:t,+rr.zo

0.56 t" E

y

'.E:29

:

30,000 psi

x

o.oo5

>

o.oo425

(0.56X0.005)(29.0 x 109 0.004(29.0 x 109/(30,000)l

+

90.00

o. = 20,021.918 psi

!: d

(0.500

rt-ru

- 0.12s)

=

0.009

Section Weights-Uncorroded Weight

-

d (1 + 0.004 E/y) '

:

t"_(0.625-0.125) :0.006

wr =

'

o l25)

16,684.932 psi

Section

Allowable Shell Buckling Stress

109

o. = 30.032.877 psi

(6,142.50)

i3o'oJ

0.00425

For Section A

5 + 30.0) + (866.25)

+

-

120

d

(2,862.0)

(136.50 + 30.0) + (10,404.0X112.0 + 30.0)

(2,598.80)(s.0

x

>

For Section B

l+-lt '\2

x

+

(0750

:

(10,174.5)

:3,672,858.86

6,142.50

!: d

li

(2.s98.80)

+

o.oo6

For Section C

5 + 10.0) + (866.25)

x (r7.0 + t0.0) r (5,270.98X157.0

120

(0.56)(0.006x29.0

3,228,045.06 ft-lb

+ 10.0) + (10,404.0)(

- 0 125) :

o,

: 10.0)

(0'875

"" _ tl + (0.004x29.0 x 109(30,000)] : 20,02i.918 psi

(866.25)

\'2

*

d

- .-. - /:+.0\ + 34) + 00.174.5) l:-jj: I

(5,270.98X147.0

2,598.80

+

(13,604.25)(26.'75

13

A

(0.2833)

''

j:

(37.0)( 12)

'n.

',[l/€)'-litt\'l', [\, / \2 I )

8,199.69 lb

Section B 106

psi;

wr

- (02813) { rzoo,rz,' " [(T)'

= 45,340.61 lb

(*, )']'"'

The Engineering Mechanics of Bins, Silos and Sacks

Section

Section C

wr

(ry ro]l_., - (0.2833); (44.0X12)'n.n [('r), [\, | \ 2 l) : 42,029.09 lb

'n

(16)(42 .0)(169 ,0s2 .44)(12)

rl (42 + @D2l(1.2.0 + 41.0X30,032,877)(1.0) 8,199.69

+

r(42.0 + 41.0X30 ,o32.877)(l .0)

Section D

t.

wt = (0.2833)

in.

--ll(30.0)(r2)

: Total

"

:

:

Mr r(D"'?+Dr'?)@"+D)oE

r(D. + D)oE

oe

:

18.25F](120.0

+

I 1 8.25X14, 182.

:

A." -

(16)(120.OXs, 138,419.76)(12) (1

, OK for buckling

l2o + 2(2.50):

=;

125.00

:

Wn

- l?!'e!6 58 - 76,84r.ros lb *,- = ottl24(125.00) 24 '']!;01?,tu'

Section D

+

[

Total tension in each bolt

Thickness

16 D"

r[(120)'?

in.

Try 24-11+-rn. d anchor bolts dec

t

1/z

Anchol Bolt Design

128,966.580 lb

Required

in. =

0.052

[(9' - (r94,)]'"

33,397 .r9 tb

wt

A

:

19X1.0)

40,000 psi

76'841 109

= |.921 in.2 <

40.0(n l3/+

1.980 in.']

in. dia, 8-thread series

128,966.580

+ 118.25X14,182.19)(1.0) in. + 7r in. [ , OK for buckling

r(120.0

t,

:

0.381

Check

[/av\ : t-wl t\d/ I ÂR:No, 1

Section C

r1r20)'?

+

r(120.0 +

, = 0.245 in. -

rl +

(24)

95,569.39 I 18.5)(16,684.932X1.0)

Ar =

t/q iI^. 'll_ , OK for buckling

Bearins pressure

+

(16)(90.0X1.8s1.388.35)(l2l (88.75f1(90.0 + 88.7s)(20,021.918)(1.0) 53,540.300

r(90.0 + 88.75)(20,021.918)(1.0) t, = 0.183 in. .r :/s-in. [ , OK for buckling

1.913 in.'?

48(s,

^'

Section B

(90),

(4X12X5,138,419.76) (12s.50)

(16)(120.0X3,672,858. 86)(12) (1 18.5F1(120.0 + I I 8.5)(16,684.932)(1.0)

1.980 in.'?

= P-- =

48Y + W :i- 7rl:in. nDu' j r Drj "

r38.419.76)

:

Base

fl

psi

<

Fb

;e

t28.966.58

7r(

:

thickness, T1

t" : " (;oiltJ

128,e66.58]

(40,000)

r( 125.00)'/(7.50)

Pt :7\3.734 Tr

<

-

125.00X7.50)

1.33(900)

:

:

1,197 psi

compression

=B* C

:

Z3tqin.

I +

thickness

Zttcin.

:

5.5o

24


=

Te

(5.50r

After one iteration,

Il,lr r l rarl "t

= 1.800 in. l:j;;:;=l I zu.uuj I

l'''

-''

:0.151

1

K:

[ :twu) o [:1zo.r+r.roenorl'' [4(20.000)el [ 4(20.000X5.5) I

1+

(61,789.8ss)

(10x1,096.373)

After six iterations,

K:0.178 B.ownell and Young Base

d

Bolt circle

P

Base

4 :di

:

f,

f"-Eq = n E' --

Method

125.00 in.

lo(1.096.373)

=

fc,-o,.area,

(1.0e6.373)

125.00 130.00 130.00

:

212.50\: (7.00) 2(7 1 16.00

130.00 in. 116.s0 1t.

: : 7.00 in.

K=

1,000;

=

I

L4

:

(1,200)

\r/2

I ^" JI. - ^1^-l

:

:

1,106.925 psi

[ 2(0.333x125.00) +

(5.138.419.76)

r,=-

'

[46.,rr'l,,rr.*,

I

t,26t. sto)1"' - ,.'' "' [:rt ,o"ooo I

2.181 in. (without gussets)

lr( ""-" h = -r 1.588; C,

= 2.316 z:0431l.

-

00l

.,"\ ll25 (128.966.58){0.r'''

12

/

559,723.403

A z'd

=

,..,,

f,'s,

gusset spacing is

7.00

1.980 in.2 (12) ?r(

125.00)

t2

n b

"' = 32.725 in.. | = A = 5.00 in.

O\

5.00 32.'125

From

tble

4-8, using linear interpolations,

My: -

O.467fcrt2

My=

0.467 (1,268.836)(5

-

r,- _ l(oJ{l+.6rr.oou)l =

- U.UOI ln.

:

t

6l,789.855

20.000

'00f :14'813.660 in.-lb 2.10g in.

I

t = use 2rls in base Brownell and Young External Chair Design

Fc

t:

:

=

I

0.333

0.782

:

7.001

2(0.333X12s.00)

K = 0.333; c"=

For

t",^ ,"8)(t25.0) +

1.268.836 psi

-

Using 24 gusset

j

t0,963.73

:

with fc,"., fc(Bc)

:

559,'723.403

7.00

-

0.061

+

128,966.58

:

6.939 in.

:

688,689 983

688,689.983

rcr6.e3e

-

(10)(0.06rI

($Q)
=

r 5.00 22 b

:

gusset spacing

1,096.373

For |ta-in.O bolts,

=

32.725 in.

t 15 : e -:" 2

t.375 in.


: :

PB

\r.

max. bolt load on upwind side fsAB

-

2r.708.185[

4r t

=

lr/+

fw

:

1.33'yn(0.55), for wind or earthquake

21,708.185 lb

fw:

*

(t + 0.30),n Izrs.ool I

[z'(L375)J

,l

I

:

i.33(20,000X0.55)

Weld size

=

14,639.99

5 154 1)1 --- = 0.396 -.'14,630.00

3,612.549 ir..-lb or

.' _ [{6x3612.549)lr" _, t 15,000 I =

:

= (10,963.73)(1.980)

in. in. f,

"^.

0.396

'2

for compression ring

= 0.198+

Va

in. minimum weld each

side

Cantilevel Vibration

'.

Calculation of Gusset f, Thickness for Compression Rings

:

(,aJo o

. (,$n',

=

5 860 rt

Corroded Stack weisht r,2

[ = 4qr2-r2 =]. t2

,=

:0

[ereL, ]

withk=%(1.250)=0.469

*,^

:

6nluurf(,sl

-

(91 :6,16'".ze4tb

*,"

:

-

(r91 :36,323217

r35 in.

h:G+H I21h n. :9 + lt/+ in. i

h 12.500 r 0.135

P

2t/c in-

tb

= l2tlz in.

*,:,ounn

Bolr Load

lttt

rl(?l- (rtl]I|l:

35,o6oe6o,b

23,905.217 tb 101,457.688 lb

18,oo0rtr-Ptt- htP I,500

18,000(5.00)t63

-

Lc

:0

(12.500),(21.708.185)

_

1,500

qt

-

q=

0.24ltS 0.40

in.

r/z-in.

f,

5.00:

13.0

= U.UtJ <

trl

0

= (200X5.8601 LD,2= 4!4:1688=

ft U.5

14.773

<

2r)

Therefore, vibration analysis r,?as, be performed.

- 0.025:0 =

8.00 +

r^ rlnn L 200

(21,708. 185)k,

_

:

Wa

is OK

Skirt-to-Base Ring Weld

':

-

,: (#ft)* (";)'0u." r:a.+ ro.76x r2)] , _ [r+xs. r-[ --;6 20"0)!-l t

r28.966.58

"(t20-00)

:

101,457.688 lb,

:

193.50

-

lr.O

*

ff

:

r'v))

ft

1.648( 193.501 L? 5r(ET, = o.gaOx:sJt-lItc

t.648

I : t: ,uB

= )'tv+ tzl

L" = 200

0.511 cps

vc :3fDrr:3(0.s11X5.860)

:

8.983 mph

seconds

26 V:o

v*


:

100 mph

:

(roo)

r-

(*J'"' :

k_

L..Ws

_

fu 13 1.

165(1.3)

:

193.50)1t

0

l5 mph

170.5

(0.0077X5.860)5(29.0 (

x

_

(

2

:

"f

it{zs.zts), -

\ /.

(34.71

(0.207X5. 86oX

x

x

t :6047 -'

106)0

5)2

5

(1.760) = 3.520

/ ss

cps

\-/l , lfl in.a :

/

77,307.326

6.047 cps

10 ft,

6o(to0l--

0.2(66)

:

2t,:2.640 <

\/ss.zs + o.zs\

<

f'" -_ 7.58(0.625X29.0 x lfff5 _

=

a)\).^<

1.320 cps

4.252

At bottom section,

in]

f,' _

7.58(0.751(2?.0

x

t06)05

60(10.01

=

5.102 cps

i,:o2t66t=1.320cos '10

8EI 8(29.0

60(7

At 120-in. dia :

0.523 in.

P"D,(LF(12)j -

_

7.58(0.5x29.0 '

10

, '=: \'oo/\ 34."111 ir. -. D.=

t.: "

2f,:2 0.107 psf

0,,,) * (,z,|(?..,")

i+r \/ +r r o.zs

r:

:

- 0.r25) + (,$,o.uro :

," = (_..)(? * :35.285 in.

0.2v 0.2\66, :D=(35;=r'l/rcPS

/.f

1.0X0.00238X 1.467P(8.983,,

(,$,o.to

vortex shedding frequency

f _ 0.2(66) _ | %n

2

,

=

. t, At 90-in. dia : 7.5 ft,

Static Deflection

^ ^ Y.-{.,o-

20.826 cps

2f"=7.54t

Therefore, the stack is free from cantilever vibration.

tt.467V

:

106)

t.457.688.)

115

:0.002 <

0-l-]06t

60(3.50F

13r.165 mph

Maximum gust velocity : 0.0077D,5E

7 58(0'3zs-iq9

l93.so)4(t2f

106)(77 ,307

.326)

=

0.164 in.

2f,:2.640

. t.rO,

Therefore, stack is free from ovaling vibration.

Dynamic Deflection Using a magnification lactor of 30. 6

:

0.164 (30)

:

4.915 in., which is permissible

Ovaling Vibration Natural frequency of free ring

''^

7.58r.(E)o

5

:t

AIICHOR BOLT TOFOUE Anchor bolt torque on stack bolts is handled exactly like tower anchor bolts as discussed in Chapter 4. Using Equation 4-66 and considering lubricated bolts we have

T:CDFi where the uplift load on each bolt, F, is

6oD2

At 42-in. dia : 3.50 ft,

(4-66)

-t,:

r2) ,2a1us.0ot

4(5, r38,4r9.76X

r0r,457.688

a

: tt't6t 'tztD


.\hich results in a required bolt torque of

r:

(0.

rs) (r.75)(77

ALL MATERIAL TO BE SA-285

_C

,987 .312)

= 20.471.67 in.lb = 1.706 ft-lb Use 1,706 ft-lb torque with lubricant grease Fel-Pro C-

or equivalent. The skirt base and anchor bolt detail for the stack is hown in Figure 5-23.

5,A,,

Design Summary Static wind shear at base = 22,355.110 \b Static wind moment at base = 1,299,115.509 ft-lb Dynamic wind shear at base = 22,844.841 lb Dynamic wind moment at base = 1,308,916.974 ft-lb Total deflection at top of original tower 4.418 in. Total deflection at top of modified tower 5.898 in. Base plate thickness:2lle-in. plate Compression plate: 1l/4-in. plate

:

:

trL_u--l ffi

ALL WELD SIZES

16) l:/+-in. anchor bolts Required anchor bolt torque: 1,710 ft-lb Total operating weight = 128,966.580 lb ,

IN

INCHES

EXAMPLE 5.3: STAGK VORTEX STRAKE DESIGN An exhaust stack 126 ft tall is to be Drovided with heli.'al vortex strakes. The length of the stack to be straked is the top portion 31 ft 6 in. long. Cornpute the radius of iurvature of the strake to be cut from flat olate. Referring to Figure 5-15 we have the following:-

D:ODofstack:7ft4in. L:31

ft 6 in.

D

7.333 : J.DO/ .i = _ = _

L _31.5 : 2ro 2rtl)

zl-tci I .t

a-tgg-'et. a THBEAo sERtEs BoLTS TO STRADDLE CEI.ITERLINES

BOLTS

t{

\ou, +b2

_

_

a2cu2

_

_

(3.66'7)2(r)2

- --;F-

:=

(5-17)

+

(5.013F

(356?X1t10.521

ft

Figure 5-23. High-pressure flare stack base support detail.

28


Check BASE PLA?E

-

3/16r

Using the approximate Morgan equation we have, Si

:

:

interior arc length

[(rDJ'? +

52:exterior arc length =

:

41.637

ft

L2]0 5

:

39.025

ft

[[?r(8.667)]'? + (31.5)'?105 STRIPS CUT FRO}I

x:9:t?'o,T:r.nt s.

(s-1e)

BASE PLATE

41.637

r

\w : ._________

(5-lg)

(0 667) r - |937)(0 - 9.966 ft = 9 ft i t.594 in. 0.937 10.521 - 9.966 _ va e:,rof = = 5.276Eo errol ff

t

0.5ft + 0,66?ft

= 11.-2.

The final product is shown in Figure 5-24.

EXAMPLE 5.4: NATURAL FREOUENCY OF OVALING HING FORIIULA IMICHELL FORUULA} To use the Michell equation (5-12) dimensional analysis must be applied to obtain Equation 5-13. The original Michell equation is as follows:

f. '' =

,

I

rtJrJ

- 'J].--.-(n'. +l+/) -.

(5-12)

2"Y PAf -r/

where p

:0.283 lb/in.3 for

A:

(t)

in.

x

steel

(1) in.

f : in.a E : lb/in.2 I - T-; . per unit lenpth ofring. t2

z

:

in.'

l/r for steel 386 lb.-in.

rgl I

z7f

'i-c'

(0.283) -.l!l

E - : 4.409r Ir ---- Vt1

1

in.2

1(36)r(in4)

1

in.a (5.333)

(5-13)

Figure 5-24. Manufactured strake elements.


: : a: B: D: A

cross-sectional area of stack, in.2 anchor bolt area, in.2 stack radius = D/2, ft critical arching parameter, dimensionless critical diameter at which piping is unstable, di-

mensionless; internal stack diameter (Equation 5-15), ft; outside diameter of stack (Equation 5-16), ft; dynamic magnification factor (Thble 5JI

E = modulus of elasticity.

psi

: material yield strength, psi ff: critical flow factor for arching in channels, dimensionless f, : natural frequency of a ring, Hz f" = stack vortex shedding frequency, Hz G : consolidation particle parameter (Equation 5-8), dimensionless H : height that solid is stored in bin, ft H, : stiffening ring spacing, ft I = moment of inertia of stack cross section, in.a L : height of tower portion straked, ft m : geometric parameter for arching (Equation 5-2), dimensionless n : flexural mode (Equation 5-12), dimensionless P"1. = air pressure (Equation 5-11), psig Pn** : maximum hoop pressure at bin-hopper tangent point, psi r : outside radius of stack (Equation 5-12), ft; nf.

S=

Low Oamping

6D

HiBh

Greek St/mbols

:

bulk density of solid. lb/ftl 6 = logarithmic decrement, dimensionless

7

Damping

=

:

modetutelt stiff soil; aormol spreadfooting or pile sup-

port soft soil; foundation on highlJ stressed Iriction piles

perpendicular to stack centerline (Figure 5-14),

: d' : dr : ot : or : p

: interior arc length of helix (Equation 5-18), ft : exterior arc length of helix (Equation 5-18), ft S. = section modulus of stiffeners (Equation 5-15), ft' t : shell thickness of stack, in. V = wind velocity, ft/min V" : critical wind velocity in which ovaling occurs (Equation 5-14), fum w : width of strake, ft; normal pressure applied on mode shapes relating translational displacements about the x, y and z axes, respectively

30

6 : piping factor, dimensionless 0_: ungle of hopper slope, degrees 0 : modal shape relating to rotation about an axis

Si

7.1

90 0.052 60 0.105

tural Itame support. Average Dampin?

So

])

Average High Damping 6D6D

Damping

2" gunite lining 0.070 45 0.100 31 0.300 10 9 4" gunite lining 0.117 27 0.r25 25 0.360 Inw Danping = rocky, very stiff soil; Iow-stressed pile suppon, or struc'

ft

bin walls by solid (Equation 5-1), psi

0.035

Unlined Stacks Lined Stacks

dius of curvature of vortex strake (Equation 517), ft over-all length of vortex strake (Equation 5-16),

XI

29

Table 5-3 Conservative Values for Logarithmic Decrement and Dynamic Magnification Factor tor Various Stacks

NOTATION AB

Stacks

dimensionless

coefficient of friction between the bulk solid and the bin wall (Equation 5-1), dimensionless kinematic angle of friction between the solid and the bin wall, degrees consolidating pressure for steady

flow (Equation 5-4\, tbflft2 allowable tensile stress of stack material, psi number of revolutions around stack made by a helical strake, dimensionless

REFERENCES 1. Jenike, A. W., Johanson, J. R., and Carson, J. W, Storage and Flow of Solids, American Institute of Chemical Engineers, New York, New York, 1981. 2

.

Blevins , R. D . , Formulas For Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New

York. NY. 1979 3. Thomas, G. B., Calculus and Analytic Geometry, Addison-Wesley Publishing Co., Inc., Third Edition, 1960.

Rotating Equipment

Not all PD pumps are purely rotary or reciprocating, but we will focus our attention on these types. PD pumps, by

Fluid movers and their use are vital to the process industries. This chapter focuses on two basic typespumps and compressors. The sizing of these units and their interaction with the other components of a process

definition, deliver fluids at a rate proportional to the speed of the pump action and this rate is independent of the pressure differential across the pump. For this reason means must be provided to limit the discharge pressure and this will be discussed under the section of positivedisplacement pumps. Typical rotary positive-displace-

system are discussed. This chapter does not address the detailed mechanical design of sophisticated equipment, such as turbine blade design and gas dynamics in a turbine. That type of material is a separate field of study and lies outside this text's objective of examining how to select and apply rotary bquipment to process systems. For further reading, see the bibliography at the end of the book.

ment pumps include screw, gear, vane, cam, and lobe. Reciprocating positive-displacement pumps include piston, plunger, and diaphragm. Selecting the type of pump to use is a function of the service to be handled. Sometimes, the selection is obvious; for example, if you wanted to pump molasses, you would choose a positive-displacement pump. In the situation where neither a standard type of pump is used for the service, nor is it obvious what type to use, a centrifu-

PUIIPS As the primary movers of liquids, pumps come in

gal pump is always considered first. The reason for considering a centrifugal pump initially is because of its low initial cost, economical cost of maintenance, wide range of materials of construction, and relatively large clearances. Factors to be considered in selecting a pump are

many types and an understanding of the various kinds is essential in successfully applying them to process systems. Pumps are used to transfer liquids from one point to another. They basically fall under two categories-centrifugal and positive-displacement. The centrifugal pump gets its name from the fact that the pump's impeller im-

as follows:

1. Efficiency

parts kinetic energy to the liquid with centrifugal force acquired by the impeller's rotation. This simple mechanism allows the centrifugal pump to be practical for high capacity, at low to medium heads. The aspect of low to medium heads will be discussed shortly. Typical centrifugal pumps include mixed flow, propeller, peripheral, and turbine. Positive-displacement (PD) pumps trap a quantity of liquid and force it out of the cavity against the pressure of the discharge by means of rotary or reciprocating action. Ideally, a PD pump will produce whatever head is impressed on it by the system restrictions to the flow.

2. Net positive suction head (NPSH) required by pump 3. Operating costs 4. Shaft speed 5. Magnitude of clearances 6. Materials of construction 7. Fluid service to be handled 8. Availability and delivery time of pump The type of pump to be used for a specified service or duty can be selected from Figure 6-1. This figure clearly indicates how different pumps have overlapping charac-

31


10

ro-

F

o I J

I

234

-l 5

Figure 6-1. Pump selection guide.

teristics. Depending on the relative importance of the previously cited criteria, a certain type of pump will be selected. Figure 6-1 will help the reader determine from a quick glance what type(s) of pump(s) will be required.

Gentrifugal Pumps Centrifugal pumps are the most widely used because of their wide operating range and the reasons previously cited. These pumps come in a vadety of types, depend-

ing on the type of impeller, casing, stuffing box, and bearings. These components are shown in Figure 6-2. The radial type impeller is by far the most common centrifugal pump in the process industries. The flow is directed by the impeller imparting motion on the fluid, driving the fluid to the periphery of the impeller. This allows the velocity head to be converted mostly to pressure head in the volute. The mixed flow pump impeller consists of vanes doubly curved or screw-shaped so that the impeller moves the fluid by both centrifugal and pushing action. The result is a discharge of axial and radial flows. The axial flow pump impeller develops head by a lifr ing or pushing hydrodynamic action that results in totally axial flow on discharse.

The impeller is hydrodynamically balanced to ensure minimal vibration. The casings can come in a variety of designs, but are either vertically or horizontally split. A vertical-split casing implies that the casing is bolted together along a vertical plane. Similarly, a horizontally split casing is bolted or connected along a horizontal plane. The advantage of the vertical split casing is that the pump is supported along the shaft allowing for thermal movements without causing shaft misalignment. Packing and seals on the shaft are the most common of failure for a pump. In low-pressure applications, soft or metallic packing will suffice in a stuffing box. In most low-pressure applications, a single seal will usually suffice. When pressures exceed about 50 psig and there can be no tolerance for leakage, a double seal is utilized. These seals come in various configurationstandem. bellows. and face-to-face. source

When process conditions get severe enough, a double inside-outside seal, where part of the seal is outside the stuffing box, is used. The disadvantage of this type of seal is that not all stuffing box arrangements allow such a configuration. For proper cooling and lubrication the seal must be supplied with a fluid, called a seal flush. Figure 6-3 shows such a system.

G:oup ll and lll Standard Pumps

Group I Standard Pump

Materials Common io all Alloys Unless otherwise Noted Parl No.

Malerial

Parl

104

lmoeller Gasket'

107

Rear Cover Plate Gasket*

Durabla

108

Bearing Housing Adapler

Casl lron

109

Bearinq flousrno Fool

111

Gland Studs or

112

Sealcaqe'(E)

PTFE

113

Molded Rino Packinq'rE)

Kevay'il

114

Inboard 0ellector

PTFE

115

Casino Studs/Hex Nuls

118

Inboard

119

Bearina Housing

Cast lron

120

Inboard Eearinq'

Sleel

121

0utboard Bearino'

Steel

122

0ilSlinoer

Steel

123

Bearino Cover

Cast lron

124

Bearing LockNut

Steel

125

Bearin0 Lockwash€r

Steel

126

Beaino Cover Gasket

Cork

127

Bearino Shim'

129

outboard

130

Shall Couolino Kev

131

Beanno Housrng Adapler'

132

Soherical Washer lor Foot

Steel

133

Trico 0iler (nol shown)

Steel-Plaslic

134

Bearinq Housino Venled Drarn Plu0

Plastic

136

Cao Screw for Foot

Steel

138

Cap Screws

139

Machine Eolts lor Bearing Housrng

140

CaD

F

Casl lron

3M S.S./303 S.S

anqe Studs with Hex Nuts

304 S.S./316 S.S.10 TFSB

0ilSeal'

Steel

oilseal'

Screws

TFSR Steel

0"

Binq

SBR

lor Eearinq cover

iorAdarterto

Steel Steel

Cover

'Pafls 10rtra'y sl0ck.d by cLsrome.lor e4erqenc/ rs 'Ppd "Trrd.name ol lnternanonal Nrrel Coooanv (A)Nor avarable In Recessed h0eller pumps (BlNor avr'abre In Seri Pnmno oumoe (Cr \or rva ubre on 4x3 LS.loii 4d US I3 o' 614 US l3A rcast sleel suotntuledr

Sleel (E) Used n Packed PonPs only {t) Trtanrum Dumos havs GraJor rmpell€. oaskels Cdro,r b a reo'9ercd lraoe name or un'on Carbrde Coro0 anon lGr Allov rs B7 Sio. Duclilp lron rnd Crlbon Sleel oumos {H) Icd€name ol E Duponl deNamoors & ComDafiy Inc

I

{01Jackeled cover oral€s are carhon sre€l

Figure 6-2. Centdfugal pump components. (Courtesy of the Duriron Company.)

Mechanical Design oI Process Syslems

A seal flush configuration. (Courtesy Durametallic CorDoration.) Figure 6-3.

The various types of seals are shown in Figure 6-4. The pump manufacturer should be relied upon for the choice of seals. Sealing technology is a subject vast enough to encompass this book and the reader is referred to Buchter [1] for additional sources. Bearings, like seals, are for the most part the main responsibility of the pump manufacturer. In all situations, the bearings should be of the outboard type (not subjected to the process fluid), unless situations prevent this type of arrangement.

Hydraulic Bequirements of Centrifugal Pumps In this section the reader will find it advantageous to refer to Chapter 1 . The most important hydraulic parameter in pump selection is the net positive suction head (NPSH), which is the total pressure at the pump suction point minus the vapor pressure of the liquid at the pumping temperature. NPSH is the energy that forces the liquid into the pump, and is expressed in foot-pounds of energy per pound of mass (normally referred to as feet of head) or pounds per square inch of absolute pressure. When values of pressure are expressed in feet of liquid, the theoretical height to which a liquid can be lifted at any temperatnre is the difference between the atmospheric pressure and the vapor pressure of the liquid at that temperature. Figure 6-5 helps simplify the calculation of the NPSH.

of

the

In selecting a pump the engineer must refer to the performance curves the pump manufacturer prepares for each model ofpump. Most performance curves are plots of flow capacity (gpm) of water versus break horsepower or total dynamic head in feet. Such a curve is shown in the examples that follow. As seen, the efficiency curves are plotted with various lines indicating impeller size and the NPSH required at various points. In reading the performance curves, it is emphasized that the extreme right side of the curve should be avoided, because the capacity and head change abruptly. Pumps are normally selected to operate in the area of high efficiency. The danger in selecting a pump on the extreme left is that at low flows the pump horsepower overheats the liquid. If low rates carmot be avoided, a by-pass may be required to prevent vaporization and subsequent pump damage. Thus, vaporization of the pumped liquid can occur two ways: (1) the NPSH required is not being met and cavitation occurs in the liquid causing vapor bubbles that can severely damage the impeller or (2) the pump horsepower overheats the pumped liquid, forming vapor bubbles that can (and normally will) damage the pump.

Excess heat resulting

in pumping a fluid can be

avoided by determining t}re minimum flow required to allow proper heat dissipation. At low flow rates or shutoff conditions, heat is transferred to the liquid contained in the pump casing at a rate representing the power losses of the pump. The power loss is the difference between the brake horsepower consumed and the water horsepower developed. The remnant energy in the pump bearinss and that lost to convection to the outside atmo-

h

O

l-o :.

9?

;7 3.: E>

.9+ 9@ E.)

I

q=

oii !

36


Pump Hydraulic Design Calculation Sheet Liquid Viscosity at P.I (Pumping Temp.) Vapor pressure at PT Sp. gr. (7) at PT. Flow at ambient temD. Operating flow at PT. Design flow at PT.

psra

gpm gpm gpm

_

Suction

Discharge

Source'pressure

psra

Terminal pressure

psia

Static

psi psi psra

Static (head)(lift) APr discharge Piping system Other Discharge press. Suction press,

psl

(+ headx- lifi) =

- APr line loss Suction pressure - Vapor pressure

psra psra

NPSH avail NPSH avail NPSH req'd

-

ft ft

[,lin NPSH avail > NPSH req'd + 2 'lnilial press., e.9., ATM or

O

-

unp at Duty condition (gpmXTDHXr) _ ono" _

psi psi

psia psia

TDH TDH

psra

leet

fl

@

Onp at Maximum Capacity

66o.," =

(3,e60Xr)

Condition

(gpm)CrDHXr) (3,960Xri)

TDH = total dynamic head TDH = discharge press. - suction press.

4 = pump efficiency,

PT.

=

o/o

pumping temperature

Figure 6-5, Pump hydraulic design calculation sheet.

sphere is negligible. The temperature rise per minute is computed by the following relation: 42.2(bhp,") W*Cp

where At : bhp," : W* : Co :

(6-1)

temperature rise per minute, oF/min 6.u1" horsepower at shut-off weight of liquid in pump, lb specific heat of liquid in pump

which is the power required if the desired head at the required capacity could be produced with zero losses. For water flowing through the pump, conditions become stabilized and the temperature rise is determined by the following:

". _

(bhp

-

whp) 2,545 m

where 2,545

:

ir :

(64)

Btu equivalent of I hp-hr mass flow rate- lb/hr-

The break horsepower of the pump is given by

.. OH"y bhp = -,::--r J,vou4

Another variant of Equation 6-4 that relates the tem(6-2)

=

:

flow rate, gpm H = total head, ft

where Q "v

q

= =

^ ô(;-,)

specific gravity pump efficiency (fraction)

':

QHI 3,960

(6-5)

In Equations 64 and 6-5 the compressibility of water is

The water horsepower is given by who

Derature rise to the total head is

(6-3)

neglected. To prevent overheating of the pumped liquid, a bypass piping arrangement is used to have the pump operating at full capacity. Such an arrangement is shown in Figure

6-6.

It is always desirable to pass the bypass liquid

Rotating

through an intercooler to cool the fluid before it enters rhe pump suction port. Under no circumstances should the bypass line connect directly from the pump discharge to the pump suction. So faq we have not considered the pumping of viscous liquids. For a liquid that has viscosity greater than about 10 cp, a viscosity correction must be made, because the pump motor must work harder to pump the fluid. All pump manufacturers' pump performance curves are based on pumping water. To correct for the pumped liquid's viscosity, Figures 6-7 and 6-8 are used to approximate the equivalent water performance. The figures, developed by the Hydrauiic Institute, are used by entering the bottom with the viscous flow rate (gpm), moving vertically upward to the desired viscous head (head per stage for multistage pumps), then moving horizontally to the left or right to the viscosity line, and proceeding vertically upward to the correction-factor curves for the head and capacity. The equivalent water-performance values are then obtained by dividing the viscousperformance values by the correction values. Thus, the pump selection can be made on those ratings established for water. The efficiency of the viscous liquid pumping conditions can be calculated using the efficiency correction factor multiplied by the pump efficiency for water. In this manner the viscous performance of the pump can

be determined using the manufacturers' performance curves, which are always based on pumping water. This procedure is illustrated in the examples later in this chapter.

Positive Displacement (PDl Pumps Positive displacement (PD) pumps are usually selected after it has been determined that a centrifugal design can-

Equipment

37

not meet the requirements. Thus, PD pumps are used where centrifugals cannot operate-under low NPSH requirements or handling a highly viscous liquid. There are several types of PD pumps, as previously mentioned,

and their positive attributes are that they at relatively high efficiencies when pumping viscous liquids. Operate under low NPSH conditions and produce high suction lifts. Operate with high heads at a wide range of capacities . Have a wide speed range, which is limited by the liq-

1. Operate

2. 3

.

4.

uid's viscosity. inherently self-priming.

5. Are

Selecting the fype of rotary pump is primarily a function of cost and the particular requirements that are to be met.

1.

Vane ptmps-normally have a capacity up to about 380 gpm and operate by trapping liquid within vane differential pressures, usually at around 50 psig. The practical limit on viscosity is approximately 100,000 SSU. Vane pumps are subject to wear and should not be used with a liquid that has poor lubricating quali-

ties.

2- Gear pumps-normally

are used up to about 1,000 gpm and can handle liquids with viscosities up to 5 x 106 SSU. These pumps operate at approximately 1,200 rpm with liquids of 10 to 500 SSU viscosity (see Figure 6-9). It is desirable to have internal timing gears and bearings since only one shaft sealing area is required. A variant of a gear pump is shown in Fieure 6-10.

INT€RCOOLEA

Figure 6-6. Excessive heat build-up is often caused by operat-

ing pumps at reduced flow rates. To prevent overheating the pumped liquid, it is advisable to pass the liquid through an intercooler before it enters the pump suction port.


l

00 .90 .ao .70

o

.60

z

.50 _40

.30 .20

."n,

B S9 .icF

CP

.\$

?p

r_':

\9, rd

^

3cP

'6

g

1s"

Hp Zro o!o -co g

vrscoslTY-ssu

'. s

u";*t*

s

g;*1"

I

15

20

25

30

40

CAPACITY.GALLONS PER I\4INUTE

50 (At

60

bEP)

Figure 6-7. Performance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)

Rotating

Equipment

ol

fil -l v,

l( o F ()

[>l

z2l

ogl

trol HEI !t ol

8el >l FI

gl o-l

5l

gt
:l tuI o-l rr lrl I

:l
-l

I

4

6

CAPACITY

810 IN lOO

15

GPM

Flgure 6-8, Ferformance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)

39


Figure 6-9. This drawing of a rotary gear pump illustrates the positive-displacement principle. The fluid is captured in the gear teeth and displaced to the suction port. The crescent acts as a seal between the suction and discharge ports. An application of this type of pump is illustrated in Example 6-2.

Figure 6-10. The internal bearing gear pump is a variant of the rotary gear pump in Figure 6-9. (Courtesy of Worthington

3.

Friction head-the pressure (psi) required to overcome frictional resistance of a piping system. Velocity head-expressed in psi, see Chapter 1. Tbtal suction /r/-the total pressure below atmospheric (in Hg or psi) at the pump suction port during pump operation and equals the following:

Screw pumps-these pumps, depicted in Figure 6- 11, are used where large flow capacities, 4,000 gpm and 3,000 psi, are required. Screw pumps can handle vis107 SSU and have bearing and cosities up to 10

x

timing gear requirements sirnilar to gear pumps.

Screw pumps come in various designs, and one type, shown in Figure 6-12, can handle highly viscous, non-Newtonian fluids such as glues, molasses, tar, asphalt, and wastewater with ease. Positive displacement ( PD) pumps come in a vast variety and you should refer to the manufacturers' literature to best determine the selection of the particular pump to be used. However, PD pumps are sized very much like centrifugal pumps, and the calculation sheet in Figure 6-5 can safely be used for sizing either type. Pump sizing

is focused upon here to illustrate the various ways in which a pump may be specified. Figure Gl3 shows various installations for a pump. Some properties and characteristics illustrated in Figure 6- 13 are

lfi-the

vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be pumped and the centerline of the pump suction port when the pump is located above the liquid level of the ' liquid to be pumped. Static suction head-the vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be pumped and the centerline of the pump suction port when the pump is located below the liquid level of the liquid to be pumped. Static suction

Pumps, Mccraw Edison ComPanY.)

1. Static suction lift plus the frictional head, or

head minus the static suction head (only if the frictional head is greater than the static suction

2. Frictional head).

Total suction head-the total pressure (psi) above atmospheric at the pump suction port when the pump is operating and is equal to the static suction head minus the

frictional head . Static discharge head-expressed in psi, is the vertical distance in feet between the centerline of the pump and the point of liquid discharge. Total discharge head (TOH)-the sum of the frictional head in the discharge line (discharge frictional head) and the static discharge head. Tbtal static head-the difference between the static discharge head and the static suction head or the difference between the static suction lift and the static discharge head.

Toial dynamic head-the sum of the total discharge head and the total suction lift or the difference between the total discharge head and the total suction head'

E -o

E.i aa E

i

E

35

Et=

,^.c!

'6'y

P:;

q .= .:.. -o

'T

0)

o !

9q) .E

CDY)

(.)c,

,*(5 .g E

r].1

o

3t*

;

i: AE F.q .?3H ;6o

b5 9E o.; -o

:", \ d 9 o.: i!-P I E.EE

oo

6-E9g

ao

E';e qIb

!E9 s

g

3

=

il

-oo

EE3

dz

=E

;-F B o-

-

bX-

€ .=o

$Egq 'EE P H:1 :..6

9? E=

=.!ebo ;.

o

t!

-

.F

c

s

9!

b;d

9=Y"t o I cg .2

o

E:0i (sYE:,il

E Xe.d"

:

r ".! 33 r_d ?E 49 &: E06: r * xE ;i

P:

EP

I ! (L

=;= 6-d

PU(J thJ rDt

5.s,b F>\ DDq O x rE F ='; I ai dE 6 crt gl'" dd E 'i-oi

E= =; F

d)


Figure 6-12. A cavity screw pump is ideal for handling higbly viscous non-Newtonian liquids. (Courtesy of Moyno@ Industrial Products, Fluids Handling Division, Robbins and Meyers, Inc.)

t|'r$|lhF..Dl$hra

When using PD pumps where a suction lift is required, remember that the theoretical height to which a liquid can be lifted at any temperature is the difference between atmospheric pressure and the vapor pressure of the liquid at that temperature, when both values of pressure are expressed in feet of liquid. However, the suction lift practical for actual pumping installations is somewhat less than the theoretical value. Figure 6-14 shows the theoretical and practical suction lifts for water. Also, remember that the higher the installation is above sea level, the lower the vapor pressure, and the lower the maximum suction lift. Application of PD pumps to practical installations is given in the examples. The unit conversions included in Appendix D are helpful in pump calculations.

Pressure Protection For PD Pumps By definition, a positive-displacement pump transfers at a rate proportional to the speed of displacing action and this rate of transfer is independent of the pressure differential across the pump. Thus, means must be provided to limit the pressure and the pump discharge side should the discharge piping become restricted or blocked. There are various methods used to prevent overpres-

fluid

sure:

1. Install a relief valve at the discharge of the pump with the relief valve discharge being piped back to the pump inlet in which an intercooler is placed in the line. Such a configuration is shown in Figure 6-15. In

Figure 6-13. The principal parameters of pump selection. (Courtesy of Viking Pump Division, Houdaille Industries, Inc. )

such an arrangement a temperature sensor device is placed at the pump discharge to detect excessive temperatures. The intercooler, or heat exchanger, is used to cool the pumping fluid. Normally, temperature becomes a problem when the instantaneous discharge

and inlet flows are equal. Gear and multiplex

Rotating Equipment

(plunger, diaphragm, and piston) pumps are examples of such pumps in which this situation occasionally de-

2.

velops. Place a pressure switch in the discharge side of the pump piping, interlocked to shut off the pump driver. Since pressure switch set points are not as reliable as relief valves, a relief valve must be added to the discharge piping and set at a pressure slightly greater than the pressure switch to ensure adequate protection. The relief valve would be piped-up similarly to that shown in Figure 6-15.

3. Install a torque{imiting device in the pump driver when a relief is not practical, such as slurry service. A torque{imiting device can come in the forms of a shear-pin or torque limiting coupling. These devices

Figure 6-14. The theoretical and maximum recommended lift for water at various temperatures, 'F. (Courtesy of Viking Pump Division, Houdaille Industries, Inc.) suction

have advantages other than protecting the system against overpressure; they protect the pump against foreign material or whenever the pumped fluid might tend to solidify. Overpressure protection

is essential in positive-dis-

placement pumps. Relief valves applied should be added to the discharge piping itself, because built-in relief valves on the pump that are not removable for testing are undependable.

COMPRESSORS The three types of compressors used in the process industries are centrifugal, reciprocating, and axial flow compressors. Like pumps, depending on the application, the type of compressor is roughly a function of the gas capacity, action, and discharge pressure. Figure 6-16 shows the operating ranges of the three basic types of compressors. As clearly shown, one type of compressor, despite its disadvantages or advantages compared to other types, is usually the obvious choice. Reciprocating compressors are normally used when a relatively low flow rate is required, but high discharge pressures are expected. This situation is common in the gas processing industry where high discharge pressures are needed for process conditions. The need and use of reciprocating compressors is unavoidable in many process system applications.

Centrifugal compressors are the most common typ€ in hydrocarbon processing plants and are to some extent the

workhorse of chemical process compression needs. There are four basic advantages a centrifugal compressor has over a reciprocating compressor:

1. Lower initial capital investment. The cost advantage is increased as the power demand is increased.

(B)

Figure 6-15, A temperature switch can be used in lieu of an intercooler (heat exchanger) in which the switch can shut off the pump driver when liquid temperatures become excessive as in (A) or can be used with an intercooler in (B) to divert

flow through the exchanger. In either case, a pressure safety valve should be used on discharge. (B) assumes the suction temperature is constant. To prevent overheating on low flow rate conditions, a flow switch is often used.

44


2. Lower

Princlples of Compresslon

3.

The general gas law that applies to all gases can be written in several forms:

4.

operating and maintenance cost. The operating and maintenance cost of a centrifugal is approximately one-third that of a reciprocating compressor. Compactness of size. Centrifugals occupy less space and make much less noise. Simplicity of piping. Reciprocating compressors can cause severe pulsation shock response in piping systems. The cost in preventing the effects of pulsation in piping systems can entail many hours of engineering and a healthy capital investment for either analog or digital simulation tests. Centrifugals do not have this problem.

Axial-flow compressorc operate at greater capacities Axialflow compressors are governed by the same formulas that apply to centrifugals. The axial units are more efficient than the centrifugals, but the latter have a much wider operating range. Axials are used primarily for and are often used in series with centrifugal units.

PV =

zmRt

(6-6)

zmRt

(6-7)

mw

: PV:

zM.Rt

(6-8)

zRt

(6-e)

where

clean gases such as air, because they are much more susceptibie to corrosion, erosion, and deposits than centrifusals.

: V: z: R: R: P

absolute pressure, psra volume of gas, ft3

:

compressibility factor for real gases (z 1 for a perfect gas) R/mw gas constant of the particular gas universal gas constant 1,545 ft-lbr/lb.

:

t= m=

: : v:

mw

mole

-

:

'R

absolute temperature, mass of gas, lb-

'R

: 'F + 459.7

molecular weight of gas number of moles of gas m/mw specific volume of gas, ft3llb.

:

Mo

A very important gas property is the specific heat ratio, k. This property is determined from the following:

.c"c" K=---j= c"

where C,

Cp

cP

:

1.986

(6-10)

specific heat at constant volume, Btu/lb.-mole-

= 4.97 Btu/lb,-mole-"F for ideal monatomic gases = specific heat at constant pressure, Btu/lb,-mole-

:

s

-

7.00 Btu/lb.-mole-"F for most diatomic gases

Reverslble Adiabatlc (lsentropic) Compression

a

The reversible adiabatic (isentropic) compression of

o

an ideal gas is obtained when no heat is added to, or removed from, the gas during compression. The process is

reversible when no friction exists. The formulations differ for a perfect gas versus a real gas.

6

Perfect Gas

INLET FLOW,ACF

souRcE:DriroPLot{ t2l

Flgure 6-16, Approximate ranges of application for cating, centrifugal, and axial-flow compressors

recipro-

[2].

PrV,K

:

(z

PtYtx

! : l&F tr \Pr/

:

1)

(6-11)

(6-12)

Rotating Equipment

Real Gas (z P1V17

t' t'

:

*

1)

: gas flow rate in standard cubic feet per minute of gas (60"F, 14.7 psia) P, : absolute pressure at suction, psia Pd: absolute pressure at discharge, psia t. : absolute temperature at suction, oR

where Q (6-13)

P2V2'y

lP:l "

(6-14)

\Pr/

_2"*24

:

mean comoressibilitv factor

where. for any system of units

: : : -y : t: P

absolute pressure

V k

volume or specific volume, v specific heat ratio isentropic exponent for real gases, Co/Cu absolute temperature

z. za

: :

compressibility factor at suction compressibility factor at discharge

For a gas capacity of Q

:

100 scfm, Equation 6-16

becomes subscripts spectively

I

and 2 denote inlet and discharge conditions, re-

[,,,-,

To determine the exponent, T, real gas properties must

k-r

kt

be used. These properties can be obtained from gas property charts and used in the following formulation:

r / \'l I-I-y =*l'*,lSll [ \atloj

(6-15)

JCp

where J

:

mechanical equivalent of heat

:

'778 ft.-lbrl

Btu

/,el : ll-l d[,l p \

rate of change of compressibility facror. z. with respect to the required temperature. t. along a constant pressure, P. path

To determine a mean value of the isentropic exponent for a real gas, ?, over a compression range, Equation 615 must be solved by iteration. In Equation 6-15 if we have a perfect gas in which

4"

: :

?

'v=k For a compression ratio PzlPr < 2.0, mately equal to k for most real gases.

t

[,

],

\k/t

t

(6-17)

qn

: :

mechanical efficiency the ratio of the actual horsepower delivered to the gas to the brake horseDower. or

shp bhp

:

:

(6-18)

overall adiabatic efficiency the ratio of the isentropic horsepower, hpr, for a stage of compression to the brak€ horsepower, or hD"

is approxi

For isentropic compression of an ideal gas the theoretical horsepower requirement is as follows:

hp':ffi|('iJ'*-', -'l['',J'

adiabatic efficiency the isentropic horsepower, hp1, delivered by the actual horsepower delivered to the gas, or

hpr

4,o

JCP

I

gnp

''''

R k-1

l\P,/

In applying these formulations that deal with the isentropic compression of an ideal gas, efficiency factors must be defined in order to apply the equations to real world compressors. These efficiencies are as follows:

l=l =0andz:1.0 then Equation 6-15 becomes

],

h._ =6.42llPdl k _rl{r,l_ -l\520/-

(6-19)

bhp

In defining the horsepower input for a single stage of . compression, utilize the overall efficiencv as follows:

6'6, bhP=*=ffi[(,t-']F;'{*) \ k /r

(6-20)


For bhp at 100 scfm, Equation 6-20 becomes

J

The isentropic energy transmitted to the compressed gas in ftJb/lb- of gas represents the adiabatic head, or

t

\t

,[,,*-,

I

- 'la \mw/ \K- r/ [\Ps/ ",: llsl{IlllSlT I

(6-2r)

The compressor driver horsepower (bhp or ghp) is related to the adiabatic head by the following:

ghp: bhp

:

(6-22)

33,000a"

frfl,

(6-23)

33.0001""

where rir

:

mass

PlVtn

=

where

n:

(6-26)

flow rate of the gas, lb./min

The adiabatic efficiency can be defined in terms of the

polytropic efficiency by the following:

PrYro

(6-27)

the polytropic exponent,

n

+ I orn +k

Expressing Equation 6-27 in terms of temperature and pressure we have

t' /p,\? t' -- \P,/ The value

gas

;H"

constant

When Equation 6-26 is expressed between the initial and final conditions we have

bhp=ffiH=-'l'H \-o /1

:

PV'

(6-28)

ofn

depends on whether the gas is a perfect

(z: l) or a real gas (z *

1) as previously dis-

cussed.

For a perfect gas the relationship between adiabatic and polytropic efficiencies is given by Equation 6-24. Similarly, the polytropic exponent, n, for a perfect gas is related to the polytropic efficiency and adiabatic exponent. k. as follows:

n-1

k-l

n

lll

(6-29)

\4el

k-1 _R

(6-30)

JCo

(6-24) sincek: Equation 6-24 is discussed in more detail below. For a single stage of compression, neglecting any changes in potential and kinetic energy, the temperature change from the inlet and discharge is given by Af : r. - r : 6.33(2,547bhp

-

q)

(6-2s)

QCo

where q

:

total heat energy lost to the surroundings or to any available cooling water or cooling jackets. This value does not include thermal enersv for intercoolers or aftercoolers.

For a multistage compressor, Equations 6-20 through 6-25 must be applied separately for each stage.

Polytropic Compression

ColC"

The relationship between the polytropic efficiency and adiabatic (isentropic) efficiency of a perfect gas is shown

in Figure 6-17. The polytropic efficiency, 4p. is usually determined by the compressor manufacturer using either an old design or testing a new design. The polyropic exponent, n, for a real gas is determined from real gas properties or with using real gas data and using the following expression:

n-

I

n [z+ t l_tl /a'\] _t_ JCo lqo \at/l

Equation 6-31 is identical to Equation 6-15 except that the isentropic exponent for a real gas, 7, is replaced by the polytropic exponent, n, and the compressibility factor for real gases, z, is divided by the polytropic efficrency, ?p.

This type of compression occurs when a gas is reversibly compressed along a path that is defined by the followins relation:

(6-31)

Similarly to Equation 6-15, Equation 6-31 must be solved by iteration for a mean value of the polytropic exponent, n, over a compression range.

Rotating

6A 70

72

74

ciency for a perfect gas (Z

lp

In Equation 6-31, if we have

l3l :

ouno z

\r/p

*'ffilett'le

= I fora perfect sas

then,

JCp4p , /r \ K l-l

@32)

\4pl

For most real gases below a compression ratio of approximately 2, then

n

=

1).

'' (,C,tffi

(6.33)

For ghp at 100 scfm,

n-l:j-:= n

47

Figure 6-17. The relationship between the polytropic efficiency and the adiabatic effi-

767880

POLYTROPIC EFFTCTENCY

Equipment

- I _k n ll\ 'K l-l

1

,no

(il t=l

: k /t[tfl

H!-1J_j1?L

\;/\

_ (,$,,, H,6.34, ]

The equations for polltropic head are similar to those for adiabatic head. Equation 6-21. Thus.

\ql

The basic horsepower and head expressions for polycompression are similar to those for isothermal compression, Equation 6-20. Thus, we have

fopic

FJ

. : (.*_)t^J IH(l

,]

"

(6-35)

48


If the polytropic head is known, the compressor horsepower (ghp or bhp) can be obtained from the following: bhp

:

ehp

:

mil

(6-36)

33,000a*

riH

bhp

t, = i&)H \P,/

(6-38)

values):

/\ I lk-ll

.

y

v

(6-3e)

./ - -t----t -4p\ K / \p

: k-l

(6-40)

k

Normally, the value of ?e is estimated from data supplied by the manufacturer. For initial or preliminary values of the polytropic efficiency, 10, Figure 6-17 may be used.

lsothelmal Gompression This compression occurs when the temperature of the gas being compressed remains constant during compression. For a perfect gas in which z 1.0 and (AzlAip 0 we have

:

P1V1

:

:

(6-41)

P2V2,

OI

PV

:

(6-42)

constant

The theoretical horsepower developed during a reversible isothermal compression process is

ho,:atz " 8.1l0hl&) \P,/

(644)

7h

where

: Ia :

isothermal efficiency

4,

overall efficiency

: Itlln

F)

.

hp, hpr

tlfl- tl:.

(64s)

Equations 6-35 through 6-38 are used separately for each stage of a multistage compressor. Equations 6-38 and 6-39 can be used to calculate the polytropic efficiency directly (provided t, ta, P,, P6 and k are known

wnere

_

: overall polytropic efficiency : IpI.

The outlet and inlet temperatures for polytropic compression are related by the following expression:

!

not

achieved, because the heat of compression causes the gas to exceed the inlet temperature. The actual performance of a real compressor can be evaluated by the following:

(6-37)

33,00040

where 4oo

Equation 6-43 assumes that the heat of compression is

fully removed by cooling. In practice this is

(6-43)

After applying Equation 644 and determining

the

brake horsepower (bhp) for a single stage of compression, the discharge temperature can be determined by Equation 6-25.

Dimensionless Reference Numbels In sizing and selecting the type of pump or compressor to be used, a logical correlation is often desirable. The following dimensionless parameters apply to pumps and compressors and are the specific speed and specific di ameter, as defined as follows:

N : '

N(Q)o

5

(6-46)

H0.75

: specific speed, dimensionless N = speed, rpm Q : capacity of flow rate, ft3lsec H : head, ft-lbrilb.

where N,

^

"":

where D.

:

D: H:

D(H)o

25

e*

(6-47)

specific diameter, dimensionless diameter of impeller ot rotor, ft head, ft-lbr/lb.

Figure 6-18 shows the dimensionless parameters as originally presented by Balje [3]. This figure is the graphical combination of Equations 6-46 and 647. Past experience often dictates what type of pump or compressor is to be used and in cases of uncertainty or new applications, this figure will be useful in equipment selection. Figure 6-18 must be applied to each stage separately, as each impeller or stage must be chosen with each separate inlet capacity or head for that stage.

Rotating Equipment

^.

10

E

G

I

4

=N

'/q/Ha1

D,= DHltalJT'

/V O D

= Speed, rpm = Flow, fr3/s

= lmpeller diameter,

0.3 0.6

ft

30

1

60

Specific speed,

r00

3m 6m 1,000 3,0()()

10,000

4

Figure 6-18. The initial selection ofa single-stage compressor is made using the specific speed and specific diameter parameters

t3l.

Gentffugal Gompressors The centrifugal compressor powered the first turbojetpowered aircraft and is still used today injet engines as a

supercharger. The main advantage

of the

centrifugal

compressor is that it produces a large pressure ratio for a single stage of compression, and is easily manufactured. Its advantages over the reciprocating design were cited

previously. Most centrifugal compressors are designed so that the gas enters the impeller axially-parallel to the rotating shaft-as shown in Figure 6-19. The gas flow is then changed to the radial direction and is accelerated in a peripheral direction as it moves along the impeller. As the gas exits the impeller, it enters a stationary diffuser where the gas velocity is reduced. This process is repeated at each stage on multistage compressors. Most of the pressure increase in the gas occurs in the impeller and the greatest pressure drop occurs in the diffuser. In multistage compressors, cooling the gas between stages is quite common and many such compressors have water-cooled separators or diaphragms. The polytropic relations, Equations 6-26 through 640, are usually preferred for centrifugal compressor calculations. Figure 6-20 shows why with a schematic plot of the centrifugal compression process on a temperatureentropy graph. Using the adiabatic (isentropic) process, the actual discharge temperature is underestimated

Figure 6-t9A. Centrifugal compressor-single-stage. (Courtesy of Dresser Industries, Inc., Roots Blower Operation.)

50

Mechanical Design of Process Sysrems

Changing the speed of a centrifugal compressor involves the "affinity laws," which apply to single-stage compressors, multistage compressors when each stage is considered separately, and to multistage machines over a narrow speed range representing no more thm a 15% change in speed. These laws are stated as follows:

1. The developed head (feet) varies to the square of the speeo.

2. 3.

The required power varies to the cube of the speed. The capacity (cfm) varies to the speed.

Figure 6-21 shows the effect of varying centrifugal compressor speed. In centrifugal compressors a phenomenon known as surge occurs when the compressor capacity is lower than a specific flow rate. This specific flow rate is shown in

Figne 6-22 as the "surge limit." The phenomenon of surging is manifested by cyclic vibration of gas flow, which can even result in reversal of flow direction, power requirement, and discharge pressure. The phenomenon normally is associated with excess noise and

1

2.

3 4 5 6 7

8.

Nozzte 9. Shaft Cover 10. Oi Fterainer Sub Cov€rSeclion 11 BeartngSrand Bearing Stand Cap l2 Coupting End Beanng SteelShim 13 tmpelerEnd Bearino r'rus Bed nq 4. Or'Ferar-e. -!run Ho-s nq 5eal t5 Sa.t Spaci.g Fing 16 Votute Discharge

Casing

17 Intetsection j8. impe|er j9. clideVane Housing ZO. In er Nozzte

21 cuideVane 22 curoevaneLrtdop moe er End ptdl;

23

24. Intet Wearing Fing

Figure 6-198. Cross-section of a single-stage centrifugal of Dresser Industries, Inc., Roots

compressor. (Courtesy Blower ODeration.)

(ideal). Since the polytropic compression process, by definition, is the path connecting the inlet and actual discharge conditions, the polytropic formulations are preferred by compressor manufacturers. This factor becomes extremely important in sizing intercoolers, since using the adiabatic discharge temperature would result in undersizing the cooler. The larger the compression ratio of the machine, the more severe the mistake ofundersizing the cooler becomes. Gas inlet conditions can change and when they do they affect a centrifugal compressor differently frorn a positive-displacement compressor, such as a reciprocating machine. Table 6-1 lists the effects of changing inlet parameters on a centilugal compressor operating at a constant volumetric flow rate and a constant sDeed.

Atidd: t2t-tl At*,-r=t2-tl

ENTROPY s

Figure 6-20. Centrifugal compression process.

Rotating Equipment

/.

:.1

9

t

.46

il

/. ,lPji: ;.J 2 t{l

I

k' "y

{

lsr N t\\

3A\ a\ 1\

I

t;

(Vtt I s,l t[t

)

>-Kl

J;Al

un

4 d .t AI

*f

\\N \E.I

NN \'lN \'l

N

/s

A

ll

N; \

w:,

I

I

.1

'=\\

E

E

${ \l

il

.lI\

'I

sI

aE:93Bs3B9BEig9S3P3e9 lstu Stnsslud

1N3?8ld

!3/VlodtsuoH

R

lNlltld

! 8

L 61 I

\ \

I

=

c

5T--r-t

N \ ii",-l

oU;

I

?;

3;t

\

3io-

\\

83q33P339 3Sll ]Unss!rd 1i!ltld

!3NrOd3S!08 1tt3U3C

ga.

_11

-t

;L al,l

L ,/a

=rl

l I I

I

.J .J :-

|t\

3\

\

t\

:9

\ \

\l \

>,

3

E33P cY3ll I rillu ld

9833P33 t3fl0dlst0lt 1r!llttd

;-n

oa. < Or^ =E ltY

5l


52

Table 6-1 E tects ot Varying Various Inlet Parameters on a Centrilugal Compressor Increasing lncreasing Increasing Increaslng value ot Inlet lnlet Molecular Weight Polytropic n or Pressure of Gas Adiabatic k Pressure Differential

Deateases Decreases Decreases Decreases Decreases Decreases Constant Decreases

Compression Ratio Inlet Density Discharge Pressure Discharge Temperature Power Required Head Developed Mass Flow Rate

r20

COMPRESSOR CHARACTERISTI(

I

B

I

,

I

s80

7

I

...

I

460 c0MPn€ss0F SURGE LIM

40

I]

I

I t

t0 0

D

0 r0 20 30 40 50 60 70 80 90

too tn

PERCENT CAPACITY

Figure 6-22, Pressure vs. capacity for a constant-speed centrifugal compressor [4].

vibration of the compressor and sometimes the compressor piping. Normal surge limits are 40% to 90% of rhe design point, with the higher range (close to 90Vo) being associated with multistage mach ines. Controlling surge in centrifugal compressors is more difficult than in centrifugal pumps, but the following factors ease the problem considerably:

1. Throttling at the discharge flange.

2. Throttling

Increases Increases Increases Increases Increases Increases Constant Increases

Decreases Decreases Constant Decreases Increases Constant Constant Constant

J. Using a variable speed driver, usually accomplished

CONSTIiIT SPEED

0

o.

Increases Constant Increases Increases Constant Increases Constant Increases

at the inlet flange, which is usually more efficient than throttling at the discharge flange.

by the turbine driver. 4. Bypassing or blowing

off

excess gas to avoid surge.

These steps will help in alleviating surge problems, but if a variable rate operation is required, the compressor manufacturer should be consulted. Antisurge devices can be incorporated into compressor systems. For nontoxic or inexpensive gases the compressor discharge can be vented to the atmosphere as shown in Figure 6-23. For expensive or toxic gases an automatic anti-surge system can be installed as shown in Figure 6-24. In this type of arrangement a heat exchanger is placed in the system to remove the heat of compression from the vented discharge gas to prevent a loss of compressor performance caused by the temperature rise above the design value at the inlet. Compressor manufacturers use standard cubic (scfm) feet to speciry compressor performance, just as pump

manufacturers use water to determine pump performance. The manner in which scfm and altitude correction is handled is discussed later. Impellers are critical in the selection of centrifugal compressors. The three basic types of impellers for centrifugal compressors are shown in Figure 6-25. The conventional closed impeller shown in Figure 6-25 is used for adiabatic heads up to approximately 12,000 ft-lbri lb-. The open, radial-bladed impeller shown in Figure 6-25 develops more head with the same impeller diameter and shaft speed. The open inducer impeller can produce heads up to 20,000 ft-lbrnb*. Whenever the head requirement becomes too great for a single impeller, then one must think in terms of multistage compressors. Each stage of compression of a multistage compressor is treated as a single stage compressor and the same formulations hold.

Rotating Equipment

Reciprocatlng Compressofs

cle. Figure 6-26 shows the reciprocating compressor cycle. This cycle involves this displacement of gas,

These compressors normally are sized according to the adiabatic expressions of Equations 6-11 through 6-25. Normal practice in calculations for reciprocating compressors is to use the adiabatic exponent, k = Cp/C,, then adjust the results according to the specific compressor design and configuration. The parameters that affect the compressor horsepower, cylinder capacity, and discharge temperature are length of stroke, shaft rotation

hence the classification of a reciprocating compressor as a positive displacement type of unit. The compressor is

speed, cooling efficiency, and fixed clearance of cylinders. All of these parameters vary for each given application, but have the same basic cylinder design and cy-

drscharge

unable to exhaust all gas from the cylinders and the residual gas remaining in the compressor at discharge conditions expands to inlet conditions. This phenomenon is shown in Figve 6-27 . The clearance voiume is usually set by the compressor manufacturer and is specified to match the specified capacity with the standard size compressor unit. Power consumption is not affected by the clearance volume or

the volumetric efficiency. The use of "clearance pockets" is used in some compressors to vary the volumetric efficiency. These clearance pockets can be sized to affect the capacity of the compressor, as in Figure 6-28. Power consumption at reduced flow rates is minimized by use of capacity control. The use of a clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor, because the re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke. This mechanism is economical, because the energy expended in gas compression is retrieved in expansion. The clearance pocket is separated from the cylinder by a stop

valve. Figure 6-28 shows how varying the cylinder clearance affects the numeric value of the volumetric efficiency at constant compression ratio. The volumetric efficiency for a reciprocating compressor is given by:

inlet

actual capacity piston displacement

Figure 6-23. Manual surge control system for centdfugal

(6-48)

comPressor.

The parameters that affect the volumetric efficiency are as follows:

l.

flow monitor

2. 3.

centrifugal compressor

Figure 6-24. Automatic surge control with recirculating bypass.

The ratio ofa relative clearance volume, e, which is the ratio of clearance to theoretical displacement expressed as percent. The compression ratio, C., of discharge to inlet pressure. The various exponents of the polytropic curve of reexpansion. Such a curve is shown in Figure 6-29.

Here the cylinder is normally cooled by a water jacket or surrounding air. The small volurne of gas that remains in the clearance volume expands and contracts with a cooling surface. Consequently, the re-expansion curve (curve 3-4) is initially steeper than the adiabatic curve (curve 1-2). With continuing expansion ofthe gas, the gas temperature falls below that of the piston and walls, and heat is transferred from these surfaces to the gas. Thus, the exponent of the re-expansion curve (curve 3-4) is variable. For reexpansion oflower compression ratios, Chlumsky [5]


OPEN BACKWARD.BLADED

IMPELLER

OPEN RADIAL-BLADED IMPELLER

CLOSED BACKWARD.BLADED

IMPELLER

'120

BACKWARD LEANING B LADED IMPELLER

e

63

RADIAL BLADED IMPELLER

si

100

80 60

(PARAMETER-

s

% SPEED)

(PARAMETER.

% SPEED)

40 149 120

EH o

o"o,

-4,

?E

40 60 B0 100 120 qoRATEO INLET VOLUME

BACKWARD LEANING IMPELLER AOJUSTABLE IN LET GU IDE

3

1?O

q

E

100

E

c'

ao

E

BLADED IMPELLER

s

ADJUSTABLE

ol

s

l

ll

opi-l RADIAL

IN LET

GUIDE V

WIDE

VANES

UIDE VAN ES G

T

100

100

Vcc

g'g .-B

d>

ro

ao

so

s9 40

20 40 60 80 100 oToFATED

INLET VOLUME

120

20 40 60 BO 100 obFATLO

l\-ET

120

VOIUMF

Figure 6-25. Basic types of impellers for centrifugal compressors. (Courtesy of Dresser Industries, Inc., Roots Blower Operauon.)

Rotating

Equipment

;

P2

= receiver pressure

P1

= inlet pressure

Compression Stages: O = start

@ = comPression @ = discharge @ = expansion O = intake

-tl @@ Figure 6-26. Reciprocating compressor cycle.

o/o

Clearance =

Clearance volume (100)

Volume

Figute 6-27. The effect of clearance capacity.

55


Clearance volume

tts

l{ts F 6.

It rsl<\

|

rls lrlo 115

I

100

o/o

Piston DisDlacement

Figure 6-28. A clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor because the re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke.

|

CLEARAT{CE :C 0O5L + O.Smn, WHENE L=STHOKE L-ETGTH

voLuME -.---------+

sourcE

:

cH urMsl(Y

l5l

Figure 6-29. A pressure-volume diagram of a compresor with clearance (zero flow resistances)

[51.

Rotating Equipment

recommends fof compression ratios of appfoximately 2; the re-expansion may be approximated as an adia-

batic process. For the volume, Va-the volume to which the gas expands during the pressure drop from P2 to Pr-we have the expression

., : ".

.. /pl,

(64e)

"" \p,/

For compression ratios of 4 and higher, the re-expansion cannot be considered as an adiabatic process. For these compression ratios the polytropic exponent m (where m denotes the difference between the re-expan-

PV'

(constant) and the compression PVn (constant). 1.25. For diatomic gases, m The value of the polltropic curve exponent, m, varies sion

:

with pressure. Chlumsky [5] recommends for a com-

pression ratio of 3:4 the following values of m be used:

Substituting Equation 6-49 into the expression for volumetric efficiency, we have

First stage Second stage

,lt

-

v"+v"-v4

-

-----------=;--

Third stage Fourth stage Fifth and further

'u'(*o]'

-

stages

m:l 20 m : 1.25 m: 1.30 m = 1.35 m:k

or These values are given at different pressure levels, as ex-

-t

-.[(,*i -

where e =

*vp:

(6-50)

.utio of the clearance volume. Vo. to the volume swept by the piston stroke.

v" ?" =

#vp: V^

expression for volumelric efficiency. Equation 6-48, the ratio of gas volume pumped to the volume swept by the piston (compressor displacement)

Figure 6-30 shows the graphical solutions of Equation G50 for various compression ratios and exponents of the polytropic curve of re-expansion and clearance values.

34

_L-

I9n

ist in multistage compressors with the suction of the first stage at atmospheric pressure. The volumetric efficiency for a perfect gas (z = 1), not realistic, is given by

4,r:100-c(cRr/k-1) where 4,, : theoretical volumetric efficiency The volumeuic efficiency for a perfect gas (z with realistic effects.

4":100-cR - c(cR'/k - l) Cs : compression ratio : PzlPr

1@Z

80

c

Figure 6-30. Curves for determining volumetric efficiency [5].

(6-s

l)

:

1)

(6-s2)

58


The difference between Equation 6-52 and Equation 6-51 is that the theoretical volumetric efficiency should be reduced by a value equal to the compression ratio to obtain an actual value for a perfect gas. This is a factor that has been determined from field experience. For a real

lv:

100

gas

(z

*

22:

_ cr _ c1(cR)i" _

(6-53)

I

rnlet and discharge compressibility factors, respec-

tively

As stated previously, reciprocating compressors follow the expressions for an adiabatic process. The work required for the adiabatic compression of a perfect gas (z : 1) is found by the following expression:

w:

1. Operating at high speeds, they can be coupled

1) with realistic effects,

where

zt,

dency has been to increase the cylinder size using a smaller number of cylinders. Multistage reciprocating compressors have the following advantages:

PV (-o_JhtJ=

2. 3.

fluctuation of torque. The more cylinders, the less the fluctuation of torque. 4. Starting multistage compressors is easier because they have small moving masses and thus can be driven by electric motors with less inertia torque and lighter construction. 5. Variations of pressure and flow velocity in the intercooler or oil separator are less, thus making these

6.

-']

(6-54)

7.

6-16 or bv the followine:

:

u [ll,I- . rl'l [,, * ,l 33.ooo k-l [\Pr/ \ 2., /

(P

Vrrr44

For an ideal

where

ga's, 21

P1, Pz

:

:

parts smaller. Machines of various capacities can be manufactured using identical parts, making interchangeability efficrent,

The theoretical horsepower may be found by Equation

6o.

di

rectly at high shaft speeds thus utilizing cheap electric motors. Better balance of inertia forces. The mass of the flywheel, which rotates at high speeds, can be made smaller, resulting in a smaller

(6-5s)

22

inlet and discharge pressures, respectively,

Multistage compressors are better suited to automatic operation.

Gas Temperature for Reciprocating Compressoas The discharge temperature of a positive displacement compressor, a class of which the reciprocating is included, can be predicted by the following expression:

psia

Vl, V2 = ir et and discharge

gas

flow rates,

respec-

tively, acfm

In Equation 6-55, the theoretical horsepower may be varied by the following parameters:

l 2. 3. 4.

lncreasing Increasing Increasing slon rate, Increasing

the compression ratio, Cp the specific heat ratio, k the inlet pressure at a constant compresthe actual inlet volume (nat standard vol-

ume).

Multiple Staging of Reciprocatang Compressors Multiple staging is the compression of a gas from one pressure to another involving more than one step. Each step acts in series with the others and entails a basic machine element. In multiple staging of reciprocating compressors, increasing the cylinder size is less expensive than increasing the number of cylinders, thus the ten-

,r

/P'\?

t-\Pj

(6-56)

where t :

absolute temperature for any system P = absolute pressure for any system

: 1, 2 : k

Cp/C', adiabatic exponent inlet and discharge conditions, respectively

Axial Flow Gompressors In axial flow compressors, the flow enters the unit oarallel to the axis ofthe shaft and the flow direction esientially remains unchanged from the inlet to the exit of the unit. Airfoil blades are located on the rotor shaft, varying in pitch and size according to the flow conditions. The gas passes through the airfoil blades in an axial direction. Axial flow compressors are used for applications of about 25,000 cfm upward. The formulas for centrifugal compressors apply to axial flow machines. Axial flow compressors can handle greater capacities, which is the primary reason why they have replaced centrifugal com-

Rotating Equipment

pressors in aircraft gas turbine units. The characteristic curve (head versus flow) for an axial flow compressor is much steeper than for a centrifugal compressor and the surge limit is a function ofdesign capacity. Contrary to a centrifugal compressor, the required horsepower for an axial flow compressor at constant speed and pressure decreases with increased flow Axial flow compressors are not as common in the process industries as centrifugal or reciprocating types of machines.

Fans and Blowers Fans and blowers are basically compressors. They fall under two types of compressors-centrifugal and axial flow. If one understands the basics of centrifugal or axial tlow compressors, fans and blowers come easy, for they are less complicated than compressors.

Specifying Gompressor Flow Gondltlons Specifying compressor flow conditions is a major source of confusion in applying compressors to process sl stems. There are three basic ways to specify compres-

:or flow conditions:

l.

flow-define the mass flow rate of the gas, Ib./ in the English system and kg/hr-m in the Sl/metric. 3. Actual, or inlet, volume flow-volumetric flow rate of the gas at the inlet conditions, expressed as acfm or icfm in the English system and m3/hr in the SI and MKGFS systems. -1. Standard volumetric flow-the volumetric flow rate of the gas at the inlet conditions expressed in terms of standard cubic feet of gas per minute (scfm) or millions of standard cubic feet of gas per day (MMscfd) in the English system and m3/hr in the SI and MKGFS systems. Mass

Iass

Flow

The method of defining the mass flow rate of the gas h terms of the inlet conditions of the comoressor is far ored by many and is mandatory in calculating gas propenies between stages. Mass flow rate ,?2uJt be specified as either dry gas or wet gas. Ifthe gas, for example, conrains water vapor, this could drastically change the compressor design. One of the problems of using mass flow is not speciffing the flow conditions as a dry gas, which ir reality is a two-phase or multiphase flow. Another disadvantage to using mass flow is that it does not allow one to appreciate the physical size of the sysrcm. An intuitive feel for any system is essential to its successful desisn.

Actual or Inlet Volumetric Flow Actual flow rate conditions at the inlet to the compressor is denoted as acfm or icfm-acfm meaning actual cubic feet per minute and icfm meaning inlet cubic feet per minute. The disadvantage to specifying acfm is in the internal components ofthe compressor, e.g., a sideJoad refriger-

ation compressor, or in a multistage compressor. In a multistage compressor the previous stage's discharge temperature is a function of the previous stage's compression efficiency, and mass flow rates are better for such conditions. Acfm is best for plotting compressor performance curves, because the impeller is sensitive only to the actual volumetric flow and is insensitive to the gas state conditions. Mass flow and acfm volumetric flow should be used because mass flow is invaluable in communicating with tle compressor manufacturer and in dealing with internal machine flow conditions, and acftn is essential in getting a feel for the physical size ofthe system. The use of mass flow and acftn should counter the disadvantages of both approaches. In computing pressure drop through connecting piping systems to compressors, it is imperative that acfm be used to avoid any confusion in designing the piping systems.

Standard Volumetric FIow Specifying gas conditions in terms of standard volumetric flow is done extensively throughout industry. The gas flow conditions are based on standard inlet condi-

tions-pressure, molecular weight, temperature, and compressibility-all based on "standard" conditions. Thus, the standard specific volume is constant being that

u.,.

: "'+J'':

constanr

(6-57)

where z.,a : compressibility factor at standard conditions R: universal gas constant, which is a function of the molecular weight of the gas

: P$d : tsld

temperature at standard conditions pressure at standard conditions

Volume flow is expressed as Q,ta

:

mV,ro

(6-s8)

where the standard volumetric flow is directly proportional to the mass flow rate.

60


As with using mass flow, when using standard flow conditions one cannot appreciate the physical size of the system. And worse still, using scfm does not provide any of the advantages of using either mass flow or acfm. To specify something as "standard" one thing is essential, that all parties agree on what is "standard." Unfortunately, this is not the case with using scfm, as the following "standards" cited by Lapina [6] indicate:

The specific volume, V, may be determined by sas\ / ' \ v = z /rl::_:l I::-::l mw

/

\

where, as before, mw

scfm

(6-61)

\1,14Pl

:

molecular weight

(379.46)mh

:

(6-62)

60

Metric system

English system

1. P",a : 14.7 psia t'ta : 60'F 2. P,u : 14.7 psia t"a:70"F 3. Pd : 14.7 psia t.to : 32'F

1

2.

P",a

=

where mh

101.3 k?a

: 0'C P"a : 101.3 kPa t,ra

and

tsa:15'C

rir

=

moles/hour

= (rfi)(mw)

(6-63)

and finally,

aclm:

qs _ = [(MMscrdx106)1 1,0

Thus, what is considered "standard," as Lapina [6] writes, varies from industry to industry and engineer to engineer. In the net result what is often gained is confu-

where

sion.

tion) conditions.

lie

nu)1/f*l*)|/t)

t--aOoz, t \-pJ\460

+

-' rJ\il .""_*,

subscript, s, denotes properties at the inlet (or suc-

Equation 6-64 may be expressed as follows:

e.=acrm=*-tltjHP*.,-J

Properly Specifying Gompressor Flow Gonditions To properly size or select a compressor, the capacityno matter how it is given-must be converted to the inlet conditions. To do this the following expressions are used:

(6-6s)

where the scfm is based on a dry gas. To convert the standard volumetric flow to mass the following relations are used:

flow

English system: PrVr

tflt

_

P2V2 tzzz

(6-66)

V: P:

where

t: z

:

volurne absolute pressure absolute

Sl/metric system:

Iemperalure compressibility factor

rir

In Equation 6-59, if z and

t

acfm

:

where

e_ = rirV

ri : V p

: :

mass

scfm fP"o

\zd

'

ro'\

(6-61)

R.td t.ld/

1.0 for a perfect gas, and P

are at standard conditions, then

:

:

: "' p

flow rate, lb./min

specific volume, ft3llb,,, density, lb./fC

PIPING SYSTEilS FOR ROTATING EQUIPMENT (6-60.)

For rotary equipment to be functional and contribute to the process system, it must be connected to the system with piping. The science of connecting piping systems to rotary equipment is a relatively new field and has drawn

Rotating Equipment

the stalwarts of academe to join with industry in solving problems of piping and equipment. The two problems focused upon here are nozzle loadings and pulsation response spectra distributed to the attached piping system by reciprocating machines.

Table 6-2

Typical Manufacturer Allowables lor Nozzle Loadings tor Inline PumPs

Nozzle Loadings In earlier years various rotating equipment manufacturers would define allowable nozzle loadings as "zero force and zero moments." Such statements were not only ludicrous, but showed how little confidence some rotary equipment manufacturers had in their products. Ultimately, the pipe stress engineer was left to use his (or her) sole judgment to determine if the piping loads were substantial enough to damage the attached equipment. There are several standards for handling nozzle loadings on rotating equipment, and probably the best known are those of NEMA (National Electrical Manufacturers -{ssociation). NEMA provides guidelines for nozzle Ioadings for steam turbines for mechanical drive service. Unfortunately, its guidelines are appiied to every prece of rotating equipment by eager customers and engineering contractors. For example, what is valid for steam turbines is not valid for inline pumps. Because steam turbines are more fragile than most types o[ rotary equipment, using the NEMA standard produces over-conservative designs for most types of rotary equipment. The American Petroleum Institute (API) also has standards for rotating equipment: API 611-General-Purpose Steam Turbines For Refinery Service; API 612Special-Purpose Steam Turbines For Refinery Service; ,\PI 617-Centrifugal Compressors For General Refinery Services; and API 618-Reciprocating Compressors tor General Refinery Service. Applying API standards to nozzle loadings on rotating equipment leads to the argument in which rotating equiprnent specialists claim that the API standards are only intended for procurement purposes, and the pipe stress engineers, having no other guidelines to follow, assert that the API standards are what is to be used in practice. The best criterion for judging nozzle loadings is experience with a given piece of equipment. For example, my several years of practical experience with turbo expanders dictate they can withstand three times the nozzle loadings allowed by NEMA (remember-only for steam turbines!) .{lowables for inline pumps, as above, did not exist a tew years ago. Such pumps were regarded as piping components, e.g., valves, and allowables were considered unnecessary. But "thinning-up" casings to reduce naterial and costs makes such allowables possible, alrhoush controversiai at times.

PUUP

SIZB

(

in)

Fa lb

Mi=

!

Mo=

Fo

2x3x6

4000

50 00

4000

3x4x6

6000

60 00

5000

2x3xo

4000

5000

4000

3x4xB

5000

6000

5000

4x6xg

6000

7000

6000

4x6xl0

5000

7000

5000

6x8x!

0

8000

9000

8000

6x6x20

500 0

6000

5000

| 0x1 0x20

800 0

9000

6

12x12x20

r 2000

F *Miao * !{oact 1to,n", F" Mi.o

Lo

-tb

t-1

13000

Li

000

10000

2.g

Hhere, F

= resultant of actual force applied,lb

Mh. u.tuut bending monent on suction nozzle,ft-1b Mou;, actual b€nding nonent on discharge noz2Ie,ft-1b

62


There are three basic options to solving nozzle loadings on rotating equipment.

1. A detailed finite element study of the equipment. Destructive testing of the equipment.

2. 3.

Close interface between the rotating equipment manufacturer and the piping stress engineer.

The problem with finite element analyses is who is going to pay for it-the client, the engineering contractor, or the rotating equipment manufacturer? Next, can the rotating equipment manufacturer disclose proprietary information often required in finite element analyses? Destructive testing poses the same question, who will pay for it? The third option-the pipe stress engineer conferring with the equipment manufacturer-is perhaps the most viable of the three, because if the NEMA and API

criteria cannot be met, then the rotating equipment manufacturer can at least expect extra loadings and can design for it, if time permits. Thus, the rotary equipment vendor working as a team with the piping stress engineer(s) can help to alleviate most nozzle loading problems.

NEMA and API standards are very safe and a piece of equipment that meets their requirements should not have any nozzle loading problems, such as leaks. The problem comes in modular skid construction, where the values provided by the standards are very conservative.

Manufacturers often give allowable values for their equipment, and Table 6-2 presents some typical ones. A generalized standard taken from several pump manufacturers' allowable standards is shown in Fieure 6-31. Reasonable nozzle loadings for turbo expandJrs worked out by the author and several turbo expander manufacturers are listed in Table 6-3. Neither Thble 6-2 nor Table 6-3 should be substituted for the manufacturer's allowables, if the vendor has his own. However, the information can be a valuable tool. Rules of thumb often are not only invalid but are often based on special situations that may not be true for every case. One must be extra careful in piping steam turbines, be-

cause these units are usually fragile. Example 2-2 in Chapter 2 illustrates a piping arrangement connected to a steam turbine. If expansion joints are allowed, the configuration shown in Figure 6-32 is ideal.

PULSATION BESPONSE SPECTRA INDUCED BY RECIPROCATING EOUIPI'ENT Reciprocating machinery often induces pulsation response spectra

in attached piping systems. This subject

alone is comprehensive to fill several volumes, so we will just outline the problem here.

Mno

=\fif,,T Mfi

Mfl

MF"

=..ffi*r N/-t+Tlg

MFN = greater of Mpo & Mp", where Mso & resultant moments applied at nozzles

MRO = resultant bending moment about

DM, DM,{ .-.-L FFs

=

= F"-(0") +

= F"y(d") +

+ M"y+

FDy(dD)

+

l\4"y

tr\arr 12 t\-a i, LtAr'.-"t_ | lL,/..r,r[Fs2"

+ F!, + F!.]o5

Fno = [F2o* + FBy + FB

FD,(dD)

= greater of

MDy

+

110.5.

)l

;

FzD.]o 5

FRs

or

l\iDy

FFD

*&*^!!'*ffi. z.o Figure 6-31. Generalization of forces, moments, and allowable nozzle loadings.

-

MRs

are

Rotating Equipment

Table 6-3 Reasonable Turbo Expander Nozzle Loadings

Nozzle Size (in 4 6 8

10 '|.,

t4

l6

Nozzle Size (in 4 6 8

10

2,436 3,654 4,870

M, 3,383

4,474

5,074

6,710

6,7&

8,947

6,088 7 ,306 8,524

8,455 10,146 11,838

I 1,184

9,730

l3,513

t7 ,870

2,436 3,654 4,870

4,474

6,088

11,184

M,

g9

l too

1

974

1,948

1,948

I,948

) q))

1,624

5q1

3,896

2,436 7 )47

3,246

4,869

?OO

too |,623

,

1,948

2,272

aa \

La \

so5

5,189

5,189

&9

r too

1,299

9',14

1,948

1,948

1

t

3,246 3,895

)

3,895

5 R4? 6,817 7 ,784

d n{q 4,871 5,683 6,486

13,421 15,658

F, 1 too 1,623

t

3,246

,)
1,948

1,624

3,383

5,074

3,896

2,436 a )L1

4,869

4,059

5,843 6,817

4,87r

,784

6,486

8,455 10,146 11,838 13,513

I O))

6,7&

6,710 8,947

,306

13,42r

8,524

15,658

9,730

r7 ,810

5,189

3,895 A \A\ 5,189

648 972

l,080

F, 1,080

|,659

2,699

r,620

2,488

1,620 2,429

2,699

1,620

4,U9

4,O49

4,147 6,220

10

|,296 |,620

2,160 2,699

3,318 4,147

4,049

10,367

L,944

4,976

4,859

6,748 8,098

6,748

12

2,160 2,699 ? )10

2,268

3,779

3,779

5,806

9,448

50?

4,3t9

4,319

10,798

10,798

4,859

r2,147

12,t47

16,588 18,661

100

4,859 < ?oo

13,497

13,497

20,735

6,486

6,486

6,63s 7 ,464 8,294 9,964

5,669 6,479 7 ,289 8,099

8,098 9,448

12,M\

t4

16,216

16,216

24,912

12

t4

l6

|,948

1 11)

t

so{

3,895

4,545

Nozzle Size (an 6 8

l6 l8 20 24

,

') cll5 3,240 3,892

<

1r10

7

5,683

l tlo

9,730

s ?oo

7

s lqq

8,294 14,514

Mechanical Desisn of Process Svstems

64

Table 6-3 (continued) Compressor Discharqe Nozzle Size (in.) 4 6 8

l0 1''

14 16 18

F,

F,

650

|,444

i

974

2,165 2,888 3,610

,

1,300 1,624 I q4q

) ,

4

)74

sqq ? ol o

PG: lA: G: HEJ: GEJ:

111

Fz

Fs

M,

rqq

2,048 3,072 4,097 5,121

1,624

,

2,436

?

1,949 soo

3,249 3,899

{ n{l

4,548

6,486

5,198 5,838

Planar Guide

IntermediateAnchot Guide

Hinge Expansion Joint Gimbal Expansion Joint

Figure 6-32. An expansion joint arrangement ideal for steam turbines where nozzle loadings must be kept low (almost always the case with steam turbines) and the use of expansion joints is practical. (Courtesy of Pathway Bellows, Inc.)

Currently, two methods are used to predict pulsation problems: (a) modeling the system on an analog computer and (b) simulating it on a digital computer. Basically, the piping system is modeled with support and soil stiffness vaiues input at every pipe support as discussed in Chapter 2. Then the system is excited with various forcing functions that represent the reciprocating machine or machines. The piping supports are moved

6,145 ,169 8,193

7

9,202

7 )49.

\

My

M'

Mp

165

3,W7

4,046

6,016

6,070 8,093

t4q

4

at)

4,060 4,872 5,684

A1L

7,5r9

10,116

6,496 '7 a'7q

9,023 t0,527

12,139

6,496

8,662

12,030

14,162 16,185

9,730

13,514

l8,

'7 1a-l

181

around, deleted, or added to decrease the amplitudes generated by the forcing functions. This analysis can be done on either an analog or digital computer. There are two methods available on existing computer software that can help head off pulsation problems. These methods arc modal ertaction analysis and time spectra (time history) analysis. Modal extraction is computing the natural frequency of the piping system, after modeling the pipe support and soil stiffness values, and comparing this frequency to that of the shaft speed of the equipment. Time spectra analysis is a transient analysis that basically does exactly what modal extraction does except on a transient basis for every time interval over a specified period of time. In other words, we compute the system's natural frequency for every second over a period of one hour. Over the period of one hour we excite the system with a forcing function that accurately defines the rotating equipment. Figure 6-33 shows a piping system excited by pulsations from a reciprocating machine. A complete investigation of the pulsation frequencies and surge capacity is normally required, which involves the compressor bottles (surge drums), compressor suction header, and suction compressor bottle, the discharge header, and discharge compressor bottle. Two companies are engaged separately in investigating these problems-Southern Gas Association's compressor analog computer at Southwest Research Institute and the Structural Dynamics Research Corporation (SDRC). The compressor bottle (or surge drum) acts as a pulsation dampener. A typical bottle is shown in Figure 6-34. The compressor bottle acts as an acoustic filter designed for all frequencies induced as the reciprocating engine speed varies. The compressor bottle cannot damp out all frequencies, but should store energy generated from the various frequencies and reduce them to produce a relatively smooth and continu-

Rotating EquiPment

Figure 6-33. Piping system excited by pulsations from a reciprocating machrne'

ous operation. Sizing the compressor bottles should be done by a specialist who has worked in this field for several years. In the days before analog and digital simulations, pulsation Droblems were solved (and still are) with orifice plates. These plates were placed in the piping system and the orifice diimeter was approximately 0.53 times the internal diameter of the pipe. These plates' distributed throughout the piping system, acted as pulsation dampeners. Although orifice plates produce huge pressure

drops, they are effective in many installations.

EXAMPLE 6-1: HORIZONTAL' CENTRIFUGAL PUIIP SYSTEM DESIGN A food processing plant is having a cooking kettle installed to process molasses into refined syrup for breakfast foods. A horizontal centrifugal pump is to be installed next to a fuel tank to supply fuel oil to a burner in rhe cooking kettle. The fuel oil tank is to have a 50 psig

Figure 6-34. Typical pulsation bottle (or drum) configurations that act as pulsation dampeners.

nitrogen pad because the tank cannot be raised for higher head at the pump. The cooking kettle is 200 ft downstream and 15 ft above the discharge flange of the pump.

desired to select and size the burner feed pump shown in Figure 6-35. The discharge pressure at the burner end is to be 40 psig.

It is

Suction Llne Pressure DloP Fluid

:

tuel oil

TemDerature

:

90'F

Pressure = 50 psig p 54.725 lb^lft3

: p: 139.53 cp : (139.53)(6.72 x 10-a) : lb./ft-sec e : 0.0018 L:1.0ft Suction line = 3 "dSch 40, Di : 3.068 in Q : 150 gpm

0.094


cooking kettle

Figure 6-35. Hot-oil pump piping scheme for Example 6-1.

fuel tank

3" x 1tlz" burner feed pump

(r5o)sar

lrj,

ll]]ry\ s€c/

min \7.479 gal/ \60

(7.393) in.:

I t n'in.r/)

Entrance and

l-3-in.d 90"

= 6.51I ft/sec

exit: K:1.78

std

ell

1-3-in.d gate valve

: K : 0.30 : K : 0.14 \-.. *

\1,14

l3

068li.,o.srr, rt (s4.72s)l9r

N.-=DVP-\ 12l r

sec lh

ft'

-

From Equation 1-4 we compute the frictional pressure drop as follows:

nur.,

r0.094;-1\

* r.leY '' : ILL \D -'l- I2e,

n-sec

With NR"

ao,

:

969.1, the flow is laminar. From Equation 1-6b we compute the friction factor

as

follows:

6L 6A f=j_: N*" 969.1

oo,

- fro.ooorrts.oorrtzr,,.rrl t (3.068) I

:0.066 rsa.72sr

K.Values (Velocity Heads) Referring to Figures 1-7 and 1-11 we have the following:

llr(6.511)? tt2

ftr

zr:z.zr Ap1

:

L524 psr

sec2

n-111

sec'-ln

I\144'o',,l in.2/

Rotating Equipment

o,,:[ry.0"']

Discharge Line Pressure DroP The conditions are the same as the suction line except

for the following:

@.64D'?#Hh)

ts+.zzs1$

Line size = 2-in. Schedule 40 for which Di For 1l/z-in. d pump discharge,

.";;;m[

:

(150)#[+r-J(#,J

2.067

^."^ -'-Apr

=

23.642

:

fr-lb. ^. -' sec2lbr

2.982 Psi

fr

:

sec

K-Values lor 2-in. Portion

2-2-in.-std90' elbows = K = 0.40

For 2-in. S/40 discharge line,

exit:K:1.0

EK:

r4o

L-200ft

-^r,r ^ ^.

For 2-in. d S/40 pipe,

t, ., ,.oOl 06zr -. -l th. 'il r14.343).. _ft2 I tfr: t

[{0.044)r200.0X

[-o

rS+.225r

I

.z \raa in.,]

fr-lh

(ry) - (14.343)A(54.72rk

S€C'-lD1

=r/.lR?

A* =

(o.os+) -.1!.

n-sec

63.72 psi

:

too high-choose a 1 r/z-in.

x

3-in'

diftuser

With 3-in.d Sch 40 PiPe,

64 64 " Nr"_ 1,438.3 _^^^^

(lso)sa,

L+fu)(,**)

(7.3e3) in.2

(r-

K-Values for 11/2-in. Portion

:

:

K 0.78 Entrance From Thble 1-7, for a 2-\t.

E*: L

:

r".

x

lll2-in. diftuser, K

:

0.055

o.srt

=

[('-ryt tz

- l\

I

|I

@ :0.037 Nt"

sec

*--L)

K-Values for 3-in. d PiPe 2-2-in.-std 90" elbow

3.0 in., d

ft

=K=

0.54

Dr:

t.so

exit:K:1.00

1.610 in.

e3.642t L,ro.rrr,

'-

10.094;.'"' tt-sec

hl tt'l

=

l1!4lr

r.zzo.s Nn"

: \l2 l

I

(6.511)

a,so.tts, l!: sec

(0.094);lb'

I

n-sec

6A f: -

Nn"

=

0.066

:

969.125

Mechanical Design oI Process Systems

68

^_t ^pf_[

(0.066x200.0)(12) (3.068)

(s4.7zs)t#(6.51rF

+

g

(,* *-)

fr-lh SeC'-lDr

Apr

:

13.309 psi

=

use 3-in.

{

S/40 pipe

New K-Values for 1r/2-in. Pipe

:

Entrance K From Table l-7 K 0.337

:

E*:

:

0.78

, for a 3-in.

x

fluid being handled should be Newtonian. Gels, slurries, asphalt, and other non-Newtonian fluids should not be considered with these charts. In handling such fluids a positive-displacement pump is usually required. (Example 6-2 is an illustration of how to handle such a liquid.) To use Figure 6-39 we must convert the absolute viscosity io kinematic viscosity. This is done as follows: use the charts, the

r.54]

: w:

p

139.53 cp at 90'F 54.725 lb/ft3

io.oooozog\tu-r.. (139.53)cpl . --"1 ;;--(32.17) -ij-i:!-.

lllz-in. diffuser,

rr-lh

\ rcp / r('

r.ttt

rDr-sec'

th

154.'725)=

L : 3.0 in.: d : 1.6i0 in. Nn.:1,720.5;f=0.037

rt"

z

:

f12

0.0017-:sec

..^.:

ji1Ii0.,

L (1.610) '-'"rll

lQ

or

ll

lh fr2 / rfr? I ,I \s4.125)'+ (23.642f ::-

0.0017

fr-1h )/1t tr " '"m

0.0000107639

Irr

V--

| '" sec? \ 144 in.2/

sec'-lDl

:

sec

centistokes

i: sec

v:

159

.261 centistokes

3.912 Psi Total pressure loss in discharge linc 13.309 3.912 = 17.221 psi

Using Table l-8 we make the viscosity conversion from centistoke to SSU as follows:

Using the pump manufacturer's curve in Figure 6-36, we can enter data on the Hydraulic Design Calculation Sheet in Figure 6-37 to size the pump.

0.226r-::::=v

Apr

-

-

The Effects of Laquad Viscosity on Gentrifugal Pumps From the previous analysis and Figure 6-36 we know the hydraulic performance required of the pump. Before the actual horsepower requirement for the motor and the

impeller size can be determined, the viscosity effects of the liquid being handled must be considered. One requirement of a centrifugal pump is that the handled liquid be relatively clean of suspended particles. Obviously, for the same size pump and motor a highly viscous liquid will tax the unit more than would a low viscous liquid. Thus, the viscosity is an important property that affects the horsepower of the pump motor. To account for this, the Hydraulic Institute has prepared charts shown in Figures 6-38 and 6-39 for determining viscosity effects. To

rq5

t

- 704.695t t : 706 SSU t2

862.832

=

0

Now, looking at Figure 6-39 we see that for 150 gpm, : 82 feet, and 706 SSU we obtain the following coefficients:

TDH

Cr:056 Ce:090 x Q^*, where QNw is the water capacity at which maximum efficiency is obtained

Cu = 0.90 for 1.0

The corrected flow rate becomes

^ Qc =

sDm"i... :-: = LO U.YU 150

166.61

=

167 spm

Rotating

EquiPment

O

o @

(o
{)

5lL a

69

70


Pump Hydraulic Design Calculation Sheet

Liquid

fuel oil

Viscosity at PT. (Pumping Temp.) Vapor pressure at Sp. gr. (.y) at PT. Flow at ambient Operating flow at Design flow at

139.53 0.010

PT temp. PI PT.

cp psra

o.477

150 150 150

_

Suction Source pressure Static head - APr, line loss Suction pressure

- Vapor pressure NPSH avail NPSH avail

Discharge 64.7 1.9

1.52 65.08

= = _

gpm gpm gpm

-

0.01

65.07 171

t

Terminal pressure Static head

psia psia psia

Piping system Other Discharge press. Suction press. =

-

-

ft ft

NPSH req'd

=

psra psi psi

71-38

psia

'1.9

psl

17.221

psi psl

96.201

psia

3'1.12

psra psra

82.017

feet

APr discharge

=

TDH

= bhp at Duty Condition

=ffi

DnpD =

= 515hP=5v+hP

bhp at Back-Pressure Condition

or'c* =

Sffi

=

*AlrffiB

=

3.7o6hp

-

4hpwithwater

Figure 6-37. Pump hydraulic design calculation sheet for Example 6-1.

centrifugal pump with a l0-hp motor and a 5-in. impeller. In selecting a centrifugal pump it is desirable for the

The total dynamic head becomes Hc

TNH R' = 'i-" =;:91. LH U.YU

= 9l

fr

Now, referring to the manufacturer's curve in Figure 6-40, for Qc : 167 gpm and TDH : 91 ft, we determine the pump efficiency as

n:63% The NPSH required

= 8 ft

To correct the efficiency for viscosity we have

r"

:

!C,t = (63%)(0.56) = 35.28% efficiency

The brake horsepower for pumping the liquid is bho,,,"

QHl- = 3,960 4.

(167)19l)10.877) (3,960X0.153)

- 9.53 ho

Referring to Thble 6-4, we see that the next larger mo-

tor size is a 10 hp rnotor, thus we select a 3

x

lllz-in.

required flow rate to fall in the middle of the pump curve. Avoid extreme sides of the manufacturer's performance curves. Select an impeller that is at least two sizes below the largest size available for the pump, because if greater head is later required, e.g. , if additional piping is added to the system, changing impellers is much cheaper and expedient than purchasing a new pump. In the final analysis the design engineer must not forget the potential problem of back pressure that the pump could be exposed to under varying conditions. For example, if the discharge line contained a bypass valve that diverted flow to either the cooking kettle or to a reservoir that collected water, the reservoir would be used if and when the pump and piping system are cleaned with water or a cleaning agent. In this situation the pump would have to be sized for handling water or whatever cleaning is to be used. When the bypass valve is shut off, closing the discharge piping connecting the pump to the cooking kettle, the flow conditions are changed, resulting in a lower TDH. With the same size impeller, as the TDH lowers- the flow rate increases as the curve shifts

Rotating Equipment

300

26 150

1(n

80 60 40

30 20 15 10

8

10,000 8,000

6,000

'4,000

3,000

tO

15

20

25

30

40

50

60 70 80

90

100

CAPACITY-GALLONS PER MINUTE

Figure 6-3g. Viscosity corrections for capacities of 100 gpm or less (Courtesy of the Hydraulic Institute, Cleveland Ohio.)

72


i F> *.2

;t ?E P,Z

E< o6

;

Figure 6-39. Performance correction chaft for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)

Rotating Equipment

Table 6-4 NEMA Frame Dimensions

___o

Ir

r--i F- E =q-

E -->l

H-SIZE HOLE

Source: Goulds Pumps, Inc.

74


to the right in Figure 6-40. Since the impeller does not change, more horsepower is required for the lower TDH. This condition is known as the break horseoower (bhp) required at the end of the pump curve. or maximum flow capacity condition. In our case we have a minimum TDH of approximately 45 feet in which the bhp becomes

'

bhp

=

{llE(s){l

0)

3.960(0.46)

:

3.706 or 4 hp with water

Thus, we see that our 10-hp motor is sufficient against back pressure. Often, the water condition requires more horsepower, and thus a larger motot than the process liquid condition. The design engineer must be always cognizant of any other fluid that the specified pump may have to handle.

:

N*"

:

DVP

'4

{lP}n : \tzl

(3.78r)

a sectes.soer k n"

(0.630)-

_lb.

'

ft-sec

193. t 16

From Equation 1-6b we compute the friction factor as

f: -:-

Nn"

=

0.332

K.Values (Velocity Headsl for Suction Line Referring to Figures 1-7 and 1-11 we have the followtns: En'irance andexit K 1.0 + 0.78 1.78

:

2-4-in. plug valves

:

:

:

K:

2(18X0.017)

1-4-in.-90" standard elbow

EXAUPLE 6.2: POSITIVE DISPLACEIIENT PUMP DESIGN A positive-displacement pump is required to transfer a adhesive coating mix from a storage tank to a bin in which the mix is dropped onto a nylon sheet (see Example 3-6). The adhesive coating mix adheres the particles together to form roofing shingles. First, we must perform a fluid analysis of the system shown in Figure 6-41.

ft-sec

(_ri'

)tr_ry sec

min \7.479 gat/ \60

(t2.73)h.2H*l

:

:30(0.017):0.510 \-r :

3.781 ftlsec

2.9O2 velocirv

From Equation 1-4 we compute the frictional pressure droo as follows:

r2) * a.M8l oo, [
k

(6.5ilr

g

fr-Ih

mix p : 95.909 lb*/fc :400'F Temperature L : 11.0 ft Pressure = 20 psig a : 150 gpm Suction line = 4 in. Schedule 40 + Dr = 4.026 in. e : 0.0018 p : 938.08 cp = (938.08)(6.72 x 10-4) :0.6:0 lb'

0.612

heads

Suctaon Line Pressure Drop Fluid = coating

:

K

LtK

(e5.eoe)

(rso) sar

:

Apr

:

J

F-!-,-

SeC'-lD1

40.822 psi

Referring to the pump hydraulic calculation sheet, Figure 6-42, we summarize our results. From this we compute a total dynamic head (TDH) of 93.76 feet. Past experience indicates that a rotary gear pump of the type shown in Figure 6-43 is excellent for handling high viscosity liquids. The pump manufacturer has the performance curves rated in terms of kinematic viscosity in SSU. Now converting our viscosity to SSU's we have

Ssu

:

ll(.1,]1 635) (938.08X4.635)

w/g

195.9091 l-l

\

32.2

l

=

1.459.78 SSU

L)

o

o o ro

q

o r)

o to N

o o GI o lo o o

o to (o

o

lt

ir

o o o o o

izu(o!@sl-

a

z E

75


//t

ir

Rotating Equipment

Pump Hydraulic Design Calculation Sheet mtx

adhesive

Liquid

VG;o;itrt

PJ. (Pumping

Temp.)

938

\/.^^r at PT qn ^;aee,,ra /_ I .r PT ^r rioriat ihbient temo. Operating flow at

08

cp

.1.537

PSla

-

not

lEn j:X

PT.

{^n,.r PT

YI:

150

Suction

-

APr line loss Suction pressure

-

=

4.0

psi

2.O

psi

Static tift - aPr discharge Piping system Other Discharge press. Suction press.

psia

8.70

psra

Vapor pressure

=

NPSH avail NPSH avail NPSH req'd

Terminal pressure

psia

14.7

Source* pressure Static + (headlift)

8.70

psia

6-90

ft ft

ri na

=

-

TDH TDH

= =

16.70

2g.g1-

= = =

psia psl

13.74

psi psi

53.75

psia

-8.70

psia

67.58

psia feet

2+2=4ltrcqulred lrin NPSH avail > NPSH req'd + 2 lt

(oom)ffDHX'v) .. bnp"c = :(38;bX4-

bhp at Duty Condition

nr"^ _

* (150X67.58X1.537) = n = (3,960Xrr) (3,s60X10)

(gpm)CrDHXr)

3g.g4o/o

TDH = total dynamic head TDH = discharge press. - suction press

4 = pump efficiency,

bhp at Maximum Capacity Condition

o/o


We now refer to the manufacturer's performance curves which, in this case, are rated to the viscosity of the service fluid. The closest curve is that shown in Figure 6-41. As a starting point, it is always desirable to start at the middle of the curve. Extreme ends of any pump performance curve should be avoided, as the pump's performance varies significantly at either end of the curve. Thus, we select a very common speed for this type of pump-155 rpm. Now for 150 gpm and 62.45 psi TDH, we find that we need approximately an 1l-hp motor. Solving for the pump efficiency we have bhp = Q(rDH)"y

(6-2)

(3,960)rt

Thus, we have (150X93.76X 1.537) ,, _

'

(3,960)(10)

:

0.496

or

49.6%

This efficiency rating is quite common with a rotary gear pump handling a highly viscous liquid. Now, refer-

ring to Table 6-4 one can observe the classifications of electric motors. From Figure 6-44 we see that the viscosity of our fluid, 1,460 SSU, is about mid-way between the two curves shown. Thus. the required horsepower is between 8 hp and l0 hp. Looking at Thble 6-4 we see that electric motors are lUz hp and 10 hp. To meet our requirements, we select a lO-hp motor, because 7llz hp is too small. Notice that the pump has built-in jacketed enclosures to match the piping, which is hot-oii traced, to keep the fluid in the piping and pump liquid. These jacketed systems are discussed in Chapter 3. In this problem we have a suction lift on the suction side of the pump. It is important to remember that the theoretical height to which a liquid can be lifted at any specified temperature is the atmospheric pressure at the installation site minus the vapor pressure of the liquid at the specified temperature minus the friction loss in the piping. The theoretical and maximum suction lift for water is shown for various temperatures in Figure 6-14. For non-volatile liquids, the maximum allowable suction lift should never exceed 15 in. Hg (7.4 psia) under ideal conditions. For volatile liquids, the maximum allowable


Complete jacketing ol casing, head and rotor bearing sleeve for heating or cooling liquids.

Hich ten Dronze

for long,

rugged service.

on head for handling

hot liquids.

Figure 6-43. The type of gear rotary pump selected in Example 6-2. (Courtesy of Viking Pump Division, Houdaille Industries,

Inc.)

Rotating Equipment

Figure 6-44. Rotary gear pump performance curve. (Courtesy of Viking Pump Division, Houdaille Industries, Inc )

suction

lift

should never exceed 10

in. Hg. If these val-

ues are exceeded, then the suction source should be pres-

surized with a neutral gas (inert nitrogen) to offset any pressure that may fall below the vapor pressure of the liquid. At the liquid vapor pressure, vaporization occurs, resulting in possible cavitation and pump damage.

A Word About Prlming

A positive-displacement pump, like the rotary gear pump in this example. must be primed when pumping low viscosity liquids. This is done by a vacuum device or by using a foot valve. Also, with a low viscous liquid, the fluid drains back to the suction when the pump is idle. For a viscous liquid, like the one in this example, the liquid is retained in the rotary gear clearances and thus acts as a seal when the pump is restarted. However, before restarting the pump, the liquid being pumped should be introduced through the discharge side of the pump to lubricate the rotating components. Since the coating mix is not a clean service, a centrifugal pump is impractical because it cannot handle a nonNewtonian fluid containing suspended particles.

EXAilPLE 6-3: CENTRIFUGAL COiIPRESSOR SELECTION A centrifugal compressor is to be specified for a gas plant, which is at sea level. The unit is to compress 3,000 lb./min of gas mixture at 50 psia at 60'F to 150 psia. The gas mixture is composed of 40% ptopane,3O% ethane, and 30% methane. The reduced pressure, P", the reduced temperature, L, the molecular weight, and the specific heat of the mixture is determined as shown in Table 6-5. Using the data in the table we calculate the ratio of specific heats for the mixture as follows:

c-. cp. - 1.986 13.08

13.08

-

1.986

(6-10)

=

1.18

The compressibility factor for the mixture is determined from the reduced pressure and reduced tempera-

ture. Thus.


80

Table &5 Tabulation of Gas Mixture Properties Mol

Gas Propane Ethane Methane

o/o

P"

(psia)

t" ("R)

Pc

40

44.t0

616

666

.64

246.q

30 30

30.07

708 668

550

9.O2

212.40

343

4.81 31.47

20Q.40

16.07

17

Gas Mixture

659.20

266.40 165.00 102.90 534.30

6.86 3.68 2.54 13.08

Table 6-6 16l Typical Centrifugal Compressor Frame Data* Nominal

Nominal Nominal

Nominal

Nominal lnlet Volume Flow

ffi (icfm) Frame

(m3/h)

l,000-7,000 B

6,000- 18,000 13,000-31,000

D E F *Wite

23,000-44,000

c

33

,000- 65 ,000

48,000-100,000 this table is based on

P

.D

50

a

(lt-lbl/lbm)

1,700-12,000 10,000-31,000

10,000 10,000

22,000-53,000 39,000-75,000 56,000-110,000

r0,000

82,000- 170,000

534.30

:

4.97 3

: : rp^ :

10,000 ft-lbfnb. 76%

|,370

150

50

(6-14)

(6-61

-

460.)

1O,339.276 icfm (or acfm at the inlet)

7,700 rpm

54

an, machinery duplicating this table woud be purely coincidenml.

t1

Using Table 6-6 from Lapina [6], we find our unit to he a Frame B with nominal values to be as follows:

N"

914 1,120

Thus, we have

Now from Eouation 6-32 we have

n-r /r- r\

T=\-o

1"

From above,

kr

Hp"

44

factor

- ,mRt, ----" V: (mw)Pi

:

30 36

406 584

:

-

Y

l6

(mm)

l), we can use Assuming that we have a perfect gas (z Equation 6-14 to find the average discharge temperature.

Using Equation 6-6 the inlet volumetric flow is

(0.972x3,000)( l.545x60 (144)(31.47Xs0)

78 78

^'' P, Pr

: 0.972: inlet compressibility

,,

77 77

30

(in,

l l,000 7 ,700 5,900 4,900 4,000 3,300

76 76

30 30 30 30 30

lmpeller Oiameter Metric

English

Computing the compression ratio we have

Now from Figure 6-45, we have zr

(%)

Speed (rpm)

(k.Nm/kg)

survey of currently available equipment, the instance of

:0.076

60 + 460

Rotaiional

Efficiency

10,000 10,000 10,000

659.20

t

Polytropic

ltp'

:

l'18 = 0'76

Thus, 18\

l0 r0.i6l u.18/

-

0.116

Rotating

t?

=

0116

tr(C " :

(60

+

460X3.0)

zz

:

0'93

or

t, :

590.68'R

:

v-22 =zt

130.68'F

Now, the average compressibility for the gas mixture must be obtained. From above the inlet compressibility, zr :

81

Using the compression ratio and pressure ratio we determine the outlet compressibility factor from the compressibility charts in Appendix E. Thus,

from which n-I

Equipment

!

zz

_0.972 + 0.93 _ 0.95

In determining the polytropic head we use Equation 633, where

0.972

Compression ratio,

p-

rc^r,=:j: P,

'-"

150

659.20

=

Pz=Pa O.228

of specific heat, k, is k = 1.18 = inlet conditions, which is an approximation. Thus, and the average ratio

Temperature ratio,

' = (-*-) (*,{,) [[&J-"*-" -'],u

,_, _tz_560.68 _ r trR,2-L-534-30-'"^<

f- compressibility tactor, Z =

1.00

PV/RT

\--

---1 ------J

NS \

N \s iK (\

S \

\-"%_ =

0.94

\*r-1 \l

I Y

x \

'1 0

-tl = riP{

N ilxl/-

-x

-0.85 BO

\t 'oS

= 2.00 1.60

401

-t

-'----

x

'r;{ I

-->

= >< \

ii( 0.60

(6-33)

>i

*al

\"'r \ \ 0.92

\ 0.91

0.01

0.02 0.03 0.04 0.05

0.06

reduced pressure, Pr

0.07

0.08

0.09

Figure 6-45. Compressibility curves for very low values of reduced pressure. (Reprinted by 0.10

permission of Chemicql Engineering, McGraw-Hill Company, July 1954.)

a2


from which

r: H=

Thus,

[(t't31srq'01

(8.62r) r(3.0f ,,6

-

*- ='ni?l lo' -

r]

29,913.143 ft-lbr/lb.

N:N"l '

by

II

:

maximum polytropic head per stage, (see Figures 6-46 and 6-47)

tttm'ntl I ^ [t26. L krzrrr I L(

=

ft-lb/lb.

^" r.t:

tzo.

r

lt: r .+zr I

)(0.972)(520t

| . t8

P,r

(6-69)

7

l3l

rpm

rir

H. '

33,000

:

(3,000)(29.913)

4o

(33,000X0.76)

3,578.11 hp

Using Table 6-7 to determine the mechanical losses, we find that

1.377

:

Il,:-"'' rqqrr lo' | r t.ooox r)l

The required shaft power is

L. :

From Figure 6-46, He.

(6-10)

I

\Ho. N.J

Lr

Using Table 6-5, we have

0

I u ..P \05

N = r7 TOOr

(6-68)

-q

where Ho.

3

The required rpm is

The required number of compressor stages is determined

: N., '.H-

2.ite =

11,000 ft-lbfnb.

(0.02sx3s78.11)

(P.rL"*r

:

P.r

+ L.

:

:

99.453

3,578.11

12,000 11,000 10,000

6:

I

limit for miled yield

9,000

slress mpeIers

8.000

I

lNTuw

ltl

I

7,000 6.000 E

5,000 4,000 3,000

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

2.1

0

Figure 6-46. Maximum polytropic head per stage-English system [6].

L.,

ta

+

89.453 :3,667.563hp

Rotating EquiPment

trl

Eru =32 ot

928

u=@ v krzlTt ttl

- I'n,J,,'*Lon"N slress impellers

Ezc e20 o

.-

16

5rz 'i^ 't.0 1.l

1.2

1.4

1.5 1.6

1.7

1.8

1.9

0

Figure 6-47. Maximum polytropic head per stage-metric system [6]'

Table 6-7 [61 as a Losses Approximate Mechanical

Percery Mechanical

Losses,

Metric (kw)

English (hp)

3

0-2,500

0-3,000

2.5 2

2,500-5,000 5,000-7,500

3,000-6,000 6,000-10,000 10,000+

L,'n

(ohl

1.5

7,500+

nents.Thistablewitt'howewr'ensurethatmechanicollossesareconsideredandtiea uselul valuas

for estittutinS purposes.

The discharge temperature becomes tz

= rr(C ("

')/"

=

(520X3.0)0.r'6

:

590.68'R

tz:130.68'F This example demonstrates how centrifugal compressors are estimated. The reader should be cautioned as when to use inlet values for the values of k and z. The value of k will decrease during the compressron process and calculations for the polytropic head and discharge temperature should be made with average values of k, including single stage compressors. Compressor manu-

facturers use the inlet values at each stage of compression, but the inlet values for each stage wi1l be different. In calculating the polytropic head, the inlet value of k can be used to achieve an approximate value of the head with some error, because the polytropic head is insensil). tive to the value of k and thus n/(n

-

The discharge temperature is much more dependent on the value of k. Using the inlet value of k will yield a conservative value of the discharge temperature, generally 25-50'F in extreme cases. For a more detailed discussion of the specification and design of centrifugal compressors, the interested reader

is referred to Lapina [6].


84

EXAMPLE 6-4: INSTALLING A COMPRESSOR AT ELEVATION 8p00

A reciprocating air

compressor is to be installed in a food processing plant, which is at an elevation of 6,562 feet. The desired capacity is 33.3 m3/min. The machine to be used is to be refitted and is of Polish make. From an

elevation-barometric conversion chart, such as Figure 6-48, we determine that the atmospheric pressure at the site location is 11.53 psia. The compressor is to compress the air to 7 atmospheres, or 102.87 psia. Now,

r' /^- ^. . rP\ ",1 : v : 33.3 rmtn l3s.314 \ m"i

2,000

t4

t3

t?

tl

Alfr o3ph.ric Pn33ur., lb./sq. in.

Figure 6-48. Atmospheric and barometric pressures at various altitudes [7].

I.175.96 cfm

Compression ratio:

For a multiple stage unit, the compression ratio is Pr

=

11.53 psia

Pi

:

102.87 psia

C-

:

t02 I

g

l.)J

:

Cnr

= 8.92 > 6. thus requiring

Crz

LD '', : iP.

wnere

D.

With an intercooler, you must consider the gas pressure drop across it. The minimum horsepower is developed when the ratios of compression are equal in all cylinders. The ideal case is with no intercoolins in which Ludwig [7] suggests

Pr P2 P3

_

Pa2_

-z

p.

cD'.J

(6-71)

: --:l Dl

^n

Pn-r

Po3_

p: rol

P,

P"

D1

'o.-l

Thus, for two stages,

and with intercooling, Po1

(6-73)

p.

two-stage

compresslon

Pr=Pr=&:...:

- CR3 :.-":[bJ

/P.

Pr.

n -P__,'-4- 4-'

(6-'72)

where subscripts 1,2,3, ..., n

subscript d

prime

: :

(') :

\0.5

t_,21 LRI : LR2 : l;l

\r

(6-74)

l,r

gas conditions across a cylinder in which I represents the first stage, 2 represents the second stage, etc.

Thus, the compression ratio per stage is approximately

interstage discharge pressure condition, directly at the cylinder represents the actual pressure to the suction of the succeeding cylinder, which

and for the

CR:(8.92)05=2.99

Pr

:

Pdr

first

stage,

11.53 psia

:

(2.99x11.53) +

rs the interstage discharge

subscript

f:

condition that is reduced bY pressure drop over the intercooler system final discharge pressure from a multistage machine

5

i

=

36.94 psia

For second stage, Por

=

(2.99r(11.53)

- i:

31.97 psia

Rotating EquiPment

:

Pr

102 87 Psia

The discharge temperature the first stage is by Equation 6-5s ta, :

bho '

=

l ','lu" / \ l.u x '=.

-. 11.203,486.3721 l (69.6)

Total horsepower

: =

ttFJ?

for

k=

tu,

:

(85

:

287 94"F

83 763 hp

+ 83.763 182.669 or 183 hp

98.906

Equation 6-75 is based on a given compression ratio, Cp, 6rake horsepower/ 106 ft3ld at 14.4 psia and suction ternperature. F,s is a constant which is a factor for the specific gravity of the gas.

1.406,

+

=

460)(2.99)0'?8e ='147.94"R

or tnt

60

based on the discharge temperature from the intercooler. The intercooler cools the air to 90'R which is the suction

54f

: tr2 :

tiiR"G tvr

=

(90

+

460)(2.99)0 287

:

48r 46r

754.80'R

pressor size is to use the "horsepower per million" iurves depicted in Figure 6-49. The "horsepower per million" ii the bhp/MMcfd and is used to determine the horsepower per stage by the following relation:

rr:#:b(MMcrd)F,,

(*)

=

(r.r75.e6){60x24)

:

I,421,068.508

:

(6e.6)

=

('-lr;(14_:#. J

(

Hi+Hfl

:

ll-

/,,/'

"'l

I

30

l-

28f 26

lllllll

Ratios below 1-4 are subiect

v

manufacturer foa best dala.

ttttttl

l-

24Y 22u

lo

signiticanl etror, consult the

1.5 1.6 1.7 1.9 1.9 2.0 2.1 2.2 2.3 2.4 2.5 Ratio of comPression

Figure 6-49. Power requirements for reciprocatmg compressors. (Courtesy of Ingersoll-Rand Company.)

q:

e8.eo6 hp

/,, ..\

t.421.068.s08\j-r:)

:1,203,486.372

3o

7/.,

69.6

'

For the second stage, MMcfd :

36

(6-75)

where F"n is determined in Figure 6-50, converting the acfm to MMcfd we have

t

40l*l 9

i.?_

2

Ml

A reliable and quick method to approximate the com-

z

.

$

o2l

For the first stage, F.,

'14.4 psia

50|.-

Selecting the Reciprocating Gompressor

bhp

to

Gas ref( 1

294.80"F

MMcrd

(

521 intake I

temperature to the second stage. Thus kz

l:

ical efiiciency, 95j 58fiMechan through valv€ Gas vek 561- :3,000 f 'city | (APl equat( rfll

The discharge temperature for the second stage is

I

1f9_!Jl) _ touo

uu /

0.60

1.5

2.0

2.5

3.0

Ratio of compr€ssion,

Figure 6-50. Horsepower correction factors for specific grav-

ity [8].

86


Next, the cylinders must be sized. This can only be done after the interstage temperatures and pressure are defined . Because of the clearance required to allow operation and permit the provision of passages, the piston does not sweep the entire volume of the cylinder. Thus, the actual cylinder capacity is lower than the

displacement of the cylinder. Relating this in terms volumetric efficiency we have

o

(6-i6t

LD

where 4" Q Cp

: : :

volumetric efficiencY capacity at inlet conditions, acfm cylinder displacement, ft3/min, where

= I4*l I \121 """ \ 144",)E'|" where L =

: A"" :

,46"

N: A

of

(6-77)

piston stroke, in.

ar€r of head end of piston, in.2 area ofcrank end piston (,46" minus the area the piston rod), in.2

of

Ipm

where

- .. [eU:l I zdtzs I

C" Cp

: :

(6-78)

cylinder clearance compression ratio ratio of specific heats colllpr€ssibility factors at the suction and discharge conditions, respectively.

k= 2., za =

For our machine we have the following design:

L = 220 mm :

in.

9.661

- 500 rpm Dr : 500 mm :

:

For the second stage, piston rod diameter

o,. =

piston stroke

:

: " (";t")' 10e.563 in.2

convenient formula recommended by Neerken [8] is

n. = o.si

,2.]2t )lr uu'),roo, .."\= lrogL:t44 : 1,512.514 ft3lmin l\t2 I

_

60 mm

:

2.362 in.

roe.563 in.?

*(.9)'

,n.,

:

105.181 in.'z

+ ro5.r8r 'l c":l 10e.563 r44 {gjutl ,roo, l\ t2 I

:

538.165 ft3/min

The volumetric efficiency is approximated by Equation 6-76 as

n, = o.si

-

(0.lr)[(2

ee)'i -

r]

= 0.81i :8t.iEa

This analysis is only a preliminary estimate of what the compressor design is to be, although in this example, data is drawn from an existing unit. The actual selection of a compressor can only be accomplished using the manufacturer's data on such items as piston displacement

and the volumetric efficiencies of the cylinders. The manufacturer's data should always be used before attempting a final design. The actual unit in this example is similar to the one shown in Figure 6-51 . A more detailed discussion on how to specifr and design reciprocating compressors is given by Chlumsky t5l.

N

19.685

in. =

diameter of first stage

cylinder Dz

:

300 mm

=

11 .81

1

in.

:

diameter of second stage

cylinder

For the first stage,

:

=

65 mm

/r o
=

304.341 in.2

-

&.

:

\21

304.34r

/r

sso\'

- " \;)

=

A cosmetic manufacturer of women's lipstick contracted a chemical company to formulate a chemical that satisfies certain specifications. The chemical process engineers determined that

piston rod diameter

A,- =

EXAMPLE 6.5: NAPHTHA PUMP SYSTEiI DESIGN

2.559 in.

2ee. re8

in.'

a light cut of naphtha would

make an excellent base for the lipstick. The pump in this application can also be used to supply the naphtha to a small chemical company nearby for manufacturing paint thinner. This second application is called the "maximum capacity condition" and will be discussed after the pump is sized for the first application. The pump must be sized

for both

cases.

Figure 6-51. Two-stage reciprocating compressor with a shell and tube intercooler. The first stage is achieved with the vertical .yiinder and the seconl stagi with tiie horizontal cylinder. Pistons of the first stage are aluminum and the second stage are cast iion. (Courtesy of Zaklady Budowy Maszyn, Aparatury im Szadkowskiego, Poland )

In the first case, a rail switcher transports the naphtha to the chemical plant from a nearby refinery The plant only needs to send one 50,000-gallon railroad tank -car once every four months to meet the cosmetic manufacturer's needs. The light naphtha cut is 68"API. The task is to design a pump and hydraulic system that will store and transport the naphtha according to the configuration shown in Figure 6-52. The reservoir is large enough to consider the fluid as having a constant head. The plant manager estimates that the naphtha head required is 12 feet, but wants to have it

resulting in a colorless liquid. Next, the naphtha is processed through an activated charcoal filter to remove the fuel odor. Finally, the finished process liquid is loaded into the 50,000-gallon tank car. In the petrochemical industry, the specific gravity of petroleum is given in terms of hydrometer termed 'API. The relation for API is as follows:

"4p1 =

(6-79)

^tp

7w

evaluated.

The basic process involves the naphtha passing throush a scrubber that contains caustic soda (NaOH). The ciustic soda removes the straw color in the naphtha,

141.5:131.5

where

: l* : .yo

the specific gravity of the petroleum product at

60"F the specific gravity of water at 60"F


88

NLL = normal liquid level

9"

g', g',

$+-Llj

g',g',2,-O,g', 9"

5',-O"r _L

Figure 6-52. Pump-piping scheme of light naphlha cut used 10 manufacture women's lipstick. (Example 6-5).

'API, temperature is given of in Figure 6-53. For our case 68oAPI, using Equation 6-79, we have

The Flow from the Reservoir to Naphtha Storage llank

ro:141 5: 7* 199.5 in which 7o :

of liquid is

The relationship between the

o.zo9

(0.709)(62.4)lb/ft3

:

44.26lbifC at 60'F

The maximum pumping temperature is controlled at 90'F. The coldest pumping temperature is at 34'F Since the density is higher at the lower temperature, that is the one used for frictional pressure drop calculations. Thus, referring to Figure 6-53 "Yp

:

0'13

45.55

Dresslon:

o

:

rr.os

o'(\)"

(6-79)

The velocity heads on the line from point @ to point @ are as follows:

and

p:

The reservoir is of such large magnitude that the head considered constant, because the railroad switch engine delivers the naphtha regularly to the plant. The flow rate from the reservoir to the storage tank in gallons per minute is determined from the following ex-

lb/ff

Values of f1 are determined from Figure 1-7.

Rotating Equipment

Entrance:K:0.78:0.78 18 fr : 18(0.017X2) : 0.612

2-4-in. plug valve: K :

Q

:

1e.65(4.026)

APr

Exit:K:1.00:1.00 sr- : LtK 2.392

:

[rrrt*J"

177.2

12

x=

38

sec

p

3.900 psi

10.5 psi nitrogen pad

)

10.5 psi

6.60 psi

=

20.308

ft

:

ft

12.35 psi

-

:

1.223 psi

I

l. 127 psi

>

10.5 psi

The new flow rate is

(1!4|-(a.a67;x A(45.ss)k =

lb. 2.640

-

:

:

Adding an additional 26 ft of head we have

ft :::-

DVp

<

x + 3.90

0.0884 ft,

-. l\Re :

ft of naphtha head = (12X0.325) psi

This pressure differential will cause the naphtha to be forced back into the reservoir. The number of feet required to deliver the liquid to the tank will now be determined. Since we already have 12 ft in the tank, then

wm

o

4.46'1

1.223 Ot'

3.90 psi

4 lb./ft-hrl : lb^ 'a = r. r co'\ [2 lcp / z.u ft-hr

:

:

I

I

hr

ft-hr \3,600

Q

:

1e.6s(4.026)

(#r)0' :

315.317 gpm

I

sec/

f l rnin I \oo r""/

93,088 0.0884 ft,

Using Np" to check the friction factor,

r-05:

(rgl*

(1-6a) Nr": \ul

-2r"r.[+. rt=*)

(7.e48rx

tb

=

'7

.948

sec

a

r" : secr+s.ss1$

- - ft-hr lt* -"*n \:.ooo

165,633

\ sec/

2.51

(93,088)(0.17875)

f:

Applying Equation l-6a,

r.-"1

0.03198

ft

aP. = l(o.o3l9x1o5.83)

Now,

t--

,,,

4.026

t12J

l- x.l4I | 16 I

aP,' = ILL +H t.t \s

\

||

(1-4)

t(Hft

I

(4s.5s)k $.46if

##j

fr-lh SeC"-lDf

f: +

0.0319

2.3921 | I

-n

'Etc

o,,: [rr1*opu"' * r.,nl

-

rrelr' ft-lb. SeC'-lOf

AP1 :

38

ft

3.364 Or'

-

APr

8.486 psi

<

=

12.35 psi

-

3.864 psi

10.5 psi pad

Select a 6-in.

{

fi

-:-

Sch 40 pipe

:

8.486 psi

90

Mechanical Design of Process Systems To determine the flow rate we must consider what the system is to service. Plant operations dictate that the loading of the tank car must not take longer than four and one-half hours. The rail tank car capacity is 50,000 gallons. We select 4.35 hours, which yields a flow rate of

Repeating the hydraulic analysis we have

2-6-in.

e

:

{

plug valve:

1e.6s(6.065) (,

K

Entrance and exit: K 18 fr 18(0.015)

:

:

or--)"

=

: :

Dr :

1.78

0.27

z.oso

s9.990 eat

513.107 gpm

-

\ 12,----7------

--

re | .57

0D(#(*J -

a4

1'79 0L')

-

(0.0884)

:

[]-::Yl(a.8a)(a5.55)

N*"=''-';

f:0.01803

t

:

r 2.6401

rll ssxs zot'?\r++/

^.^lt+s - ffiAPr:l l(0.0r803x105.83) -r, ^-.U)Urz\rz'z

APr

= re2 spm

will size a centrifugal pump 192 gpm,

,r,

lll t*tr-oj

Ir

r

with 192 gpm capacity. For

sec

19'ut\,r.rouo, rr ne

:

We

fr

5.700--

0.2006

hrs {+!!) \60 min/

4.35

l6.o6sl

I I

\-rzl

I

f+

I

:

0.032 (from Equation 1-6a)

./ r\ l.---. tt'd'*l@

r

38 ft - APr : 12.35 psi - 0.930 psi :

11.42 psi

>

10.5

pst

So there is 0.92 psi (11.42 - 10.50) net positive pressure head of naphtha entering the storage tank.

or,-ll+.oze\ - l,o.orrt,zr.rtr, * ,.rrnlI | t I I I 't APlo

For a 3-in. Iine,

_ -

Suction Line

:

23.313

2(32'2\

= 9.5110t'

Naphtha Pump Hydraulics

L

:100.863

\3,600/

9.939 Ot'

For 4-in. Sch 40 portion of line,

i

4.84 ftlsec

L:

1.0

,rnr,l-l\[) \7.47e1 \601

(0.0s130)

ft

-

8.34 ft/sec

ft 3',0168),s.:0,,+s.:s,

K-Values

Entrance and exit: 1-4-in. plug valve: 4-in. x 3-in. reducer:

K : 1.75 K : 0.306 K=0.163

srLtK

=

2.219

For 3-inch Sch 40 portion of line: K-Values

(18)(0.018) : 0.324 3-in. diffuser: K:Kr:0.055

3-in.d plug valve: K

4-in. x

:

D*-*"

|

tl".: I}-

1 2.6401

..

=

t32.449

I

\3.600/

f:0.0344 re,.'' =

APi.

=

t ol'l4t(t or la5.5sl,t.r,'(,;) o 3791l(o lr /r.oos\ r| 2\32 2) \,2/ 9.175 ntt

Rotating Equipment The total pressure drop for the suction line

AP.

=

APlo

+

APr3

:

:

AP,

,0,,0, ,r, i1,uti,, I 1) |

N^".'"-'; -ttl

0.686 Psi

i

z

60.708

ft, 4-in.

rl

Sch 40

aP,, :

l(o

: 170 : 0.136 4-4-in. plug valves: K : (4X18X0.017) = 1.224 5-4-in. std 90' elbows: K = (5)(30)(0.017) : 2.550 1-4-in. swing check: K: (100)(0.017) 1-4-in. gate valve: K : (8X0.0i7)

Entrance:K=1.0:i.00

D" :

oôto

t*. = E*'

AP1,

:

APp

=

AP1,

I

too.8b3

l(o

:

ol2'(6oi7o8)

|t 14.0261 I r?

select

+ o.oro

2(32.2)

r

: | 42'7 + 0 460 :

-

APo

1 887 psi

+x+

friction

static head (psi)

oressure

\ = i/ tiquio uupot

x

:

\preisure

'i

rpsiarJ

minimum pad pressure required, pslg 20.85

+

21.361 psi

x = Tpsig

Referring to Figure 6-55 and 6-56, we re-evaluate the pump performance. Since the light naphtha cut has a low viscosity

1.427 Ot'

For the 3-in. portion of the discharge line, For 3-in. Sch 40 pipe, d1 3.068 rn.

:

K-Values

4-in. x

34r(*)

I

14.7+x+3.557:0.511 +

|

APlo

o.e43l

line tAP.rf \arop on suction

I

where

ar,, =

+ APi.

/ =

0.032 (from Equation 1-6a) t

*

5r(8

The total pressure drop for the discharge line

\3,600/

:

(45

0.460 Psi

ATM. pressure (psia)

s+x+s.ssr

2.6401

f

934'(i

o)

From Figure 6-54, the pump hydraulic design calculation data sheet, it is obvious that the available NPSH is much higher than the required NPSH. This means that the 10.5 psi pressure for the nitrogen pad is excessrve. The minimum pad pressure required is

(0.0884) 026'1,+.

roo/

It lr.068l I 17 I

K-Values

14

132'449

fi = 0.0344

Discharge Line

L=

e+o[3

=

Entrance: 3-in. reducer:

K

:

0.780

K:0.163

DK = o,sa3

L

:

3 ft.

bhp

:

bhe

-

QHr

(6-2)

3,96Ou (19?)(6172)(9 73) (3,960x0.61)

= 3.i

or a4 hp motor

The Maximum Capacity Condition The small chemical company nearby that manufactures paint thinner needs the naphtha only about once a

year. However, when the naphtha is needed, it must be delivere.d quickly. Consequently, delivery time is crucial to the client.


Equivolents of Degrees APl, Degrees Boum6, Specific Grovity, Weight Densily, ond Pounds Per Gollon ot 6OF/5OF Degrees

Values for API Scale

API

oil

Baum€ Scale

!peci6c

Values for Baum6 Scale

Liquids Lighter Than water

W€ight

Pounds

LblFt3

Gallon

D€nsity,

per

6 8

,,.

'.: ,.oooo

l8

0.9861 0.9725 0.9593 0.9465

61.50 60.65 59.83 59.03

0.9340 0.9218 0.9100

57

0.E984

56.03

20 22 '),4

'].6

28

0.8871

30

0.8762

32

0.8654 0.8550 0.8448

34 36 38 40 42

Lb

8.337

a.xll

8.108 .998 .891

7 7

.043 6.960

0.8235 0.8140 0.8046 0.7955 0.7865

0.7883

49.

50

0.7796

48.62 48.09 47.57 47 .07 46.57

6.499 6.429

0.7778 0.769X

6.359 6.292

0 .7

0.7389 0.7313 0.7238

46.08 45.61

6.160 6.097 6.034

0.7165

5.973

70

0.7022 0.6953

43.79 43.36 42.94

0.6E86 78 80 a2 84

1.1789

0.8537 0.8434 0.8333

6.646

0.7093

l.1600

.679 7.579 7.48X

7.124

0.8642

49.7?.

68

.781

0.8750

o .797

44.64 44.23

7 7

.305

6.799

45.14

1.1069 1.1240

7

6.879

5E

.994 .886

0.8861

5l .46

0.7547 0.7467

8.105 7 7

.396

0.81 55

o.7624

60.63 59.80 58.99

7

0.8251

54

l.o74l

56.70

0.E348

o.77tl

8.337

6t.49

0.909r 0.4974

7

l6

oa.s

7.587 7 .490

52.69 52.06

t

''.

1.0140 1.0284 1.0432 1.0584

58.20

.787

0.8063

7X

Gallon

Specific

Gravity

Weight Density,

Lb/Ftx

0.7609 527

0.7447

E.Zt9

7

54.57 53.90 53.L4 5L.60

.387

.295 .205 7.117 7 7 7

.03r

5t.97

6.947

50.76 50.18 49.61 49.05

6.786 6.708

48.51 47 .97 47.45 46.94 46.44 45.95 45.4E 45.00

5.913

0.7368 0.7292 o.7216 0.7143 o.7071

5.854 5.797

0.7000 0.6931

43,66 43.22 42.40 42.34 41.98

0.6E63

7E.64 80.03 8t .47 42.96

.29

10.512 10.698 10.891

1r.091 11.297

1.3810 | .4078

86.13 67.80 89.53 91.34

|.4356

11.513 11.737 11.969 12.2rO 12,462

I1.64

14.924

r

14.46

t5.302

1.EE31

t17.44

15.699

1.9333

120.57

16.118

5.836 5.774 5.722 5.666

39.84 39.4E

39.69 39.33 38.98

5.306

5.274

5.096

1.2609 1.2832 1.3063 1.3303

77

I

5.454 5.404

95. 1.5591

97

5.506

s.ttl

3E.63

34.29 37 .96

75.99

1.7901

0.6482

5.r41

1.2185 1.2393

9.828 9.990 10.159 10.332

I . E354

5.424

5.186

1. 1983

6.016 5.955

40.80 40,42 40.05

38.79 38.45 38.12

L67r 73.52

14.22?

o.6542

39- 13

9.518

106.39 108.95

5.474

0.6275 o.6120 0.6166 0.6112

9.371

7r.20

1.7059 1.7470

41.58

0.6364 0.6306 0.6250 0.6195 0.6140 0.6087

l.t4t7

9.XX8

6.079

6.143

0.6667 0.6604

0.fl3r.

70.10

13.895

6.209

4t .72 41.33 40.95 40.57 40.20

0.6388

8.955 9.0E9

13.244 r3.583

0.66S0

90 92 94 96 98 100

66.99 67 .99 69.03

4.8L4

12.998

0.6731

0.6422

4.697

99.37 101.60 103.94

0.6796

0.6446

65.06 66.01

1.5934 1.619L 1.6667

42.12

88

8.337 8.454 8.574

l9 .2]

47..53

E6

1 0902

6.484

6.413 6.344

44.10

4t.19

62.36 63.24

64.t4

1.4646 1.4948

0.68r9 0.6754 0.6628 0.6566 0.6506

Pounds per Gatlon

.s

0.9333 0.9211

7

,87

54.64

1.0000 0.9859 4.9722 0.9589 0.9459

46 48

64 66

/Ft3

Pounds pef

','

50.86 50.28

60

Weight

Density,

r.0000

l0 t7 I4

Gravity

s

s 0 2

Specific

Liquids Heavier Than Water

5. 1r9

..'

,'.

Figure 6-53. Relationship between 'API and temperature. (Courtesy of Crane Company.)

'..

Rotating Equipment

Pump Hydraulic Design Calculation Sheet Light Naphtha

Liquid Viscosity at PT. (Pumping Temp.) Vapor pressure at PT. Sp. gr (-y) at PT. Flow at ambient temp. Operating flow at PT. Design flow at PT.

Cut-68'

API

_cp

'1.1

psia

20.85 0.73

gpm

't92 't92

gpm gpm

Discharge

Suction Source pressure Static head - APr, line loss Suction pressure

-

Vapor pressure NPSH avail NPSH avail

25.20

Terminal pressure Static head (litt) APi discharge Piping system Other Discharge press. Suction press.

psra psi

-

= =

0.51 'l

28.248 20.85 7.398

-

1.3

NPSH req'd

-

psi psia psra

psia

-

ft ft

psra

= =

= =

6.313

psi

1.887 20.o 44.90

psl psl psra

28.244

psia psia

feet bhp at Duty

onpo

=

Condition


Q{l(IPr)1! (3,960Xn)

onp"" =

QSTrylI1 (3.960Xr)


Referring to the pump manufacturer's pump performance curve, Figure 6-55, we see that approximately 400 gpm is the maximum limit. Using this flow rate we re-evaluate the pump for the maximum capacity case.

Suction Line

:

APr,,

2.200 ps

For the 3-in. portion of the suction line,

u.- :

lq)

r8.34r

\t92l

**. :

= r7.37sa sec

:275,e35 (,rr4) 032,44s)

Referring to previous calculations on the suction side we have the following:

u.

From Equation 1-6a,

: {gl r4.84r = io.o8jl sec \tvtl

1n ORI N^. : l',"i,'l r100.863) \ +.d4 /

f:

0.03395

It

I

210.062

From Equation 1-6a we obtain

f :0.0315

or,.

:

APr

o1le1'"'r * r,nl (4s.ss)(ro.osf(1-L; [ro 2(32.2)

rffi

I

o:'n''lt o' * o rrnl

rffi

on,. = ['o

:

9.759 Ot'

AP,:APso*APi.

AP,:2.29*a.trt AP,

=

2.959 Ot'

l

2(32.2)

I

..1

E

.z

=if, =

(oEn E

\J

ii

tal

2

ab L,' 9 -r6 G+i \r l, ,i

.2 H ...i

^ :>,

(J I +: EE O.;\ =!

c.r

Ei (\t l!,, \J

9?ts

E ,6

tr!J

o.E : R .b lrt.:i

9X ttc

o ooooo o @(o\fc\l

Rotating Equipment

Pump Hydraulic Design Calculation Sheet Light Naphtha Cut-68o API

Liquid Viscosity al PT. (Pumping Temp-) Vapor pressure at PT Sp- gr. (1) at PI Flow at ambient temp. Operating flow at PTDosign flow at P.T.

1.1

cp psra

20.85

0.73 't92

gpm gpm gpm

192 '192

Suction Source pressure

Discharge

=

21.70 3.559

Static head = APr, line loss Suction pressure = Vapor pressure = NPSH avail NPSH avail NPSH req'd

-

psia

-

0.51

24.744

psl psi psra

-

20.85

psia

12.3 1.3

ft

1

Terminal pressure = Static head aPr discharge Piping system

-

Other Discharge press. = Suction press. =

psra

-

tt

bho"

=

psra

psi

1.847

psi psi psra

24.744

psia psia leet

20.'152 63.77

TDH

= bhp at Duty Condition

'16.7

6,313

bhp at Back-Pressure Condilion

(SPmXTDH)(?)

bho"" =

(3,960X4)

(gPm)[rDH)(?) (3,s60)(a)

Figure 6-56, Re-evaluation of pump hydraulic design calculation sheet of Example 6-5.

Discharge Line Referring to previous calculations on the discharge side we have the followins:

v.

sec

(lryrt (100,863)

I' l4ql \ /

: zto,o6z

12

AP6n :

I

--"-'--'\r44l l,or.rrxro.oo,{*} -^^+ 6.610l

[+.ozo\ IrrI

| )

6.143 O.'

: APo :

lgl(8.34): \t>Ll

2(322\

AP6o

*

AP1,

=

6.143 psi

+

1.989 psi

3.132 ntt

Referring to Figure 6-57, we reevaluate the pump for the maximum capacity condition.

Normally, we would use a 9.5-in. impeller, as indiIn this case, being that the application is infrequent, we keep the 8.Gin. impeller. As the flow rate increases with the same size impeller, the TDH decreases and the required NPSH increases. As we see on Figure 6-55, the available NPSH of 4.589 ft is slightly exceeded at 400 cated on the pump manufacturer's curve, Figure 6-55.

For 3-in. portion,

u, =

2(32.2)

I

J

APlr:1.939

ap,. _ l(0.031sx60.708)

-l

f:0.03395

APp

^".- ..^

(,1q; 032,44e) :275,e35

Al-h = l------l--------- + U,y4Jl

f:0.0315 t.^

:

II ,or.rr,,rr.rrrr(r{) l(0.03395X3.0) ^ ^.^l

: {g} (4.84) = ro.o8l \t921

N* :

*""

r7.37sa sec


96

Pump Hydraulic Design Calculation Sheet

Maximum Capacity Condilion Reevaluaiion Light Naphtha

Liquid Viscosity at PT. (Pumping Temp.) Vapor pressure at Pl Sp. gr- (r) at PT. Flow at ambient temp. Operating flow at PT. Desion flow at

cp

0.73

pT.

Suction Source pressure

=

4no 4uu

gpm

Terminal pressure

Psia psl psi

Static (lifi) APr discharge Piping system Other Discharge press. Suction press.

- 20.85 1.45 4.589

psia

psia

-

ft

ft

NPSH req'd

16.70

=

TDH TDH

8.132

= = = = =

bhp at Duty Condition


ono"=9##

.

.

Psia psl

6.313

-

psia

NPSH avail NPSH avail

gpm gpm

Discharge

21.70 3.559 - 2.959

Static head - APi, line loss Suction pressure = - Vapor pressure =

psia

20.85

20.00 51.145

psi psl psra

22.300 24.845 91.282

psia psia feet

(oom)fiDHXr)

bnp"" = =.(3GbX4.

Figure 6-57. Maximum capacity re-evaluation of pump hydraulic design calculation sheet of Example 6-5.

gpm. It is suggested that a flow rate of375 gpm be used to avoid cavitation. From Figure 6-55 the actual TDH is

TDH

:

34

ft

The required brake horsepower rs

..

'

necting the reservoir to the storage tank, considering the pipe to be 4-in. schedule 40, is as follows:

(375 x34.0X0.73)

(3,960X0.65)

-

J'v'

,, _

(3?r " -'

(ciL)(=*-] tl+tl \min/ \7.a79 eau \60 sec/ 0.0884

ft?

= 9.45j a

sec

ttv

:

A 4-hp motor is sufficient for normal and maximum ca-

2.640

pacity operations.

lb'

lnr

fchr

From Equation l-6a,

Re.evaluation of Reservoit Line f-05 Since the nitrogen pad on the naphtha storage tank was

:

-lr"c. [+ .

decreased from 10.5 psi to 7.0 psi, we must reconsider

the line size. With 38 feet of head in the reservoir, we incurred a pressure drop of 3.9 psi, yielding an entry pressure of 8.5 psi. In the back-pressure condition, we need a flow rate of 375 gpm. The new presure drop in the line con-

f:0.031s

*]-tt)

196,992

Rotating

k

From Equation 1-4 we have

aP.:lLL*rrl \d -

or, =

m Pv'

l2e"

1+s.ss1

: mw : n: N: N, : NPSH : P: Q: R: R: scfm : fiIo

olualgrl,o

p

* r.rnrl I

1r.+s:;,#

(*q-J

fr-lh SeC'-lDf

APr

:

5.41f Or'

38ft:12.008psi

:

:

ratio of specific heats CplC,, dimensionless mass, lb. and re-expansion polytropic expo-

flow rate, lb-/hr moles of gas m/mw molecular weight mass

:

polytropic exponent speed, rpm specific speed, dimensionless net positive suction head, feet or psia pressure, psi

flow rate, gpm or ft3/sec R/mw : gas constant of a particular gas universal gas constant : 1545 ft-lbr/lb. molestandard cubic feet per minute, ft3lmin-see discussion under standard volumetric

With 38 feet of head in the reservoir we have an entry pressure to the storage tank of

Entry pressure

97

nent

dl =

I (r!flr [,o

: :

Equipment

12.008 psi

-

5.411 psi

:

6.597 psi

Because 6.597 psi < 7.00 psi pad, we keep the 6-in. schedule 40 pipe. The 6-in. line was evaluated for 513 gpm, so it is adequate for the 375 gpm in the 4-in. line. The system is now completely designed for hydraulics, using a 4-in. x 3-in. horizontal centrifugal pump.

t: temperature, "F At : temperature differential, oF V : volume of gas or cylinder, ft3 v = specific volume of gas, ft3/1b* w* : weight of fluid whp = *ur". horsepower, hp y : constant : (k_ lyk z : compressibility factor, dimensionless

flow

Greek Symbols

: : €: p: ? 4

NOTATIOl{ acfm bhp

=

: e: Co : C. : C" : D:

D" ghp

= =

: icfm : J: H

actual cubic feet per minute, ft3lmin 6.u1" horsepower, hp clearance volume, in.3 specific heat at constant pressure, Btu/lb-mole-"F compression ratio specific heat at constant volume, Btu/lb.mole-'F diametef of impeller or rotor, in. specific diameter, dimensionless gas horsepower : horsepower delivered to gas, hp head : energy per pound of mass, ft-lb/Ib., or better known as feet of head, ft actual cubic feet per minute at compressor inlet, ft?/min mechanical equivalent of heat: 778 ft-lbrl Btu

specific gravity, dimensionless efficiency, expressed as percent ratio of clearance volume to the volume sweot by the piston stroke density, 1b./ft3

REFEREilCES 1. Buchter, H. Hugo, Industrial Sealing Technology, John Wiley & Sons, New York, N.Y., 1979. 2. Dimoplon, William, "What Process Engineers Need to Know About Compressors," Compressor Handbook for the Hyd,rocarbon Processing Industries, Gulf Publishing Co., Houston, Tx., 1979. 3. Balje, O.8., 'A Study on Design Criteria and Matching of Tirrbo-machines-Part B," Trans. ASME, J. Eng. Power, Jan. 1962.

The Mechanical Design of Shell and Tube Heat Exchangers

A heat exchanger in process systems allows the transfer of energy as heat from one source to another. Witlout this essential piece of equipment most industrial processes would be impossible. There are various types of heat exchangers, each of which is designed to accommodate the requirements of the specific needs at hand. Shell and tube heat exchangers are by far the most common because of their relative simplicity and ability to handle the largest variety of fluids. Plate fin heat exchangers have become quite popular in cryogenic gas services and have largely replaced shell and tube exchangers in gas processing plants. Finned-tube exchangers are used for gas-gas heat transfer, such as in waste heat recovery units, and have gained popularity in the past few years because of emphasis on cogeneration to satisfu energy needs.

bottom shell-side nozzle cooled to the desired temDerature. The tube bundle is supported between two iubesheets with baffle plates spaced at intervals to support and brace the tubes. In this figure the tube-side flow enters the tube bundle on the bottom left side and exits on the top left side with a horizontal baffle plate separating the two tube-side flows. This type of arrangement is called a l-2 exchanger, one shell-side pass and two tubeside passes. The various configurations of exchangers will be discussed shortly. Figure 7 -2 shows a reboiler in which isobutane vapor is formed by heating liquid isobutane. This type of reboiler is called a "kettle" type reboiler because ofthe excess area above the tube bundle that is provided for vapor separation. Figure 7-3 shows another type of reboiler where the shell and tube exchanger is mounted vertically alongside a process tower. Here the heat energy of steam is used to separate the propane and propylene liquid into a gasJiquid two-phase mixture. This type of arrangement is common in the gas processing industry and, as will be discussed later, one must be very careful in designing the support(s) for such an exchanger, because of the tubes' thermal expansion. All shell and tube heat exchangers are exposed to internal pressures, tube-side and shell-side. Thus, in the United States the ASME Section VIII Division I Pressure Vessel Code governs the vessel design of such exchangers. The detailed design of shell and tube exchangers is governed by TEMA (Tubular Exchanger Manufacturing ASsociation), whose published standard classifies exchangers by the severity of process requirements. The three classes are Class "R," Class "C," and Class "B" exchangers. Before discussing these classes, we must clariry heat exchanger design types and terminology (see Figure 74).

FUNDAMEHTALS OF SHELL AND TUBE HEAT EXCHANGERS A shell and tube heat exchanger is a cylindrical vessel housing a set oftubes (called the tube bundle) containing a fluid at some temperature and immersed in another fluid at a different temperature. The transfer of heat occurs between the fluid flowing over the tubes and the fluid flowing inside the tubes. The fluid flow inside the tubes is said to be "tube side" and the fluid flow external to the tube bundle is said to be "shell side." The simplest type of shell and tube heat exchanger is the type shown in Figure 7-1, where warm kerosene enters on the top shell side. The kerosene's flow path is guided between the tubes by baffle plates and exits at the 99

100

Mechanical Design of Process Systems WARM WATER OUT

KEBOSENE IN

KEROSENE OUT

(cooLED) COOL WATER IN

Figure 7-1. An example of a fixed tubesheet heat exchanger. (Courtesy of Howell Training Company.)

ISOBUTANE VAPOF

LEAVING AT

2OOOF

orL ENTEBTNG AT 6650F

LIOUID ISOBUTANE LEAVING AT 2OOOF

LIOUID ISOBUTANE ENTERING AT I95OF

Figure 7-2. This U-tube exchanger represents a kettle type reboiler. (Courtesy of Howell Training Company.)

The Mechanical Desien of Shell-and-Tube Heat

Exchangers

101

PAOPANE & PAOPYLENE 50% VAPOR - 50% L|OUTD

FRACTIONING TOWER (DE ETHENIZERI

PROPAN€ AND PROPYL€NE 50% vaPoR 50% LroulD

CONDENSATlON

Figure 7-3. Iilustration of a thermos]phon reboiler. (Courtesy of Howell Training Company.) PROPANE ANO PFOPYLENE 100% Ltouto

Design Classifications of Heat Exchangers Typical shell and tube heat exchangers and their functions are as follows:

Reboiler-transfers heat to a liquid to produce a twophase, gasJiquid mixture used in a distillation column.

Thermosiphon Reboiler-provides natural circulation of the boiling

fluid by a static liquid head shown in Fig-

ure 7-3.

Forced Circulation Reboiler-a reboiler in which a pump is used to force the liquid through the heat exchanger (reboiler) into the distillation column. Condenser-a heat exchanger to condense vapors by removing heat from a gas. Partial Condenser-only partially condenses a gas to provide heat to another medium to satisfy a process

condition. The residual gas is recirculated through a heater and recycled. A common application is using excess steam to heat up a process fluid. A typical application of a partial condenser on a distillation column is to condense only enough liquid for the reflux when the overhead product is vapor. Final Condenser-an exchanger where all the gas is condensed and all the heat is transferred to the other medium. Steam Generator-a device that generates steam, such as a boiler. to provide energy for process requirements. The most classic example is the old stearn locomotive, which is a shell and tube exchanger "mounted on wheels" with the steam used to Dower the locomotion. (This unit is a fired vessel and is not covered by ASME Section VIII Division.) Vaporizer-an exchanger that fully or partially vaporizes a liquid. Chiller-an exchanger in which a process medium is cooled by evaporating a refrigerant, or by cooling and heating with little or no phase change.

102


HEAD IYPIS

'AIIONARY

I A Uff ' "

ANO iEA{OVA8TI COVEP

tn

F

WTh

B

G

LONGIIUOINAT

Ul(E "4" STATIONARY HEAO

3AFFIE

N LIKE

BONNST (INIEGRAI COVER)

H

SIAIIONARY HEAO

'1T STAIIONARY

HEAD

P OUI5IOE PACKED FTOA'ING

c

'IFAO

CHANNET INTECFAL WITH IU8E. SHETT AND RE/nOVASIE COVTR

s J

T

N

PUIT TIiROUGH FIOATIIIG HEÔ ''UBT-

CHANNEI INIEGRAL WIIH 5HEET ANO REITOVABLE COVER

K U

D

x SPEC|AL

hICH

PREsSURE

CTOSUI€

Figure 7-4. Nomenclature of shell and tube heat exchangers. (@1978 by Tlrbular Exchanger Manufacturers Associauon.)

These classifications are the major types of services that shell and tube exchangers provide in the process industries. Process requirements dictate the type of design to be used. Figure 7-4 shows some of the major types of con-

struction. The standard TEMA classification of ex, is to use the shell identification and number with the exchanger designation type. For example, an 18- 150 BEM is an exchanger having an 18-in. shell with 150 tubes, a bonnet (integral) cover with a fixed tube-. sheet at one end (B in Figure 7-4), a fixed tubesheet and a stationary head at the other end (M), and a one-pass changers

shell between both ends (E).

Fixed Tubesheet Shell and Tube Heat Exchangers Fixed tubesheet shell and tube heat exchansers are the simplest of the shell and tube designs. They ionsisr of a tube bundle attached to a tubesheet on each side of the tube bundle. The tubesheets are welded to the shell pro,

viding an absolute seal to prevent the shell-side fluid from leakage. Often the tubesheets extend beyond the shell diameter and have flange bolt holes that allow the tube heads to be bolted to the tubesheets. In fixed tubesheet exchangers, tubes can fill the entire shell to achieve maximum heat exchange (of course, this

The Mechanical Desisn of Shell-and-Tube Heat Exchansers

also increases shell-side fluid pressure drop) such that tolerances between tubes are minimum. However, this factor limits the shell-side fluid to a relatively clean service, because the exterior of the closely-packed tubes cannot be mechanically cleaned or inspected. Another limitation to the design is that there is no allowance for thermal growth of the tubes , except if an external expansion joint is used, which is quite common for this type of exchanger. Normally, single convoluted bellows are used since the maximum temperature differential is 200"F and the cyclic loading is insignificant. Tube-side headers, channel covers, and internals of tubes can be cleaned quite easily and the shell side can be cleaned only by circulating a cleaning fluid or backwash-

ing.

U.Tube Shell and Tube Heat Exchangers U+ube shell and tube heat exchansers consist of one tubesheet with tubes bent in a U-shipe atrached to rhe single tubesheet. This type of exchanger is used for large temperature differentials where there is a lot of tube growth. This type of design allows for easy access to the

shell side of the tubes and removal of the tube bundle. The inside of tubes must be cleaned with soecial tools and then only when the bending radius is fairly large. This tne of design is also very suitable for chemical cleaning.

The maximum number of tubes per tubesheet is less than the fixed tubesheet design beciuse of the minimum bending radius required to form the U-shape. The Utube design is also very applicable to high-pressure servlces.

Floating Head Shell and Tube Heat Exchangers This type of shell and tube heat exchanger has a floating head that is designed to accommodate thermal expansion of the tubes and to provide access to the tube-side and shell-side exchangei components. This type of design is expensive and its use should be considered against other possible designs.

Packed Lantern Ring Exchanger (Figure 7-5a). This construction is normally limited to design tempera-

gland tollower

floating-head cover

(B) Outside-packed floating head exchanger

(A) Packed lanternring exchanger

flange floating-head cover

backing ring shell

f

tlange gasket

shell

cover

floating tubesheet

floating tubesheei

floating-head cover

gasket (C) Internal floating head

exchanger

103

(D) Pull-through lloating head exchanger

Figure 7-5. Several configurations of floating head exchangers.

'lO4


< 370"F and design pressures < 300 psig. This type of design is used only for mild services, such as steam, air, low viscous oils. In this design the shell-side and tube-side fluids are sealed by separate packings which, in turn, are separated by a lantern ring. The lantern ring fits between the packings that separate the shell and tube-side fluids and normally contains weep holes that accommodate any leakage through the packing. Such leakage, which is passed to the outside and drops to the foundation below, will not cause shell and tube-side fluids to mix. The tubesheet must be designed such that it is large enough in diameter to encompass the packingJanternring ensemble and differential thermal expansion of the tubes. Occasionally, a skirt is attached to a thin tubesheet to act as a bearing surface for the packingJantern-ring tures

ensemble.

Outside-Packed Floating Head Exchanger (Figure 7-56). Rings of packing contain the shell-side fluid, which is compressed by a gland follower that is guided by a tube sheet skirt. The skirt is integral to the floating tubesheet. This removable-bundle construction allows for differential expansion between the shell and tubes. This design is normally limited to 600"F and 600 psig, which is one reason why it is the most commonly used removable-bundle type exchanger in the petroleumchemical industry, even though usage has decreased over recent years.

Internal Floating-Head Exchanger (Figure 7-5c). This design consists of an internal floating tubesheet held by an internal backing ring, which is bolted to an internal floating head cover. The internal backing ring and internal shell cover are beyond the end of the shell containing the tubes. To remove the tube bundle, the shell cover, split backing ring, and internal floating head cover must be removed. The internal floating head cover acts as a return cover for the tube fluid with an even number of tube-side passes. with an odd number of tube-side passes, a nozzle must be extended from the in-

ternal floating-head cover through the outside shell cover. Clearances between the shell and the outermost tubes are 1rla in. for pipe shells and 17re in. for mediumsized rolled plate shells. This design is more suitable for higher shell-side temperatures and pressures than for pull-through bundle types of construction. This design has been used extensively in the petroleum-chemical industry, but there has been a decline of use over the past few years.

Pull-Through Bundle Floaiing-Head Exchanger (Figure 7-5d). This design consists of a floating head directly bolted to an internal floating head cover. The tube

bundle can be removed without removing either internal floating head cover or shell cover when bundle is pulled out an opposite end of shell cover facing internal floating head. This feature reduces down and maintenance time during inspection and repair. The clearance between the outside of the tubes and shell inside must be sufficient to allow space for both the gasket and bolting at the internal floating head cover. This clearance is usually twice that required for the split ring design used in the internal floating head in the previous section. This type of design is normally limited to services where leakage of the internal gasket is tolerable. With an odd number of tube-side passes, a nozzle must extend from the internal floating-head cover through the shell cover. The number of tube-side passes is simply limited by the number of tubes. This design is generally suited for lower temperatures and pressures than that of the internal floatine head exchanger described earlier.

General TEIIA Exchanger Glasses-Rr Ct and B There are three basic categories of shell and tube heat exchangers in TEMA-Class R, Class C, and Class B. The difference in class is the degree of severity of service the exchanger will encounter. Descriptions of the three classes are as follows: Class

R

C/css

C

includes heat exchangers specified for the most severe service in the petroleum-chemical processing industry. Safety and durability are required for exchangers designed for such rigorous conditions. includes heat exchangers designed for the gen-

erally moderate services and requirements. Economy and overall compactness are the two essential features of this class. Class B are exchangers specified for general process

service. Maximum economy and optimum compactness are the main criteria of design. Rubin [3] described the TEMA classes of exchangers in terms of the various components and how they vary from one class to another. This data is given in Table 7-1. Ludwig [4] described various types of heat exchangers, their applications and limitations, which include shell and tube exchangers as well as other types. This data is -oresented in Thble 7-2.provide a comprehensive view of tbles 7-1 and 7-2 and their applicaof heat exchangers various types the of the on the components can now focus tions, so we shell and tube design.

Table 7-1 Comparison of TEMA Classes R, C and B Exchangers [31 Para-

graph

Toplc

1.12

Definition

1.51 2.2 2.5

Corrosion allowance on carbon steel

3.3 4.42 4.7 | 5.11 5.31

TUbe diameters

Tirbe pitch and minimum cleaning lane

for the generally severe requirements of petoleum and related processing applications. r/s inch

for the generally

for g€neral process

moderate requirements of comrnercial and general process applications.

sefvrce.

3h, 1,1\+, 1tlz, and 2

R+%,

inch od 1.25 x tube od. r/+ inch

R+5/E tubes may be

lane.

located 1.2

8 inch tabulated

6 inch tabulated

tho inch

3/s, rlz, and

5/e

xtube od

r/ro inch

R*5/e

R*lane may be 3/re inch in 12 inch and smaller shells for s/s and 3/+ tubes.

Minimum shell diameter Longtudinal baffle

V+

inch minimum

t/8 inch

3/s

inch

% inch in 6-15 inch

r/+

alloy,

hch CS

thickness

Minimum tie rod diameter Floating head cover cross-over area Lantern ring construction

6 inch tabulated. Va inch alloy, r/+ inch carbon steel r/+ inch 6-15 inch shells.

shells

flow

1.3 times tube flow area

Same as tube

375"F maximum. 300 psi up to 24 inch diam shell

600 psi maximum.

(same as TEMA R)

Metal jacketed or solid metal (a) internal floating head. O) 300 psi and up. Asbestos permitted for 300 psi and lower

(same as TEMA C)

150 psi for 25-42 shells

a.rea

Same as tube

flow area

irch

75 psi for 43-60 inch 6

.2

shells Gasket materials

Metal jacketed or solid metal for (a) internal floating head coYer.

(b) 300 psi and up. (c) all hydrocarbons.

6.32 7

.131

pressures.

Peripheral gasket contact

Flatness tolerance

No tolerance specified.

No tolerance specified.

surface

specified. Outside diameter of the tube.

0.75 xtube od and smaller.

(same as TEMA C)

Minimum tubesheet thickness with expanded tube joints

.44

Ti.rbe Hole Grooving

.51 7.7

Length of expansion

7

7

Ttrbesheet pass partition grooves

9.3 9.32 9.33 9.1

Pipe Tbp Connections

10.1

Pressure Gauge Connections

Thermometer

for 1 inch

z/s

TWo grooves

inch for 1% od inch for 1tlz od 1.25 inch for 2 od Above 300 psi design

(same as TEMA R)

Smaller of 2 inch or

pressure: above 350'F design temp.-z grooves Smaller of 2 x tube od or

(same as TEMA R)

tubesheet thickness 3/re inch deep grooves

Over 300 psi rAo inch

(same as TEMA C)

I

required 6000 psi coupling with bar stock plug required in nozdes 2 inch

&

uP.

lequired in nozdes 4 inch

deep grooves required or other suitable means for retaining gaskets in place 3000 psi coupling

(shall be specified by (shal1 be specified by

purchaser)

Nozzleconstruction

no reference to flanges

same as

Minimum bolt size

3/a

t/z inch recommended,

inch

(same as TEMA R)

purchaser)

6a up.

Connections

3000 psi coupling with

bar stock plug

TEMA R

smaller bolting may be used

(same as TEMA R)

All

nozzles larger than one inch must be flanged. 5/s inch

106


Table 7-2 Selection Guide Heat Exchanger Types l4l

Relatlre Cost Type Deslgaatlon Fixed Tube Sheet

SlEnlficant Feature Both tube sheets fixed to

shell

Applications Best Sulted

Llmltatlons

Condensers; liquidJiquid;

Temperature difrerence at extremes of about 200" F. due to differential expansion

1.0

Jnternal qasketsofter danqer

t.2a

Bends must be carefully

1.08

gas-gas;

gasliquid; cooling

and heating, horizontal or vertical, reboiling

Floating Head or Tube Sheet (Removable and nonremovable bundles)

One tube shea "floats" in shell or with shell, tube bundle mav or mav not

be removable from shell. but back cover can be rej moved to expose tub€ ends.

U-Tubei U-Bundle

Only one tube sheet required. Tubes bent in Ushape. Bundle is removable.

Kettle

Tube bundle removable

High temperature differedtials, above about 200' F.

extremes; dirty fluids .equiring cleaning of inside as well as outside of shell, hori-

zontal or vertical.

High t€mperature differentials. which migbt require provtslon tor exDanslon ln 6xed tube units.elean service or easily cleaned coodi tions on both tube side and shell side. Horizontal or vertical. Boiling, fluid on shell side,

as U-type or

as relrrgerant, or

(r!9engagrng.

flu-id in

floating head. Shell €nlarqed to allow boiling and vapot

proc€ss

fluid beioe vaporized. Chilline or co6lini of tube side

Co[structlon

of leakine. Corrosivenesjoi fluids on-shell side floatins parts. Usually confined t-o horizontal units-

made or mechanical damase

and danqer of ruDture ctn result. fube side'velocities

can cause erosion of inside

of bends. Fluid should

be

free of susp€nded particles.

For horizontal installation. Phy.sically large for other

applcatrons.

retrig;rant evapora-

tiofl on shell sideDouble Pipe

Each tube has own shell

forminq annular for

aliy

she-il side use

soace

fluid. ijsu-

externally finned

ba[ks for

larger applications. Especially suited for high prcs-

sures in tube above 400 psig.

tuDe.

Pipe Coil

Relatively small transfer area service. or in

Pipe coil for submersion rn coll-trox ol water or

with water is simplest type of exsprayed

Services suitable for 6nned

tube, Piping-up a

0.8-1.4

large numDer olten r€qurres cost

and space,

Condensins, or relativelv low heat l;ads on sensiblir transfe!.

Transfer coefiicient is low,

Condensing, relatively low heat loads on s€nsible trans. fer.

Transler coefiicient is low, takes up less space than plpe co{.

0.8-1.1

Condensing, high level heat transter.

Transfer coefiicient is low, if natuaal convectiol cir-

0.8-1.8

requir€.s, space

lt

relatively

0.5.{}.7

l.arge

heat loaq rs hrgh,

changet.

Open Tube Sections (Water cooled)

Tubes require no shell,

only end headers, usually long, water sprays over surface, sheds scales on outside tubes bv exoansion and contraciion.tan also be used in water box.

Open '(AirTube Sections

Cooled) Plain or finned tubes

No shell required, only

end headers similar to

'w'ater untts.

culation, but is improved

with forced air flow

across

tubes. Plate and Frame

Composed of metal-form-

ed thin plates

separated

by gaskets. Compact, easy

to

Viscous fluids, corrosive fluids slurries, High heat transfer,

clean.

Not well suited for boilins

or

condensing; limit 350500'F by gaskets. Used for Liquid-Liquid only; not

0.8-1.5

gas-gas.

Spiral

Compact, concentric Cross-flow,

condensing,

Process corrosion, suspended materials.

0.8-1.5

Chemical resistance of Clean fluids, tubes; no tube fouling.

condensing,

Low heat transfer coefrci-

2.0-4.0

plates; no bypassing, high turbulence. Small-tube Teflon

heating.

ln

C.arbon Steel

The Mechanical Design of Shell-and-Tube Heat

Baslc Gomponents of Shell and Tube Heat Exchangels There are various components to a shell and tube heat exchanger, but the following are the essential ones:

1.

Tubes

2. Baffles 3. Tie rods 4. Tubesheets Tubes There are basically two types-finned tubes and bare tubes. Finned tubes have external fins mounted by various mechanical means. The necessity of having external fins mounted on tubes is to provide more heat transfer area and thus more heat influx to the tube fluid. Finned tubes are most common where there is a gasJiquid or gas-gas transfer of heat with the gas always being external to the tubes. Typical applications of finned tubes are waste heat recovery exchangers, waste heat boilers, gas turbine regenerators, and air-cooled exchangers. Examples of some finned tube designs are shown later. Plain or bare tubes are the most common in shell and tube design. These tubes come in two basic types-solid wall construction and duplex construction. The duplex design consists ofa tube within a tube in which the outer tube is mechanically drawn over the inner tube. The solid wall tube is what the name implies, a simple tube of solid wall construction. Tubing is available in almost as many materials as piping and is available in standard gauge sizes listed in Table 7-3, along with diamerers and section properties. In applying the U-tube exchanger design, tubes must be bent 180'. Thble 7-4 lists the recommended minimum bend radii.

Baffles Baffles serve several functions and consequently the design of each is dependent on its purpose. Baffles can act as:

l

2. 3.

Structural supports for the tubes. Dampers against vibration. Devices 1o control and direct flow Datterns of the shell-side liquid.

Baffles as Tube Structural Supports. Like piping, tubes behave as structural beams and consequently will develop excessive deflection, or sag, if left unsupported. Baffles act as the structural supports in the shell and tube exchanger. Another structural function of baffles is to add stiffness to the tubes so that each tube. in effect. is

Exchangers

1o7

constrained at each baffle. Thus, the hole in the baffle, being larger by varying amounts than the outside tube diameter, acts as a limit stop for the tube. In piping mechanics (see Chapter 2) a limit stop is a restraint that limits the amount of pipe (in this case, tube) movement to the distance between the hole diameter and the outside diameter of the tube. In other words, the tube can translate in the lateral direction perpendicular to the tube axis only by the amount of clearance between the tube OD and the hole diameter. Translation is mentioned instead of rotation because even though the tube rotates, it is insignificant. Thus, the baffle hole acts as a limit stop and prevents lateral buckling of the tubes when they are induced to thermal expansion by temperature differentials. In this sense the tubes are much stiffer and stronger than

they would be without the baffle supports. The consequences of strengthened tubes affect the integrity of tube joint connections in the tubesheets and this will be discussed shortly. We see from this discussion that the baffle plates act as both structural supports and as buckiing stabilizers.

Baftles as Tube Vibralion Dampers. Figure 7-6 shows baffles of circular rings with rods that run vertically in the first two rings and horizontally in the second two rings, thus damping vibration much in the same way as helical vortex strakes on stacks (Chapter 5). The rods break up forming vortices that induce vibrations, a phenomenon discussed in Chapters 4 and 5 called vortex shedding. The rods also reduce turbulence to below res-

onant levels of the natural frequency of the tubes and they reduce fluid elastic vibration.

Baffles Conlrol and Direct the Flow Pattern of the Shell-Side Fluid. There are various types of baffles that direct and/or control the flow ofthe shell side fluid. Fieures 7-l and 7-2 are examples of baffles guiding or d'irecting the flow in the vertical direction. Fig]ure 7-7 shows baffles diverting flow in the horizontal direction. The flow direction is a function of the orientation of the baffles and their respective geometries and is dependent upon process requirements. The arrangement in Figure 7-7 is said to be vertically cut and the arrangements in Figures 7-l and 7-2 arc said to be horizontally cut. Often, process conditions require the shell-side fluid to flow horizontally, parallel to the longitudinal axis of the exchanger. This arrangement, called a longitudinal baffle, is shown in Figure 7-8. Figure 7-8a shows a twopass shell-side arrangement and Figure 7-8b shows a four-pass shell-side arrangement. The baffles control the flow in the sense that both the direction and flow rate are dependent on orientation and number of passes, respectively. With the same inlet flow rate, the fluid velocity

108


Table 7-3 Characteristics of Tubing

Sq.

tt.

Sq. Ft.

o.D.

Y.

tt

B.W.C. Gage 22 24 2?

yt

t8

% % Yl

20 22 ?4

h

l8 20

v,

22

% %

t2

% vs %

%

l3

l4 l5

Sq.Inch .028 .018 .016

.0360 .0313

.049 .035 .028

.0603 .0731 .0799

.0962 .09E2 .0982

.0725 .0798 .0835

.022

.0850

_0982

.0E57

.065

.1075 .1269

.1309

.035 .028

.t452

.1309 .1309

.1546

.1309

.109 .095

.1301 .14E6 .1655 .1817 .1924 .2035

-049

.0E3

17

.05E

x

20

t/.

l0

.134

.1E25

.t20

.2043

.109 .063

.2223 .2463 .2679

.0t2

.2884

.055 .056 .049 .035

.3019 .3157

.165 .134

\2 % % 1A

l3 l4 l5 t7

l8 20

I

.0508 _0539 .0560

.022

l6

II

lengrtl

.0655 .0655 .0655 .0555

.072 .065

l8 l9

LenAtlr

.0295 .0333

.049 .042 .035

',|

WGisht

len8th

Tube

.095

.218t -2298 .2419

.1636 .1636 .1636 .1636

.0570

[21

Steel

Tubo t.D.

Ssctlon

.194

.054 .045

.26

.00012 .00011

.2t4

.040

.218

.00009 .00008

,lil

.277

.00083 .00071

.0810 .0E?4

52

t.2t4 l.16E

LI46

.0195 .0159 .0t31

1.354

.0502

1.233

.0374 .0305

.00064

.0829

56 56

_l164

94

.1556 .1606

_305

.319

.00045

.083

.331

.00036

.0969

.302

.0022

.00E5

.1052

.236

.0018

.l t26 .l162

.@72

.171

.370 .402 .430

.00t4

_0056

.0012

.0046

.1066 .1139

.602 .537

.019i

.t202

.479 .425 .388

.0061 .0057 .0053 .0049 .0045

.l4I

.350 .303

.407 .435 .459 .461

.495 .509

.0042 .0037 .0033

.t636

_1453

.262 .221

_555

.0028

.1963 .1963 .1953

.1262 .1335

.884 .809

.482

.0129

.510

.0122

.1393 .1466 .1529

.748

.532 .560

.t587

.520

.1623 _1660

.4t6

.0116 .0107 .0098 .0089 .0083

.367

.t963

46

.104

.1380

.1963 .1963 .1963

.9792

.t27

.1636 .1636

.1963

.00098

,0036 .0029 .0025 .0020

.14t6

.3339

.1953

.3632

.1963

.\107 .1780

.3525 .4?AE .4536 .4803

.2618

.1754

_2618 .2618 ,2618

.51t3 .5463

.666 .592

.428 .269

.521 .541

.5E4

.606 .620 .634 .652 .680

.0076

.0163 .0170 .0155 .0145 .0131 .0118 .0105 .0091

.12t3

lt4

.\227

125

.\248

134

.1649 .167r .1864 .1903

.1938 .1971

.I993

198

227

241 232 258 283 300

.2016

3V

.2043

340

.2068 .2089

358 377

.0344 .0326 .0309 .0285

.2229

285 319 347

.0262

-23/6 .24t0

.0238

.0221

.2267

.2299 .2340 .2433 -2455

384 416 450 471

.649

.6390

.26t8

.2361

20

.035

.6793

.2618

.2435

.496 .360

tt/t

1

t% t%

.6221

.3272

.2330

.32t2

_2409

.890 .920

_\425

.6648

2.057 1.921

.0E90

l0

.180 .165 .134

_0847

.1355

.t20

.7574

_25t

I.59E

.982 1.010

.0741

.u86

.8012 .8365

.0666

1.a32

.4612

1.094

.3272 .3272 .3212 _3?t2 .3272 .3272 .3212 .327?

.3089

.456

Ll80

.0579 .0521 .0426 ,0334 .0247

.1100 .1027 .0926 .0833 .06E2 .0534 .0395

Ll92

_3927

1.232

.3927 .3927 .3921

.3225 .3356

1.955

1.291 1.398

l.6lE

t.2E?

.3492

1258 .996

1.334

l_370

.0755

_1008

.5079

2,410

1_760

.3144

.6660

2.201 t.934

t.182

.2904

_6697

3890

.4739

.2586

.3141 .2904 .2586

.6144

4014

_4801

1.6s9

.2300

.2300

,6784

1t/t

II

lYa

t2

tYl

ty.

l3 l4

t%

t6

t)A

t\

IE 20

.083 .065 ,049 .035

t\t tw t\t

l0

.134

\2

.i09

tk

l4 l6

z

lt

z 2 2

t2

l4

.109 .095

.0E3

_8825

_9229 .9852

'\.042

.065

t.471

.120

2.433 2.494 2-513 2.642

.t09 .095 .0E3

.5236 .5236 .5236

.2644

.?t02

1,448 1.329

.2715

Ln3

.2E36

1,033 _823

1.060 1.0E4 1.120

.629

1.t52

.2932

.3587 _4606 .1665

1.810 1.834

.103

l_186 1.155

.089

L125

.065

1.556 1.410 1.339

.260 .238 .220 .196

t.284

_174

l.?3E

.153 .140

.0t7

t.411

t.2t0

.t26

0t24

_z?t8

_049

I

1.228

1.235 1.199

.5755 .5945

E

1.263

.079

.813

I

.125

.430 .364 .332 .305 .?10 .239

.2183 _2241

l8

.l4l .ll4

1299

1.493 1.366 1.316

.2618 .2618 .2618

.714

.158

1.352

550

.9lE

l5

.t7l

1.43i

.3009 .3098

.2t21

I I

.0415

.0784 .0700 .0654 .0615 .0559 .0507 .0455 .0419 .0332 .0241

_2518

l3 l4

1.126 1.536

1.103

.760 .782 .610 .634 .856 .870 .902 .930

I

1.241 L163

Ll50

1.037

-132

-0244 .(]EE6 _0694 .0511

521 567

.0051)

Lt29

.109 .095 .083 .072 .065

l133

.2484 .2532

.0067

.1990 2041

.t20 t2

1.176

1.183

.19t6

l0

.0!t7

{92

.0203 .0178 .0134

.670

I I

1.289

1.351

L46? 1.2t1

E

5q. Inch

t.D. _066

.00068 .00055

.1259 .1296 .1333

o.D.

.0392 .0350 .0321

.0307 .0280 .0253 .0227 .0210 .0166

.1354 .1159 .0931

.3140

.3V4 .3211 .3255 .3291

555 708 749 E04

852 898

.l0E

1.279 t.167

_210

.3314

921

1.149

.191

.3366

997

1.t09

.146

.341{

1060

1.075

_106

.3836 .3880 .3974 .4018

970

1.404 1.359

.565

.4052

1037

ll82

.605

'\.273

1250 1305

1.238

I440 I537

I.153

t.2t

_470 _426 .391

I

.4097 .1136 .4196 _4250 .4291

I31l

1.0E5

.185

t707

L059

_134

.1806 ,1546

_4853 .4933

1860

.t241

.50tE

.575 .476 .370

2299

1.218 1-170 1.121 1.095

3795

1.136

.709 .647

l5?6

2014

2l6l

4t2l

Ll79

.315 .304 .212

t.ll6

.293

l.\22 Ll05

.559 .500

t.090

l.0i 1.09

l

t3

l.I4

The Mechanical Design of Shell-and-Tube Heat Exchangers

109

Table 7-4 Minimum Tube Bend Radii l4l Tube Outside Dia. (in.)

Duplex, all sizes *Plain:5/s

I

Bend Radius (in.) 3 times Tube O.D.

Center-to-Center Oistance (in.) 6 times Tube OD

t3/te

15/s

1

2

131t6

2z/s

*For bends this sharp, the tube wall on the outer circumference of the tube ma\ thin down lt/z to 2 gauge rhicknesses. dependin| on condition and specific tube materiaL Morc genercus ndii \9ill reduce this thinning. TEMA presents a formula for calculating the minimum wall thickness.

VAPOR IN LET

FLUID

IN

LET

FLUIO OUTLET CONDENSATE OUTLET

Figure 7-7. Baffles can divert flow horizontally. (Courtesy of Howell Training Company.)

Figure 7-6. Although complex, this design eliminates tube vi-

bration. To use this configuration, one must be cognizant of pressure data [5]. (Courtesy of Heat Transfer Engineering, Hemisphere Publishing Corporation, New York, Washington,

D.C.)

Figure 7-8. Longitudinal baffles direct flow in the axial direction. (Courtesy of Howell Training Company.)

1

10


flow area decreases, that is, the velocity increases with an increase in the number of oasses. The control of flow in exchangers is accomplished as increases as the

well with orifice baffles. Figure 7-9 shows an annular orifice baffle. To utilize this type of design a very clean shell-side fluid is required, since the fluid must flow in the annular space between the tube outside diameter and the hole in the baffle forming the orifice. The flow at the orifice is very turbulent and the pressure drop through an orifice-baffle arrangement is very high. Consequently, these baffles are not used often in industry. Also, since the orifice baffle requires a very clean fluid, non-Newtonian fluids are completely ruled out. We will see later in the chapter that the plate fin type of exchanger is superior to the shell and tube design for many clean services. The reason for the shell and tube desisn to be dominant is because of the wider variery of fliids it can handle versus any other design. Other baffle arrangements are possible with varying baffle shapes and orientations. Figure 7-10 shows baffles in disc and doughnut shapes, which disperse the flow in a radial direction. Baffles can be cut to allow for horizontal or vertical flow in varying amounts as shown in Figure 7-11.

Figure 7-9. Annular orifices between tube outside surface and hole in baffle plate [6].

Tie Rods These are structural rods that run oarallel to the exchanger tubes through the outer perimeter of the baffles. fastened to the tubesheets such that they space and support the baffles. Tie rods, being attached to the baffle plates, also prevent them from vibrating and damaging the tubes. Table 7-5 lists what TEMA recommends as a minimum number of tie rods and rod diameters for a set of shell diameters.

Figure 7-10. Doughnut and disc type baffles [6].

Tubesheets These are the structured plates in which the tubes are connected at each end ofthe exchanger. Tubesheets come

in two basic types-single and double. Double

tube-

sheets consist of two tubesheets mounted together at each end of the tubes with a clearance between the two sheets. The reason for using two tubesheets at each end is to reduce the possibility of a leak of the tube-side fluid. Dou-

ble tubesheets are quite common with highly toxic services, where a leak cannot be tolerated. Single tubesheets are much more common than double tubesheets because ofprocess applications and economy. Typical tube-tubesheet connections are shown in Figure

1

1a

Of great immediate concern in tubesheet design is the loading induced by the tubes thermal movement, which

Table 7-5

TEMA Tie Rod Standards (in.)

Nominal

"R" Exchanger

ShellDiameter 8-15 r6-27 28-33 34-48 49-60

"c"

"R"

Exchanger Tie Rod Dlameter

& "8" Exchanger Tie Rod

irinlmum

Dlameter

of Tie Rods

3/z

3/t

4 3/a

tlz tlz tlz

Number

rlz

tlz

o o 8 10


Exchangers

is a definite problem in fixed

% Cul Bd!.d on Diomehr

tubesheet exchangers. TEMA gives two equations for determining the compressive stress induced on tubesheets for all three types of exchangers-Classes R, C, and B:

Ihis Areo Cll Ool to Arlor Vopor Passog.. Siz€ of Cul Set by Combiiolions ol Heol Troisf€r Co€llici€nt oid Pressure Drop.

: :: when Cc < ktlr z\Ku r _ | ,,-,,-,1 o. = : ll - llllJ I when C" > k#r t I lLc I o,

This Areo Reooead lron Soiil€ lo Allo* lor Liquid D,oinoqa,Sire Sel to Slil Erp€cl.d Fkr

Soltb

{iidor,

Voror Possoq. Areo

where

rl Bollh Cll or lor 0.oininq olrer lfoshout.sir. ro Suil Flor.Ihis b l'lol Becohriended tor

Should be Rrhoved

coidensed liquid

=

oy

:

t

Tubes)

rh.n

rhr

C"

: : tr : ki = :

Mun be Horironlor,

Ihe. S€dionlind0ding

(7

is High.

tloriron16l Condenseri.

I8) tlorkonlol C!l 8!ftle

Figure 7-11. Baffle details [4].

(7-2)

[rf,:i" minimum yield stress oftube material ofdesign remperalure radius of gyration of tube 0.25[d3 + (d" - 2t,)2]0 50, in. tube wall thickness, in. equivalent effective unsupported length of the

tube. in. unsupported tube span, in.

Applied Process Design for Chemicol ond Petrochemicol Plonts

Flush lo

Tube Shee

Clod Tobe Sheet

I

Ferrule,some

l/l6"to l/4' nne

0s tnner

Tube Woll 8= l5'Avirose

Beoded or Belled

Flored

We ld ed

Dupler Tube

Beoded or Eelled This Tube Moy olso be Inslolled Ploin End (No Ferrule)or Flqred With or Withoul Ferrule,

l/8"

5/16' Minimu m

I

Minimum

p-tre'' Uinirr.,Usuolly l/4"

ssq+ $\

-r)

f

lA) VeflicolCul Eoltle

Ploin

111

usn"

Typicol Grooved Detoil

Figure 7-12. Typical tubesheet-tube connections [4].

112


r {o' ['o : 4 : oc : Et

for unsupported tube lengths between two tubesheets

for unsupported tube lengths between

where f" : C:

mode constant from Thble 7-6 span length, in.

I: E= I = W: Wt : Wq : W6o :

a

tubesheet and a baffle for unsupported tube lengths between two

baffles

modulus of elasticity of tube material at mean tube metal temperature, psi outside diameter of tubes, in. allowable tube compressive stress, psi, for the tubes at the outer periphery of the tube bundle

Equation 7-1 is based on Euler's columl equation and Equation 7-2 is based on the short column formula developed by Professor J. B. Johnson during the nineteenth century. Other TEMA formulations are summarized in the following sections. The reader is urged to be familiar with the TEMA standard and follow its guidelines in designing a shell and tube heat exchanger.

tube natural frequency, Hz

modulus of elasricity. psi moment of inertia, in.a (Table 7-3)

Wr

+

Wn

+

MWr", lbs/ft

weight of empty tube (Table 7-3) weight of fluid inside tube 0.00545 p"d"'?

M : added mass coefficient from p : fluid density, lbs/ft3 d : diameter of tube, in

Table 7-6

subscripts:

i :

o:

inside outside

Allowable Tube Compressive Stress-Periphery of Bundle. The allowable tube compressive stress, psi, for the tubes at the periphery of the bundle is given by:

TEMA Formulations

a,:ffi-28

Baffles and Support Plates Natural Frequencies ot Straight Tubes on Multiple Equal Spans

-r

s"=\l - 21r -

when C.

-. I (kur)l 2C"l

s

kf/ror

whenc >kur

/:*

3.36C

where

C"'Vsr = l/

^

Table 7-o

Mode Constant-C Extreme Ends Supported No.

of Spans

lst

I

2 3

4

Mode

31.73 31.73

3r.73

5 6 7

31.73

9

31,73 31.73

a

to

2nd Mode 126.94

[21

Extreme Ends ClamDed

,l-r+r

Fr-l-'-l*,.1 |--___l /T-7\--lzf-R lst

Mode

2nd Mode

49.59

49.59

37.O2

37.O2

198.34 72.36 59.56 49.59

34.99 34.32 33.67

34.99 34.32 33.67

40.52 38.40

&.52

33.O2

33.02

72.36 40,52

33.02 33.02 33.02

p1d1,

weight of fluid displaced by tube 0.00545

Extreme Ends Clamped-Supported

r-fr-fr

lst

Mode

49.59 37.O2

34.32

44.r9

37.O2

34.99

znd

Mode

160.66 63.99 49.59 42.70

39.10 37.O2

32.37 31.73 31.73

35.66 34.99 34.32 33.67

The Mechanical Desien of Shell-and-T[be Heat Exchansers yield stress, psi, oftube material at design metal temperature used. radius of gyration of tube

0.25

KT:

.vu +la" -

2tJ1,

only, may be calculated as follows: 2.74C" R2

where

fnu

R

=

: :

U-tube natural frequency, Hz mode constant for U-bend bend radius, in.

spans between two tube-

Note: For other than simple support conditions the calculated frequency may be estimated by multiplying the above

spans between a tubesheet

value for f,, by the appropriate ratio of mode constants from Thble 7-6 using single span values.

sheets.

0,8 for unsupported

quency, assuming simple supports and for the first mode

in. (Table 7-3)

equivalent unsupported buckling length of the tube, inches. Use the largest value considering unsupported tube spans. unsupported tube span, in.

0.6 for unsupported

113

and a baffle. 1.0 for unsupported spans between two baf-

fles.

Note: The value of S" shall not exceed the Code allowable tensile stress of the tube material at desisn metal temperature used.

Effect ot Longitudinal Tube Stress

ASME Tube Joint Load Grlteria

I

The ASME Secrion VItr Division Dressure vessel code lists formularions in evaluating tube forces exerted on tubesheets. Referring to Figure 7-13 and Table 7-7 the formulas for the maximum tube force are as follows:

Dt2

'Er.,j where fnp

:

tube natural frequency in stressed condition, Hz tensile, negative for compressive)

P = axial force, lbs (positive for

Natural Frequencies of Straight Tubes on Unequal Multiple Spans

f" :

For

F, :

joint types a, b, c, d,

(7-3)

A,o,11f,

For joint types

F,

:

e:

f, g, h, i, j,

k: (7-4)

A,o"11f,f"f,

where

:

maximum tube joint force, lb1 cross-sectional metal area of tube, in.2 oall : ASME maximum allowable stress. psi f= joint reliability factor

Ft

10.83 t'z

f. (no tesg = maximum value without test given For a tube on multiple unequal spans with the extreme ends fixed and simply supported at the intermediate supports, ki can be obtained by solving the following characteristic determinant for an n span system.

Natural Frequencies of U-Tubes. It must be recognized that each tube is a continuous beam that has a single fundamental frequency. This frequency may be largely governed by the lowest "stand alone" frequency of either the longest straight span or the U-bend. It is suggested that both be calculated and that the lower value be used, keeping in mind the approximate and somewhat conservative nature of the result. The straight span frequency may be determined from Thble 7-6 using the appropriate mode constant. The U-bend out-of-plane fre-

f, (teso

:

in

Table 7-'7

maximum value with test as specified in

the ASME Section

VIII Division

1

code, per section UA-002

Figre 7-14 shows how the tube joint load varies for various tube gauges of various process conditions. Naturally, as the tube wall increases, the tube stiffens and, consequently, the force exerted by the tube on the tubesheet joint increases. The engineer should evaluate the tube loads with the various process conditions possible and use the worst for determining the maximum tube joint force, as shown in Figure 7-14. The TEMA standard gives the formulations to determine the tube ioint lorces and the user is referred to this standard for these expressrons.

The buckling of exchanger tubes can be a problem if thermal expansion is not properly accounted for in de-


114

Table 7-7 Reliability Factors, f,

Joint

Type

Notes

Descriptions Welded only, a> 1.4r Welded only, tsa
a

b

(1)(7X8) (1X2) (1X3) (1X6) (1X7X8)

Brazed, examined Brazed, not fully examinable Rolled, welded, a> l.4t Rolled, two or more grooves, and welded, a< l.4r Rolled, single-groove, and welded, a < 1.4r Rolled, no grooves, and and welded, a < 1.4r Rolled, two or more grooves Rolled, single groove Rolled, no grooves

c

d

f c h I

j

k

[71

l. (tesr)

f, (no test)

1.00

0.50 1.00

0.80 0.55 0.80 0.40 0.80

0.95

o.75

0.85

0.65

0.70 0.90 0.80 0.60

0.50 0.70 0.65 0.50

0.70 1.00

(1X4)(s) (7) (l

)(4)(s) (7)

(l)(4)(5) (7)

(l)(4xs) (l)(4x5) (l)(4)(5)

Notes: (l) The use of f. Ceso factor requires qualification in accordance with UA-003 and UA-004. (2) For welds where a is less than t, fi (no test) 0. Tubes with Type (b) joints where a
-

P=

d" + 0.165 (d" + 2r)

= nominal pitch (center-to-center distance of adjacent tube holes), = tube o.D_, in. I = nominal thickness of average wall tube, in.

in.

except that:

(a) nominal pitch shalt not be less than 4 + 2t unless the joint is qualified in accordance with UA-003 and UA-004; and (b) 96% of the ligaments between tube holes throughout the thickrcss of the rnachined tubesheet shall not be less than 0.85

(P-4). Ligaments which do not meet this requirement shall be evaluated and €orrections made as may be necessary. (6) A value of .50 for f, (test) or .40 for f, (no t€so shall be used for joinls in which visual examination will not provide proof that the brazing filler metal has penetrated the entire joint Isee US-14(b)1. (7) The value of f. (no test) applies only to material combinations as provided for under Section IX. For material combinations not provided for under Section IX, f. must be determined by test in accordance with UA-003 and LIA-0O4. (8) For joint types involving more than one fastening method, the sequence used in the joint descriptions does not necessarily indicate the order in which

the

oDerations are Derformed.

sign. One such formulation to predict the critical buckling load is as follows:

P.,

q'' t0.5216r - , " ,, I L** l' \Ns + t/

where L,u6"

:

NB :

t7-51

total length of tubei between tubesheets number of baffles

Equation 7-5 is based on the Euler column formula. In situations where there are several baffles, such that the effective length, L", divided by the radius of gyration, k, is between 30 and 120, exclusive, then the Johnson short

column equation is more accurate. For a tube to be considered as a series of short columns constrained by fixed ends, one must be certain that the baffles constraining the tubes allow practically no translational or rotational movement. The stiffness of the baffle plate should be

analyzed, as small translational and rotational tube movement allowed by the baffle plate could considerably alter the buckling characteristics of the tube. The evaluation of a baffle plate containing several tubes can be a somewhat detailed analysis, and it may be faster to consider the tube as a continuous beam in determining buckling characteristics. For further details on the mechanical design of exchangers, the reader is referred to TEMA. We will discuss tube vibrations shortly.


PBOCESS EVALUATION OF SHELL AND TUBE EXCHAI{GERS

mechanical engineering coincide. Thus, the mechanical engineer must be cognizant of process evaluation of heat exchangers in order to design these units. A thermal evaluation of shell and tube heat exchansers concerns primarily two modes of heat transfer-conJuction and convection. In Chapter 3 we considered heat transfer through piping and vessel components as well as jacketed systems. As described in Chapter 3, the basic expressions used in conveetion are as follows:

We are concerned here only with any particular heat exchanger and determining whether it can transfer heat energy as required. How the unit affects process conditions of the entire system is not our concern here, because we are interested only in the proper performance of the unit. Evaluating the exchanger in relation to the process system is the primary concern of the chemical engineer. The thermal evaluation of the exchanger is one area where chemical and mechanical engineering overlap; just as in Chapters 2 and 4 we saw how civil and

: q: q

rhcpat

(3-24)

UA(LMTD)

(3-26)

t2l

{1t Some ecceptable weld geometriea where

t

is not less

(61

lhan

Exchansers t15

l.4t

l7l

(81

Figure 7-13. Joint types [7]. (Courtesy of ASME.)

116


J

;

sooo

l! F

=

-

7t)00

U ul .o

*

6000

.o5 .o5 st

.oa .o9 Jo 11 12 13 .1+ .15 16

t7

TUBE WALL THICKNESS Iin|

Figure 7-14. Tube joint loads.

Equation 3-9 is a variant of Fourier's heat law of conduction in which,

q: KAAI

(7-6)

The treatment of shell and tube exchangers requires the same basic theory for use in Chapter 3, but a different application. In these types of exchangers we are pri-

marily concerned with the heat duty or heat load required in the same general sense as the jacketed vessels

in Chapter 3. Process requirements are the criteria used to determine the heat duty. The two basic components of heat transfer in the shell and tube exchanger are sensible heat and latent heat. These concepts are described mathematically with the use of Equation 3-24. Using this relation we have:

q = r;cp(ao q

:

rimrg

(7-7) (7-8)

The Mechanical Design of Shell-and-Ti.rbe Heat Exchangers

Equation 7-7 determines sensible heat change and Equation 7-8 determines latent heat change and is a form of Equation 3-13. You will recall that sensible heat is the amount of heat energy required to either heat or cool a given mass (solid, liquid, or gas-without a phase change) to a measurable degree. Thus, if we have a kettle full of water and we heat the water mass at atmospheric pressure to 212'F, adding additional heat to the kettle will not raise the temperature. Thus, the sensible heat is the amount of heat required to raise the water temperature to 212'F. The additional amount of heat required to convert the water to steam is called latent heat. Sensible heat can be detected by the human senses and thus physically measured, as with a thermometer. Latent heat is heat energy that cannot be detected by the human senses and is more intrinsic to the basic nrocess-the hot steam plus the additional heat provided- to rhe kertle to convert the water to steam. While these terms are rudimentary, their importance is fundamental to heat exchangers. Combining Equations 7 -'7 and 7-8 we arrive at the total heat duty of the exchanger as:

q:rirco1a9:rirtrr,

\'7

117

pass to another in a muhipass exchanger. Figure 7-15 illustrates how a different LMTD occurs for each oass. showing that using the inlet and outlet ofrhe rubesid; and

shellside would not produce an accurate LMTD value. Thus, the value obtained from Figure 3-10 must be multiplied by a correction factor, F, as provided in Figure 716. These correction factors were tabulated by TEMA and are determined by the "P" and "R" parameters shown in Figure 7-16. For a true counterflow or parallel exchanger a correction factor is not necessary. Use of these tables is demonstrated in the examples which follow.

It should be pointed out that the straightline exchanger curve in Figure 7-15 is for a single-component fluid. Most industrial applications are multicomponent mixtures. Chemical engineers do vapor-liquid equilibrium calculations that show vapor and liquid compositions in multicomponent mixtures to be different and changing within the exchanger. Thus, real curves are not straight, but often can be approximated as such in multicomponent flow. Assuming a straight line is a source of many oesrsn errors.

-9)

The first term on the right side of Equation 7-9 represents the sensible (cooling or heating) heat and the sec-

ond right-hand term represents the latent (condensing or boiling) heat. In Chapter 3 we discussed the LMTD and the reader can use Figure 3-10 to quickly determine this parameter. The difference between that value used in Chaoter 3 and the application here is that the LMTD will vary from one

Tube Wall Temperature and Caloric Temperature Chapter 3 dealt with the LMTD in the computation of heat transfer problems. One of the assumptions used in defining the LMTD is that the overall heat transfer coefficient, U, remains constant. With multipass exchangers this is certainly not always the case, as indicated by Figure 7-15. Even with counterflow exchangers, as the cold fluid gets hotter, the viscosity decreases, changing the

overall U-value. In many instances, the U value will vary more than the inside tube coefficient. Colburn [8] addressed this problem by assuming that the U value will change linearly with temperature and deriving an expression for the temperature differential. Colburn thus elected to obtain a single overall coefficient, U,, at which all heat transfer surfaces can be assumed to transfer heat at the computed LMTD. In this way the overall U-value, U*, can be expressed as

r. E

P

\|TTD/

Toral Heat Transler, Btu

Figure 7-15. The amount ofheat transferred varies from to another [4].

pass

a_ ,, IGTTD - LITD ;- uxt,l I\ r" lcrrDl

I

(7-10)

I /

Such a value of U* exists at a temperature, t", known as the caloric temperature. It is this value of t" at which the inside and outside tube film coefficients, h1 and h., respectively, are evaluated. The caloric temperature is found by multiplying the respective hot and cold temper(tert continued on page 122)

118

Mechanical Design of Process Systems r.0

5 F

o.s

2 (l

o -.'

:

P .TEMPERATURE EFFICIENCY

I

/tL--.....-.-,

lr-t' l.-+<_

LMTD CORRECTION FACTOR SHEIL

PASS '

D

!

EVEN NUMBER OF TUBE PASSES

-.:l-J

Gl=

T,-t,

r

'2

-l/ oa

o

F

O.9

z

9^"

o 0.7

= o.6

P

.

03

0.5

0.6

T€MPERATURE EFFICIENCY

LMTO CORRE

2

SHETL

PASSES 4 OR MUTTIPLE OF 4 TUBE PASSES

P'++

I:I Q-tr

Figure 7'16. LMTD correction factor. (@1978 Ttrbular Exchanger Manufacturers Association.)

The Mechanical Design of Shell-and-Tlrbe Heat

Exchangers

5 o.g F

z

I

o.e

o o.7 F

o.6

P

'

TEMPERATURE EFFICIENGY

3 SHELL

LMTD CORRECTION FACTOR PASSES 6 OR MORE EVEN NUMBER OF TUBE PASSES

P'++

I:l

R' tr-1r

P o.s 2 o

tr

o.8

o

O.7

F

t

o.6

T-

4

SHELL

LMTD CORRECTION FACTOR OR MULTIPLE OF 8 TUBE

PASSES 8

gHELIS

I I

-r_

"'++ Figure 7-16. Continued.

]-J

tr- tr

PASSES

119

'120

Mechanical Design of Process Systems t.o

E

P o.g

z tr o.8

tr o.7

:

5

SHELL

PASSES

10 OR MORE EVEN NUMBER OF TUBE PASSES

r'#-+ .t

o.3

0.4

Tr-Tr

"=

0.5

0.6 P = TEMPERATURE EFFIoIENcY

LMTD CORRECTION FACTOR 6 SHELL PASSES T2 OR MORE EVEN NUMBER 9:-]3-J ' T,-t' Figure 7-16. Continued.

R

=

-l--3

OF

IUBE PASSES


Exchangers

P =TEMPERATURE EFFICIENCY

I

DIVIDED FLOW SHELL

PASS

o. -13--:!

'

I

T,-t,

EVEN NUMEER OF TUBE PASSES

I-I,

o.g

z

P o.t

o F

o.7

= o.6

P.IEMPERA

LMTD CORRECTION FACTOR

SPLIT FLOW

SHELL

e'f{ Figure 7.16. Continued.

2

''r-rE

TUBE PASSES

121

122


ature differentials by a caloric fraction, F". That is, the fraction, F., is multiplied by the temperature rise of the controlling stream and adding the resulting rise to the lower terminal temperature of the stream. Figure 7-17 helps in determining the controlling streiim. Colburn [8] correlated the data for the insert in the top left-hand corner of Figure 7- 17. The fluid stream, either shell-side or tube-side, that has the largest U-value corresponds to the controlling heat transfer film coefficients, h1 and h., which are used to determine U*. Basically, rhis implies that we must find the values of U6 and U" for both separate streams, and the stream that has the largest c value, based on Figure 7-17 is the one used to compute h. and hi in computing U,, where Uh is the overall heat transfer coefficient at the hot end of each respective stream and Uc is the overall heat transfer coefficient at the cold end of each respective stream. In equation form we express the caloric temperatures as derived by Kern [9] as follows:

t* =

The hot fluid caloric temperature ls

h1"

:

ho

:

tqh:th.*F.(th,-th")

(7-1 1)

The cold fluid caloric temperature is

r.c: tc + F"(t." - r") where tch : caloric temperature ofhot fluid, .F th" : outlet hot fluid temperature, oF 1,, : inler hot fluid temperature. .F t.. = caloric

t" :

tc"

F"

: :

(7

-r2)

temperature ofcold fluid, .F

inlet cold fluid temperature, .F outlet cold fluid temperature, "F correction factor determined from Figure 7-16

Outside tube wall temperature for the hot inside of the tube is

fluid on the

hi^

,

nio

f-

no

(t.h - t".)

(7-

l5)

or

t.h

h +. ]:.

n,.

+

(r.r, no

- l.)

(7

-16)

Thus, the pipe wall temperature can be computed when the caloric temperature values are determined. The temperature difference across the tube wall is customarily assumed to be negligible because the entire tube is at the outside surface temperature. The terms in Equations 7-13 through 7-16 are as follows:

t* :

tube (outside surface) wall temperature, 'F inside film coefficient of tube using outside surface temperature, Btu/hr-ft2-' F outside film coefficient of tube, using outside tube surface temperature, Btu/hr-ft2-'F

The tube wall temperatures are to be used in computing thermal movements of the tubes and all other mechanical computations. As explained previously, these tube wall temperatures are based on the caloric temperature values that truly reflect the mean value of the varying values of h1, ho, and U,. It is a common oversight in exchanger design to use the arithmetic mean rather than the caloric values. Equation 3-26 should not be used because Equation 7-10 more accurately describes the true mean values in the exchanger.

Overall Heat Transter Coefficient Once the hot and cold caloric temperatures are determined we can now compute the tube wall temperature, because the caloric temperatures represent the true mean values for the varying values of U^, hi, and h". Kern [9] has expressed the tube wall temperatures in the follow-

ing forms: Outside tube wall temperature with hot

fluid external

to tube is

The thermal duty of an exchanger cannot be discussed without first defining the overall heat transfer coefficient, or "U-value." This parameter is referred to in the previous discussion and it is noted that this value can vary with various types of configurations. Now, after discussing how a variable U-value is handled on multipass units using the caloric temperature, we are ready to treat the overall coefficient in detail. The overall heat transfer coefficient, denoted as U, is defined as follows:

hi..

t" = t.r, .n,o + -

(t"n nu

-

r...t

(.7

-13)

or

t" = t.r,

u=

l,TuT,tT" -r-

hi Kr, k" h" n,o

-

+

(Lr, no

-

t".J

(7

-14)

where

hj

Tn

(1- 11)

-h.

-l-

-k.

= inside tube film coefficient, Btu/hr-ft2-'F = thickress of inside tube deposits. ft

The Mechanical Desien of Shell-and-Tirbe Heat

Exchansers

123

E

ut

e 3 t4 ul

g

4

= F

u,l

e 3 |'|-

ul

() e ul

tlll .f J

.9

s'

F o\

o o

t\ to tt

;l; lJ 110 J0

rr|ivr9 'l 'd'v

:

124


kn

:

T" = k* : ho Tro k,o

: : =

thermal conductivity of foreign deposits on inside of tube, Btu/hr_ftr_.F tube wall thickness, ft thermal conductivity of tube wall,

it contacts tube surface, resultinq in a coating effect. Thus, the depositing of foreign miterial adds to the resistance of heat flow from the tube and she side flows. Fouling can occur inside and outside of tube surfaces. The complexity of fouling and how it occurs does not easily allow this phenomenon to be treated analytically. There are far too many variables involved for one to accurately compute fouling factors. Thus, this phenomenon is treated in a more subjective light, using experience as a guideline. Years of experience with various services have resulted in the use of accurate foulins facphases when

Btu/hr-ft2-"F outside tube film coefficient, Btu/hr-ftr-.F thickness of outside tube deDosits. ft rhermal conductivity of deposits on outside of tube, Btu/hr-ft2_oF

The terms in Equation 7-17 , llh, T/kf, and T*/k*, are known as film resistance, fouling resistance (we will refer to this as fouling factors), and tube wall resistance, respectively. These parameters represent the resistance to heat flow through the fluid film, foreign deposits, and the tube wall. This is shown in Fisure 7-18 where the temperature is shown varying throGh the various resistance zones. This figure is a conceptualization of the temperature profile, as the degree of gradient change in temperature is a function of the flow conditions daminar versus turbulent) and on the type and amount of foreign deposits. To understand Equation 7-17 we will discuis each resistance separately.

Fouling of Inside and Outside Tube Surfaces Fouling occurs when deposits are made on the walls by particles contained in the fluid medium or bv the fluid itself forming a layer on the tube walls. This can occur two ways, either by adhesive characteristics of the deposited matter or by the foreign material being bonded to the tube surface by thermal gradients between the tube wall and the foreign material, so that the latter chanses

tors.

Fouling factors are very important in the design of shell and tube heat exchangers. Bare or plain tubes, which are almost always used, generate low U-values when compared to those generated by tubes with fin attachments. Finned tubes, especially those with fairly high fins, experience very little fouling unless the deposIts cover an appreciable portion of the fin height. With the normally accepted long periods between tube cleaning in plants, fouling certainly must be considered in the calculation of the U-value. One must be aware of the shell- and tube-side fluids and select those foulins factors thar best reflecr the op{imum fouling thar williffect thermal duty. The fouling factor in Equation 7-17 is T/fu. This term is the inverse of the thermal conductance of heat throush the foreign matter. denoted by k,/T,. Thus, the reciproial of the thermal conductiviry of the foreign material is known as the fouling factor. Fouling can exist on both or one side of the tube. Typical values for fouling factors for common services are siven in Table 7-8.

Direction

+ Att

At1 = Temperature drop through inside

Att

Atz = Te6p"tu,ur" Orop through laminar boundary tayer inside

Atr At. At"

-----T At,

turbulent boundary

rayer

tube

Ats = Tsrnpsr.lrra drop through fouling layer inside tube At4 = Temperaiure drop through tube wall Ats = Tsrnpg,.1r,a drop through outside touling layer At6 = Temperature

drop through outside laminar boundary

rayer

Atz =

T66p"r"rrr" drop through outside turbulent boundary taver

Figure 7-18. Temperature profile through tube wall.

n

fl


Table 7-8

Recommended Minimum Fouling Resistances Fouling Factor

Gases and vapors Cenrrifugal compressor exiaust Reciprocating compressor exhaust Reciprocating compressor refrigerant vapor Centrifugal compressor refrigerant vapor

Oil-free and clean high-quality steam Oil-free and clean low-qualitv steam Oil-bearing steam Compressed air

-

l-,iatural gasl

Liquiafs Bay water

-

0.002s 0.0015 0.0003 0.0005 0.001

-

Acid gas ;olr€rt rapors

0.001 0.01

0.002 0.001 0.001 0.001

Fuel oils

0.0025 0.0005 0.0033 0.0033 0.0015 0.0012 0.0015 0.006

Clean organic solvents

0.001

Vegetable oils

0.004

Refrigerant liquids Industrial heat -transfer oils

0.001 0.001 0.001

Distilled water Hard well water Untreated cooling tower water Treated cooling tower water

Engine jacket water Treated boiler feed water

Hydraulic fluid Natural gasoline and liquefied petroleum Rich oil Lean oil

gases

and Tate as fbllo$

N-,"

:

coetTicienr

\\:, : \r. : :

\p.

L

=

greater heat transfer between the shell-side and tube-side fluids, resulting in higher film coefficients. For a more detailed discussion of boundary layer theory one is referred to a basic text on heat transfer, such as the l/andbook of Heat and Mass Transfer, Volumes I and 2, N. P

Cheremisinoff, ed., Gulf Publishing Co., Houston, Texas, 1986.

oi thernal conductivity of fluid

rn,lde rub('. lJlu hr-ft- "ts \usselt number (see Chapter 3) Re) nolds number Prandd nunber (see Chapter 3) total tube lensth. ft lluid viscosity at bulk tenperature. Ib,,,/ft-hr

or cp

fluid viscosity at wall, lb./ft hr or cp The viscosity at the wall, p,", should be evaluated using either Equation 7-15 or Equation 7-16. The bulk temperature of the fluid is in practice the average of the inlet and outlet tube fluid temperatures. For turbulent flow inside tubes wall effects can play a role in the film coefficient value. The correlation that is widely used is the one developed by Sieder and Thte, which is as follows:

In the region close to the tube wall the fluid becomes stagnant and forms a film around the tube surface-on inside and outside surfaces. This stagnant region is called the "boundary layer" because it forms at the boundary of the tube wall. The size and properties of the particular boundary layer are a function of the fluid properties itself and whether the fluid flow is either turbulent or laminar. Turbulent fluid motion always leads to

(7-18)

inside pipe or tube diameter. ft

where

i

Tube Film Coefficients

s:

= r 86{Nn.)r' (\,.)'' (q)'" (4)'''

T

0.002

-

125

Inside Tube Coefticients. In Example 3-5 we used correlations to determine film coefficients inside tubes. Here, we will give a more comprehensive treatment of film coefficients inside tubes. In laminar flow there is more fluid stagnation around the tubes because in the boundary layer itself the flow is laminar, whereas in a turbulent boundary layer the sublaminar boundary layer is only a small percentage of the total layer. Thus, fluid properties at the walls in laminar flow must be evaluated. The laminar film coefficient is largely dependent upon the viscosity and, thus, the temperature (which controls the viscosity) of the wall controls the value of h. The most commonly used correlation for laminar flow inside pipes is that given by Sieder

0.001 0.00

Exchangers

NN,^

"

:

for 0.7

/ \o 14 0.027(NR"ro

<

Np,

<

\N.,t' '

l4l \4"/

(7-

le)

17,000

As for Equation 7- 18, the value of p*, should be determined using temperature values calculated using Equations 7- 15 or 7- 16. McAdams [10] suggests that for temperature differences between the bulk fluid temperature and the pipe

wall surface temperature the following expression can be used:

Nu, = 0.023(NnJo 8(NrJ"

(7 20)

126 where

Mechanical Design of process Systems

n = 0.4 for heating n : 0.3 for cooling

Nr,

And the temperature differences are as follows:

At At At

: pipe surface temp-bulk < lO'F for liquids < 100"F for gases

fluid temp

Outside Tube Film Coefticients, Forced convection around immersed bodies is a complex subject, especially when a bundle oftubes is involved. We will only give L rather brief discussion of how one can obtain a s;neral

magnitude of film coefficients. The -reader should be aware that process design is not addressed. Thus, for solving problems dealing with condensation,

order

of

nucleate boiling, and film boiling-to name a few_the reader should consult other sources that treat Drocess de-

sign in detai[ [4.81. For gases flowing normal to circular cylinders a simple relationship is contrived by M. Jakob [1] using an dyercge Nusselt number for the gas. An empirical version of this expression is given by hd,

where h

:

= C(NIJ"

('7

-2r)

hd'

-

:

Kf

Forced convection normal to tube bundles is mucl: more complex than that of a single tube. The size of the bundle and how the tubes are oriented (tube pitch ar_ rangements) in the bundle are of prime importance. First. we will discuss an approach io determining the film coefficients for bundles and then discuss the mr-erits of arranging tubes in various geometries. There are four basic types oT tube arrangements-tri-

angular pitch, inJine triangular pitch, inJine square pitch-, and diamond-square pitch. These four geomelries are shown in Figure 7-19. Tubes arranged in bundles are more complex than a single tube becaule the flow vortices formed by the flow around the first tubes affect the

flow around the tubes farther inside the bundle. Mose

researchers agree that this transient effect is substantially dampened after the flow passes over the first ten tubei.

Numerous research studies have been made that analyzed flow effects on tube bundles. E. D. Grimson [12] concluded from several studies that for tube bundlei ai least l0 tubes in depth the following expression can be used to predict the film coefficient: hd,

:

B(pvd"irr.r)"

-23)

average

where

pf

: _: h p: ki :

A variant of Equation 7-21 is widely used for forced ofair normal to a cylinder is given by the fol-

B and n do

Range ol Reynolds Numbers 0.989

40 < NR" < 4000

0.683 0.193 0.027

4000
: =

Reynolds number at maximum fluid

velocity,

0.91

I

V.",

film coefficient, Btu/hr-ftr-.F air density, lb./ft3 thermal conductivity of fluid, Btu/br-ft-'F average

constants given in Table ?-10 tube outside diameter

(4, Triangular pitch,

NR" <4.0 NR" <40

lb-/ft-hr

Figure 7-19):

Circular Cylinders

40,000
absolute viscosity,

The Reynolds number in Equation 7-23 is evaluated at the maximum fluid velocity. This velocity is obtained at the minimum flow passage between the tubes. This minimum distance is shown in Figure 7-19. Tbe minimum distance is expressed in terms of the tube bundle geometry for each of the four configurations. as follois isee

Table 7-9 Parameters for Fluid Flow Normal to

0.40<

:

V : velocity of air, ft/hr

Nx"

convection rowrng:

<

(7

k1

film coefficient for gas, Btu/hr-ft2-.F dt = tube diameter, ft ks : gas coefficient of thermal conductivity, Btu/hr-ft-.F C and n : parameters from Thble 7-9

4

C(PJ'/r(NRJn

d-,"

: * 2''

0.330 0.385

(b) InJine triangular pitch, dni"

0.466

(c.l

0.618 0.805

.

=W

-

d,

InJine square pitch, dmi. = W (d) Diamond square pitch, d.;" : P cos 45' 0.707p - D

-

D

:

The Mechanical Design of Shell-and-T[be Heat

Exchangers

127

(B) Inline triangular pitch-apex facing nor-

(A) Triangular pitch-apex facing tlow

mal to flow

l

Flow

+

+

+++ 9-

(D) Oiamond squars pitch

(C) Inline square pitch P=

Pitch

Figure 7-19. Tirbe bundle anangements.

Table 7-10 Grimson Constants for TUbe Bundles Containing 10 or More Tube6 w/do Ratlo Tube

wdo

Bank Geometry

Flgure 7-19)

Inline

t.25

.348

1.50

.JO

2.00 3.00 0.600 0.900 1.000

Staggered

1.25

(see

/ .418 .290

2.0

1.5

.5E2 .586 .570 .601

Bn

B .275

.608

.100

.7U

.250

.620

.101

.299 .357

.@2 .584

.229

.702 .632

.cgl

.))a

.581

.063 .068

.752

.74

.198

.&8

.286

.608

.213

.636

.446

.571

.401

.581

.565

.Jl6

.560

.srs

.so

.478

1.250

.505

.ssc

.519

.451

.4U

.460 .416

.562

2.000 3.000

.568 .572

.452 .482

.522 .488

.562

1.500

.556 .s68 .556

.310

.592

.356

.562

.421

t.125

.568 .580

.40

.449

.568 .570 .574

128


The cross-flow are for various types oftube bundles is shown in Figure 7-20. From the concept of continuity, where for two points . along a flow path, or streamline,

: V2A2 where V1 : velocity of fluid at point I, ftlsec Al : cross-sectional area, ftz VrAl

'A )
e-24)

\@

we can deduce

For staggered and iniine tube arrays,

:

With all tubes being placed at a constant pitch and Vr Vr : fluid velocity, we have

v.,, = v'l+l

(7-2s)

\o.,"i

o,

=

o'10 - p,"" * 9!: *]44 [o" Pn - [

o,yl "l

,rc

For triangular layouts,

.= B n. r++

[^ - -D," + o,^-dr. ..1 .^ (P - dJl [D"

+---i

,rt'?

where, DL = OD of tube bundle D" = lD ol shell dr = OD of tube

Equation 7-25 represents the fluid velocity that would be used in Equation 7-23. For tube bundles containing less than l0 tubes, values

of the film coefficient in Equation 7-23 must be multiplied by the correction factors in Table 7-1 1. Each tube pitch arrangement has its own advantages and disadvantages. A listing of these facts is given in lable 7-12. Whatever the tube arrangement selected, the tube arrangement in the tubesheet should be made verv carefully. Clearances, which could be such items as impingement baffles, channel and head baffle lanes, must be considered. Table 7 -13 is a compilation of various industrial standards for tube sheet layouts. Fipure 7-21 shows a typical tube sheet layout. One of the easiest and most common methods used to calculate shell-side film coefficients is that proposed by Kern [9]. The Kern correlation, which is used for all fluids. is as follows:

'lu l' ' o ro lq"o)"'l,9url' k \p/ \t/ \pJ

h"&

B = baffte spacing

Ar = flow area-cross-llow area for one s€ction tween two baffles

Figwe 7-20. Tube bundle cross-flow

area.

(7-26)

or

h"rD":

o.:orN""f

t,*rr"t

(")o''

Equation 7-26 is divided into two components, jH and Np" in which

Figure 7-21. Typical tubesheet layouts.

T

:iw


j":+H'(,+) Table 7-1

where h.

-27)

film coefficient, Btu/hr-ft

"F

G,

flow rate of fluid, Iby/hr

mass

thermal conductivity of shell-side fluid, Btu/hr-

ft-"F D. = shell-side equivalent tube diameter, in. C, : sPecific heat of fluid, Btunb-"F

123456789

0.64 0.80 0.87 0.90 0.92 0.94 0.96 0.98 0.99 Staggered 0.68 0.75 0.83 0.89 O.92 0.95 0.97 0.98 0.99

('7

outside tube bundle

: k:

Kays and London Constants for Tube Bundles Containing 9 Tubes or Fewer Number of Tubes

In-line

:

1

129

For a square pitch tube arrangement,

l(p: -

nd; )

l

i-

(7-28)

?iorn

Table 7-'12 Pros and Cons of Various Tube Arangements Tube Pitch

Arrangement Advantage Disadvantage Yields higher film Medium to h igh Pitch coefficients than pressure drop. in-line square Cannot be used in pitch. More tubes foulrng serrice.. can be contained in Can only have shell becau.e of chemical cleantng.

For a 60'equilateral triangular arrangement,

D.

:

.1(0.-13o:

-

-_:

0.5rdi

ilt

(.7

in

29)

a

(a) Triangular

(b) In-line Triangular Pitch

compact arrange-

g rcB'

ment.

p(144)

Film coefficients

Medium to h igh

are not as high

pressure drop. Can only have chemical cleaning.

as

triangular pitch, but greater than inline square pitch. Suitable for fouling conditions.

(c) InJine

Good for condi-

Relative low film

Square

tions requiring low

coefficients.

Pitch

pressure drop.

Ar-

for easy

access

of

Square Pitch

pitch. Easy access for mechanical

cleaning. Good for

fouling service.

ft:

17-30

r

D, = ID of shell, in

c: clearance bgtween tubes nleasured along tube pitch, in. B : baffle spacing, in. G, : mass flow rate of fluid, lb,/hr G.:th p : viscosity of the shell-side fluid at the caas

at the tube

wall

temperature, lb/ft-hr

tubes for mechanical cleaning. Good

for fouling service. Better film coefficients than inline square pitch, but not as good as triangular or in-line

ft:

loric temperature, lb/ft hr p* = viscosity of the shell-side fluid

rangement allows

(d) Diamond

uhere p : tube pitch. ir. d,. = ID of shell. in a, : flow area of tube bundle,

Relative low film coefficients. Does not have as lowpressure drop as

the inline

square

prtcn arrangement.

The parameter js is plotted against Nx" in Figure l-22a. The value ofjH is determined from the figure after the Reynolds number is calculated. Then from Equation 7 -27 the film coefficient is determined. The use of baffles is extremely important in directing the shell-side flow, tube support, and controlling the shell-side flow rate. As the number of baffles is increased, the flow rate increases. Likewise with an increased flow rate, the pressure drop increases substantially with an increasing number ofbaffles, with the film coefficient increasing as well. Ludwig [4] reports that for a constant flow rate, the velocity across the bundle is doubled with an increase in the film coefficient of approxirnately 44%

.

(text conttuued on page 139)

130


Tube Count for TEMA

Fixed Tubesheet

Outside Packed

No. ol Passes

No. of Passes

Head

668

588

18 t2 26 24 52 48 98 84 142 t28 168 156 232 220 798 292 388 3s2 484 456 570 s48

922

902

812

808

22

10.02

0

12.N

170 212

21.25 23.25 25.00 27 .00 29.00 31.00 33.00 35.00

P

70 t6 30 28 66 60 106 96 164 148 196 r88 270 252 348 332 440 420 554 524 646 612

5.047 6.065 7 .981 13.25 15.25 17 .25 19.25

Table 7-13

in. OD Tr.rbes on 13^6-in. A pitch

TEMA

LorM

Shell lD in.

g/a

68

283

3&

454 562

1230

868

l2t2 lt72

1590 1560

1516

TEMA Type s Head No, ot Passes

l106 1092 1040 1438 1430

1496 1468

6l 104 151

178

24r 316 396 490

764

1336

Tube Count for s/s in. OD Tubes on Z8 in, TEMA

TEMA

LorM

Fixed Tubesheet No. of Passes

Shell lD in. 5.047 6.065 7 .981

l0.02 12.N 13.25 15.25 t7 .25 19.25

21.25 23.25

25.W 27.W 29.W 31.00 33.00

3s.00

P

18 t6 30 24 61 s2 48 96 94 80 151 138 132 187 176 168 241 232 224 302 292 396 384 352 482 472 456 568 554 536 792 780 752

Outside Packed Head No. of Passes

418 506

14 t2 26 16 48 44 82 76 124 t12 148 t32 196 184 266 252 334 312 4t6 396 492 472

704

700

22

19

31

26

1062 1030

1008

13s6 t346

13c4

55 88 130 151

206 270 JJO

946 930

660 896

1234 1220 n80

U

Inside

t9 14 t2 31 26 16 56 52 44 96 90 76 lsl 138 t28 187 184 160 258 242 224 336 326 304 421 412 392 s26 502 480 608 s98 556 868 836 804 t152 lt24 t088

t9 JI

TEMA

U-Tube

No. of Passes

1424

A pitch

TEMA

Tvoe S Inside Head No, ot Passes

14 t4 t2 22 20 16 51 48 40 85 76 72 130 120 112 163 152 144 216 2r4 196 288 282 264 358 350 340 450 436 416 526 506 484 724 720 696 994 978 948 1288 1252

1220

TEMA U

U-Tube

No. of Passes

The Mechanical Design of Shell-and-Tube Heat Exchangers Table 7-13

Continued Tube Count for s/s-in, OD Tubes on ZB-in.

TEMA M

Type L or

Shell lD in. 5.047 6.065 7 .981 r 0.02 12.00 13.25

t5.25 .25 19.25 t'7

21.25 23.25 25.00 27 .00 29.00 31.00 33.00 35.00

Fixed Tubesheel No. ol Passes

21 16 26 26 52 52 89 82 128 124 158 158 2r3 208 277 266 344 332 420 404 502 4't6 694 668 922 910 1181

1166

TEMA

Type P Outside Packed Floating Head

908 I 160

1070 l0g

52 80

r20 148

208

264 336 400 488

664

l2 16

44 68 92

r20 164

220 284

TEMA

TEMA

TYPe S

Type

l2 2l '74

109 138 188

246

TEMA M

316 394

432

456

.1.18 14

608

6.10

636

62.1

812

86? 8.18

8,10

Fixed Tubesheet

Shell lD in. 5.O4'7

6.065 7.981 10.02 12.00 13.25 15.25 t7 .25 19.25

2r.25 23.25 25.00 2'7 .00 29.00 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00

No. ol Passes

19 14 t2 27 26 20 55 48 40 85 76 72 126 118 104 151 148 140 206 196 180 268 266 240 340 330 320 416 408 392 499 480 460 576 558 530 675 661 632 790 ',7',13 736 896 875 858

1018 1011 976 1166 I137 1098 1307 1277 1242 1464 1425 1386 1688 1669 1618 1943 l9t2 1878 2229 2189 2134 2513 2489 2432 2823 2792 2752 352'7 3477 3414

TEMA

Type P Outside Packed Floating Head No. of Passes

U-Tube

No. of Passes

12 12 16 16 38 32 10 68 92 88 136 128 18,1 t'76 241 210 308 30,+ 388 38,1

360

1048

U

Inside

I122 1112

Tube Count for 3/4-in. OD Tubes on 1sA6-in. Type L or

Pitch

Floaling Head No. of Passes

No. of Passes

13 t2 22 22 45 44 76 76 109 104 137 t28 \'77 t76 241 236 293 284 366 364 436 432 612 608 828 812

t6

!

1100

A Pitch

TEMA

Type S lnside Floating Head No, of Passes

TEMA

Type

U-Tube

No, ot Passes

l0 104 64 t4t48 t9 18 12 t4 8 l8 22 18 16 38 42 40 36 32 42 40 32 30 32 24 68 14 72 60 54 73 66 60 54 56 52 98 109 106 96 86 109 106 92 86 92 80 134 130 124 112 108 140 138 124 108 114 104 r'76 114 168 156 152 187 184 168 152 83 74 230 24t 222 2t6 2r0 253 242 224 2tO 220 204 302 288 282 2@ 260 320 294 280 2@ 290 268 384 384 368 344 338 400 380 352 338 360 340 456 469 449 430 418 454 436 416 410 220 21.O 516 544 529 500 490 514 498 471 465 506 488 s96 @3 616 600 s1s 607 s87 560 558 614 580 720 744 132 '704 695 707 690 '769 663 657 720 684 760 830 804 859 83s 812 800 816 79'7 9'13 959 926 900 931 910 876 870 944 916 1118 1093 1054 l0l0 1062 1039 998 993 1076 940 1253 t224 ll84 1150 1200 lt77 tt35 |24 1218 1184 1392 1359 l3l8 1286 1341 1318 1282 t2g 1366 1324 1616 1602 1552 1482 1558 1554 1870 1833 1800 1770 1875 1834 2145 2107 2060 2025 2132 2100 2411 2395 2344 2305 2431 2392 273'7 2683 2@2 2612 2730 2684 3400 3359 3294 3220 3395 3346

U

1502 1482 1600 1552 1'736 1708 1854 1800 1998 196/. 2122 2064 2286 2250 2410 2356 2574 2536 2732 2668 3228 3196 3398 3336

131

132


Table 7-13 Continued

Tube Count for 3/a-in. OD Tubes on 1-in. TEMA

TEMA

LorM

5.047 6.065 7 .981 10.02 12.00 13.25 15.25 17 .25

t9.25 21.25 23.25 25.00 27 .00

29.N 31.00 33.00 35.00 37 .00 39.00 42.00 45.00 48.00 51.00 54.00 60.00

14 14 t2 22 20 16 42 40 36 7372& 109 86 80 139 134 124 187 180 168 241 232 220 296 290 280 372 354 344 434 420 404 507 489 476 604 s94 s68 689 679 660 808 804 772 906 891 860

1030 1152 1273 1485

r72r

1026 1000 1134 1090 1259 1222 1461 \434 1693 1650

1968 l94l 2221 2187 2502 2465 3099 3069

1902

2134 2414 3010

TEMA

Outside Packed Head

Head No. ol Passes

10 108 10 104 64 19 18 16 19 14 l2 108 40 38 36 32 28 37 32 28 26 28 24 64 &62 6058 61 60 48 46 56 44 98 95 94 84 78 96 94 80 78 86 72 122 12L ll0 100 98 r21 ll8 104 98 106 96 t& 151 146 140 138 163 1& 144 140 148 136 212 208 196 188 160 216 214 196 158 200 184 270 258 242 232 230 276 270 260 235 254 240 330 320 316 296 298 338 338 324 3m 3r4 300 404 380 372 364 33s 396 396 376 339 388 368 482 475 466 452 430 460 440 420 4r4 452 432 582 530 526 508 49s 558 554 536 494 538 524 672 653 &2 620 610 624 605 s89 581 632 612 724 696 688 669 7s6 744 '116 669 732 708 859 848 818 805 818 797 783 771 838 808 946 922 9M 880 980 978 944 880 950 916 1106 1081 1054 996 tU1 1039 1001 996 1074 rO40 1218 1208 tr74 1r2s rt72 1164 1130 1125 1200 1164 1426 1399 1376 1306 1367 1350 1322 13M 1406 1364 1652 1620 1586 1635 1608 1536 1s04 1632 1s84 1894 1861 1820 1887 tUz 1768 1740 1870 1832 2142 2101. 2060 2143 2lA4 2019 1992 2122 2076 2417 2379 2326 2399 2366 2270 2244 2396 2340 29W 29s7 2906 2981 2940 2932 2800 2992 2936

TEMA

LorM

6.065

2l

.98r

38 61

7

10.02 12.00 13.25 ).5.25 t7 .25 19.25

2r.25 23.25 25.00

27.N 29.N 31.00

97 117 158

zlo 262 J10 370 442 524

602 698

f-in.

!

Pitch

TEMA

TEMA

s

P

U

Fixed

Outside Packed

Tubesheet No. ol Passes

lnside

Head No. ol Passes

No. ol Passes

l2 t2 16 16 38 32 60 52 90 88 I 16 112 158 148 208 188 256 244 316 308 372 368 432 428 524 500 596 580 692 688

U-Tube

No. of Passes

22

TEMA

5.U7

U

Inside

No. ot Passes

Tube Count for g/q-in. OD Tubes on

Shell lD in.

TEMA

s

P

Fixed Tubesheet No. ol Passes

Shell lD in.

A pitch

12 16 37

t2 16 32

)/ )t) 89 82 9'7 94 t37 128 177 176 224 216 274 270 333 332 414 406 464 456 570 562 628 620

Head

98 16 16 32 12 52 24 56 52 76 56 89 82 88 80 104 104 120 lt4 r45 140 164 160 188 184 208 198 238 236 268 260 304 292 316 308 344 332 392 344 398 386 448 424 484 472 548 496 554 532 612 576 650 @8 4

12

U-Tube

No. of Passes

64 88 32 t2 24 20 'tA
t2

Exchangers


Table 7-13

Continued Tube Count lor s/+-in. OD Tubes on 1-in'

LorM

Fixed Tubesheei No. of Passes

Shell lD in.

33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 s4.00 60.00

782 768 894 892 1004 978 I102 1096

768 880

964 1076

1283 1285 1270 1.484 1472 1456 l70l 1691 1610 1928 1904 1888 2154 2138 2106 2683 2650 2636

s

P

Outside Packed Head No. of Passes

TEMA

M Fixed

Tubesheet No. of Passes

Shell lD in. 5.047 6.065 7 .981 10.02 12.00

t3.25 t5.25 .25 19.25 17

21.25 23.25 25.00 27 .00

29.00 31.00 33.00 35.00 37.00 39.00 42.OO

45.00 48.00 5l .00 54.00 60.00

\2

2r 37

l0

8

18

16 28

32

61 54 97 90 113 108 156 146 208 196 256 244 314 299 379 363 448 432 522 504 603 583 688 667 788 7'70 897 873

1009

983

48 84 104 136

184

236 294 352 416 486 568

654 756 850 958

1118 1092 1066 1298 1269 1250 1500 1470 1440 1714 1681 1650 1939 1903 i868 2173 2135 2098 2692 2651 261.2

682 824 882

1062 1045 1026 972 1048 1028 996 1232 1222 1218 1140 1224 1200 1170 1424 1415 1386 1336 1421 1394 1350 1636 t634 1602 1536 1628 1598 1548 1845 1832 1818 1764 1862 1823 l7'/9 2080 2066 2044 1992 2096 20.+8 2010 2582 2566 2556 2476 2585 2552 2512

TEMA

No. ol

f in. '

668 724 160 836 8'72 940

't20 8L2 924

9'72 1048 10/10 1140 1222 1204 1336 1420 1400 rs36 1624 1604 t'164 1852 1820 1992 2084 2064 2416 2596 2564

TEMA TYPe

S

TYPe U

Inside Head

Passes

No. of Passes

1864 1837 1804 2098 2062 2026 26W 2560 2520

No. of Passes

Pitch

Head

t2 10 8 16 t2 8 32 28 24 52 46 40 81 74 68 9't 92 84 140 134 128 188 178 168 241 228 216 300 286 272 359 343 328 42t 404 392 489 472 456 575 556 540 660 639 624 749 728 708 849 826 804 952 928 908 1068 1041 1016 1238 t2t6 tt96 1432 1407 1378 1644 t6Il 1580

U-Tube

Head

No. ol Passes

742 732 732 668 '130 112 816 8r2 804 760 848 828 952 931 928 8'72 931 918

Type P Outside Packed

U

lnside

Tube Count tor 3/4-in. Oo Tubes on Type L or

TEMA

TEMA

TEMA

TEMA

n Pitch

U-Tube

No. ol Passes

108 24 20 42 36 66 64 86 80 124 116 174 164 2t8 202 272 260 334 320 390 380 468 452 550 532 626 '720 608 700 818 796 928 904

1036 1016 1220 rr92

t4t2 1384 804 788

1834

1804

2584

2544

20'72 2036

133

134


Table 7-13

Continued Tube Count for TEMA

M Fixed Tubesheet

Shell lD in.

5.M7 6.065 7

.98r

10.02 12.00

t3.25 15.25 .25 19.25 17

21.25 23.25 25.00 27 .U) 29.OO

31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00

864 14 148 26 26 16 42 40 36 64 61 56 85 '76 72 ll0 106 100 147 138 128 184 175 168 227 220 212 280 265 252 316 313 294 371 370 358 434 424 408 503 489 468 576 558 534 643 634 604 738 709 6U 8M 787 772 946 928 898

1087 1069 1042 1240 1230 rl98 t397 1389 1354 1592 1561 1530 1969 1945 t90/.

OD Tubes on 11/a-in.

TEMA

Type L or

No. ol Passes

l-in.

Type

TEMA

P

outside Packed Floating Head No. of Passes

TEMA M

Shell lD in. 5.O47

6.065 7 .981 10.02 12.00 13.25 15.25 17 .25 19.25

21.25 23.25 25.00

27.W 29.00 31.00

Fixed Tubesheet No. ot Passes

86 12 24 37 57 70 97

r29 t62 205 238 275 330 379 436

l0

4 8

20

l6

32 53

28 48

70 90

& 84

r20 r52

1t2

193

184

228 264

220 256

315 363

300 360

422

410

142

TEMA

Type S Inside Floating Head No. ot Passes

Type

U

U-Tube

No. of Passes

74400 l0 104 44 22 18 16 14 l8 t4 812 14 8 38 36 28 24 33 28 16 18 26 24 56 52 48 46 51 48 42 44 44 36 13 72 60 44 73 68 52 44 56 52 100 98 88 80 93 90 78 76 86 76 130 126 116 104 126 122 112 192 114 104 170 162 148 140 159 152 132 136 152 136 2r2 20r 188 176 202 r92 182 172 19? 176 258 2s0 232 220 249 238 21.6 2t2 232 220 296 294 276 250 29r 278 250 240 270 256 3ss 346 328 300 345 330 298 288 322 3U 416 408 392 360 400 388 356 348 378 3U 475 466 446 420 459 450 414 400 444 424 544 529 510 498 s26 514 484 4& 508 492 619 604 582 s66 596 584 548 536 s78 560 696 679 660 646 672 68 626 608 660 632 768 753 730 723 756 736 '7M 692 740 '1r2 908 891 860 840 890 878 834 808 872 836 1041 1017 990 968 1035 lm8 966 948 1010 980 1189 1182 1152 1132 1181 l162 lll8 tO92 1156 tt24 1348 133'1 1300 1280 1350 1327 1277 1254 1322 1284 l53i 1503 1462 r4r'iO 1520 r49Z 1436 1416 1496 1452 1906 1879 1842 1802 1884 1858 1800 1764 1866

Tube Count tor 1-in. OD Tubes on 11/4-in. Type L or

A Pitch

TEMA

Type P Outside Packed Floating Head No. ot Passes

54 12 2t l)

4

l0

8

18

16

lt

52 46 61 58 89 82 113 1r2 148 138 180 r74 22r 210 261 248 308 296 359 345 418 40r

28

40 56

76 104

128 168

2N 236

286 336 388

1828

v Pitch

TEMA

TEMA

Type S Inside Floating Head No. of Passes

Type

U

U-Tube

No. of Passes

00

44 108 24 i0 36 32 50 44 70 64 96 88 124 t20 156 152 200 188 232 220 282 268 330 320 382 368

{l The Mechanical Design of Shell-and-Tube Heat Exchangers

Table 7-13 Continued Tube Count for 1-in. OD Tubes on 11/4-in. 0 Pitch TEMA

Type L or

Shell lD in. 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51 .00 54.00 60.00

M

Fixed Tubesheet No, of Passes

495 556 632 705 822 946

478 472 552 538 613 598 685 672 '799 786 922 912

1079 1061 1052 1220 t159 1176 1389 1359 1330 1714 l69t t6&

TEMA

Type P Outside Packed Floating Head No. ol Passes

477 540 608 674 788 910

1037 1181 1337 1658

Tube Count

TEMA M

Type L or

Shell lD in. 5.O4'7

6.065 7 .981 10.02 12.00 13.25 15.25 17 .25 19.25

21.25 23.25 25.00

27.N 29.N 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51 .00 54.00 60.00


964 L2 l2 12 22 20 16 38 38 32 )o )b Jz 69 66 66 97 90 88 t29 \24 120 t64 158 148 202 l9l 184 234 234 222 272 267 264 328 317 310 378 370 370 434 428 428 496 484 484 554 553 s32 628 621 608 708 682 682 811 811 804 940 931 918

1076 1218 1370 1701

106l

l0,l0

1202 tt92 1354 1350 1699 1684

460 526 588 654 765 885

TEMA

Type S lnside Floating Head No. ol Passes

&O 7s6 866

1138 1292

r@4

OD Tubes on 1tA-in.

TEMA

Type P Outside Packed Floating Head No. ol Passes

U-Tube

1002

1018 1000 1160 1142 1307 1292 1626 1594

!

U

No. ol Passes

440 498 562 630 144 872

448 508 568

lor 1-in.

Type

424 484 548

620 728 852

980 1116 12@.

1576

Pitch

TEMA

Type S lnside Floating Head No. ot Passes

TEMA

Type

U

U-Tube

No. ot Passes

544-544-00 1264-126444 21 16 16 12 t7 12 812 12 8 32 32 32 18 30 30 16 18 24 20 52 52 44 24 52 48 42 24 38 36 61 60 52 50 61 56 52 50 52 48 8984806485786264.7268 l 13 112 rt2 96 108 108 104 96 98 96 148 144 140 114 144 136 130 tt4 t28 124 t'18 178 t'72 156 1',73 166 154 156 166 156 216 216 208 192 217 208 194 192 200 196 258 256 256 212 252 240 230 212 240 232 302 300 296 260 296 280 2'70 260 284 276 356 353 338 314 345 336 310 314 332 332 4r4 406 392 368 402 390 366 368 290 384 476 460 460 420 461 452 432 420 442 436 542 530 518 484 520 sr4 494 484 254 248 602 596 580 550 588 572 562 548 574 560 676 649 648 625 66r &0 624 620 W 628 782 780 768 730 776 7s6 738 724 758 748 9M 894 874 850 900 882 862 844 872 868 1034 rO27 101,2 980 1029 i0l6 984 9'72 1002 988 1178 1155 1150 1125 1170 1156 tt26 1114 1146 ll40 1322 1307 1284 1262 1310 1296 t268 1256 1300 1288 1654 1640 1632 1585 t64t 1624 1598 15'76 1620 1604

135

136


Table 7-13

Continued Tube Count tor 11/4-in, OD Tubes on 1sfi6-in. TEMA

Type L or

shell lD in. 5.047 6.065 7 .981 10.02 12.00 13.25 15.25 1',7 .25 19.25

21.25 23.25 25.00

27.W 29.W 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00

M

Fixed Tubesheel No. of Passes

744 864 t9 14 12 29 26 20 423834 52 48 44 69 68 60 92 84 78 121 1l0 104 147 138 128 r74 165 156 196 196 184 237 226 224 280 269 256 3t3 313 294 357 346 332 4t6 401 386 461 453 432 511 493 478 596 579 s70 687 673 662 790 782 758 896 871 860 1008 994 968

1243 1243 l2l0

Type P Outside Packed Floatlng Head No. of Passes

TyPe

LorM

Shell lD in. 5.04',1

6.065 7 .981 10.02 12.00

t3.25 15.25 17 .25 19.25

21.25 23.25 25.00

S

TYPe U

Inside Floating Head

U-Tube

No. ol Passes

No. ol Passes

00 00 64 14 22 32 48 64 86 tt4 138 t62 196 232 268 310 356 4M 452 534 626 720 822 930

00076414 14822 20 16 37 36 28 22 44 44 36 28 64 62 48 45 85 78 72 69 109 w2 96 86 130 130 116 1r2 163 152 r44 130 184 184 1"12 164 22r 216 208 196 262 252 242 228 302 302 280 270 345 332 318 305 392 383 3& 3s7 442 429 4r2 407 493 479 460 449 576 557 544 5r2 657 640 628 596 756 745 728 696 859 839 832 820 964 959 940 892

1199 1195 1170

1160

1116

Tube Count for 11/4-in, OD Tubes on 11fi6-in' TEMA

A Pitch

!

t20 144 164

296

3M 388

440 522

6t2 700 800 908 1140

fvoe

rtinq Head

88

184

220 256

TEMA

No. ol Passes

52 76

132 152

Tvpe S lnside

I Head

42

104

l'vDe P

No. ol Passes

32

60 80

TEMA

No. of Passes

16

44

Pitch

Fixed Tubesheet

12

28

TEMA

Outside Packed

444 664 12 12 24 22 37 34 45 42 61 60 80 76 97 95 t24 124 t45 145 172 168

12

20

0000000 6640664 t2 12 lZ 21 16 16 32 32 32 38 38 32 52 52 52 70 7o 68 89 88 88 rr2 112 ll2 138 138 130 164 l@ 156

0r2 12 21 18 29 24 38 48 52 s0 70 80 85 96 108 114 136 136 154

12 12 28 34 48 66 84 108 128 rs4

4 8

16

34

44 56

70 100

128 142

U

No. of Passes

000 000 064 12 128 18 20 20 24 28 28 48 42 36 50 56 56 80 74 68 96 98 96 114 124 120 136 140 136

n The Mechanical Design of Shell-and-Tube Heat

Exchangers

Table 7-13

Continued Tube Count lor 'l'tlq-in. OD Tubes on l/rs-in.

TEMA Type L or M Shell lD in. 27 .OO

29.00 31.00 33.00 35.00 37.00 39.00 42.00 45.00 48.00 51.00 54.00 60.00

TEMA


210 202 24r 234 272 268 310 306 356 353 396 387 442 438 518 518 602 602 682 681 7'.70 760 862 860

1084 1070

202 230 268 302 338 384

434 502 588 676

756 8s6 1054

!

lnside Floating Head

U-Tube

No. of Passes

No, of Passes

No. of Passes

1042 t034 1026 1008

5.047 6.065 7 .981 10.02 12.00 13.25

t5.25 t7 .25

r9.25 2t .25 23.25 25.O0 27 .O0

29.00 31.00 33.00 35.00 37.00 39.00 42.O0

45.00 48.00 51.00 54.00 60.00

544 664 13 108 24 20 16 37 32 28 45 40 40 60 56 '79 56 76 '16 97 94 94 t24 tt6 ll2 148 t42 t36 174 166 160 209 202 t92 238 232 232 275 264 264 314 307 300 359 345 334 401 387 380 442 427 424 522 506 500 603 583 572 682 669 660 1"t"t '762 756 875 857 850

1088 1080

1058

<

,

TEMA


Type S lnside Floating Head No. of Passes

,l

,tl

12 108 2t 18 16 32 28 28 3',7 34 32 52 52 48 70 70 64 90 90 84 tt2 108 104 140 138 128 162 162 156 191 188 184 442 ,130 416 26t 249 244 300 286 280 34t 330 320 384 372 360 428 412 404 497 484 4'72 5',75 562 552 660 648 640 743 '728 716 843 822 812

1049 1029 t0t6

U

Pitch

TEMA

No. ot Passes

Type

184 180 158 r12 176 176 2t7 212 204 198 200 196 252 248 234 236 232 232 289 2',76 270 264 272 268 329 316 310 304 312 296 312 368 354 340 348 348 420 .102 402 392 396 392 485 116 468 464 472 456 565 55J 5+6 544 552 536 653 616 628 ',705 620 '7t2 628 620 738 126 ?20 708 837 820 811 80.+ 808 804 1036 l0lE i0r2 1008 l0t2 992

Tube Count tor 1tlc-in. OD Tubes on 1el16-in.

Shell lD in.

TEMA


193 184 184 172 224 224 216 198 258 256 256 236 296 296 282 264 336 332 332 304 378 3'70 370 358 428 426 414 408 492 492 4U 464 570 566 556 544 658 648 648 620 742 '729 722 7t2 838 823 810 804

TEMA Type L or M Fixed Tubesheet No, of Passes

Pitch

TEMA Type S

TEMA

Type

U

U-Tube

No. ol Passes

00 00 44 12 20 26 40 56 74 96

t2 20 24 36 52 68 88

120 ttz 142 136 170 164 200 192 228 220 268 256 306 296 346 336 390 380 456 448 542 528 618 604 708 692 802 '784

l0l0

984

'137

-o9.

9.

"

.

?

9o

o

o

a

P

6

N |

ld

o"l-: -l

| F F 6 0 d €; ci <;

;.rsso , , Rsg$ lo

!9 INrl N < trli-:

! 3 i

li

t.tc o "1.;o

{ o"l;;;;

i:aic;e';<; tr-'

F!::"i j

d<;d

.r (9l
i

<;
.9

:

,'€ t2

i ;

i"'c:!i::gl:: onoofs{{{{

,''i€e-i3t
rD^

iiH

xl:.:.*;ia++l+a{

ii .El* ?l

*

i |.e "" t. -_.i

=' a"

i.i;

c;

':

Ea

:<

ol" / l14

ii:a

|

_

aa a;

ri,i*;;ital:i;

rs

6|-=

.9n lI-:

Eo i6

t4> oo|.

\ .oor -_,,' len-\dt I

/11 y-s-\ i

/or

o,t

E The Mechanical Design of Shell-and-Tube Heat

iGlD.(NB +

1)

(5.22X10)roD"7

r

where (p/p,,). G,, D., D. NB

Polh ot Fluid

A. Shell side fluid baffling showing segmental cut baffles.

^l

t. Fluid Flo13 Poroll.lhTubrs os,t Po3r.3 /From one Bolll.d A..o io N.rr. eorrrr

"wintoi' or "co'l 03 %cu!,{hkh

O O J Eac$ed

sotlrs Ooid

O

B. Segmental baffles showing window are for fluid flow.

oootoo ooolooo ooooo ooooo ooooo

ooooo )OOOooO oo

Iilol.:Ar0o Avo,l0bla tor Cror! Flor

i:l:1if.' 4,i! *, C. Cross

orhe'

L3ed Cort,r,!rr r .' peler*ce I . oth.t a,,olq!-e.rt ro ooh . E3se"',- ||e so-.

flow area for iube layouts.

Figurc 7-228. Various baffle *indou schemes

[,1].

Baffles neveq except for unusual designs such as orifice baffles, extend a full 360" around the shell. The baffle plate is cut such that the shell-side fluid can flow around its edge. The open area between the baffle edge and the shell wall is known as a baffle "window." Baffle windows are commonly referred to in terms of percentages of the entire circular shell area. Figure 7-22b illustrates various baffle window schemes. Shell-Side Pressure Drop. There are several methods to calculate the frictional pressure drop across tube bundles, and the reader is referred to Ludwig [4] or Kern [9] who give comprehensive discussions of the various techniques. The method we

will

(7 31)

: :

are previously defined

number of bafiles

= specific gravity of

:

shell-sidc

fluid

combined friction factor deter mined from Figure 7 23

is

{%XSherl 10.). Ner Fror Ateo ol Wiido* is Full Windor A/.0 Diius Ar.o

Boftr.s @0,'d@

139

Kern [9], where the expression for the shell-side pressure drop is given as follows:

Sallle Pilch or Stoci.q

;9 ]

Exchangers

use is the one developed bv

TUBE VIBRATIONS Chapters I and -1 described how fluids moving around objects can produce r ibrations. The same thing happens in shell and tube heat exchangers, but it creates a different problenr. Chapters I and ,1 were primarily concerned with Yorte\ sheddrng. This chapter covers vortex shedding and sereral olher t\pes of vibration phenomena. Also. the problen is difterent from rhat in Chapter 4 because the boundarr conditions of the system have chansed. Chapter I used a cantile\er beam to show how a til\\ er or srack is restrained several different ways at the ends." There have been nrany research studies made in the field of tube vibrations. Probably the most numerous stem lrom the nuclear industry. The problem is complex and no one method proposed is a full and complete anal-

ysis of tube vibrations. Consequently, research is still being done to better understand the causes and prevention of tube vibrations. Here we will outline the causes of the phenomena and present some quanlitative approaches to the problems. Presented first is a simple and quick approach to pre, dict tube vibrations caused by shell-side flow. This approach was originally developed by John T. Thorngren [14] in 1970 and is called the "maximum velocity method." We will present a modified version of the method proposed by Thorngren to encompass a wider range of applications and to specifically define all the variables in the equations. This method addresses the tube vibration caused by vortex shedding when the shellside fluid alters direction at the baffle plate and strikes the tubes. The arrows in Figure 7-l show how flow di, rection of a fluid turns at the baffle plate and strikes the tubes midwal between rhe bafile plates. Thi5 causes rhe tubes to deflect and the hole in the baffle plale acts as a fulcrum for the tubes to deflect against. Two types of problems can result a fatiguing of the tubes at the baf: fle hole and eventual tube rupture, or the tubes colliding

For low-Finned Tubes f" (sq. ft)/(sq. in.)

'

oooF

iol)

6 a

||'

F

^z.E ^z,E

.!.

l-€-e;; - -- g rtx

3: :-

=l

-';

;

.3 -i 3 q "- :E -al -- ? F 3l; tree lli:E fr xla E I -.j i; xlo :i X -. --:'i 3; 5 'rli :lu,r, 5c; -= ;= 6e= < --- --=: =F= "el "'59 -tr -c6; 'r =-Ft* {SS s5- E} î' i;t--E E\.E tl+ P; tld ES.= E c* E E :lr=-E zl x Sooo -o9= eElDF;

o.

-8

.

= g:: -E+xld.FsE:;.E-E€ ;l: @ ;9-e A;o.9 g ol -

-:;-

:1:;5#!=sji5Fi; ^6+ - oo !: c(r(-)oE

I go

-oo

;

6r9 0'--jzz,

o,<

@-1. ! E5

j: r: ri=\= gi 99

;E

e: :5

P

=

-

=t

d

>

o

::

"l ,: E=.E

EEP

;€ rj6tr

:d*+ o._ !2.f

--;;;

!{E-

--es ;==* !ii; 3= i;

iE s r !'EE

Ess_ii3;S ; t -: a*:L:L+:

oooF
lo |.l rt

n)

-ooFtoI'

t

ro

N

x: ..!A .9: fri

{.)

N ": tl.E

oti

ii,

The Mechanical Desien of Shell and-Tube Heat

with each other resulting in abrasion and rupture. This phenomenon can be offset somewhat by anticipating shell-side velocities. The velocity of the shell-side fluid can be kept reasonable if the entry and exit nozzles are properly sized. To determine the force exerted on the tubes by the fluid vortices we refer to Equation 4-80, the von Karman eauation as follows: E_

Co pY212

(4-80)

2g"

In the case of tubes the characteristic area, f2, can be replaced by the outside tube diameter, d. (ft), and the value for the force becomes: CFpV2do

:

force per unit length of

tubes

(4-80a)

Chapler 2 introduced the concept of the Strouhal number as 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 written AS:

f.d"

()-31)

Exchanqers

141

7 -24, we notice how the drag coefficient varies over a wide range of Reynolds numbers. For viscous liquids moving at low velocities, it is very possible for the Reynolds number to be low, making the drag coefficient high. Thus, we keep Cp as a variable in Equation 4-80. In Figure 2-32 we see that at NR" > 3.5 x 106 the vortex street is again developed. At this Reynolds number the fluid flow velocity would be too high to consider wind design as discussed in Chapters 2 and 4. Also, those two chapters were only concerned with a single cylinder, whereas here we are studying the effects of vortices on an array oftubes. At values of Nn" ) 3.5 x 106 for tube arrays we would be more concerned with flow-induced vibration. which is discussed in the next section. Also. Reynolds numbers in this range rarely, if ever, occur in heat erchangers. In an arral oftubes the maximum velocity ofthe shellside fluid occurs at the minimum cross section between the tubes. Thus. V increases such that as the tubes get closer together the ralue of Nq. approache\ 3.0 x 105 and the rorter street is broken up as previously described. Thus. the effect of vottex shedding in tube arrays is onl1 si-enificant for tubes spaced such that the Relnolds number falls within the appropriate range. The effects of tubes being spaced closer are discussed later in this chapter.

viscous liquids. Now, observing Figtre

For considering vorteK shedding, Equation 4-80 represents the maximum force exerted on the tubes. To ana-

As observed in Figure 2-32 the vortices break up when Nq" approaches 3.0 x 105. Referring to Figures 4-21 and 4-29 we see that the force or drag coefficient is constant in this range. However, in Chapter 4 rve are dealing with air as the flow medium. In our application here we are dealing with a wide range of fluids-gases to heavy,

lyze the tubes, one must consider them as continuous beams supported by baffle plates. The baffle plates act like beam supports as the fluid exerts a force in the tubes forcing them against the baffles. The general equations for the shear force and deflections of a continuous beam take the following general forms: FiE)re 7-24. Drag coefficients versus Reynolds number for long circular cylinders in crossflow.

'to

'142


F. : aFrL

^

bFI L4

EI

(7

-32)

(7

-33)

The values for a and b are dependent upon the boundary conditions of the continuous beam. Typical values are presented in Figure 7-25 and are fairly comprehensive for most shell and tube exchangers. For cases not covered in Figure 7-25, the specific values must be solved for using the analysis for a continuous beam.

As the shell fluid exerts pressure on the tube, the tube deflects at mid-span forcing the tube at the baffle against the baffle hole. The stresses induced in the tube are a resuit of localized forces at the tube-baffle contact points. At these points the tube behaves similarly to a horizontal vessel such that only a portion of the tube wall offers effective resistance against collapse. Thus, Equation 4-2 predicts the amount of tube wall that effectively resists the baffle wall reaction, and is written as

a:11{\12+ :olI

(4-2)

180

Continuous Beams dmar

br"r

I

l .200

2 3

0.550

0.0059 0.0099 0.0069 0.0094 0.0097 0.0065

1.100 1.223

4

0.572 1.143

5

6

4

[.r.

(0,130 r

fton A] =

t.005r

,rrlsl

A

€ comtruous

! il.r. (0.tt , tioE ^

.'

a

r.&

o.raa I

rroi

A

o. D)

-

0,0rl

!r.

(0,415 r

koh

E,

5

o.m!a

!r./al

BEAM-FoUR Eeual spaNs-LoAD FtRsr aND THrRo spANs

o) a 0,00n &,4/El

a

6.

rr.r.

tl.r.

(t az

rlr.n

A) E 0.6tt

{,r/al

coNTlNuous BEAM-FoUR EeuAL spANs--{LL spaNs LoAoEo

r

^

.L

(Gaa I lr.h A .na a)

Figure 7-25. Boundary conditions of continuous beams

u5l.

-

O.Ol5

d./s

The Mechanical Design of Shell-and-Ttbe Heat

where d

=

A=

angle of contact

where

sisting tube wall area

:

that neither the tube nor baffle hole will deform to reduce stfesses, which is the worst condition. For determining contact stresses between the two bodies, Timoshenko [16] has shown that for the case in Figure 7-26 the diameter of the circle of contact is

:

149

constant that represents the amount of effective re-

radians

Thorngren [14] proposed that about 40% of the tube metal is effective in resisting wall membrane stresses. In Equation 4-2 this would make the value of 0 144' , greatef than most saddle-shell connections for horizontal vessels . To take the problem furtter we consider the tube wall as a ring shown in Figwe 716. The assumption is

d

:

q

Exchangers

1.76E(qi_e")g4" l"' [ 2EEB(d, + dJl

Now combining Equations 7 -32 and 7-35 we have the followins:

: " I--Lil--qe-)||--t')' \aF,L/ \4 + dB / \0.798/ r-v! l-u$ where c = z,

= hisson

ratio for the tube material, dimension-

less

/B

= hisson

ratio for the baffle plate material, di-

mensionless

E=

Ea

From Equation 7-34 one can deduce that the tub€-bafalLalyzed as point loadings. For such loadings as shown in Figure 7-26 the contact force representing the shear of the tube against the baffle plate

:

modulus of elasticity for tube material, psi nodrlus of elasticity for baffle plate material, pst

fle interface should be

*. (#,.J"L,,*',J'

c = constant, in./lbr cr

:

constatrt, dimensionless

To arrive at the modified damage numtrr damage we solve for F1 in Equation 7-32: Q-3s)

(7-37)

EB

Q-34)

ts

(7-36)

F,: -

for baffle

F"

o'al-

Evaluating the relationship for shear in Equation 7-32 we have

F.

=

aaFrl-

Now dividing this relation into Equation 4-80 we obtain Cpd,p\Palc _ 1.0 2g"F.

Letting the baffle damage number be represented by Nss, a dimensionless parameter, we have:

*, ^"" -

Cpd.pV2alcv --fdE-

where Nss

(

Q-38)

1.0

If NBE > 1.0, then tube damage at the baffle is very probable and a tlicker tube should be selected and the analysis repeated. The analysis of determining the dimensionless parameter, NsD, which governs tube damage induced by excessive displacements in tube movements, is similar to that for the baffle damage parameter. Solving for F1 in Equation 7-33 we determine F1 as follows:

Figule 7-26. Fluid foroe causing tube to impinge on

plate.

baffle F"" : E bL4

144


Dividing this expression into Equation 4-80 we have Ded,pV'?bLa

_

2g.6E,I

1.0

We define N6p as rrcD -

CDd,pv2bL4 2g.6E

where NcD

<

(7

I

-39)

1.0

>

1.0, then thicker tubes should Once again, if NcD be selected and the analysis repeated. Equation 7-39 is similar to that obtained by Thorngren [14] and Coit [17]. The dimensionless parameters, Nss and N6o, in Equations 7-38 and 7-39 should be regarded as mere rules of thumb. Even though they are dimensionless, they do not have the same firm basis as do dimensionless parameters used in fluid mechanics and transport phenomena. One can approximate the tube behavior by using the principles in Chapter 2, Example 2-6. Using the baffles as supports and spacing them (either equally or unequally), one can simulate the tube displacements. However, since we are not dealing with a single tube, vortex shedding around tube bundles can presently only be accounted for in design by being conservative. Flow-induced vibration of exchanger tubes is another mode different and distinct from vortex shedding. In

vortex shedding a component of the flow, the vortex, is the contributing cause to the tube vibration. In flow-induced vibration, forces are exerted on the tubes that are caused by flow field interactions around the tubes. Fluid that flows normal to the tubes is forced into a smaller area between the tubes resulting in a Venturi effect known as "jetting" or "jet switching." This phenomenon is shown in Figure 7-27 where a control volume of fluid is shown being compressed between two tubes. The result of this 'letting" effect is the fluid exiting the narrow area between the tubes diverges into a diffused mass that whips or whirls around remaining tubes. This "whirling" effect is another mode of vibration. Vibration induced by turbulence is the most common mode. This phenomenon is commonly confused with the other modes because the term turbulence is viewed synonymously with fluid flow and vibration resulting from such flow. However, vortex shedding, jetting, and whirling are different from turbulence because even though they exist in turbulent flow, they can all be final causes of failure and each must be controlled. Turbulence can be best viewed as a pressure field around a tube shown in Figure 7-28. Herc we see a pressure dis-

FigUJe 7-27. Jet switching in tube arrays.

F-+

6= futr) p = p_(t)

where t= iime

(r\ Figure 7-28. The magnitude of the direction of the fluid striking the cylinder can be thought of mathematically as a forcing function, F-, mapping a pressure distribution around the cylinder over region R.

'wi


tribution around a cylinder in much the same way as an aircraft airfoil. This pressure field, or distribution, varies all through the flow regime and is also a function of time. As this pressure distribution fluctuates and changes, the tube is subject to vibration as the fluctuation frequency approaches that of the natural frequency of the tube. It is this fluctuation frequency that is referred to as the turbulence response spectra. As the pressure distribution changes over random time intervals, vibration is generated. We will describe briefly the methods to analyze these modes of vibration. The subject is exhaustive and is far from being a perfected science. One could spend many volumes the size of this one and not adequately cover the subject. For this reason the reader is referred to Blevins [18] for more details. As previously stated, turbulent flow induces continuously varying pressure distributions all around the tube surface(s). The efficiency as to how the pressure forces excite the tubes in each mode (first, second, third, etc.) of vibration is termed 'Joint efficiency," denoted by J;(<,r). This parameter represents the model efficiency of the pressure forces at a given frequency c,.r, where col is the natural frequency ofthejth mode. Figure 7-29 shows the joint acceptance of a single tube plotted against cull V. (U in Figure 7-29), where L is the tube length between spans and V is the fluid velocity. The ratio of the

t 5 :

3

0.01

fluid velocity to the turbulence frequency, as the correlation length ard is given by

145

r,r, is known

(7-4o)

> I, then the varying pressure forces that act

If L. >

along the tube oscillate in phase. Also, ifthe value of L" is much smaller than the length of the tube, such that coL

_ >> I then the joint acceptance is independent of the mode shape and is proportional to the value of LclL. The mean response of the tube is the average tube displacement induced by the mean flow over the specified time interval. The greatest percentage of the response exists in the fundamental mode. For a tube that spans several baffle supports the following expression is used for the mean response:

6-, = 0 036cv'd, (*)(*) where C

=9.7x10

p=

'(*.)""'" ('.J

(7

-4r)

1(sec)05/(ft)r5

density of fiuid external to tubes, slugs/ft3 slue 32.2 lb.)

:

(1

/''i V""-;''\ ,,, ,,,

Figure 7-29. -Th€ joint acceptance of a simply suppofted tube subjected to turbulent flow. (From FlowJnduced Vibration by R. Blevins @ 1977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.)

146


V : fluid velocity of fluid external

: dr : L: Lr : fN : m

mass density of

to tubes, ft/sec

fluid external to tubes, slug/ft

tube OD, ft tube length between baffles, ft total length of tube between tubesheets, ft fundamental natural frequency of tube portion between baffles, Hz sum of structural damping and the fluid dynamic damping distance along tube, ft

I : x: d" :

4Rs

:

4(hydraulic radius)

:

4 (flow area between tubes) wetted perimetel

- ;] ".

tubes on an equilateral

triangular pitch of P

_ -;

+0,

[/r\ t\-dJ

- f] -

ro.,"0",

on a square pitch ot P

t2

o*": E-Cp1*-y 6.*

: :

2.586.-, (for

x

: L/2)

F i,l2 -L

,lZ r0

(7

4=

=

(7

-46)

/\

."^ _ pv'0, 6"" 16,l

2e,

where

K,

:

\d,/

2T-

tn

D

T

/nVfor :r ) l 5 \T/ D'

Kr: l:l

(7-43)

5

- ;;; 6L-

dti

-4s)

(P\'", \T/

r< D

1.5

drag coefficient of tube surfaces

The value for the natural frequency at the tube in

: mr :

(7

\o,/

K, = C'(D/T)

Equation 7-41 takes on several forms. The easiest to use is the formulation developed by Blevins [18]:

where E,

zE"

(7-42)

Equation 7-42 represents the maximum tube deflection to be incurred. The factor 2.58 represents the ampl! tude of the highest one percent of cycles.

"7( rN

pv':d, -. 16,l ru' : -N" l=l

-

Using Figure 7-29 the value of thejoint acceptance for the appropriate mode and the first mode are obtained. The ratio of the joint acceptance of the mode being considered to that of the first mode is multiplied by the value of 6.*, obtained from Equation 7 41. The relationship in Equation 7-41 is based on the theory of tube turbulence developed by Wambsganss and Chen [9], which yields the followins maximum stress value:

where Ce

port end conditions, and tubes that have equal spans and unequal spans. These expressions were presented earlier in this chapter and in Thble 7-6. Equation 7-44 is simplest to use because it requires less input. However, when the information is available and time permits, the expressions recommended by TEMA should be used. The phenomena of "jetting" and "whirling" are not as well founded as vortex shedding and turbulence. This does not say that vortex shedding and turbulence are solidly based, but relatively speaking, they are compared to the other vibration modes, such as jetting and whirling. From Figure 7-28 one can predict that when the tubes are inclined to the fluid flow, the results are force components about the x and y axes. Equation 4-80 illustrates how one can determine the force induced per unit length of a circular cylinder. In the case of whirling and jetting the term CD is a variable. This term is called the force coefficient and is used in Equation 4-80 to evolve the following expressions:

-44)

modulus of elasticity of tube metal, psi mass density of tube metal. slugs/ftl tube OD, in tube ID, in.

TEMA gives a listing of expressions for the natural frequencies of the tubes based on several types of sup-

-(,n)'.,(,n)' where D and T are parameters defined in Figure 7-30 and Fig-

ure 7-31.

Values for K, have been plotted against the parameter T/D. These values are shown in Figures 7-30 and 7-31 to represent the whirling parameter 2(2?r)0 5/(C"Kr)0 '?5. Experiments indicate that the lower the whirling parameter the greater the probability that whirling (and jetting) will occur. To determine

if the tube deflections are within a safe range one must estimate the components F, and F* at their maximum values using Equation 4-80. From the tube spacing determine the force coefficients K, and C* from Equation 7-46. Then solve for 6, and 6" and determine if those deflections are acceptable. After determin-


ing that the deflections are in a safe range, use Figures 7 -30 and7 -31 to determine the whirling parameter. If the parameter is on the low side, then the tube spacing should be increased to raise the whirling parameter. Unfortunately, at the current state of technology, there are no critical values to decide whether the whirling parameter is critical. One manner in which to avoid nroblems with whirling is to use Table 7-14 in derermining the maximum shell-side fluid velocity flow. This table and the previous discussion will eliminate any problems with jetting or whirling. If the velocities cannot be controlled, because of someone else's design or a client's requests, then this procedure can give one an idea of whether whirling can be anticipated. The main focus is to keep the tubes spaced such that the maximum velocity will be reasonable. It has been confirmed bv exneriment that the critical velocity for whirling increises'rapidly wirh the minimum spacing between the tubes and that inline tube arrangements have lower critical velocities than staggered tube arrangements (refer to Figure 7-19 for the various illustrations of arrangements).

PLATE.FIN HEAT EXCHANGERS These units use have been on the increase the past sev-

eral years because of an increasing number of liquified gas and cryogenic plants. The plate fin heat exchanger is

1

147

more efficient than the shell and tube exchanser because the comparable shell and tube exchanger req-uired to re-

fin would be eight times the volume and twenty-four times the weight of the plate fin if constructed of aluminum. The reason for this is that if the plate-fin is made of brazed aluminum, the aluminum place a plate

conducts heat better than most materials and can be used down to absolute zero (-460'F). Since the ductility of carbon steel is lost at -20"F, one must revert to expensive nickel alloys or stainless steels in the shell and tube design. Thus, for cold services, the plate-fin offers some advantages. It is here that the advantages of the brazed plate-fin exchanger end. For the plare-fin to be applied, a very clean

service is required. Even in clean services, these units can accommodate certain thermal shock and fatisue. It is quite possible after continued and repeated therrial loading in excess of differential temperatures of 50'F that internal components can fail. In addition, because these units are aluminum. external nozzle loadings induced by the piping can cause pipe stress problems. One must be extremel! careful ho\\' much loading is induced to the nozzles. because even if failures do not occur, leaks are common if overloading exisrs. Thus, if the service is not clean. a shell and tube design must be used. In gas processing and cryogenic services, the plate-fin exchanger suffices because in these applications the ser-

--loF \JT rl-L o

Oo

./

./

,-7

-rlA

---_ -

i,

. -2 . 5,onr-3ro'2 '

xY

-lDt'3

(0,1,3

Figure 7-30. Whirling parameter of a tube row expressed as a function of transverse spacing.

(From Flow-lnduced Vibration by R. Blevins @1977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.)

148


!M!!

"F

A

o

o

o

.-1'h >; -/l

,r1

o

--r.

h

-- u+ I

o

Figure 7-31. Whirling parameter for tube ar-

rays. (From Flow-lnduced Vibration by R. Blevins Oi977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.)

With newly developed techniques in vacuum brazing, stronger bonds have been achieved that reduce failures of internal components subjected to thermal shock and

Table 7-14 Maximum Recommended Shell-Side Velocities All liquids in 10 fusec Gases and Vapors-in fl/sec Pressure

(psi)

18 30 50 100 150 200 2'7 -tn.(vac) 250 185 160 110 100 90 15-in.(vac) 130 100 85 65 60 52 0 100 80 70 50 45 40 50 65 55 45 35 30 25 100

200 500 1000

fatigue.

Molecular Weight

55 45 35 25 20 18 50 40 30 23 19 t7 40 30 20 20 15

400 77 45 35

20 16

vices are relatively clean. However, it must be noted that shell and tube exchangers are more popular because of their flexibility ofuse. Certainly with moderate to heavy viscous fluids, the shell and tube exchanger is the only design to use. Figtre 7 -32 shows a plate-fin exchanger with rectangular boxes containing an assortment of plates and fins

resembling honeycomb structures. Fluids flow in tubu-

lar channels formed by fin attachments between plates (Figure 7-33). The plates that separate the two services vary from approximately 0.006 in. to 0.023 in. in thickness, depending on the pressure of the service. This design is commercially available at a temperature and pressure of approximately

-

452"F at 1,400 psig.

The aluminum flanges used on these units are designed per ASME Section VIII Division I and, quite commonly, are identical to ANSI 816.5 flanges. For further discussion on the thermal analysis and design of plate-fin units, the reader is referred to Kays and London [20].

EXAMPLE 7.1: REGENERATED GAS EXCHANGER DESIGN A gas-gas shell and tube heat exchanger is to be designed. The exchanger is to be used to exchange heat between a hydrocarbon process gas and a gas used for regeneration. The unit is to be designed per specification sheet in Figure 7 -34. The exchanger is shown in Figure 7-35. The process gas is to be cooled from 965'F to 705'F. The regeneration gas is to be heated from 200"F to 661'F in a parallel configuration. Thus, 975'F 200'F

GTTD:775"F

750'F

tiITD

:

625"F

125'F

.M


LMTD:

'7'75

-

125

149

:356"F

h (E,l

u25/

now,

q

:

riCo(LMTD)

The shell-side mass flow rate : 22,050 lb,/hr for the shellside gas, Co : 1. 10 Btu/lb.-'F. The required heat duty of the

unit is

q = 122.050r ' q

:

l!hr rr. ror j'l= 1:so.r"r lb",-'F --

Rfr

8.634.780

I

nt

The available tube area in the exchanger is determined follows: From Table 7-3, we determine that for a l1/+in. tube the square feet of external surface per foot of tube is 0.3272 ft:. Thus. as

Figure 7-32. The plate-fin exchanger. (Courtesy of Albraze International, Inc.)

Available area

=

(0.3171)

'ft

T (ZS:),u0., (tr) ,,

=

1.38E.95

it:

ng Sh€el Bar

Turning Distributor Fin

Figure 7-33. Tubular channels in plate surfaces result in excellent heat transfer in plate-fin heat exchangers. (Courtesy ofAlbraze

International. Inc.)

150

Mechadcal Design of Process Systems

I

HEAT EXCHANGER SPECIFICATION SHEET

2

5

5 7 a 9

lo

ll t2

l3 l5

l6 t7 t8 t9 20

2l 22 23

?1

27 2E

?9

30

3l 33

34 35 36 38 39

40 41 42

43

1t6

47 4E

19

T"b"-T,rb".h".t

J.i.t

50

Bundle

Entranc€

Bundtc Erir

52 53

57 5a 59

6l

Figure 7'34. Heat exchanger specification sheet. (O1978 Tubular Exchanger Manufacturers Association.)

The Mechanical Design of Shell-and-T[be Heat Exchangers

151

For the tube-side gas, 1%-in.-11 gauge tubes sa-tua-600

: k:

osME)

0.7, obtained ftom Process data

Np"

P

0.03 Btu/hr-ftL'F 0.01 Cp : 0.024 lb/ft-hr

=

Tirbe-side mass

r.gu;riil{

flow rate = 41,884 lb./hr

For each tube,

. ----

41:qq4 9./hr 283 tubes

:

148

rb-ihr

: O.1524lbJft3 ' 4 =: l'25 in" 1'010 in'; di Ar : 0.8012 in''? P

:

48.48 ff/sec

From Table 7-14 this velocity is reasonable sa-ra8-6lrt (^snE)

Flgure 7-35. Vertical gas-gas exchanger.

Shell-side nozzles C and makes the flow area

l. = a'(16)'z=

D are

16

in. in diametel which

_: Nr" : Nr"

2ol.o6 in.2 : t.396 ftz

(48.4D

a

93,278

>

(1.oro) in.

ffi

,o

tou

*

10,000 and Equation 7-19 applies

0.027(93,278)0.8(0.7)t/3(1.0)

:

226.78

h..1.

Shell-side mass density

v:

22,050

:

p.

rr. / rr,. \ + nr l=.:;r-l Ijbtt, secl j::--l:i:-

:

0.09 lb./ft3

Nr" ::+:1

From which,

:

48.75 ff:/sec

------o.os !!r n.396) ft, ftr

From Table 7-14 we observe that this is a reasonable velocity.

ftrbe.Slde Film Coellicient

Btu : ro -- hr-ft2-"F -- lt

For turbulent flow inside tubes we use Equation 7-19, the Sieder-Thte correlation,

Shell-Side Fllm Goefficlent

Nu"

N.,"

=

0.027(NrJ03(Np.)18 (rJrJ''4

:

?

= o.:o (Ps,

)"'rN*,',,

(;)"

Q-26)

152


For 60"-4 arrangement, p

:

1.75 rn. 1.r.

^"" _ -

-

8[0.43P'z

0.52'd"'z/4]

-- -

c= B

:

0.119

:

L75

-

1.25

:

_I

0.50 in.

80.83

-.

- -^.

I

-

ln.

n 8 baffles

:

=

(1.75xt44)

in

j\

hr-ftr-"F

1.lso;"n

1,384.91 ft':

From previous calculation,

- l. t9 rt'

-ft'

Available area

:

1,388.95 ft'z

In most applications the available area should not be

n

: p

0.09 lb-/fC average for tem0.05 lbm/ft-hr

:

Shell.Side Pressu:e Drop

Ap-

lh

12.348.00-15

hr-ft2

D.G, {0.119) fr (12.J48.00) lb./hr-ttz ^, _ 4 __. 0.05 lb./ft-hr

NR":29,388.24

Ns

D. G,

=

: :

ure 7-22,

8 baffles

t)

(7_Jt)

:

:

3.333 40 in. shell ID 12,348.00 lb./hr-ft2

=

For Np"

29,388.24,

f = 0.0022

ft from Figure 7-23.

f

f,=::=0.00t8 t.1. : 'y :

D"

100

/ rr.re,r"t

f C.rD,(l_.,t8__t

(5.22X10)!oD"1d

For plain and bare tubes,

The exchanger has baffles with 25 % cut, thus from Fig-

=

:

.

+nr

10% greater than the required area, such material is not wasted.

c"" - .=^.+ = 1.79 11'

Np.

8,634,780

1tz.st,)

as

ff

"l/'\l--- hr-ft2-'F

a,,

2

For the shell-side gas, p peratures specified, and

:

I + 23.40

Btu

:

(7-301

(40) in. (0.50) in. (22.50)

rt

+ 0.001

Area required :

D.(cXB) . , a\=-ll" p(t44)

^rn

0.001

22.50 rn.

Computing the flow area of tube bundle

n"

+

distance between baffles

B:

:

Btu hr-ft2-o F

IT _

ft

tube clearance

._

jn

tnnll l^',',"=l t0.8tr/\tt \u. r lvl

For gases used in this application the fouling factors are 0.001 shell-side and 0.001 tube-side. Solving for the overall heat transfer coefficient,

or

:

1100)

(7-2e)

"dr,

8[0.43(1.75)7 - 0.5rr1.25r']l41 _,/1rr^' _ r(l .25)

D"

=

\o

t+

[aJ

0.119 specific gravity of shell-side gas

r

0.8 from process data

d

:

r.0:

/

\o t+

tl]

= 0.9

Exchangers

The Mechanical Design of Shell-and-Tube Heat (0.0018)(12,348.00f (3.333X8

aP" = AP.

+

From Equation 7-35 we compute the shear force induced on the tube at the baffle hole,

1)

(5.22X10)ro(0. l 19)(0.9X1.0)

=

0.0015 psi 7-34

<

<

10 psi allowed on data sheet, Figure

I ^" \ /R:l#kltto-.tnr] V

t=''

qEB + --l --f",&:

"= EXAIIPLE 7.2: VIBRATION CIIECK FOF

c_

2(1.00

span between baffles

=

Shell-side gas density

4

:

:

=

22.50 in.

16.015

1.25 in.

ds

:

= =

*

in.

1/o+

Fr.

:

1.200 lbr/ft

F.

:

eaF,

1.156, where t/e+ in. is the baffle hole clearance (s€e Figure 7-34)

A,'

: + [o," - o,"* + D'= d'te - al nz t44t P I

^, Ar

210.0

in., D,o : 37.125, P

=#[oo :

- rr.,r,

=

G":

18,522.0 (5.145)

(1. 1ox1.2oo)

rtBE ^, -

-

117.236

A

sec

b

:

0.0069

o

SeC"

F

+ (zig*")

-

=

6.471

CpdlpV2ale

(7-38)

------;----zE"r

'

r.2s)]

lh

.:"'

!-: lDf

J-(l6.0lt - SeC-

+n

ft'-sec

,

(2.0s1) ft, 5 n'-sec 0.0e

:

:5.14s

-;l tt'-hr

1.10 and

aFrL

2(32., l|1

:

-

Nse

2.051 ft2

*,0-', (oryJ

16.015 lbf/ft

1.75

.tf#6.?s

1trpsi

10_E

p orr.rrur$ (9 z1tzz1 !": tDf

L = q:

From Figure 7-20 we compute the shell-side gas velocity bgtween tubes.

:

x

ft=

in.

D.

27.0

crPP4

Fr:

18,052 psi at shell-side conditions

1.25

=

lbr/ft

Frorn Figure 7-25, a

0.09 lb-/ft3

*

= '. [.' ?]il''"l,o

From ASME Section VIII Div. I (see Chapter 4) for the tube rnaterial at design temperature, o"n,

= 4.941 x

7-l is to be checked for

possible vibration problems. To accomplish this we compute the damage numbers of equations 7-38 and 7-39.

B = tube

-

Es

(7-35)

0.?33)

27xlop

REGENERATED GAS EXCHANGER The exchanger in Example

153

5

betwe€n tubes

NeB

:

rr.rr

(lJoJ

ft6.471)

1.00

Cedp\Pbla ,.." ", _ _EJE;_

(7-39)

154 ^


bF, L4

For the tube-side,

E,I/\ (o.oo6ex t.2o)

6

:

N.o

l]i I (22.50)a \Lz ln.i

106)::] (0.06881 in

f(

x l0-5

9.520

rt

th-

\

(27

ry

M,:1.448f:o.o+sf

fr

0.036 r4.94r

6..,

:

7.553

in.

\ 12 |

:

0,.. :

x l0 7 ft

1.000

H (;9" [.J",r [.)

o.o36cV2d,

(7

-4r)

(1-44)

d,

=

1.25

dt

:

1.084

'"

- 8(rrjo4:

9.063

x

10-6 in.

in. = in.

0. 104

:

EXAMPLE 7.3: CHLORINE SUPERHEATER DESIGN A plant wishes to use hot oil to heat chlorine sas. The exchanger unit. a chlorine superheater. is to be i TEMA 18-150 AEL. The chlorine gas is to be heated from 77oF to 158'F and the hot oil is cooled from 250.F ro 176.F. The exchanger is to be rated and analyzed for tubetubesheet loading. The exchanger specification is shown in Figure 7-36. The thermal duty is 600,000 Btu/hr. The exchanger is a parallel flowing unit.

ft

0.090 ft

., ,0"" lb. " "*- *l

ttt.zsF in.2 +

(1.084)2 in.2

/ r ,rug \ /rzza in.r\ 1:z-z ruJ \--

ft-/

LMTD =

For shell-side fluid,

crrD -

(with

a

lbJ|

LTTD

\tttol

_

173 'n

-

t8

:68.496.F

irz:\ \-tr /

parallel exchanger no correction is needed for LMTD)

Tube-Side Film Goefficient For chlorine gas,

frr \ 32.2

250'F 77"F

:

. /crro\ '"

1.710 Hz

,'^ /,^,..^\ r:!,llils

in. 176'F out in. 158'F out 173'F LTTD: l8"F

Shell-side (hot oil) Tube-side (chlorine gas)

GTTD

(27 x. ro6)-,-]k

o.oe

:

With this magnitude of tube displacement and Nss and Nsp being in the safe zone, we conclude that the exchanger will not have vibration problems.

With NBE and NcD not exceeding 1.0, we do not expect vibration trouble. To be certain we compute the maximum tube deflections as follows:

p ' =

ol

x t0-)(t,r.rru,2 lit,ltl F \ 12 / \0.04s/

- fr I 9.520 x l0-5

lb.

rt2 /rr
f" =

:

:

",

Nco

d-,

4

:

rb-/fc o.oo3:15

ft'

q

:

rirCog-Uf O;

Co:0. l16 Btu/lb.-'Fi p:

|.667

The Mechanical Desisn of Shell-and-Tube Heat H

Exchansers

EAT EXCHANGER SPECIFICATION SHEET

I 2 3

Add.€ss Plaht Locarion

Prcposal No.

Dale

Rev.

5

6 7 a 9

Siz.

(Horlvert)

TypG

Surf/Unii (Gross/Eff.)

In

Pa.allet

Series

So rl

PERFORMANCE OF ONE UNI'I ShcllSid€

Ffuid Ouantitv.

Total

Tube Side

Ur:T otL

to

ll

Connected

Surr/Sh.ll (Gross/Eft.)

So Ft: Shells/ Unit

Lb/Hr

EEDfuflE

GA-

72

Liquid 14

t5

l6 t7 T€mper.tur.

l8 soecific

(lnlo!l)

,

cravitv

lC

l9 Viscosity, Liquid 20

2l 22 23 21

25 26 27 2E

29 30

3l 32 33 31

ÎEg

I ^fiO

Cp

Molecular W6isht, Vapor Molecular Weighl Noncondensable

o.+zao

Specitic Heat Btu/Lb "F Thermal Conducalvity Btu Ftltlt Sq Fr ' F Latent Heat Btu,/Lb @ "F

Inlet Pressure

O.11to

Psia

Ftls Pressur€ Drop, Allow. Calc. Foulins Resisranc. (Min.)

Psi

(D O O.OOO Heat Exchansed Bru/Hr: MTD (Correcr€d\ b ,t,5 Transler Rate. Service CONSTRUCTION OF ONE SHELL sletch (Bundle,Noz:le Orientation) Shell Side D€siRn,/T€st Pressur. Psir 15U

DesiEn

TemD€rature

35

No. Passes Der Shell

36

Corrosion

Allowance

t

'F

/,79

ln,

ln

37

3a 39

7{6

'F

Sizo &

Out

Ralins

op I

rube No.,5O 4l Tsbe Type

1to

4Z

Shell

13 11 45 46 47 4a 49

Channel or Bonnet Tubesh€ct-Stationary FloatinE Head Cover

Bafites.cross

In.;rhk

(Min/^vs)

In.r r€nsrh r5Ff': Ft; Pitch Material

If{

In.

+30 a.50€-so

€>a5

Tubesheet.Floating

lmpins€menr Protectio!

b

Supports-Tube Bypass Seal Arransem€nt

TvDe

4h

% cut (Diam/area) 1 .j/4"spacine:

U-Bend

cuc

tnlet

In

Type Tube-Tubesheet Joint

50

5l

Bundle Exit Gaskers-Shell Side

Code Reo0irem€nts Weight/sherl

TEMA Class

55 57 59 50

5l

Figure 7-36. Chlorine superheater heat exchanger specification sheet.

Lb

155

156


P nr

700,000

ft:

Btl,

9.116 _

t*

88.0ee.783'u.( hr \3600

^

5nr

88,099.733

(68.496).F

-r

rDm-

:

(.42o

) sec/

lh

ftr

For each of the 150-l-in.-14 BWG tubes, 14,680

:

25.'796 ft/sec

Llg{'o)

sec\12 / ',

(1.667r

'

The smallest shell-side nozzle is the 3-in. outlet, where

!!r

Ar

ftr \ lhr"''l/ {:ooo

'frhr

(5.0

'

=

0.027(298,860.527)0E(0.835)r/3(1.01

(re)'

'', 0.7 <

(610.464r(5.0

N",:\!i =h,

lqi,t\n l

-+nr-n'- -f

Shell.Slde Film Goefficient

p

fiCP(LMTD)

:

lh

Np,

:

<

17,000

^ _

619.a64

D"

:

8[0.43 p')

0.5rd!4]

8(0.43)(1.2sf - 0.5 r(l.0)z l 4l r(1.0) 0.711 or De : 0.059 ft

c: |.25 - 1.00 : 0.25 in. B : 30 in. for 6 baffles D, : 18.00 in. : shell ID D.cB I-" = _-

(

18.00)(0.25 X30)

p(144)

\1.2s)(t44)

: t-t.11 ll.

as

.a^ iI (3.600)::: lh sec hr : 31.987.20 ^ : ______=-_:=_______j:: -G. .+ (J. /) rt' hr-tt'

(6.664)

k=

-

Tdo

^rn

0.426 Btu/lb,-"F; 62 46 -;T:

Btu

hr-ft- "F

t l0-,) Bt' hr-ft-'F

\12

:

Btu

For 60" A arrangement,

NN"

cp

=

lb^

ft-hrro.426rlb.-'F = t4.075

0.077

Btu x l0 3) 'hr-ft-"F

'

Very reasonable

u = 2.544ltt^tft-hr

,0.116r ' ft-hr lb^-'F _____ =Aal(

tN.,l,'

ft2

v : _-- !g :2.092:! 0.051 ftr sec

Np,

0.027(NrJo

:

in.'?:0.051 fr3

Btu

:

q

7.393

12.5+4t

N*"

h, = 41.866

:

r'l'.: &,

u".:l.Cp,k=5.0x to-r-gu ^' k hr-fc'F =_

0.10? ft3/sec

Reasonable

:298,860.527

lb'

:

ftr

-

lb'

(0.036)

-r'

l9r E9

62.46=

Nq. = j:l; I = 0.0148 Cp = 0.036 lb./[t-hr

ro.036r

6.664

ft3

I

Nn. =

!r sec th

v = -........- 2( J9c = (0.0037941ft 50)tubes

r2s.7e6t

6.664

sec

:!

| .667

:

i-frl

14.680

d+ (68.4e6).F

0.077 Btu/hr-ft-'F

lh

The Mechanical Design of Shell-and-T\rbe Heat Exchangers

Nn"

: DG _

(o'059)ft(31'987.

P

z.su

,0#

lb^

'v

=

741.842

ft-hr

r,.12

I

h- -

ratio of OD to ID of tube 1.199

h' 73'629 ot.+os Blu : Ar = l.l99 - --"-'br-ftL'F

\0.14

U" =Jx!11-trr:l "' Pl

D.'

:

Ar =

1-JJ

in=

1.001

d=1.0 Aa

The exchanger has baffles with 45 % cut, so from Figure

=

\p",

(l2xo.o77)

Btu tt t tt ;$:F o.o5964.025)r/36)

Since both gases are relatively clean, the fouling factors for both sides are 0.0001.

-

h=

196.720

t* =

161.436"F

6r.M + 107.480

Maximum allovable tube joint load

1

-

99.680)

= L"*"

1..* = A,ouf, For SB-l6l-2fi) at 162"F,

* o.oor + o.ooo8 * 43.866 ,1 .. 37.779

(196.720

61.,109

r -, :

o"n:

10,000 psi

g

=

(0.239)in.1lo,m)

tn.'

(1.0)

2,3e0.00 lbr

U=19 700,0m# Area required

:

=

521.875 ftz

(re.582h;h(68.4e6) Available area

=

(0.2618X150X15)

:

589.050 ff3

This implies a 12.87 lo excess, which is acceptable.

The tube wall tenperature is used in a method developed by Miller [21], which is a more exact approach than most and consequerdy results in a more economical design.

P,

:

shell-side pressure

At = tw -

:

D"

ID =

18

in.

=

1.5

ft

ft,gSZ.Z0,l\. nr-n'

shell

=

, . ..

18.0

ID =

-

f

i=

0.w225

D" = 0.059 ft

70'F

Ds

0.0

-

:

91.436'F

CA

18.0 in.

(looxg'o) PR -= og - qfp-
Use ta'a

=

34rc-in.

For the shell,

f"=

:

70oF

CA = corrosion allowance = 0 for pure helium (inert)(erosion is negligitle)

'st'ctt

C"

-

:

+ l) o)'D.rd

6 baffles shell

161.436"F

ambient air temperaturo

Plessure Drop f"G.,D"(N"

\ : D, :

=

100 psi

: D. : At

^'' = iSzrl

ta; ta

:

aPs =

=

F.+

=

=

0.1875 in.

27.546

x lffpsi

(0.w2zs)(3r,987.20f(1.5x6

at 161.436'F

+ l)

(s.22X10)ro(0.059)(1.00lx1.0) 0.008 psi which is acceptable

158


Tube Metal Temperature

: : ar : : n: na, :

where E1,

modulus of elasticity of tubesheet metal tubesheet thickness 1.1875 in. cross-sectional area of tube (see Table 7-3)

:

T

For parallel flow,

Atn:259-77:173.F

At: tla - 158 : At": 18 =o,no Atn 113

lS.F

600,000

rt I Ol2 /rtr'vr-

4

B=

:6.794

(s 10.510x173)

6oo'o00

' = (s 10.510)(18)

ltl ^'-l_ luh

A =

-u"l _

6.794 U[ ,-i-5i%

From Figure 7-1"1, F"

:

65.2e41

176

L":

t"i

+

+

(0.28X250

F"(t""

-

O.28 (7-11)

-

176)

:

tljOt :

Pri

:

= 99.6t0",

C

:

254.469 in.2

-t2)

I'

Ler

= !4a,

E,B-

dt

=

- 70"F :

Ul8.J75P .{l8.r2s),J

-

Let APn

=

(13.79q t21.546

86.394 in.2

:

168.075 in.2

:

:

100 psi

^y

106X35.850) 106X7.1668)

-)

sosr

equivalent pressure difference. psi D rri

in./in.-'F at 161.436"F

tube-side (channel-side) pressure

At = 161.436'F

total cross-sectional Area or tube holes

^

For the shell material, 10-o

-

(A-C) tl :--

coefficient of thermal expansion, in./in.-.F

o, : 6.090 x

shell cross-secrional area

86.394 in.z

-o3r = I

t*=t"i,-,n,o!.+ tt.n-r".t n. :

:

.1668 in.2

r96.jZO.F (7

711

254.469 in.2

expressed as

t"i)

t-=77 + (0.28X158 -

ct

=

The ratio of the inside shell bore area to the net tubesheet area minus the tubes is the net area that resists the tube and shell reaction forces and moments. This ratio is referred to as the ligament or deflexion efficiency and is

l=u6eo

Lr,=tr,o*F.(tr-tm) t"i -

7

-

6s )q^

(Di"

{

:

For cold end,

g-

:

4

c-

:

number of tubes 150 (ls0)(0.239) 35,850 in.2

rr lR Or2 A = ':A

For hot end,

Ul:

0.239 in.2

n

ar

:

100

-

100

-

(100)(35 850) 168.075

-21.3298 psi

Computing the differential thermal expansion

:

Ac

Aa=e,A,-o,A.

4*:

91.436.F

(7.010

x

10 6X91.436)

-

(6.090

x t0 9(91.436)

:0.000084

0.834 PE

:

the effective pressure differential induced by the equivalent pressure difference, APs, and thermal expansion,

Aq

P,:P+(ao)

qna'

A_C

(7

47)

fl The Mechanical Desien of Shell-and-Tube Heat Exchansers

Pe:

:

(13

-2r.32e8 + (0.000084)

7e?l

159

lq6)(3s 85)

168.075

226.263 psr

Assume ihe normal tube projection beyond the tub€sheet to be r/a

in.,

L

:

(13X12)

-

2(1.1875)

-

2(0.125):

Defining the dimensionless parameter, tr,

\

|

:

1.08

as

t025

-

:rr-l l--[Lr -DTdA -

153.375 in.

(748)

D.

L,J

a

1.08

"I

(13.799

x

i09(3s.8s0) (153.37sX1. 12sf(27.s46 x 109(168.075)

4

6

A

'10.25

I

(18.125)

1ot2

\

Figure 7-37. Tube stress factor

14

Ir

16

versus

\.

\:2.696

: 4r-*r : q,(.-r

-415.968 psi for

| :

f+

:

-0.046

-415.968 psi is well below the maximum allowable stress, which means that the tubesheet is of sufficient thickness.

One could repeat the process if it was desired to use a thinner tubeshe€t. Had o.1-o*1 exceeded the maximum lowable stress for the.tubesheet material, then a greater tubesheet thickness would have to be selected and theprocess repeated.

al-

From Figures '7 -37 , 7 -38,

fI

:

1.55;

lz:3.12l,

l: :

7 -39

,

and 7 40:

-0.046; f+ = 1.970

The maximum radial stress in the tubesheet is expressed

.'-.,,ffi11,9' f-"

I00){2s4.469X2.sOs8)

:

I (rg.rz5\t

(168.07s) I \ 1.125 i

4[(2.50s8X1.ss) o.1."";

as

(7-4e)

4(Vfr + fr)

l,o,o.,, -- -{

1oo

q

-1,418.659 compression for the tubesheet material

+

<

3.12]

16,?00 psi allowable

2

4

6

a

lo12

14',r6

X

Figure 7-38. Tube stress factor 12 versus tr.

|a

160

Mechanical Design of Process Systems The maximum stress in the tubes is the sreater of the follow-

ins:

", :u-[^,.na,

(n,

APt* - A_C

(7-50)

({ + lr)

I

or

[

-\- -:t'e (A-crl]l ",{t" _clAP,_ =A nu,[ (* + |.4)

o.2

q

o.o

(7

-sr)

I

-o2

;.lr"-l-,,,,n

-ot -0.6

(100x254.469X2.50s8) ro^ -,lrr^ 168.075 t-" -'

-oa -1.O

(2.5058

+

1.970)

T

Figure 7-39. TUbe stress factor f3 versus

\.

o,1^

1:

-92.62 psi for Equation 7-51

EXAMPLE 7-4: ASPHALT COATII{G lllx HEATER-A NON.IIEWTONIAN FLUID APPLICATION A roofing manufacturer needs a shell and tube heat exchanger to heat an asphalt coating mix from 425'F to 500'F to improve flow characteristics. The fluid to heat the asphalt coating mix is a leading manufacturet's hot oil heat transfer fluid. The asphalt coating mix is to be tube-side and the hot oil is to be shell-side. Determine the size of unit required with the design to be counterflow. The process is described in Example 3-6. The exchanger heat duty is to be 1,000,000 Btu/hr. See Figure 7-41 for complete exchanger specifications. First we compute the LMTD for a counterflow exchanger, Shell-side (hot oil)

650"F in

550'F out

500'F out

425'F rt

150'F LTTD:

125"F

TLrbe-side

(asphalt coating mix)

GTTD: 2

4

6

8

rO12

I

14

16

Figure 7-40. Tube stress factor f4 versus

18

\.

- qrp . lcrrDl '"\rt-/

LMrD: crrP

_ l5o_- l?5 : r.7.t2"F ,

11501

'\*/


Exchangers

161

HEAT EXCHANGER SPECIFICATION SHEET

I

Job

No.

2

Addr€ss Plant Location

Proposal No.

Date

Rev.

5

6

Siz.

7

Surf/Unit (Gross/E f.)

(Horlv€rt)

Type

9

HOT otr-

to t1 Ffuid OuantitY, Total t2 t3 Liquld t1

2l

Lb/Hr

Tsmpe.ature (lnlout)

t8 sDecific cravirv @ l9 Viscosity, Llquid 20

gtu/Lb "F Btu Ft Hr Sq Ft ' F Btu/Lb @ 'F

26

Ftls Pressure Drop,

2a

Foulins Resisranc€ (Min.) Heat Exchanaed

r-".r".

n"r",

4z€ q3*

7

l-lz,

d.<2b

a.7b

a.7>

Ft

0.52b

q4?

D:47

t

I

IO

Psi

b

t0

tO

atu/Hri MIO (Correcied)

"F

S"-i."

so

32

DeEisn/TestPressurc

Psis

l
rt " r

Sketch (Bundle/No:?le Orientation)

CONSTRUCTION OF ONE SHELL Shell Side

3l

EO

/ 226

O.sasn Temperature

35

No. Passes D€r Shcll

36

Corrosion

3a 39 40

Si2G & Ratins

Allowanc€

ln.

Out

op 74 tp 274l

luge !o. 5gt Tubc Type

42

sh€l

11

Channel or Eonnet Tubesheel-StationarY Flo.lina Head Cover

16 47 4a 49

So

Psia

Allow.,/Calc.

27

41

a

h.4)

Cp

Specitic Heat Thermal conductivity 24 Latent tleaa 25 Inlet Pressurc

31

Se.i€s

ASHJNLTCd'NN6FNIf,

Molccula. Weipht. Vaoo. Molccula. Weisht, Noncondensable

23

30

5=

//.60

t.60

656cp

22

29

Parall€l

PERFORMANCE OF ONE UNIT ShellSide

a

77

Connected In Su.r/Shell (G.oss/Efi .)

Sq Ft: Shells/Unit

Baftles-Lorg Supports-Tube Bypass Seal ArranAem€nt

In.:rhk (Min/^ve

lIl 8ly6

In.; Len$h

20

Fr;

Pitch

I.A

In. <-

30

fgl+119 9 !!

Material

op

In. lshen

cover

0nt€s.) (Rernov.)

I Channel Cover Tubesheet-FloatinE lmoineement P.otection o/o Cur (Dia6lA.ezt Seal Typ€

U'Bend

Spacina:

c/c

Inlet

In

Type

Tub€-Tubesh.et Jolnt

50

5l pvt-lnlet Nozzl€ Gaskets"shelr 53

side

Bundle

Entranc€

Bundle Exit

Tube side

-FloatinE Head

codc Requirements

TEMA Class

55

59 50 61

Figure 7-41. Asphalt heater heat exchanger specification sheet. l@1978 Tubular Exchanger Manufacturers Association.)

162


In a counterflow exchanger we must correct the LMTD. Using Figure 7-16 we have for a one-shell-pass, two-tube-Dass.

P=

500 6s0

-

425

-

=

425

0.333; R

:

(0.93X137.12)

650 500

:0.93.

From Figure 7-16, F LMTD becomes LMTD

:

:

127

-

550 425

Thus, the corrected

For asphalt coating mix at 450'F we have the following properties:

q

: :

:

0.368 Btu/lb.-'F; 2,251.20 tb^/ft-hr

fiCo (LMTD)

=

1,ooo,ooo rO 16Rr ---'''lh

-i:L

r

-oF

p

:

89.2321b.ift3; p

:

933 "O

1,000,000 Btu/hr

9!! hr

l--t?

:

2l,309.196 lb^/hr

{t)\oF' '---'

/\ thf 21.309.196 "' l ' '" hr \3600 sec/ ^ ^,, _tt3 i u.uob th I

Nn"

l-4x13*xal3 1-xa

I

lh co,'tt'"m

sec

where

x

We will try 594-3lq-in. tubes-14 BWG. Checking the tube wall thickness for internal pressure, 150 psig

PD) - 0.6P

o"11E

: E: P: ID :

where o1

t-," "- = t""r4

:

maximum allowable stress for tube material, psi tube weld joint efficiency l.g internal pressure, psig tube ID, in. 150)(0.584)

(17.s00x1.0)

-

:0.005

0.6( 150)

0.083 in.

Flow velocity through each tube is

v

i: - =j!L (0.0019)ft'z(594)tubes -0.066

=

fi3

0.059 frlsec

ratio of the fluid particle yield stress to the shear

Lab tests reveal that

fluid particles at the tube wall

x : 0.5 (0.5r

.I 4 (U.)) .^ - - -. + -:-------" n= 1l (u.)f := - =:;

=

and

1

:

3.9 for which

O.378

Now,

:

(

:

stress in the

It,

t-,":

(1-7 )

When working with non-Newtonian fluids, rheological data are necessary. The reader is encouraged to refer to Govier [22], but will often find that rheological data are not available in literature. In this situation a samole of the fluid must be sent to a testing lab. Do not attempt to approximate a non-Newtonian fluid with Newtonian equations and assumptions-the results can be a catastrophe. At the current state-of-the-art there are no simple answers for such complicated subjects such as non-Newtonian fluids. Samples of our fluid were sent to a testing lab to have the properties evaluated. Some of these properties have already been given. The fluid is determined by the lab to be a Bingham fluid, in which the shear stress and velocity gradient ofthe fluid particles are linearly related. For a Bingham plastic, n in Equation 1-7 is

I

^

DiV2 - ip

:

.522"F

Tube.Side Film Coefficient

Cp

To obtain the tube-side film coefficient we must obtain the Reynolds number. The asphalt base coating mix is a non-Newtonian fluid (see Chapter 1), so Equation 1-6 is not valid. So, to compute the Reynolds numbet we must use Eouation 1-7.

(0.584)0 r78(0.059)?-"

N.'* =

€r -1 (89.232)

sec

8.0

th

+n"

:

0.092

in.

The film coefficient is determined from Figure 7-42, which is the Metzner-Reed-Reynolds number (Equation 1-7) versus friction factot f. From this figure we obtain

f

:

180

Now, we must compute the pressure drop through each tube to determine if a 3/+ in. 14 BWG tube is adequate.

-


Exchangers

163

with a viscosity of almost 1,000 cp. The Prandtl number for our fluid is (2251.20\

f

N".: Np,

o

=

lb' ,0.368' Btu ft-hr lb--"F

Btu (o.lo) ' - hr-ft-"F

8284.416

For laminar flow, the Sieder-Tate correlation is

lt-

c

N", =

.9 .9 u-

N", hrD k

Meizner Reed Reynolds Number' Re"*

:

T: r.86

,

eo

kl''

ffi]"',t.,

[,o.or,,rrro.o,u,

= 2.r85 Rr,r

(- j6) ){{l ll

Figurc 7-42. Friction factors for flow of non-Newtonian fluids [22].

[6*.16.,;[n)]''

"L_,|

hr-ft-'F

10.5841

\ '-''

12 /

-^

Btu

hr-ft2-'F

For our velocity heads we use the entrance and exit loses

Shell-Side Film Coef ticient

and get

:

!f

O.ZS

+

1.00

:

1.78 (see Figure l-1

l)

q

Using Equation 1-4 we compute the pressure drop over 2O-ftJong tube as

* r* )qr ' : ILL \d - lze,

:

p!g(zo{l?I'* *

(t -4)

: r.zr ]

(8e.82)k(o.o5eFg(,-iI--J 2(32.2)

=

2.47gpsi

: :

0.526 Btu/lb--'F; 62.213 tb^/tt' 0.076 Btu/hr-ft-'F;

: Acceptable

_/-\ l'tu I

p: p

:

t

Looking at this pressure drop one realizes that a flow velocity of 0.059 ft/sec is not so slow for a bulky fluid

0.30 cp

I

tb.-'F

It-lD;T sec'-rDl

(O.997)(O.a)

:

0.720

nr hr \J.600 sec/ , ... Rf {0.526) "'- 1127.522\'F t.000.000

m

aP,

rirCp(LMTD)

For the hot oil at 600"F the following properties exist:

a

Ce

op,

ae,

:

4.141

62.213

th :! sec:

th +tt'

^.-

^ U.UD/

ftt

-Sec

lb-

lb.ift-hr

164


The smallest nozzle shell-side is a 3-in. nozzle, making the maximum shell-side velocit) 0.067

Fouling factors are as follows:

i:fr3 sec

' - boslF :

Btu

h-" = 155.959 hr-fta'F

Asphalt coating mix

1.305 ftlsec

-

Hot oil

Very reasonable

: :

0.01

0.004 1

(0.720) lb'

,,., rrpr _ -

Btu ro.526r ft-hr lh -oF

ACp

k

_ rl + 0.004 + 0.01 + 155.959

Btu (o.o76t ' 'hr-ft-'F

"

-"

4.695

Elr,r

hr-ft2-'F

Fora60'Aarrangement,

n

810.43

p']- 0.5rdl/41 810.4311.00) -

-

r4 D" = 0.127 or De :

0.5rrl.0r/41

?t

"(0

D.(c)B

(27.00X0.25X

15.0) ^ -^^

144p (1.00)(144) . 4.t41jl t3,600r l ^msechr U<=-: as

=

0.703

21.201 .920

*, _ D.G, _

1\Rc---

fl

th

p

5 nr-It"

lh

'

jH:

\o

'

Available area

=

323.918

Tlr,r

- i27.s22f nr-rt'- -|:] -'.-

:

1,830.308

:

(0.1963)

F

ft'?

iIt

(zo)

rt 694)

:

2,332.94^ tt

extra margin is needed, so25% to 30% excess area is not unreasonable. For more heat exchange it would be better to consider a surge tank with interior and exterior heating elements, since we are at t}te limits of the shell and tube design and, with a more viscous fluid, a surge tank of the type in Examples 3-3 and 3-4 is more practical.

ft-hr

12 for baffles

with 15% cut

Shell-Side Pressure Drop tGiD,{NB + l) ^. _ (slt(t0t6.1d

rq

From laboratory tests it was determined thar plp* = 2.0.

Ns

=

16 baffles

D. = shell ID (

nr

Twenty-seven percent of the excess area can be eliminated by reducing the number of tubes. This would increase the flow rate in each tube and thus the pressure

,

:'*L

n" = lo4rNr,f ':[aJ

(4.284)

!!

drop, which already is at 2.5 psi. For non-Newtonian fluids, properties can vary from sample to sample and

(0.011) fr (2t,201.9201

/

"

nr-n'

From Figure'1-21

:

0.011 ft

c: 1.00 - 0.75 = 0.25 in. B : 15.0 in. for 16 equally spaced baffles over 20 ft D. = 27.00 : shell ID "

Area required

1,000,000

Btu- ft l2)(0.076) hr-ftr-'F (4.983)'/r(2.0)o (0.011) ft

:

27 in.

:

2.25 ft

G, = 21,201.92 lb./hr-ft2 r4

Nr" = 324 and from Figure 7-24, f =

O.0O75


f o nn75 F_'-"'"--nnn
'

t.2

:

dT(t)

d:

specific gravity

/

a, and if the ratio of dT(t)/dt to

_l

dt

:

0.997

-:

L{r, = ln l2oo

\o t+

-

t\

\80/ dl(r) / ao \/-r\

1.0: (E

dr

(0.0062s)(2 r,20 l. 9D, Q.2s) (r7 )

(s.22)(10)'0(0.01 1)(0.997)(1.0)

:

165

T(t):(200-0-(140-60)

1.2

D" = 0.011 ft "y

:

L(t) : 0 when t dl(t)/dt exists, then

:

For plain and bare tubes,

Exchangers

\200

-

ri \80i

-1

200-t

I'Hospital's rule states that 0.188 psi, which is acceptable

EXAMPLE 7.5: ZERO LMTD EXCHANGER A candy manufacturer wishes to cool hot molasses to 140"F for the food processing of various confectionaries. The molasses is coming from a heating-blend kettle at 200'F. Spring water is to be used and it never varies ( + t/+'F) from 60'F. The water is to be heated to 120'F, and held at that temperature to heat honey. Determine the LMTD. The exchanser is a counterflow desien. Tube-side

Shell-side

at:

200'F in 120'F out 80'F

140"F out 60'F in

At

=

,. T(t.) .. dT(r)/dt 1.'t L(t) i-= d dl(r)/dr or, witha : 120'R

r1 |

-1 liml r.al _I l= I |

troo

lim t-uu

- tl

Therefore,

LMTD

:

to-Ro

.lnt/so\

- t)

80"F

80'F

With this value of LMTD, the exchanger can be designed, using the correction factor in the case of a counterflow unit.

80'F

Now using Equation 3-23 we have

LMTD:

(200

o

NOTATION

A

:

tube surface area, ft2

At : cross-sectional area of tube, in.2 a = constant for a continuous beam shear, dimen-

o

I

\80/

This problem is somewhat similar to that of Example 3-4 in its formulation. We must define the LMTD as the ratio of two functions T(t) and L(t) for which

b: c= c: C

:

sionless

constant for a continuous beam deflection tube clearance, in. constant, in.2/lb1 (Equation 7-37) 10 a(sec)05/(ft)'5 (Equaconstant

:9.7 x

tion 741)

1141P

:

T(t)

Lt)

: (200-0-(140-60)

.ln l-l1200 \80/

rl

As temperature t approaches a certain value such that T(t) and L(t) become zero being divided by zero. The derivatives of T(t) and L(t) exist when t approaches this value of t, so we can apply I'Hospital's rule that if T(t)

g" = 12fE t or)o 5 (Equation

7-2)

: drag or force coefficient for a body immersed in a fluid, dimensionless Cp : specific heat at constant pressure, Btu/lbn'-'F D:4 x hydraulic radius. in. D : tube diameter, in. D : parameter (Equation 7-27) ds = diameter of baffle hole, in. di : inside tube diameter. in.

Cp

166


: outside tube diameter, in. : 4 outside tube diameter, ft Ea : modulus of elasticity of baffle material, psi 4 : modulus of elasticity of tube material, psi F" : correction factor, dimensionless (Figure 7-16) F". : critical buckling strength for tubes, lb. Fr : force induced by fluid flowing around immersed body, lbg F, : shear force against tube at baffle, lbr used in determining tubejoint force, ; I constants lbs (Equations 7-3 and 7-4) i' I f" 1 fundamental natural frequency of tube, Hz gc : gravitational constant : 32.2 lb.-ftilbr-sec,

: parameter (Figures 7-30 and 7-31) Tn : thickness of inside tube deposits, ft Tro : thickness of outside tube deposits, ft T* : tube wall thickness, ft t"" = caloric temperature of cold fluid, 'F t"1 : caloric temperature of hot fluid, "F Li = inlet cold fluid temperature, oF t"" : caloric temperature of cold fluid, 'F thi : inlet hot fluid temperature, 'F th. : outlet hot fluid temperature, oF t = tube wali thickness, in. t* : outside tube wall temperature, 'F ar = temperature differential (tr - tz), .F U : overall heat transfer coefficient for exchanger, Btu/hr-ft2-'F U, : the value of the overall heat transfer coefficient at the caloric temperature. Btu/hr-ft2-.F V : flow velocity, ft/sec T

do

GTTD = greatest temperature difference between the shell and tube side fluids, 'F h = film coefficient, Btu/hr-ft -'F hi = film coefficient inside tube, Btu/hr-fl:,-'F h" : film coefficient outside tube, Btu/hr-ft -'F hi, : outside film coefficient of tube, using outside

I:

: k: k: k* : Ir

tube surfaces temperature, Btu/hr-ftl'F moment of inertia, in a moment of inertia of tube cross section, in.a structural constant, dimensionless (Equation 7-2) equivalent effective unsupported length of the

tube, in. coefficient

of thermal conductivity of tube wall, Btu/hr-ft-'F kr = thermal conductivity of fluid, Btu kn : thermal conductivity of foreign deposits inside of tube, Btu/hr-fi-'F kso : thermal conductivity ofdeposits on outside of tube, Btu/hr-ft-'F L = tube length or span length of tube, ft LMTD : logarithmic mean temperature difference, "F LTTD : lesser temperature difference between shell and tube-side fluids, 'F / : typical dimension of body immersed in fluid, n rir = mass flow rate, lb-/sec mt : mass density of tube metal, slugs/ft3 NB = number of baffles Nna : baffle damage number, dimensionless Nco = critical damage number, dimensionless (Equation 7-39) Np, : Nusselt number, dimensionless

: : P: p: q:

Np.

Nr"

r=

Prandd number, dimensionless Reynolds number, dimensionless

axial force, lbl tube pitch, in. rate of heat transfer, Btu/hr radius of gyration of tube, in. (Equation 7-2)

Greek Terms

: 6: p:

ct

factor of effective tube resistant area, dimensionless

deflection or displacements, in. dynamic viscosity of the fluid inside tube, lb./fthr p* = dynamic viscosity of fluid at tube wall, lb-/ft-hr uB : Poisson ratio for baffle material ut : Foisson ratio for tube material or : frequency of a given mode, Hz p = density, lb*/ft3 d"1 = allowable stress for tube, psi o" : allowable tube compressive stress, psi, for the tubes at the outer periphery of tube bundle (Equations 7-1 and 7-2) o, : minimum yield stress of tube material at design temperatue, psi : f sum of structural damping and the fluid damping, dimensionless

REFERENCES

l.

Heat Exchangers, Howeli Training Company,

2.

Houston. Texas. 1975. Snndnrds of the Tubular Exchanger Manufacturers Association (TEMA), 6th Edition, Thrrytown, New

York, 1978.

F. L. . "What's the Difference Between TEMA Exchanger Classes," Hydrocarbon Processing, 59, June p. 92, 1980. Ludwig, E . E., Applied Process Design for Chemical and Petrochemical Plants, Volume 3. Second

3. Rubin.

4.

The Mechanical Design of Shell-and-Thbe Heat Exchangers

Edition, Gulf Publishing Company, Houston, Texas. 1983.

5. Small, W. M. and R. K. Young, "The Rodbaffle Heat Exchanger," Heat Trans. Eng., I, ro. 2, Oct. Dec. (1979), p. 21.

6. Skrotzki, B. G. A., "Heat Exchangers,"

Power,

June, 1954.

7. ASME Boiler and Pressure ry'essel Code. Section VItr Division 1, American Society of Mechanical 8. 9.

Engineers, New York. Colburn, A. P., Ind. Eng. Ch.em.,35, pp.873-877, 1933. Kern, Donald Q., Process Heat Tlansfer, McGrawHill Book Company, New York, 1950.

10. McAdams, W. H., Heat hansmission, Third Edition, McGraw-Hill Book Company, New York,

ll.

1954.

Jakob, M. Heat Transfer, Yol. l, John Wiley & Sons, New York, 1959. 12. Grimson, E. D., "Correlation and Utilization of New Data on Flow Resistance and Heat Transfer for Crossflow Over Tirbe Banks i 'Tiansaaions of the ASME," Yol.59, pp. 583-584, 1937. 13. Engineering Data Book, Wolverine Division of UOP, Inc., A Signal Company, 1959. 14. Thorngren, John T., "Predict Exchanger Tube Damage,' Hydrocarbon Processing, I*l,l. 49, rc. 4, p. 129, r97o.

167

15. American Institute of Steel Constrtclion, Mantal of Steel Construaion, Eighth Edition, AISC, Chicago, trlinois, 1980. 16. Timoshenko, S., and J. N. Goodier, Theory ofElastr:ciry, Second Edition, Engineering Societies Monograph, McGraw-Hill Book Company, 1951. 17. Coit, R. L., C. C. Reak, and A. Iohmeier, "Design and Manufacturc of Large Surface Condensers-Problems and Solutions," American Fower Conference,

April

1965.

18. Blevins, R. D., Flow-htduced Wration, Van Nostrand Rheinhold Company, New York, 1977. 19. lbmbsganss, M. W., and S. S. Chen, "Tbntative Design Guide for Calculating the Vibration Response of Flexible Cylindrical Elements in Axial Floq" Argonne National Labomtory Report ANL-

ETD.7l-{r/, l9r. 20. Kays, William M. and A. L. Lofron, Compaa Heat Exchangers, Third Edition, McGraw-Hill Book Company, New York, 1984. 21. Miller, K. A. G., 'The Design of Tirbe Plates in Heal Exchangers," Proceedings of thz Institwion of Mechanical Engineers, \bl. lB, pp.215-231. 22. Ctovier, G. W. and K. Azrz, Thc Flow of Complex Minures in Pipes, Robert E. Krieger Publishing Company, New York, 1977. 23. Metzner, A. B. and J. C. Reed, AICLE Joumal, I, p.434, 1955.

External Loadings on Shell Structures

where

In a book about the mechanical design of process sysit is impossible to ignore the phenomenon of external loadings on shell structures. Such loadings occur when piping is flanged to pressure vessels and the vessel nozzle is exposed to loads induced by the piping, and when vessels are erected and the force of gravity induces loads at the lifting lugs. We have already discussed external loadings in the design of piping supports in Chapter 2. Vessels require a simiJ.ar analysis, but the phenomenon is different because in a vessel the loadings are more localized. particularly in a large vessel. In the case of external loadings on vessel nozzles one must consider primary stresses induced by internal pressure and secondarv stresses induced by the external loadings. In the design of the lifting lugs only secondary stresses need to be considered, since vessels being lifted almost never have internal

diameter of the branch diameter of the header

Also. \\'RC 197 and WRC 107 do not consider the case of erternal ioading combined with internal pressure. Current studies are being made to accomplish this task. Stress induced by internal pressure at the nozzle-shell intersection are extremely complex, so an analytical solution is impractical. Discontinuity stresses at the nozzleshell juncture are caused by the change in geometry from

the nozzle shell into the vessel shell. Consequently, a stress concentration factor, ko, must be applied when using the following expression for internal pressure stress:

"n

pressure. The two "standards" that are most widely accepted for external loadings on pressure vessel nozzles are the WRC (Welding Research Council) Bulletin 107 [1] and the WRC 297 l2l. The latrer is an expanded version with more curves to cover more cases, but it is only for cylindrical shells. Neither WRC 107 nor WRC 297 are considered standards per se. Therefore, one must take the results of the methods outlined here and add the primary stress, which is the internal pressure stress. The reader is cautioned that the WRC 297 Bulletin is under evaluation at the time of this writing. Shell theory was used to develop the WRC 297 , and the results are being compared to finite element studies currently being made. The reader is especially cautioned to use the Bulletin when the ratio of the dianeter of the branch to the diameter of the header is between 0.5 and 1.0. exoressed

P(ID)k"

(8-1)

2t

where

P

ID I kP

: : = :

internal pressure, psi inside diameter of shell, in. shell thickness, in. internal pressure stress concentration factor, dimensionless

Values of

\

are far too exhaustive to be listed here, but

are available in a work by Forman [3]. For many years reinforcing pads have been used for external loadings and it has been accepted practice to assume that such pads remove discontinuity stresses at the nozzle-shell juncture. While this is true, one must realize that the reinforcement decreases the flexibility of the nozzle-shell attachment. As shown in Figure S-la, the nozzle with the reinforcement will have maxirnum membrane stresses occurring at the nozzle-shell juncture (assuming the circumferential bending stresses are negligible compared with the membrane stresses). As Figure 8-1b shows that as the reinforcement thickness increases,

mathematically as

0.5 < db/DH <

= :

db

DH

tems

1.0

169

170


c

r tiryrcJtl F----'1

M-'x'i€m5'mm'n'|ll

ll

I

r,

--------|B w>

1.6s(arf.

r5

ll

HI

__-____1---r

I I

l

|

I

--'_;J

II

tN_

i

R-r

Figure 8-1. simple schematic of maximum combined stress disribution, as supported by field tests and finite element studies.

the maximum stress shifts towards the edge of the pad, and as the ratio of the reinforcement pad to the shell thickness approaches a "critical value," the maximum stress induced by external loading occurs at the reinforcement edge-shell juncture point, shown in Figure 8lc. Considering this it would intuitively appear that a tapered pad would ideally be the best in application, especially for thick pads (pad thickness relative to shell thickness), as shown in Figure 8-1d. The disadvantage of such a pad would be the increased difficulty and expense to fabricate such a pad. Analytical, finite element studies, and field experience bear the previous facts out. The width of a pad, from the nozzle edge to the pad edge' should not exceed 1.65VRT. Beyond this range a pad has been shown to be ineffective. Pads can be even dangerous on thin-walled shells. In many instances, adding a t/z-in. pad to a nozzle on a thin-

walled pipe, such as Schedule 55 (0.083 in. on a 4-in. pipe), is prohibitive. Such a pad could very easily transier the maximum loading to the pad edge as shown in Figure 8-1c, resulting in crack propagation or even ruptuie. Caution should be taken in working with thinwalled shells, where the flexibility of the shell is often sufficient to decrease induced stresses from external loadings.

LIFTING LUG DESIGN The design of lifting lugs can become an arduous task one is not familiar with the erection of equipment. Lifting lugs must be designed to withstand the stresses inducad from all the loading conditions; allow lifting and

if

setting the equipment in one operation without readjusting oi re-rigging the crane or other equipment' and proteit equipment and personnel. The lugs must not interfere with vessel components, such as platforms, ladders,

or piping. advantage to lifting lug design is that only secondary stresses must be considered-primary stress, such as internal pressure stress, can be ignored. We can assum€ that the vessels are not lifted while they are pressurized.

Thi

Consequently, the AISC Manual of Steel Constructi.on (unlike [4] can be used in which the factor of safety is 2: I

ASME's 4:l). The vessel is to be considered as a simply supported horizontal beam. All non-shell components, head, ladders, etc. are considered as concentrated loads. The total erection weight is the sum of the concentrated loads and the distributed loads of the shell weight and internals. Various types of lifting lugs are shown in Figure 8-2. Lifting and'election procedures are shown in Figure 8-3 Techniques for designing the lugs are given in the following examples.

EXAMPLE 8-1: LIFTING LUG DESIGN At{D LOCATION and tube heat exchanger is to be onto an offshore structure' The exa dock lifted from lbs, which is the total erection 158,750 weighs changer to locate and design the lifting is objective weight. The chocker length and minimum the lugs, and determine angle. chocker maximum

A 96-in. ID shell

Mechadcal Design of Process Systems

172

t

1T A norizontal

It

+

lili

.l

J\

U

+ "1" or

"W" beam

Figure 8-3. Lifting lug and erecting procedure (moments induced by lift load at choker angle d can be avoided with a spreader bar or with the lug design in Figure 8-28.

c spreader bar rig avoids €xcessive bending moments on lilling lugs

First, we construct a free body diagram, as shown in Figure 8-4. Each lifting lug is located such that the point of lift is located on a hypothetical vertical line that passes close to or through the centroid of the ellipsoidal head, shown in Figure 8-5. Summing moments to zero and solving for the reactions we have

GDt. : 0 :

-Rnt46.542)

+

Rr and

Rr.

: :

(2,283)(40.7 (2,094)(46.7

+

(346x44.000)

A = 16.50in.,B E

:

6.50 in.

Hole diameter Lug width

:

:

Wr

:

=

:

(4.50

+

:

4.50in., D

:

0.125)

mmlmum

3a

:

3(4.50)

wL

_

13.50

=

1.688

88

75,888.874 lb

For lug supporting the fulI vessel weighing 158,750 lb, referring to Table 8-1 we write

a

6.50in., C

:

:

4in.,

4.625 in.

13.50

in.

:

minimum

Lug Thickness, t1

s) + (346)(2.542) 5) + (1s1,587)(23.27 r)

75,698' 126 lb

:

tL :

Larger of

w _

1.6ao,

in. r/ use 1.75 in. 158,750

(1.6X4.625X38,000)

= 0.565 in.

174


For lug material SA-516-GR 7O, o,

Table 8-1

Anchor Shackles

: * - (". " | (?.,)['

n tl

H: R":

where,

ll /\

D'

,\ -)

*({* \2

50.0 + 1.75

n tl |l

"["-( H:

1"b

lvt

Pin Dia.

D

(in.) (in.) (in.) (in.) (in.) rh trys rlz shd tllrc ,1, tl" t1o

,t"

1 1tl4

lrl^

71rc 5/s

3/c

r'lrc lrl, 2rltu ltlrc ZIz lh

ls llrc

rlz

5/a 3lc 1ls

Yt^ 171rc |

33lq 111/to 1Vs 4r1o tt3lrc ltlc 43h Ztlta 13/e

rr-r" stlo 2tls lvz

-/" lrlz 1t/" 2

53lq 2tlq

27lt 1 7rl" 3tlc 3?'1" zrh qu" tou it, -9V^

i1o tluz 4lz

lslt

15

3t/z

15Vz

4118

5t/z

Safe Lilting

Load-|9!

|

4.00

Lslrc le/rc |1ha

4,500 6,400 8,700

2tla

23lg 25lL 3

1I

=

I'

:

greater of RR or R; for horizonal vessel

reaction at lug when lifting at skirt and lug end

5(19.690) in. (75,888.874) lb ll. (38,000) t13 50)2 in'

+ ln.'

:

1.079 in. < 1.75 in. Lug thickness is sufficient

'4OO

___J3_5W

351rc

35la

16'500

Minimum Weld Size

2!,59q

u,w 33,600

R[0.47

44,800 56,000 67

'2w

81,ooo

6tlz

100,800

63/q

125,000 t

where

o,*

:

lTtlz

6tlz

4tlz

7)lz

200,000

181/z

6tt/rc

43/q

73lc

224,N0 313,600 448,000

0.45(h/w)]

ra

:

allowable shear stress in weld

weld minimum yield (7s888.874)

stress/

in tension

I ot . o.ot rr2jry\l

\ir.roo1 [o (0.30)(70,000)(13.50)(0.707)

r79,200

41lt

+

re(wr)(0.707)

50,000

6tlq

5tlz

where R

R

2,200 2,900

23lq 6 6t/+ 3 33/q

r, ) *. or w'

1,675

lrlrc

16l lz

21

+ n JO

-

19.690 in.

.79-91'100

r3/rc

451rc 2 211+ 5 5Vq 2tlz

13

3tl+

50-00

6. 50

Check lug thickness

ft+l

,l*

- ")']"

insulation thickness shell outside radius, in.

(b) round Pin

lttn Itl,

;f

;'

lug height, in.

t:?

f-et r

q* ,1"

38,000 psi

Lug Height (assume 2 in. fireProofing)

(a) screw Pin

THWP,

=

r* =

0.426 in. minimum

Actual weld size

:

t*u

:

0 3q*

External Loadings on Shell

:

r*a

Larger

and twr

where

f t, ot ,, -_ I

t, =

=

: Ds: du: H: Kp: L.:

A,B,C,D,E vessel thickness, in.

1.75

in.

>

tv, so that

-

0.0625

=

175

NOTATIOil

,t,u in.

>h

In this case, tL

t*"

t/ro in.

Structures

1.688

constants (Figure 8-6) header diameter, in.

branch diameter, in.

8-l) internal pressure stress concentration constant (Thble

factor, dimensionless minimum chocker length,

ft

Ml= moment resolved about the left

Mr:

For each side of weld

end (Figure 84), ft-lb moment resolved about the right end (Figure 8-4), ft-lb

t-,:l'688:0.844 --2 since

t*" > > t*, A

a/+-in. weld is sufficient

Choker Angle (0)

o

:

arctan

[----tlt' I -,

l3w(H.A.;ll U: "r*rI

(38,000x13.50)(1.75F 3(1,58750.00) (rn.uno

*

r6.s0 +

4t0)

0:4.905" R"

I.:

12 sin d

, : t"

:

minimum choker lensth

50.00 12

rin (4.90t

A = 16t/z in., B =

61/z

in., C = 4!z in., D = 4 in.. E = 6t/z in.

= '+6'/rl n

Because of height restrictions, the lug had to be lowered from 19.690 in. to 11.00 in. Thus, we now have the

following:

I

l3.soxl.7sy I lrrtst.zso.ooy {rt.oo * ro.so * 4ll zll

"

.:qrt.grt-l

(38.ooox

\

t

0

:

6.327'

and

LC:

12 sin (6.327)

=

37.807

ft

Figure

&6. Detail of choker

and shackle.

176


P RL

R" RR

t t1

t* wL

: : : :

constant (Thble 8-1) reaction at left side (Pigure 8-4), ft-lb shell outside radius, in. reaction at right side (Figure 8-4), ft-lb

= shell thickness, in. = lug thickness, in.

: :

weld size, in.

lug width, in.

Greek Symbols o,*

:

: 0=

7A

minimum weld yield stress in tension, psl

allowable shear stress in weld, psi chocker angle, degrees

REFERENCES

t.

Welding Research Council, Welding Research Council Bulletin WRC 107 bcal Stresses in Spherical and Cylindical Shells Due to External Inadings, Match,

New York, 1979. z. Welding Research Cotncil, Welding Research Coun' cil Bulletin WRC 297, Incal Stresses in Cylindical Due to External Inadings on Noales-Supplement to WC Bulktin No. 107, New York, August, 1984. J. Forman. B. Fred. Incal Stresses in Pressure Vessels, Second Edition, Pressure Vessel Handbook Publishing, Inc. Tirlsa, OK., 1979. A American Institute of Steel Construction, Manual of Steel Constructior, Eighth Edition, AISC, Chicago,

Illinois,

1980.

178


Example-Spherically Dished Horizontal

(a)

Head

A spherically dished head with a I l4-in. { OD is spun from 1-in. plate. Determine the partial volume of 10 in. of liquid. From vessel head manufacturer's catalog we determine the following: IDD

R:'2

e: L:

Figure A-2. Partial volume of vertical hemispherical (B) Partial volume of horizonral hemispherical head.

:

p

16.786 in. (Figure A-5),

l14 o\ " - -)/t.'"'= 159.43" 108

-

:

:

108 in.

56.0in.

2.78

16.786

:

91.21 in.

head.

-_T---T

-+l itv ln' tl tf

I

PARTIAL VOLUMES OF SPHERICALLY DISHED HEADS

--

J___

--.-{,>--

_

Horizontal Head The partial volume of a horizontal head (Figure A-3) is (A-3)

Figure A-3. Partial volume of spherically dished horizontal neaos.

Vertical Head The partial volume of a vertical head (Figure A-4) is

., v=' nv(3x2 + -vr) 6

atl

P"l

x

v----i\:-7lTv

(A-4)

-v----T

-<--E--------i-:--rllDD

ot

I

.. .v) y: nv2(3o 3

(A-5)

Figure A-4. Partial volume heads.

of

spherically dished vertical

Appendix

Yr

A:

Pressure ry'essel Formulations

179

= 6.786"

Flgure 4"5.

_ V

:

--i86at -

lV(r08,

.,-

v?ro8r

-

5-dF

IJ

(9t.2r)(562

38,893.21 in.3

-

6.7862)

=

168.37 gal

t\

Itr t\

t\

ti

Example- Spherically Dlshed Vertical

ll

Head

;;=*--:-__T,

For the same head above, determine the partial volume

-_-

of a head of liquid of 9 in.

x

:

u

-

55.456 in. zr(9)[3(55 416)'?

+ 9'z]

in.t = = A.874 "'

6

64.4 gal End View of Horizontal Head

PARTIAL VOLUIIES OF ELLIPTICAL HEADS

Figure A-6. Partial volume of horizontal elliptical head.

The exact partial volume of a horizontal elliptical head (Figure A-6) is as follows:

..

(IDD)q

(A-6)

Venical Elliptical Heads Volume of top portion @ of Figure A-7 is

-a

Y'

'" 2 l"l' - 3(rDDFl

v,.' = 'Ri'

(A-7)

I

Volume of bottom portion .

,

2r(IDD)R,2 rRl

I

O

- "-----: lw

2(

is

u3

I

3(rDDll

(A-8) Figure

47,

Partial volume of vertical ellipticat head.

180


Horizontal Head Example

A

Find the partial volume of a 2: I (R;/IDD = 2) elliptical head that is 108-in. OD. The level of the liquid is 35 in., and the head is spun from l-in. plate.

vertical head

IOR - ?rl O\ IDD -- '"-______:rr:', = 26.50 in. KR

From Equation ,4-6 and Figure A-8 we have the followlng:

IDD

-x

y = (IDDI a vm7 --tl'6R, a=

138.80" =2.42

v _ ( 19.0)(2.42t !463r- * 6(53)

V

:

17,512.94

B

{Iqy-rr

horizontal head

in.r:75.81

gal

Vertical Head Example For some head above, determine the partial volume for a vertical head with 19 in. ofliquid. Using Equation A-8

we have the following:

c

., _ 2a'(IDD)R1'?

vertical knuckle region

o

v _ 2?r(26.s0x53.01 _ 1(5i.0)

6

V=

Y :76,641.06 in.3 : 77,951.81 in.3

n 2 [,o t--"

_

trq.or, ] 3(26.s0),.j

13i0.75 in.3 331.78 gal

H=IDD-KR

D horizontal knuckle region

Figure A-9. Partial volumes of torispherical heads: (A) vertical, (B) horizontal, (C) vertical knuckle region, (D) horizontal Figure A-8.

knuckle resion.

Appendix

A:

Pressure Vessel Formulations

PARTIAL VOLUIIES OF TORISPHERICAL HEADS For Figures A-9 and A-10,

: Vo : Vk

KR =

volume volume radius

knuckle dish knuckle

Figure A-1o.

: IDD : y

p=

height of liquid inside depth of dish inside dish radius

For vertical heads (Figure A-9c) the knuckle-cylinder Dartial volume is

v*: ?rtJ

+ 4ry2 +

(A-e)

r,2;

The partial volume ofthe dish region of a vertical head is ?ry(3x2 + y2) .,vD_-6-

(A-

l0)

The total partial volume in a verticil head is

nH Ty(3x2 + y2l ,. +. -----6-------:,, vu : -6- (ro' + 4rM' + ri')

(A-ll)

whereY=IDD-KR Horlzontal Torlspherical Heads Partial Volume of Dish @ (Figure A-11)

VO:

o

./(p, -y-il.t

V(pt-7F_L(Ri,. yi,) = JZ

|

,o_,r.,

Volume of Knuck-Cylinder Region @ (Figure A-12)

uo = "[#

+

Ri-

KR) +

(R,- KRr]

end view of dish volume

Flgure A-11, Sketch for example partial volume calculation of horizontal torisoherical head.

(A-13)

The total partial volume for a horizontal torispherical head is as follows: V1

: V6+ V6 -

.

.vG,

- R-iT

L(Rr2

"lry + Ri- KR) + (& - KR),]

wherel: p _ IDD

-

yi2)

(A-14)

Flgure A-12.

182


Horlzontal Head Exampte

A

102-in. S 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

ltut

= :z

:

6.125 in.,

IDD

= 50in.. L = 96.0

-

:

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:

p

:

R,

l?R trl 5l = '-" - 2=-"'-' = 67.50 in.;

x

:

17.562 in.

17.562

=

132 in.,

67

.50

KR

:

IDD

3 in.,

- (3f -

H2lo 5

=

:

20.283 in.

66.446 in.

78.438 in.

For knuckle-cylinder region, From Equation A-14 we have

vr

:

Q.532)

_

(78.438X50'

- ls) |

+

ro:

,4%t_ 1s+ _\@6r:50it

(5o.oo

-

6.12s)

Vr = 34.093.44 in.r =

r-

67.50;

11

J?r'

+ (s0.00 - 6.l25fl 'J

h Yv

147.59 ga.

:

138-in. d OD F&D (flanged and dished) head nor made to ASME specifications is spun from I l/z-in. plate.

120.283

-

Ri

=

r.= 67.50 +,[email protected] (3.0

*

KR:67.50

=

ob.u;

+

15.0)l

r(I'1 .283)[3(64.500)'?

:

-

3.00:64.50

2.283 in.

:

146,893.558 in.3

+

(17.283)2]

6

vv:31,247.726 in.3 + Vv

-

+() 19,4\ + 4(66.0), + (64.5011 = " -;-"-'l(67.501 b

Vertical Head Example A

=

in.

r /,'' <1r, 14(6.125)

[

Ri

:

115,645.832 in.3 635.903 gal

I Appendix A: Pressure Vessel Formulations

INTERNAL PRESSURE ASME FORMULATIONS WITH OUTSIDE DIMENSIOI{S

Cylindrical Shelt Longitudinal Joint

.PR

-

oE + O.4P

oEt

-

R

0.4t

Circumterential Joint

r=

PRo 2oE + '1.4P

2oEt - 1.4r

^

Ro

2:1 Ellipsoidal Head

^

r=2oEPDo + 1.8P

2oEt - 1.8t

Do

Sphere and Hemispherical Head

-

'-2rE+0,8P

2oEt - 0.8r

R.

ASME Flanged and Dished Head when UR = 164s s

0'885P1

r =0.885L

= oE + 0.8P When

PLM t= 2oE+P(M-0.2)

UB <

-

0.8t

16ry3

2oEt ^ ML-(M-0.2)

Section PDo r= - 2 cos o(oE + 0.4P)

^

2SEt cos d Do

-

0.8t cos o

183

184


INTERNAL PRESSURE ASME FORMULATIONS WITH INSIDE DIilENSIONS

Cylindrical Shell Longitudinal Joint PRi

'-rE-O.6P

Ri + 0.6t

Circumferential Joinl

t=

PRi

^

2oE + O.4P

1-\ i-r-----T;-',-il /l\

2oEt Ri

-

0.4t

2i'l Ellipsoidal Head

2oEl

^ Oi

+ 0.2t

Sphere and Hemispherical Head

{,;ft \<=]li

-

}
2oEt R + 0.21

ASME Flanged and Dished Head when UR = 1 6?3

P=0.885LoEt+ 0.1t

oc-v.tr I

Ft

When UR

pt FOR VALUES OF

M

<

164s

tu

2^tr1

SEE SUPPLEMENT

-./L-

#+\ \-__=-2, F--- q--l

LM + 0.2t

\

Conical Section PDr

2 cos d(oE

F.-t

p

-

0.6P)

2oEt cos

=Di + l.2l coso d

Appendix

A:

Pressure Vessel Formulations

185

Supptement for ASME Formulations 't. For a cvlindrical shell, when the wall thickness exceeds one half the inside radius or P > 0.385dE, the tormulas in ASME Code AoDendix l-2 shall be used. For hemisoherical heads without a straight llange, the efficiencv ot the head-to-shell ioint is to be ussd it il is less than lhe efficioncy ot the seams in the head. For elliDsoidal heads, whsre ths mtio ot the maior axis is other than 2:1. retsr to ASME Code Appendix 1'4{c). 4. To use the fomulalions lor a conical seclion in the table, the halt apex anqle, d, shall not exceed 30o. ll d > 30o' then a soeci;l analysis is required per ASME Code Appendix 1-5(e).

5. Foian when

ASME flangsd and dished haad (torispherical head) used:

Ur< 164r the tollowing values ot M shall be

Values ot Factor M

Ul

1.00 1.00

M

Ur

7.00

M

1.41

'

1.25 1.03 7.50 1.44

'1.10

1.13

8.00

8.50

9.@

9.s0

1.46

1.48

1.50

1.52

The maximum allowed ratio:

M= '('.

1

2.25

1.75 1.08

2.00

'1.06

1.50

L-r

=

2.50

2.75

3.00

.15 10.0 1.54

1.17 10.5 1.56

1.18 '| 1.0 1.58

1

D When L/r >

162/3

3.25 1.20 11.5 1.60

3.50

4.00

1.22

1.25

12.O

r3.0

1.62

't.65

4.50 1.28 14.0 1.69

5.00 1.31

15.0 1.72

5.50 1.34 16.0 1.75

6.00

6.50

1.36

1.39

16?s

1.77

(non-ASME Code construction), the values ot M may be calculated by

Appendix B

National Wnd Design Standards

A standard is a collection of current practices, past experiences, and research knowledge. Standards that are developed by consensus groups (e.g., ASTM, ANSD, trade associations (e.9., 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 desien

of buildings and other structures. Local and region-al building codes adopt portions of the ANSI srandard 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 authoritv as the ASME vessel codes. and, unfortunarely. does not have a referral committee or group to officially interpret the document. Therefore, one must rnake 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 miminum 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 care use another standard for design purposes.

147

One of the most widely accepted international standards

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 determined, 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 velocitv and the eradient height. Therefore. the exact nutur" of the suriace 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

188


the temperature gradient, modify the gradient wind to the surface wind. Wind motion is lurrher complicated by rhe rorarion o[ _ the earth. which induces additional forces that cause the alr movrng across the earth's surface to be subiected to a force at righr angles ro the wind velocity vecior. These additional forces are known as Coriolis iorces. Each country has adopted its own standard for measur_ ing wind velocity. The U.S. National Weather Service and U.S. codes use the fastest-mile wind speed, which is defined as the arrerage speed ofone mile ofair passing an anemometer. Thus, a fastest-mite wind speed of 120 mph means that a "mile" of wind passed the anemometer dur_ ing 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 bv a cuo anemometer. The mean gust speeds are recorded over a period of time such that a mean recurrence interval is de_ termined. The mean recurrence interval is the reciprocal of the probability of exceeding a wind speed of a'given magnltude at a particular location in one year. The risk. or probability. R. thar the design wind speed will be equaled or surpassed at least once in the life ofthe tower is given by the expression

R:l-(l-P,)" where P"

:

n:

annual probability of exceedance (reciprocal of the mean recurrence interval) life of the tower or stack

The risk that a given wind speed of specified magni_ tude will be equaled or exceeded increaies with the Deriod 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 rhe 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

0.

l0

0.05 0.01

0.00s

r

5

0.100 0.0s0 0.010 0.005

0.410 0.226 0.049 0.025

l0

15 25

speed will be exceeded during the life of the structure. The United States and Australian wind codes use rhe 50_

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 oper_ ated by rhe wind striking rhe cups, which drive a small permanent alternator. The indicator, which incorporates a rectifier, is simply a volrmeter calibrated in miles oer hour. [n most recent cup-generator models the generator output is used to activate a pen-chart recorder w-hich oro_ vides a record of continuous wind speed.

WIND SPEED RELATIOIISHIPS As stated previously, another method can be substi_ tuted for the appendix in ANSI A59.1. What this means is that another code could be used instead of the appen_ dix. 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 A58. I we wish ro determine the equivalent fastest mile wind speed for a 2-second gust using either the Australian or British code. From Fis-ure B-2 we read from the ordinate 1.54 for 2 sec. Knoiins that one mile of wind moving ar 100 mph will pass thi anemometer in 36 sec, we read 36 sec on the curve and arrive at V,/V366 1.30. Thus, the equivalent fastest

:

Pr = 1-(1 - PJ"

PA

Figure B-1. Cup generator anemometer

mile wind speed is

I 54t : tffil (100y rnp6 = 118.4 mph " I

50

100

0.651 0.794 0.928 0.995 0.999 0.401 0.537 0.723 0.923 0.994

0.096 0.140 0.222 0.395 o.634 0.049 0.072 0.rr8 0.222 o.394

for a 2-sec gust. For I l0 mph, the values becomes

V:

(l.l8x1l0) mph =

129.8mph

n Appendix B: National Wind Design Standards

189

110

Figure B-2. Ratio of probable maximum wind speed averaged orer t seconds to hourlr mean speed. Thus, the gust code

1.

if

l8 factor would

have to be used in the 2-sec that code were to be substituted for Appen-

dix A of ANSI A58.1-1982. Similarly, the Canadian code we must convert to ob tain an equivalent fastest mile wind speed from the mean hourly. The mean hourly implies that the rvind moves an :verage of 100 mph across the anemometer in a period of 1.600 sec. Reading Figure B-2 we have V,/V,,o, : 1.9. Thus

!! : 1.3

o.ros

rvhich 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 rvith ANSI A58.1. A comparison of the major wind codes is given in Thbles B-2, B-3, B-4, and B-5.

A-A verl restricted category in which the rvind speed is drasticalll 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 terrain 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 Categorl

alrport.

ANS|

A5A.r-r982 W|ND

Category D-A classificarion for wind moving over water. A beachhead, in which there is flat beach up to a

CATEGORTES

In the ANSI A58.1-1982 there are four wind categocategories are described as follows:

ries-A, B, C, and D. The

row of buildings would be rn 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.

190


Table B-2 Maior U.S. and Foreign Building Codes and Standards Used in Wind Design Code or Standard Australian Standard I170, Part 2-Wind Forces

British Code of Basic Data for Design of Buildinss (cP3) Wind Loading Handbook (commentary on CP3) National Building Code of Canada (NRCC No. 17303)

The Supplement to the National Buildins Code of Canada (NRCC 17724) ANSI A58.1- 1982

Uniform Building Code

Edition 1983

Address Standards Association

of Australia t972

80 Arthur Street/North Sydnev.

British Standards Institution

1974

Building Research

1980

Establishment National Research

Council of Canada National Research Council of Canada

1980

t982 1982 1982

Canada

Ottawa, Ontario

KIA

OR6

Canada 1430 Broadway

Southern Building Code Congress International

Building Officials and

1984

London, WlA 285, England Building Research Station Carston, Watford, WD2 7JR, England National Research Council of

New York, New York 10018

1983 rev.

Basic Building Code

2 Park Street

Standards Institute

International Conference

with

N.S.W. Australia British Standards Institution

American National

of Building Officials Standard Building Code

Standards House

Code Administrators International, Inc.

5360 South Workman

Mill

Road

Whittier, California 9060 I 900 Montclair Road Birmingham, Alabama 35213 17926 South Halsted Street Homewood, Illinois 60430

Table B-3 Reference Wind Speed Beletence Averaging time Equivalent reference

wind speed to fastest

mile 100 mph

Australian

British

1

2-3

second gust speed

I18.4

1

2-second

gust speed 1

18.4

Canadian

I Mean hourly 76.9

United States 1

Fastest mile 100

Appendix B: National Wind Design Standards

191

Table B-4 Parameters Used in the Maior National Standards Parametel

Australian 1983)

(sAA,

Brltlsh (BSr, re72)

Canadian (NRCC, 1980)

Unlted States (ANS|, 1982)

Wind Speed 4

3

Yes

None

Yes

Yes

Terrain roughness

Local terrain Height variation

Ref. speed Wind Pressure Pressue coefficients

Yes Yes

None Yes

2-sec gusts

z-sec gusts

Mean hourly

Fastest mile

tbles in

Tables, includes figures

Figures and

Tables, figures and notes

Gust speed Reduction for large area Dynamic consideration

Gust speed None

Gust effect factor Gust effect factor

Gust response factor Area averaging

Dynamic consideration not included

Dynamic consideration

Dynamic consideration

for h/b

appendix includes figures

tables in commentaries

Gusts Magnitude Spatial correlation Gust frequency

>

5

for h/b > 4 in. or for

for h/b

>

5

h>400ft

Analysis procedure

This standard is consid- Overall a very good ered by many the best code, its weakest part for us€ in the process is the lack of dynamic industries. Figures and tables are easy to read. The standard actually

provides the user with equatrons to curves. The analysis procedure is straight-forward.

consideration.

An excellent wind Although the appendix standard. The analysis procedure is straight-forward and the docu-

is technically not considered a part of the standard, it contains figures difhcult to read,

ments-code and

namely Figure 6. For

supplement conmany structures the tain tables and fig- data extend beyond the ures easy to read, limis 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.

192


Table B-5

Limitations of Codes and Standards Code or Standard

Australian Standard

I170, Part 2 1983 National Buildinq Code of Canada (NRCC, r980) British CP3

United States

ANSI A58.I

Uniform Building Code

Basic Building Code (BOCA, 1984) Standard Building Code, 1982 (SBCCI, t982)

statement ot Limitation "Minimum Design Loads

Location Title

on Structures"

"...EssentiallyaSer

Guide to the Use of the Code

of Minimum Regulations . . ."

". . . Does Nor Apply to Buildings. . . Thdt'Are of Unusual Shape or Location

Section

I

(Scope)

For Which Special Invesrisations May Be Necessary . . ." -

"Minimum Design Loads . . ." "Specific Guidelines Are Giyen For. . . Wind Tunnel Investisations ... ForBuildinss.. . Havin--s Irregular Shapei. . ." "The purpose . . . is to provide

Section 102

"The Basic Minimum Wind Speeds

Section 912.1

TitIE Paragraph 6.1

minimumstandards.._"

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 Desisn Pressures Used-in rhe Designof Structures Not Includedln This Section."

Preface .',

Article 1205.2(a)

194

Mechanical Design of process Systcms

PROPERTIES OF PIPE * The tollowinq lormulds C're used lhown in the toble:

in ihe computotior ol the volues

i weight ol pipe per toor (pounds) weighl ol wcter !'€r toor (pour&) squdr€ leet outside iurloce per toot Bqucre leet ilside surloce p€r toot inside qrea (squqre inch*) olea of Inetdl (squcte hches) momert ol inertid (inch6s.)

i tbo fsrridc steels rlay

b€ qbout S% les., @d tbo dultesitic stoh. l6ss ste€ls dbout 2/o qred'ler th@ the values lhown in this tqbl€ which dre bdsed o! weights lor carbon steol.

10.6802(D-r) 0.3{05d

: =

r schedul€ Du.Ebers

0.2618D 0.2618d

Stotdord weigbt pipe ond schedule 40 dle the sqme in dll sires througb lo-inch; Irom l2,iach through 24-iach, stondqrd weight pipe hcB a wdll thicble$ oI %-inch.

0.78sd

0.78s{Dr-d) 0.049r(Dr-d.)

Ertro Btlong eeight pipe (r|td sch€dule gO q!6 the sdme in sll siz6! lhrough 8-inchr trom 8-irch thlough Z4-irch, ert ci sttoag weight

A^n;

sectio! boduluB (inchest) rodius oI glrotion (illches)

=

0.0982(D.-d.)

=

o.zs

pipe hds c wdll rhjcLdess ot %-irch.

D

l ozlp-

Double enrd stloEg weight pip€ bas no cor*ponding scbedule

nu.Eb6r.

A, = dreo of Estcrl (Equa.e nocles) d = inside dida€ter (iach€6) D = outsids didnete! (bchos) R, = lodiu! ol gFotior (irches) t : pip€ wdU thicloess (inchss) DoEinol

piF rize

% 0.405

% 0.540

thick-

b

40 80

;;

% 0.840

std

std

l0s

0.049

40s

0.068

0.0740 0.0568

0.095

l0s

0.065

0.410

0.1320

40s 80s

0.088

0.364

0.1041

0.119

0.302

0.0716

ss

0.065

0.710

l0s

0.(E5

0.396 0.2933

40

t;

{0s

0.091

0.54S 0.493

80

xs

80s

0.t26

0.423

0.1405

0.065

0.710 o.6't4 0.622 0.546

40 80

;; XS

40 80

;; xs

0.466

o.2s2

0.u99

0.065

0.920

0.655

0.2011

l0s

0.083

0.884

0.6t4

10s 80s

0.1l3 0.I54 0.2t8

0-s21 o.?42 0.614 0.434

0.533 0.432

o.2521 0.333 0.435 0.570 0.718

1.185

1.103

1.097

0.945 0.864 0.719

0.083

40s 80s

0.109 0.147 0.187

;;; xs

0.308

l0s 40s 80s

t60

xxs

r%

{0

;;

J.660

80

xs

0.t{0

r.380

xxs r%

l0s

0.0r395

0.1716

0.01197 0.00586 0.00730 0.00862

0.0285 0.01737 0.02160 0.02554

0.2150 0.2159 0.2090

0.0120

0.0285

0,01431

0.0341

0.0407 0.0478 o.0527 0.0577

o.2750 0.2692 0.2613 0.2505 o.2102

0.2409 0.2314 0.2157 0.1943 0.1607 37

0.344 0.344 0.344

0.310 0.2872 o.2716 0.2s20 0.2134 0.1570

0.06s

t.?70

2.461

0.t09

1.682

0.37s 0.613

0.197 0.497

0.1271 0.1215 0.1146

0.00378

o,275 0,273 o.275 0.275 o.275 o.275

1.534

0.00437 0,00525

0.01230

0.0660

1.107

0.00088 0,00106

0.01032

0.671

1.057

in

0.00331

0.1765 0.1628 0.1433

0.63r

gYrd-

0-00600

0.538

1.160

I

UorL

0.00I22

0.I859

0.896

0.8b

lus,

0.002?9

0.220 0.220 o.220 0.220 0.220 0.220

0.250 0.382

r.496 r.283

0.0321

lodiu!

0.0572 0.04s1 0.0310

0.1295 0.1r06

0.

lb

a6clioE Erodu.

0.330 0.425 0.535

o.t77 0.t77

0.t220

|'roEeDt ol inertio.

0.3ts

o.t427

0.3{{ 0.3{{

designctioD

0,0246 0.0157

0.t77

0,434 0.434 0.434 0.434 0.134 0.434

1.27a

0.186 0.245

0.538 0,423 0.568 0.739

0.326 U.53I 0.669

40s

0.0s04 0.070s 0.0563

lbf

0.1859

r.839

1.530

lt

0.0794

0.341

t.442

per

0.220

1,076

0.109

It

il|3id€

0.141

0.2818

0.065

Bq

0.I4t

0.s22

1.049

0.957 0.815

wdl ihicla€ss

ANSI835.19 stainless sloel piF,e scbedule du.Dclors

0.1073 0.0955

0.599

0.133

0.1?9 0.250 0.358

55

,::

0.1479

0.r06

0.2553 0.113 0.4s4 0.639 0.836

r0s

160

1.900

0.065 0.109

0.2961

0.r06 0.106

0.1582 0.1246 0.1670 0.2173

0r9{

l0s

836.10 steel pipe rtoEinql

"q.tt.. ouardo

0.141

0.1583 0.1974 0.2503 0.320 0.383 0.504

xxs

40 80

0.19t0

b: ANSI

lr'6ight weight ol wcler , | auddc.€! sur{dc6, Fr It, p€r lt,

|I |

0.0970 0.12s0 0.1s74

0.3ss9 0,357 0.304 0.2340 0.1706

160

I

0.0364

0.0548 o.0720 0.0925

836.10 steel pipe schedule Dumb€rg

e

|3cr'l|r" I pertr

0.307 0.269 0.215

xxs

.1.3r5

cleq, ldred, . I _ 3q.In.

in-

160

1.050

inside didm- io"ia. |l -.tot

in.

xs

80

% o.675

wcll

Bchedul€

oulside diclmeter, ll|"

o: ANSI

0.t011 0.0827 0.0609

0.17t 0.rs47

0.851

0.1316

0.0ttl0

1.0€8

0.10I3

0.02010

r,301

0.0710 0.0216

0.022\3 0-t2125

0,684 0.857

o.2aa2

0.02451

0.2661

0.02970 0.0370 0,0448 0.0527 0.0579

't.7t4

l.l3t t.414 1.937 2.441

0.2301 0.1875 0.1284 0.0541

0.858

0.478

1.404

0.{09

0.1t04

0.2810

0.0760

0.ll5l

0.443 0.42A 0.407 0.387 0.361

1.679

0.374 0.311

0.I056

2.811

0.2281

3.659

0.t221

o.1252 0.1405

0.1329 0.1605 0.1900 0.2137

0.1038 0.1605 0.1948 0.2418 0.2839

0.1250 0.1934 o.2346 0.2913 0.312

1.r07

o.797

1.805

0-7al

0.361

2.273 2.997

0.648

0.2t92 0.349 0.343 0.334

2,t72

0.401

0.l9sl

0.0467 0.0566 0.0706 0,0853 0.1004

0.0500 0,0757 0.0874

0.378

0.1594 0.1628 0.1547

0.335 0.304 0.2346

5.2t4

0.458 0.2732

0.341

0.41I

0.469

t.274

1.067

0.I580

0,{40

2.085

0,962

0.2469

0.1663 0.2599

0.32r 0.30{

0.42t

0.564 0.550 0.540 0.524 0.506 0.472 0.649

0.63{

tCt,kne\) ,'f ITT Ctinkll.

Appendix C: Properties of

PiPe

195

PROPERTIES OF PIPE (Continued) noEitrol prpe

qumber'

outside

diomelet

ia.

thick-

srd

xi

40s 8os

xxs

2

2tl

0.154 0.218 0.343 0,436 0.s62 0.687

2.875

80

";; xs

40s 80s

160

)o(s .''.

1;

;;;

80 3.500

160

10s

3h 40 80

i;xs

80

4'JU)

xs

5.563

D-622

0.541

1.411

0.822 0.622 0.822 0.622 0,622

0.508 0.442 0.393 0.328 0.262

5.O22

1,280

0.868

0.731

7.444 9.029

0.971

1.163

0.979

0.76S

I.312

1.I01

t0.882

0.533 0.311

L.442

1.2140

1.5130

t2110

0.753 0.?s3 0.753 0.753 0.753 0.753 0.753 0.?s3

0.709 0.6s0 0.646 0.608 0.556 0.464 0.3s9 0.334

2.499 2.361 2,016 1.837 1.535

0.710 0.988

0.4s4

1.530

1.064

1.925

1.339

13.70 15.860

1.067

l.ss8

t1-729

0.554

2.872 3.0890 3.2250

0.873 0.s53 0.803

3.03 4.33 7.58

3.78

1.301

3.6r

LazZ

1.154

10.25

tl-32

2314

18.58

1.801 1.431

2-226 2.476 3.43

1.136

0.687 0.602 0.537 o.171

3.02 3.90 5,03 5.39

t.724

0.75S

3.20 2.864

7.O73

0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916

1.021

t.o47

1.004

1.463

1.047

0.984

3.41 4.91

2.680 3.68 a,721

1.047

t.o41

0.92S 0.881

12.51

1.047

0.7t6

22.850

3.8S 2.S30

3.92

6.40

2.1s0 2.556 3.199 3.641

0.083 0.120

3.334 3.260 3.068 2.900 2.626 2.300 2.050

8.73 8.35 7.39

0.89r

r.s00

2,5,13

0.r20 0.188 0,237 0.337 o.437 0.500

160

0.62S

)o(s

r.075

o,z6s2 o,420 0,561

s.2t2

0.674 0.800 0.925

4os 80s

0.499

1.276

t20

xs

0.3rs

1.582 1.455

t.275

0.109 0.134 0.258 0.375 0.500

80

r.715

2.638 3.653

1.826

0.531

;; ;;;

0-622 0,622

0.472

2.184

0.226 0.318 0.636

r0s

0.787

0.7s0 0.875 1.000

3.834 3,760 3.548 3.364 2.72A 4.334 4.260 4.L24 4.026 3,826 3.626 3.S00

3.138 3.152 2.900 2.650 5.34S 5.29S

5.(X7 1.813 4.563 4.313 4.063 3.813

3.553

6.6r 5,12 4.15 3.299

11.10

9.89 8.89 5,845

r.704

1.2?4 2.224 3,02 1.2L

5.4t 6.317

1.178

14.7S 11.25 13.357

t2.73

It.50

2.547 3.17 4,41

r0.33 s.521 s.28 7.80 6.602 5.513

0.817 0.802 o.741 0.755 o.129 0.703 0.6710 0.6410

0.t23

1.525

40s 80s

:o,s

t,229

1.001

0.58I

1.60d

t.771

0.I20

r60

r.251

0.508 0.598 0.6470 0.6670

8.6?8

2.945 4.03 4.663

10s

120

1.774

0.{12

0.588 0.565

4.19 4.24 3.55

0.2I6

40s s0s

l.5m

0.326

0.39r

0.I57

1.039

0.083

;; ;;

1.689

I.939

0.623 0.50s

0.310

0.246

o.724

0.300 0.437 0.600 0.725 0.850

IGS

o.176

tio|1.

inJ

in..

7.7tO

2.635 2.469 2.323 2.L25

80s

xrs

0.{97

lus,

lb

0.483 0.568 0.6140 0.6340

2.r09

0.083

1,qn

2.551

rodiue gYrc-

o.4tz

1.885

0.083 0.120 0.203 0.274 0.3?5 0.552 0.675 0.800

40s

xi;

2.247

rnodu-

6.40€

I.{29

80s

lt.

a6ctioE

ol wsler oI p€r It, in€diq,

1.859

r.406 0.950 0.567 0.283

{0s

per

w€isht

0.882 0.765 0.608

1.I00

xs

suatcce, EurIqce, pe.Il po. ft

rrreight

3.631

1.338

;; ;;

It

itrlide

2.7t8

0.400

3.96 3.65 3.36 2.953 2.210

rq

0.3s3 0.350 0.288 o.223

0.281

2-245 2.157 2.081

lt

outsido

o,42r

r.058

0.850 0.600

eq

0.497 0.497 0.497 0.497 0.497

0.799

1.767

0.109

;;

rD.

2,036

0.06s

l0s

rq.

1.500

5'S

xxs

3q. in. 1.6r0

0.650

160

metol

0.200

los

80

iriide

0.I45

0.52S

.:

2.375

diqa-

in.

160

L90{)

inrid€

!646.

b

q 40 80

1%

wcll

rchedule

rir.

6.283 6.62 8.10 9.294

12.385

2.175 3.531

5.793 7.661

I0.01

zt-447 24.0s'l

9.r!

t.178

l.ll5

1.178

1.082

1.178

r.054

10.79

1.178

1.002

14.98

1.178

0.94S

r.178

0.916 0.900 0.825 0.759 0.694

r8.96 21.360

1,178 1.178

10.384

1.r78 t.178

8.560

0.792

o.111 r.041

1.208

t.t96

1.094 1.0,17

6.50r0

3.7t50

1.0140

6.8530

3.9160

0.9810

5.01 4.81 4.28

1.960 2.756 4,19 6.28 s,8d80

0,980

1.38s L.312

5.800 5.51 4.98 4.48 4.160

1.378

2.394 3.14 4.9240

1,337 1.307

1.2100

2.811

t.249

1.562

3.96 5.8500

L.762 2.6000 3.21 4.27

1.549

123 11.65

t2.17tO

4-O2

13.27

21.54 31,613 35.318

3.38 2.864

15.29

2.391

t7.?130

1.399 1.386

6.35 7.77

9.73

6.95 8.43

l{.62

16.66t0

1.868

1.456

2,285 4.30

t.456 1.4s6

r.321

18.19

6.ll

1.456

1.260

20-74

t.89

I6.35

1.456

1.t95

27.O4

14.6r

7.95 9.70

1.456

1.129

32.96

t2.97

I1.34

1.455

r.064

38.5S

7.(x) 6.33 s.62

rt.4l3

12.880

l.{s6

0.998 0.933

43.8t0

{.951

36.6450

17.7s1

4.232

39.lll0

1.156

2.I4S0 2.2430

0.988 0.975 0,947 0.924 0.894 0.844 0.8140 0.7860

1.103

22.44 22.02 20.01

1t.328

0.68t

0.549 0.5200 0.4980

15.17

20.68 25.74 30.0

5.6760 5.90 6,79 7.4050 7.8720 2.494 3.03 5.15 7.13 9.25 10.80

1.5250

t,510 t.177 1.445 1.1250

t.116 1.37{ 1.3380

r.3060

1.920 1.878 1.839 1.799 1.760

I2.10 13.1750 11.0610

1.6860

1.5s20

196


PROPERTIES OF PIPE (Continued) pipe Biz€

schedule

in.

wall

inside

thick-

diom-

l0s

0.109

6.407

32.2

0.134

6.357

0.219

6.187

3t.7 30.r00

5.761

28.89 26.07

40

sia

40s

0.280

80

xs

80s

0.432

tItetol

sq. in.

rn.

b

6

inside

3q.

rL

aq

lt

outside

sq ft inBide

surrcc pe! It

per

lt

weighl per It,

lbf 5.37

r3.98

ll.8s

3.58

1.664

9.29

t3.74

14.40

4.4I0

4.35

t.734 t.734

1.620

22.6600

6.8400

1.588

15.020 18.97

r3.100

5.58

12.51

28.\4

8.s0

8.40

I.734

1.508

28.57

It.29

t2.2s

2.I95

L440

36.39

I0.30

40.5 49.6

14.98

2.153

1.358

5S.0 66.3

r7.8I

2.r04

20.03

72.r190

21.7720

2.060 2.0200

76.5970

23.t240

1.s850

5.50r

23-77

10.70

5.189 4.897

18.83

15.64

1.734 1.734 1.734

L000 L t25

4.62S

16.792

t7.662

t.734

r.211

45.30 s3.16 60.076

4.37S

Is.02s

19.429

t-734

1.t45

66.0S4

0.109

4.407

9,91

8.329

2.180

r3,40

0.219

8.187

2.258 2.258 2.258 2.258 2.258 2.25A 2.258 2.25A

2.2A1

0.I48

2.916 3.94

2.150

19.640

2.t27 2.1t3

22.36 24.70 28.55

r.282

8.17 7.284

24.07 23.59 22.500 22.48

8

20

0.250

8.125

s4.s 52.630 51.8

8.625

30

0.27',|

8.07r

51.2

0.322

7.991

0.406

50.0 47.9

10.48

0.s00

7.813 7.625

45.7

t2.78

100

0.593

7.439

t20

0.718

7.18S

I

l{0

t7.44

2.25a 2.258

1.882

0.8I2

7.001

43.5 40.6 38.5

19.93

8.625

2.2s8

L833

160

0.906

6.813

2t.9?

2-2s8

1.784

74.69

15.80

1.000

6.625 6.375

23.942 26.494

2.258 2.258

t.?34

81.437 90.1r4

14.945

r.669 2.744 2.728 2.70

r8.70 24.63

2.683

28.04

a;;

80

XS

4;; 80s

l0s

;; 30

5.800 6.58 8.40

14.96

2.089

2.045 1.996

L948

22.t8

18.84

t21.4

28.t4

2.847

17.60

140.6

32.6

2.807

r6.69

1s3.8

35.7

2.117

38.5

2.7 4A

4r.0140

2.7I90 2.68I0

13.838

10.250

9.25

0.307

r0.r38

2.815 2.815 2.81s

2.654

34.24

10.020

82.s 80.7 78.9

2.623

40.48

)0.750

80 100 120

2.938

50.87 60.63

0.250

xs

2.962 2.953 2.S09

0.219

60

I3.39 t4.6S r6.81

2.578

36.9 36,2 35.8 35.0

l0

63.4

24.52

2.815

l.9l

ll.s000

r05.7

2.815

10.07

3.00 2.9700

sr.3200

19.80

5.49 7.24

l

8.2I

20.58

4.52

0.365 0.500 0.593

3.0r

35.4

88.8

85.3

;,;

6.13

20,79

86.3

2.815

26.4S

21.69

r0.420 r0-312

83.52

2.304 2.295 2.2700 2.245

35.64 43,39

t0.482

0.134 0.t 65

40

40s 80s

34.454

3L903

luB,

r.677

0.562

40 60

inertia,

tb

1.734

0.7I8

I0s

per It,

rddius gyration, in.

1.734

160

0.864

oI

2.231 2.733

t20

xxs

w€ighl

37.4

177.t320 r90.62I0

44.2020

63.7 76.9

I1.85 14.30

3.75 3.74

100.46

r8.69

3.72

I13.7

21.I6

3.7r

137.S 160.8

25.57 29.90

3.69

34.1

9.750 s.564

'14.7

16.

t0

2.815

2.5S3

54.74

32.3

7t.8

2t2.0

39.4

3.53

t8.92

2.815

244-9

9.314

68.I

45.6

3.60

22.63

2.815

248.2

0.843

53.2

9.064

64.5

3,56

26.24

2.815

0.87S

27.t4

2.815

2.36

L000 t.125

28.0 27.6

324

9.000

64.33 76.93 89.20 92.28

31.1

0.718

2.504 2.438 2.373

8.7S0

60.1

30.6

2.815

2.:91

104.13

26.1

368

8.500

2.815

2.225

37.3r

2.815

2.16

t26.42

428.t'I

1.500

7.750

47.r5

3.52 3.50 3.47 3.43 3.39

43.57

2.8I5

2.03

148.19

24.6 23.2 20.5

399

8.250

56.7 s3.45

34.0

1.2s0

60.3 62.04 58.4 74.3 79.66

478.59

89.04

3.31

0.156

12.438

rzt-4

t22.2

12.390

r20.6

19.20

7.11

3.24

52.2

I40.S

0.2s0

!2.250

u7.9

22.t3

3.34

3.21

3.34

3.17

43-77

19.1

191.9 248.S

30.1

12.0S0

ll4_8

5r.l

0.330

9.84 r2.88

20.99 24.20 33.38

52.7

0.180

3.34 3.34

0.375

12.000

I

3.14

49.S6

4S.0

279-3

11.938

llt.9

3.34

0.406

14.58 1s.74

0.500

u.750

3.34

3.08

0.562

I1.626

106.2

2t-s2

3.04

362 401

11.376

r0t.6

56.7 62.8

0.687

26.04

3.34 3.34

48.5 47.0 46.0

47.1

19.24

53.53 65.42 73.16

300

108.{

4.45 4.44 4.42 4.39 4.38 4.37 4.33

2.978

88.51

44.0

0.7s0 0.843 0.87s

1r.250

99.40

.28.27

3.34

2,94

96.2

43.1

475 510.7

11.064

96.t

41.6

562

t20

3.34

2.897 2.88

07.20

t0.9

4I.l

578,5

1.000

10.750

l{0

36.9

3.34

2.8t4

10.500

4l.l

3.34

642 70r

1.250

10.250

45.16

150

r.3t2

35.8

755.5

10.126

3.34 3.34

2.749 2.68

25.49 39.68 53.6

39.3

r,125

95.00 90.8 86.6 82.50 80.5

31,5 32.64

3.34

I1.000

2.651

4D.27

34.9

781

140

I60

l0s

;i 30

40

t2

;;

12.750

80

I00

;;;

4;;

.-.

80s

t3.l

41.1

3.34

3?.S

333.46

39.0 43.8

?

4.5

80.1 90.7

4.31

4.27 4.25 4.22 4-21

I09.9

4-t7 4.I3

118.5 122.8

4.09 4.01

100.7

3

'1'


Pipe

197

PROPERTIES OF PIPE (Continued) aoniaal pipo riz.

rchedule

outtide

woll

iDsid€

thicL-

diqn-

inside

metal

h.

sq. it!.

11646,

iD.

b

Frlt

13.688

147.20

6,78

3.67

3.58

145.80

13.580

141.80

3.67 3.67

3.57

0.2r0 0.219

r3.562

144.50

8.16 9.10 9.48

to

0.2s0

t3.s00

143.I

10.80

;;

0.281

13.438

141.80

l2.tt

140.5 139.20

t3.42

;; 40

0.312 0.344

0.375 0.437

;; 80 100

13.312 13.250 13.126

137.9

14,76 16.05

I35.3

18.62 19.94

0.469

13.082

1s4.00

0.500 0.ss3 0.625 0.750 0.937

13,000

t32-7

12.8I4

129.0

24.94

12.750

t27.7 t22.7

26,26

12.500

woisht trrr fL tb

trlo|ne|''t ol

modu-

i|'ertiq,

luB,

tioD.

iD..

in.t

i!-

aectiorr rcdiu6 9Yra-

3.55

23.0 27.1 30.9 32.2

3.67

3.53

36,71

62.1

3.67

3.52

4t.2

6I.5

285-2

40.7

3.50

45.68

60.9

3.48 3.4J 3.44

s0.2 s1.57 63.37 67.8

50.3

3r4 34{.3

14.9 49.2

58.7 s8.0

429 456.8

55.3

1-79

72.09

57.5

484

69.1

84.91

55.9

562

80.3

s8s

81.1

4.18 4.14 4.73 4.69 4.63 1.58 4,53 4.18

3.67 3.57

3.42

3.67

31.2

weight

3.67

3.67

12,t28

3.40 3.35 3.34 3.27 3.17

r62.6 63.1

62.8

130.73 150.67

30.9

225.1

t2.2

4.47

36.S

4.86 4.85

59.7

89.28 106,13

2t8,2

4.90 4.88 1.87

194.6

53.2 s0.0 47.5 45.0

27.8

53.3 61.2

687

94.2

825

117.8

tr21

132.8 146.8 159.5

4.84

4.8s 4.82 1.80

1.093 1.2s0

It.8l4

109,6

44.3

I1.500

103.9

50,1

3.67

180

1.406

lI.l88

98.3

55.6

3.6'r

IS.670

I92.90

8.21

i;

0.16s 0.188 0.250

15.624

r5.500

191.70 188.7

9.3{ t2.3?

1.19 4.19

0.312

1s.376

185.7

15.38

0.37S

1s.250

182.6

15.000 14.688

t76.7

4.19

3,93

60

0.500 0.656

18.4I 24.35

4.IS 4.I9

4.10 4.09 4.06 4.03 3.99

4.19

80

0.843

14.314

160.9

40.1

4.19

100

1.03r

13.938

1s2.6

48.5

{.19

120

1.218 1.437

13.564

144.5

13.126

t35.3

65,7

4.19 4.19

3.85 3.75 3.65 3.55 3.44

1.593

12.814

129.0

72.1

4.I9

5S

0.r65

17,670

4.71

4.63

106.2

368

40.8

6.31

l0s

0.188

t7.624 I7.500

245.20 243.90

4.',1L

4.61

36

105.7

4t7

46.4

5.30

41-39 59.03

104.3

5{9

61.0

6.28

102.8

75.S

6.25

70.59

t01.2

678 807

89.6

8.23

82.06 93.15 r04.75

99,9

93r

103.4

6,21

98.{

1053

117.0

6.19

97.0

rt72

130.2

120

140

20 30

40

l0s

;;

xs

t40 t60

;; 30

;; 80

169.4

t7,34

4.71

0.375

17.250

233.7

20.76

4.71

230.4 227.0 223.7

24.11

4.71

4.58 4.55 4.52 4.48

21.49

4.71

{.45

30.8

4.71 4.71

4-42 4.32 4.22

0.437

17.126

0.500

17.00

0.562

16.876

0,750 0.937

16.500

213.8 204.2

40.6 s0,2

1.7r

16.126

193.3

61.2

4.7

r

182.6

4-71 4.7

|

4.7

!

3.89 3.78

140

1.562

r60

1.781

14.438

163.7

71.8 80.7 90.7

0.188

I9.634

302.40

I1.70

0.218

19.564

300.60

0.250 0.375

r9.500 r9.250

30 40

0.500 0.s93

t9.000 18.814

60

0.812

I8.376 18.2s0

80

0.875 1.031

100

1.281

17.438

298.6 291.0 283.5 278.0 265,2 261.6 252.7 238.8

1.375

s;

2.929

237,r

r5.688 r5.250 r4.876

l0

ts

240.5

r.r56

20

4.

3.01

u.376

r00 I20

l0s

3.09

9.24 r0.52 13.9{

0.2s0 0.312

20

20 20,000

rurlqce,

lt

ingide per lL rurldce, lbt per lL

13,624

l{

18,000

sq

0.188

t1.000

t8

3q.

It

outside

0.1s6

l0s

16.0U)

iD-

sq

17.938

173.8

23.t2 30.6

36.2 48.9 52.6 61.4

s.21 5.24 s.24 s.24 5.24

t10,22 I89.12

42.8

I0l7

28 32

83.5

25?

8S.0

292

42.05

81.8 80.s

384

52.36 62.58 42.71 10r.50

79.1

36.5 48.0

473 562

59.2

?32

9t.s

?0.3

136.45

73.4 89.7

ll57

114,6

164.83

66.1

1365

170.6

58.5

I?60

220.0

1894

236.1

933

192.29 223.81 245.11

138.17

92.7

t70.75

88.S

1834

4.ll

207.96

2180

3.9S

244.14 274.23

83.7 79.2 75,3

203.8 242.2

2499

z'17.6

2',150

308.5I

7

r.0

3020

306 335

168.3

40

131.0

574

5.12

46

r30.2

663

5.ll

s2.19 78.60

129.5 126,0

1I

104.I3

5.24

4.97 4.93

5.24

5.24 5.24 5.24

5,{8 5.43

194.5

5.14

s.60 5.59

5.37

5.21 5.17 5.12

6.10 6.01 s.97 5.90 5.84 5.77

7S?

7S-7

7.00 6.99 6.98

l4

lll.4

6.94

t22.8

t457

6.90

r22.91

120.4

1704

145.7 170.4

4.8r

I66.40

115.0

6.79

178.73

Ir3.4

2257 2409

225.?

4.78 4.70 4,57

208.87 256.10

109.4

2772

240.9 277.2

103.{

3320

332

5.0{

57.4

198

Mechanical Design of Process Svstems

PROPERTIES OF PIPE (Continued) nominol pip6 rire

wcll

schedule

b 20

20.ooo

in.

iD.

16.500 16.064

227.0 213.8 202.7

2r,624

367.3

t.968

s.24 5.24 s.24

4.45 4.32

296.37 341.10

4.21

379.01

17.18

0.37s

2t.250

354.7

25.48

0.500 0.625

346.4 339.2

33.77

5.76

322.1

41.97 50.07 58.07

5.?6

0.875

21.000 20.750 20.s00 20.250

80

l.t2s

I9.750

306.4

13,7A

5.76

r00

1.37s

19.2s0

291.0 276.1

8S.09

5.76

104.02

5.76

30

xs

0.750

;;

18.7S0

330.r

?.70

l0l0

91.8

87

153.7

1490

lls

135.4

7.69 7.65

150.2

1953

t77.5

7.61

t43

146.6

2t8-2

1?0

143.t

2400 2829 3245

434

18.65

5.76

5.76

5.99 s.96 5.92 5.89 6.17 5.83 5.78

140.80 156.03

t76-2

3140

26t.4

174.3 172.4

3420

285.2

37I0

309

r88.9

I152

96.0

216 238.11

168.6

4256 4650 s670

354.7

t73

8,07

6850

571

7830 8530 9460

719 788

7.95 7.47 7.79 7.10

41.{

6.28

6.28 6.28

398

45.9 50.3 54.8

436.1

16.29

388.6

63.54 70.0

6.2S

I42.1

6.28

150

19.314

293

159.4

6.28

0.2s0

2S.s00

t0

0.3I2

25.376

0.37s

510.7 505.8 500.7 490.9

0.625

24.500

0.875

24.250 24.000 23.7s0

20

std 20 30

xs

6.54 6.48

2S6.36

158.3

367.40 429,39

149.3 141.4

483.13 541.94

t34.S

t27.0

388

8.18 8.15

22t.4

1646

126.6

s.l0

88

2t9.2

r59.7

9.08

I03

217,1

2076 2479 3259 4013 4744

2t2-8

190.6

9.06

250.7 308.7

9.02 8.98 8.93 s.89 8,85 8.80

6.41

202

6.81

235

452.4

6.8I

6.35 6.28

267

20s.6 204-4 200.2 r96.1

443.0

87,91

6.81

6.22

299

ts2.t

594.0

71 92

2s1.3

2098 2601

149.8 185.8

9.81

2S5.0

22t-A

9.77

520.8

94.98

252.6 248.0 243.4 238.9 234.4 230.0 225.6

3l0s

530.9

21.80 z',t.t4 32.54 43.20 53.75 64-21 74.s6 84.82

1.20

0.875 r.000 1.r25

27.500 27.376 27.250 27.000 26.750 26.500 28.250 26.000 2s.750

0.375 0.500 0.625

t0s

6.81 6.81

r55.8

8.22 8.41

6.81

0.750

l0

6.68 6.64

55

8.29

a.z7 8.25

49.82

0.3r2

xs

6.81

186.24

1316

59.49 69.07 78.54

0.250

30

6.8r

t7t.I?

188.0

471-4 461.9

1.000

std

19.8S

25.18 30.19 40.06

5.48 5.33 s.20 5.06

63.41

481.1

1.t25

l0

8.35 8.31

7.07

16I.9

126.3

0.750

8.10

212.5 231-0

310

26.000

109.6

7.t5

1943

326

0.500

t07.2

2550 2840

1s.876

20

45t

7.31 7.23

183.8

1.812

25.250 2s.000 24.750

119.6

7.39

180.1 178.1

2.062 2.343

srd

351 403

4?58 5432 6054

s4.62

406

87.2 108.1

t26.2

125.49

4

344

303

7.47

6,09

21.83 36.S

365

40i29

7.52

295.0 366.3 432.6 493.8 550.3 602.4

6.O2

425

140

L2l8 1.53t

132.8

237 -2

6.r5

t20

80

5.04 4.91

I97 2Sl

6.28 6.25 6.28

6.28 6.28 5.28 6.28 6.28 6-28

100

5.56 5.50 5.43 5.37 5,30 5,17

4.78

415

382

6.41

157.4

23.500 23.250 23.000 22.816 22.750 22.626 22.500 2s.564 22.250 22.064 21.s64 20.938 20.376

0.968

459

't.71

0.250

0.8?5

6.56 6.48

80.4

l0

;;

422

885

132.68

0.218

376

1s8.2

118,55

402

4220 4590

5l

26t.6

0.750

98.3 92.6 87.9

14.92

247.4

0.687

tb

69.7

17.750

io

9yra. lion, in.

Eroduinerlid, lus,

756

r8.250

0.62s

rqdiur

oI

r59.t

r.875

0.562

per lt,

lnoEent rection

44

2.t25 0.375

n eight

12.88

140 160

0.500

tbt

perlt

363.1

;;;

lt

lt

per

2r.500

20

sq

lreight in8ide gurlqce, surlcce, per Il,

0.250

30

30 30.000

lll.s

lt

oubide

21.564

XS

2A

87.2

Bq

0.188 0.218

20

28.000

I00.3

17.000

120

28

aq rr'"

1.750

160

metdl

sq in.

1.500

l0

24.000

inside

140

I0s

22

inaide dicm-

r20

5S

22.004

lhick-

588.6

583.2 572.6 562.0 s51.5 541.2

0.250

29.s00

683.4

23.37

0.3I2

29.376

477.8

29.19

0.375 0.500

29.250 29.000 28.750

672.O

34.90

660.5

46.34

649.2

57.68

0.62S

7.t7

'1.33

7.33 7.G) 7.33 7.85 7.85 7.85 7.8s 7.8s

lll

?.13 7.07 7.00

t17

6.34

2tg

6.87

183

253 288

6.74

323

7.72 7.69 7.66 7.59 7.53

79

99 119 158

!96

296.3 293.7 291.2 286.2 281.3

364.9

5458

419.S

6149

473.0

6813

524.1

4085 5038 5964

6855 714D 8590

9.79

23 1.8

359.8 426.0 490.3

6t3.6

9.68 9.61 9.60 s.55 9.51

t72.3 2t3.4

10.52

3201 3823

254.8

10.18

s033 6213

335.5

I0.43

4t4.2

10.39

258S

10.50

n-. Appendix C: Properties of

Pipe

199

PROPERTIES OF PIPE (Continued) nominol schedule

pipe size oulside

wcll thick-

inside dicm-

irBide sq. in,

didmeteL

metal Bq.

in,

sq It

sq It

outside

inside

weighl pe! ft,

lbt

weight per It

!(rdiug

ol ilrerlio.

lb

lus,

gvrqiion,

per It

per rl 7.46

234

276.6 271.8

137

|

491.4

10.34

272

84S4

566.2

10.30

310

2E',t.O

9591

639.4

10.26

347

242.2

10653

t0.2

t0.22

in.3

0.750 0.875

28.500

637.9

68.92

30

28.250

620.7

80.06

7.85 7.85

30.000

I.000

28.000

615.7

9t.Il

7.85

7.39 7.33

l.l2s

27.',750

6D4.7

r02.05

7.85

'1.26

0.250

31.500

'179.2

24.93

8.38

8.2S

85

337.8

11.22

3I.02

8.38

8.21

106

335.2

3l4 t 38gl

196.3

773.2

243.2

11.20

766.9

37.25

8.38

t27

332.5

4656

291.0

11.18

7

54.7

49.48

8.38

B.l8 8.l l

168

321.2

383.8

u.l4

473.6

I1.09

40

l0

0.312

std

0.375

xs

0.500

31.250 31.000

7

32

30

0.625

30.750

7

42.5

61.59

8.38

8.05

209

321.9

6140 7578

32.000

40

0.688

s0.624

736.6

67.68

8.38

8.02

230

319.0

8298

518.6

11.07

0.750

30.500

730.5

73.63

8.38

7.98

250

316.7

8990

561.9

I1.05

0.87s

30.250

8.38 8.38

7.92 7.85

10372

648.2

lr.0l

30.000

85.52 s7.38

291

1.000

718.3 706.8

33t

306.4

I

I680

l0.ss

l25

29.?50

694.7

8.38

7.',19

371

301.3

I3023

730.0 814.0

0.250 0.312

33.500

881.2

26.50

8.90

8.1',|

90

382.0

3173

22t.9

33.376 33.250

874.9

32.99

8.90

8.7 4

1r2

379.3

4680

2',t5.3

IL33 I t.9I

867.8

39.61

8.90

8.70

sssT

329.2

11.89

33.000

s5s.3

52.82

8.S0

8.64

t79

370.8

7385

434.4

r 1.s5

841.9

65.53 72.00

8.90

8.57

365.0

I1.80

3M.l

587.8

I

78.34

LS0

8.54 8.51

9124 9992

535.7

8.90

223 245 266

359.5

1082s

637.0

11.76

20

L

t0

st; 20 34 34.A00

XS

0.62s

40

0.688

32.7s0 32.624

0.750

32.500

0.875

32.250

829.3 816.4

91.01

8.90

8.44

310

3S4.1

12501

735.4

tt.12

1.000

32.000

804.2

I03.67

8.90

8.38

353

348.6

l4l t4

830.2

t.125

3t.750

791.3

lI5.I3

8.90

8.31

395

343.2

15719

924.7

I1.67 I1.63

0.250

35.500

s89.7

28.11

L42

9.29

96

429.1

4491

24S.5

t2.84

0.312

35.376

982.S

9.42

9.26

lIs

426.1

12.62

3s.2s0

s75.8

L42

9.23

143

423.1

5565 6654

309.1

0.37s

310.2

12.59

0.500

35.000

962.1

34.95 42.D\ 55.76

9.42

9.16

190

417.l

8785

488.1

12.55

30

0.625

34.750

948.3

69.50

9.42

9.10

236

4lt.t

10872

504.0

12.51

40

0.750

34.500

934.7

83.0I

9.42

9.03

242

405.3

12898

7I6.5

12.46

0.875

920.5

96.s0

9.42

399.{

I4903

82',t.9

907.9

109.96

9.42

8.97 8.90

324

I.000

34.250 34.000

374

393.6

I6S5I

936.2

t2.42 I2.38

1.125

33.750

a94.2

123.19

9.42

8.89

419

387.9

18763

t042.4

12.34

0.250 0.375

41.500

1352.6

32.82

tt2

586.4

r28

339.3

14.?3

1336.3

4S.08

10.80

t320.2

65.18

t0.99

10.73

s79.3 s't2.3

I0627 I4037

t4.7r

0.s00

I67 222

506.r

XS

668-4

t4.67

1304.r

81.28

10.67

276

565,4

1288.2 1256.6

97.23

r0.99 I0.99

330

558.4

427.3 985.2

14.62 14.59

128.81

10.99

10.60 10.47

17373 20689

1.000

41.250 41.000 40.7s0 40.500 40.000

10.99 10.99

10.86

std

438

544.8

210a0

39.500 39.000

t225.3

160.03

t0.99

10.34

1194.5

190.85

10.99

10.21

s44 649

531.2 517.9

33233 39181

r2s9.5 rs82.5

14.50

1.250 1.500

1865.7

14.33

20

36.000

10.92

30

l0 36

0.375 0.500

109.0

2i 42

30

42.000

40

XS

0.62S 0.750

835.S

7

I.78

14.41

200


INSWATION WEIGHT FACTORS

To determine the rveight 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 fl by the density of the insulation in pounds per cubic foot.

Nominal Insulation Thickness

Nominal Pipe Size

2rt"

1%"

I 1% 1%

10 12

.051 .066 .080

2

214 3

.09r

.r9

.10

.17 .24

.21

.24

.!7

.31

,41

.30

.39

.34 .38

.45

t2

.50

.46 .44

.66 .59

.68

l4

.70 .78

.88 .90 1.0r

16 18

.6{

.87

l.t2

20 24

.70 .83

.96 1.13

1.44

.58 .56

.58 .64 .80 .93

.70 .68 .78

.83 .81

.s7

.88 .97

.71

.83

1.17

1.07 1.34

1.24 1.37

1.49

.96

1.10

1.04

1.20 1.34

1.13 1.36 1.54

t.12

1.1I

5t4"

.59

.63

.o.t

.34 .43

.30 .38

.36 .34

4%"

.40 .39 .48 .47

.31

.29 .29

.21

4

10

3%"

.23

ll l4

3%

6 8

Example. For 4" pipe rvith 4" nominal thickness insulation, f : .77. Il the insulation density is 12 pounds per cubic foot, then the insulation rveight is .77 X 12 : 9.24lb/lr.

1.99

1.52

1.74

r.s9

1.57

1.81 2.01

2.07 2.29

2.40 2.80

3.16

1,64

1.92

1.50

t.7s

1.77

2.10

2.09 2.44

2.24 2.34 2.58 2.82

2.50 2.62 2.88 3.14

3.06 3.54

3.40 3.92

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

% .068

lz

V+

%

.126 .202 .302 .419

610 1130 1810

1

.1ya,

ry4

.693

.889

1y4 1.293

2

1.144 2.300

2l+

2

3.023

3.719

2y4 4.619

3

3r/t

3

5.621 6.124 ?.918

27t0 3770 4960 6230 8000 11630 15?00 20700 21200 33500 41580 50580

71280

3

v


1tt

WEIGHTS OF PIPING MATERIALS

Pipe

2O1

prpo r.Brs, o.D.

{?

t-2

{.J-r'

z ?

z B

{\ {;\ f,.-l ,4L, E=:r L+!

!-r__--,

{--J--r

\.lJ Temperature Range "F

FiberSodium

s$ z

i

sr_r_u$

NJM {N:IS 4

z

/.4

F

4l

z

/>

Soldface

tvoe is weieht in

pounds. Lighifice type b6neath

weight,

is weight fa.ctor Ior

insulation.

Insulation thicknesses

and

\.reichts are based on averase conditions and do not constiiuie a recommendation for specific thicknesses of mrterials. Insuhtion iveights are based on 85/, magnesia and hvdrous cdcium silicate at 11 lbs/cubic foot. The listed thicknesses and rveights of combination covednq are the sums of the inner laj'er of diatom{Lcecus earth at 21 lbs/cubic

fooi end the outea layer at

,N.

11

lbs/cubic foot.

Insulation rveights inciude al,]O\llnces lol wIIe, cemen!, can-

vas, bands and paint, but not sbecial surface 6nishes. -

To find the weight of covering

on flanges, valves or fittings,

multiply the \r'eight fuctor by the

@ +€ nCI

tsO

* 16 h cu. ft. den-.ity.

SJrr

weight per foot of covering used on straight pipe.

Valve \reights are approxi-

m:Lte. When possible, obtain

veights from the nranufacturer. Cast iron valve Neights are for flinged end valvesi steei weights for rvelding end valves. All ftanged fitting, flrnged valve and flcnge $eights include the oroDortional Ncieht oI bolts or siulli to make up all joints.

202


lYn"

z F

PIPE r.660" o.D.


w'

4\

z

di

F

t_L_,

Tempcrature Renge

Fiber-

'F

Nom. Thick.,In.

Sodium

Nr$

is \eight in t)pe benexth is weight factor for

Boldface

.ty"pe pounos. Lrghflace

weight.

Insulation thicknesses and weights arc based on averaqe mnditiors and do Dot constituie

ts-ts$ {l.-.-tis z F

,41 /A

# ,N

z

Jrtd

-J

a

recommendation

tr

@

IrtJ

@ FsO

specific

combination coverinq are ihe sums of ihe inner layer of dia-

2l lbs/cubic foot and the outer laycr at tomaceous earth &t

1l lbs/cubic foot.

Insulation weiqhts include al-

lowances for

wiri,

cement, can-

vas, bands and paint, but not special surface

@

for

of materials- Insulation lveights are based on.85/p magnesra ano nl drous c3lclum silicate at 11 lbs/cubic foot. The listed thicknesses and neights of thicknesses

fi

nishes.

To find the weieht of coverine

on flanges, vatvds or fittings]

multiply the weight factor by the

\aeight per foot of covering used on straight pipe.

Valve rveiqhts are loproxi-dbtain

mate. When

possible,

lreights from the manuf&cturer. Cast iron valve weiqhts arc for

flanged.end valves; stiel weights lor weldrng eno valves.

All flanged fitting, flanged valve and flange weights include the proportionrl weight of bolts or studs to makc up all joints,

* 16 lb cu. ft, density.

] Appendix C: Properties of

.IVEIGHTS OF PIPING X{ATERIALS Schedule No.

{,1

t2 nuj >f\ i

t />

LLP

tij

e i

-1/

40

80

Wall De,
std.

NS

lhickness-In. Pipe-Lbs/Ft lVatcr-Lbs/Ft

.145

.200

.281

.400

2.72

3.63

4.86

6.41

.88

.77

.61

.41

.8

1.1

1.4

I.E

.6 .3

.7 .3

L.R. 90" Elbow S.R. 90' Elbow

L.R. 45" Elbow Tee

4,

.E

1

.2

.2

2.5

3.L

3.7

.6

.6

.6

5.4

Latera.l

1.3

.6

q--- 1_

-0

dti

Reducer

,2

c"p

.7 .2

.9 .2

.2

.5

.7

.7

.3

.3

.3

Temper&ture Range Nlaqnesia

'F

\om. Thick., In.

t00-199 200,29e 300,3c0 .100-.199 ;00-it)9 000-0119 ;00-;,1,1 s00-sf)1r 1t00-!r!9 11000-1099 1

I

\)t

.84

.84

1.35

2

2

214

!:

Caliium Siili.crp

Lbs,/Ft

{

Combina-

\om. Thick.,In.

2tt

Lbs/Ft,

1.t0

z

Fiber-

Nom. Thick., In.

Sodium

LbslFt PressLrre

,MS A rtr za|

lg

tsrj_ri}

{rrTs ..4 a /:) Z tt!4\ -

?41 | /A

3,\

1.07

Ratiig

250

SIip-On

1.5

7 1.5

\eck

S.R. 90" nlbow

lltn

FrO * 16

h

G:rt{!

I)tessure Seal

Borrrret-(-irte Pressurc Seal Ilonnet Giobe

cu. ft. density-

r.85

3.50

3.5 1.5 10

3.7

I

7 5

4.52

4.s2

4.52

21 ;

2)1

3

3

3

1.20

1.20

5.62

5.62

5.62

2\l

2%

3

3

4.76

4-16

3.50

6.16

000

900

r500

9

l9

l9

1.5

9 1.5

1.:)

1.5

I

\2

l2

l9

l9

34

1.5

1.5

1.5

1.5

1.5

*eights

9 1.5

9

t9

19

31

r

9

10

l0

1.5

1.5

1.5

t2

23

26

3.8

3.9

l9

t7

20

5.6

19

1.5

rveight

is

insulation.

tl pc bene&th

rveight iactor lor

Insul&tion thickncsses rnd based on :rverage and do not constitutc conditions^te rocommcnd&tion

for

spocilic

of m"rtorial-q. Insulation Neishts :rre bstxl on 85f6 mrgnesia ud hrrlrous lrrlcium

3l

l

46

!-.. , ,,,,1,i

^ f^^r

Tl-

listcd lhiclinesses orxl \\'cights of combinltion covering rte the sums of the inner l.rver of dirtomaceous

errth at 21 lbs .ubic

foot anrl the outcr hl cr at 39

23

30

70

5.8

6

70

1.2

.l.il

125

40

45 .t.2

t70

4.2 30

35

40

I

4.1

.1.1

6.8

tlpe is weight in

pounds. Lightfi.ce

thicknesses

4

ll

2500

1.5

t.5

9

Roldf.rcc

400

8

1.5 3.5

Flanged tsonnet, GLrlrc or Angle Irlanged Bonnet

1.8s

3.47

300

Ilanged lJonnet

Clheck

++I

1.5

L.R. 90' Elbow

Tee

2

3

blecl i j;0

L5

Lap Joini

Rlind

1.01

1ta

Casl lron 125

45'Elbow

j=
1.07

1%

1100-L:00

tl i

2.52

1

ps' Screled or \Yelrling

erce

xxs

.2

.6

l/2"

r.eoo'o.D.

203

160

_5

.2

Pipe

5

42

1.9

l0

t.2

11 ltls/cubic foot.

Insuhtion \\'ci,ahts inrluclc cllouanr:rs for \\'iro, ccmcnt. ernvlt'\, brnds llnd l)rint, but not st'ccirlsrrrf,,rc ti n rs)'cs.

Tu lin,l tlLe \, iHl,t .f,1,v, ring on flugcs, vrlvos or fittings,

rveight f.|rtor l)y thc rvcight lrcr fooi of covcrir)g uscd or) strLright pipe. \'.rlvt} \ 0iJahts lrre appro\i-

multiplt thc

mcte. \\'hcn lrossiblc, obtrin

rveights f|om the munuf:rcturer. (iust iron vrlvc \!eights:Lro for lhnged cnrl vxlves: stecl $eighls for \eldins end vrlves.

,\ll firLneed fittins,

flrnjaed

vrlvc ond 1|Lngc *cights includc iho I)r'otxJrtional \!1'ighi, of bolts

or studs to make ur) !.lL joints. ioints.

2O4


2" ptpn z',s,, o.D-

wErcHTS oF pIprNG MATERTALS

Schedule No.

A

40

80

Wall Designation

std.

XS

Thickness-In. Pipc-Lbs/tr 1,

.154

.218

.343

.436

5.02

7.41

9.03

I4'ater-Lbs/Ft

1.46

L.R. 90" Elbow

q

t!-/

S.R. 90' Elborv

F !w t/>

L.R. 45' Elbow

zf.

A^

'HJ

.5

.5

1

1.3

.2

Tee

.6

.6

Lateral

5 1.4

7.8

\i/

crp

Nom.

2.9 .5

.3

r.1

1.6

1.8

.6

.6

1.6

1.9

1.2

t,2

,+

.+

1.4

1.2 .3 .5

Temperaiure Range "F

z I

1.5

.2

Reducer

xxs

1.2E

.E

!_l--__,

160

Thick.,In.

Megnesia Calcium Lbs/Ft

silicate

100-199 200-299 300-399 400-499 500-5s9 600-699 700-7c9 800-899 900-9s9

I

I

L%

1.01

1.01

t.7l

2.53

2.53

Nom, Thick., In.

* uomDlnx; tion Lbs/Fb z Fiber-

Nom. Thick.,In.

Sodium Silicate

Lbs/Fb Pre-ssure

psl

sffi O

Z

,h

d-ir

SIip-On

'|1'elding Neck

6N_l-M

Lap Joint

ryi:-s

Blirrd

,-{l

t?.4

E II' Y ll_______.rl

ru ",1.{l

3m

+
rc

I

I

1%

1%

1.26

1.26

1.26

2.20

2.20

Cast Iron

or

trLrlS

2t4xJ i rlt E,N e /9S z

Scre* ed

Rating

I

L.R. 90' Elbow 45"

lllbow

2%

3

3

3

3.48

3.48

4.42

4,42

4.42

2%

2%

3

3

3%

4.28

4-2E

5,93

5.93

7.80

2

2

4.57

3

3

5.99

5.99

150

300

400

600

900

1500

2500

9

6

9

ll

ll

32

32

4E

10

13

t3

3l

3l

{E

type is weieht in weigii. is yreight factor for Boldface

pounds. Ligh[flce type bineath

lnsul&llon. 1.5 9

12

4E 1.5

6

10

4-8

l0

3l

t2

3l

1.5 19

35

3.8

3.8

3.8

3.8

1E

27

22

4.r

3l

4.1

4.1

14

l6

3.4

3.4

23

37

83

4,2

Gat€

6.9

7.1

Flanged Bonnet Globe or Angle

30 7

64

Flanged Bonnet Check

26 7

5t

190

4

4.5

5

40

3.8

for

specific

combination coverins

arl

the

sums of the inner Iajer of diatomaceous eerth st 21 lbs/cubic

l1

los/cuorc loo!.

on

EO

45 4

recommendation

thicknesses of materials. I-nsulation weights are based on.85/, magnes,a anct nydrous c&lctum silicate st 11 lbs/cubic foot. The listed thicknesses and weiqhts of

129

40 30

a

Insulation weishts include allowances for wird, cement, canvas, b&nds and paint, but not

3.9 41

3.8

49

fnsulotion thicknesses and weights a,re based on average COnOrtlons ancl do not constitute

foot and the outet layer at

73

6

I'langed Bonnei

235 4.5 60

300

4.2

5.8

Pressure SeaI

150

Pressure Seal

165 3

Bonnet-Clobe

4.57

3%

Steel

1'ee

Bonnet-Cste

214

250

16

S.R. 90' Elbow

1000-1099 1r00-1200

2%

special surface finishes.

To find the weisht of coverins flanqes. valvds or fittincs]

weisht factor by tle wergnt.per too! ol coverrng usecl on srrargn! prpe. V&lve weishts are aooroxi-dbtain

muhipltth!

mete. When possible,

weights from the rnanuf&cturer. C&st ircn valve weiqhts are lor flanged,end valves; sGel weights IOr Welolng eno valves.

All

flanged fitting,

flanged

valve and flange weighls include the proportional weight of bolts or 6tuds too make up uD all s.ll joints. ioints. 16 lt cu. ft. density. '

nr Appendix C: Properties of


2.875'o.D.

Pipe

2/2"

2o5

Ywn

A

(.!-f z

w

F

fl\ F-:l

z

F---i -2t"

J

' /-\ !-L-t

(--r..}

\.u Temperature Range

z

I )

z

'F

Magnesb, Calcium Combina-

tion

FiberSodium

,ffi 9+

i ${lit$ N-ls$

N ()

z

I

/A) ,4"1

,N z

g!4

l-{

.t

@ +€

flt' )

|
type is seight in \r'eight is weight factor for Boldface

pounds. Lightfece type beneai,h insulation.

Insulation thicknesses and weights are besed on everage conditions and do not constitute

a

recommendatioD for specific thicknesses of materials- Insulation weights are based on 85/6 magnesia and hydrous cclcium silicate at l1 lbs/cubic foot. The listed thicknesses and rveights of combination covering lrre the sums of the inner laver of diatomaceous earth at 2i lbs,'cubic

foot and the outer l:r|cr at

lbs/cubic foot. Insulation weights include allowances for wirc, cemcnt, canvrs, bends rnd print, but, not special surftce linishes. To find the rveight of covering on flnnges, valves or fittings, multipiy the \reight factor by the weight per foot of covering used on straiqht DiDe. 11

Valve *eiftrts are approximate- When possible, obtain

weights fronr the manufrcturer. Oast iron valve weiehts ere for flanged end valves; stiel weights for *elding end valves. AII flanged fitting, flenged valve and Iiange \\eights include the proportionel iveight of bolts or studs to rnake up all joints.

206

3


tt "tpr

B.boo" o.D.

WEIGIITS OF I'IPING NIATERIALS

rt? 8

z F F

z B

uf

/\

{_0

{l} L:-I -{\ fl-\

ri\ {----fr \iJ l

z

cnrpentLurc Rcngc "F

Magnesia Calcium

Nom. Thick., In.

F

z

(--oDlbi tron

r-

FiberSodium

weight

${rn$

Insulation ihicknesses and weights are based on average

Njs

a

/A -11

z

is weight in

ffi qN z

Boldface type

,N /9N 49!S

pounds. Lightface type beneath

is weight Jactot Jor

insuLation.

conditions and do not constitute

recommendation for specific of materials. Insulation $eights are based on 85/p magnesia and hydrous calcium silicate at ll lbs/cubic foot. The listed thicknesses and weights of thicknesses

cornbinetion covering are the sums of the inner layer of diaiomrceous eerth at 21 lbs/cubic foot and the outer la] e. at 11 lbslcubic foot.

Insul{rtion Ncights include al-

for \\'irc, cenrent, canvas,.bands- and prlitrt, but not

lorvarrces

suf tace hnrshes, speclsL -

t
@ 0 J{

a

Fs3

To iind the ueight of covering

on flanges, vs,lves or fittings,

multinl\' the weishtfactor bY Lhe weighi irer foot 6f covering'used

on straight pipe.

Yalve weiehts are aDDroxi-dbtain

mete. Wben-

possible, weights from the ma,nufacturer. Cs.st iron valve weights are for flanged end valves; steel weights for rveldinq end valves.

All

flanged

fitting,

flanged

valve and llanee weiqhts include the Drooortion;l weriht of bolts or siudi to meke u[ all joints. * 16 lb cu. ft. deDsity.

fl



4.ooo"

o.D.

Pipe

3/2"

202

ewy

{f (.-!-f z

/'h t4J

F

tij

z

&>", f,l-\

ri\

Temperature Range'F

z

Celcium

F Combina-

z

\om. Thick.,In.

tion

FiberSodium

Boldface

z J

in

ffir$ 4(|l_M

\Yeights are based on average conditions and do not constitute lr, rccommendxtion for specific thicknesses of materitls. Insuletion \Yeights are b.r,sed on 85% magnesir and h\'drous calcium silic&te at 11]bs./cubic foot. The listcd thicknesses and leights ol combin.rtion covelir)g lLIe thc sums of the inner hler of diltomrceous earth lt 2l Ibs,/cubic

Nls TNN /

z F

,11

-4

N

/>

1

1-
'

type is \leight

poun,ls. Lightfece tl pe beneath

neiglt is Beight insulation.

fscLor lor


and

foot end thc outer l:ryer at

ll

lbsrcubic foot.

Insulation weighis include allorv:rnces for \rire, cemcnt, .r,nvas, b0nds and l)l!inl, but not

spccitl surfrlce linishes. To find the $eiglrt. of covering on llrnges, volves or 6iiings,

multit)l]'the weieht frctor bv tho

@ ff1

weight per foot of covcring uscd on straight pipe.

+
flangcd cnd valves: steel ueights for *eltlirrg end valves.

rc

16

lt

cu. fr. density.

Vrlve weights irrc appro\i-

matc. \!'hen possiblc, obtrin

neights from the mxnufs(iturer. Cut iron valve s'eights are lor

lll

flarrged 6tting, fir.ngerl

valve lnd flrnge seiglrts include thc proportional rveight of bolts of studs to make up all joints.

208

Mechanical Design of Process Sl stems

4" ptpn 4.boo' o.D.


\\'stcr-Lhs/l t

/a) tu z k o

&?

h

1: ,t

{l\ tr;:I tr:JI

/\

\JJ 'li,mtx'nrluro

z

trlagnesia Calcium ComLirur-

I

rngo

"I

\om. 'l'hick., In. Nom. T)rick.,In.

iioIl

IiberSodium

NrS z {Nj+ln}

N_ts

rx:w ,.'Nl

7

/

F

,41

,l)

Boldface type is weight in pounds. Lightface tvpe bene&th

rveight

is \reight fsctor Jor

insulation.

Insulation thicknesses lnd

weights are based on average conditions and do not conslitutc a recommendation for specific thicknesses of mgterials. Insulation weights are based on 8596

magnesia and hydrous calcium silicate &t 11 lbs/cubic foot. The Iisted thicknesses and \reigllts of combinstion covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic

foot and the outer ieter'at

N

z

/\

1

ll

Ibs/cubic fooi, Insulation weights includc allowances fo wire, cement, canvas, bands and paint, but not speciel surlace 6nishes. -

To find the weighl of cover;ng

F<3 3

@ fi\

+
on flanges, velves or fittings,

multiply the weight frcior by the seight per foot of covcring uscLl on str{righi pipe.

Vrlve weights are approrimate. When possible, obtoin

$eights from thc mxnufacturer. Cast iron valve Ncights are for flanged end valves i steel $eights

for rveldinq end valves.

All

flanged

fitting,

flrnged

valve and flangc wcights includc the proporbionxl \\eiglrt of bolts or studs to mrke up all joinbs.

I

16

li

cu.

ft.

density.


WEIGIITS OF PIPING MATERIALS Schedule No.

ul ,a g.I/ zf\ F ! li

E4\ o

f'+ 3 4/4-

40

80

Wall Designation

std.

XS

Thickness-In. Pipe- Lbs/ Ft,

.258

t4.52

Water-Lbs/Ft

8.66 14.7 1.3

21

L.R.,90" Elbow

9.8

13.7 .8

S.R. C0" Elbow

L.R. 45' Elborv

.8

7.3 .5

20.78 7

120

160

.500

.62'r

27.M

32.96

38.55

7.09

6. J3

5.62

.89

r

0.2

15.6

.5

.5

t7 .7 .5

43

26

39

1.2

1.2

1.2

Laterel

3l

50

2.5

LJ---.D

Reducer

6 .4

E.3 .1

\tJ

cop

.7

.7

t4.2 .4

{---J--r

Nom. Thick.,In.

Z Sodium Silicate 9 F-

Lbs/Ft

B tion

Lbs/Ft

Nom. Thick.,

85% !Iagnesia Calcium

Lbs/Ft

,ffi O -'r-

Screu ed

or

'|r,\'elLling

2.92

2.92

I

I

2.34

2.34

i50

20

32

l8

1.5

1.5

+
ft.

3

3tl

3ti

4

4

7.01

9.30

I1.8

I1.8

14.9

14.9

2%

2%

3

3

4

4

9.31

9.31

14.31

14.37

t.5

l

58

94

80

5

73 1.5

100

1.5

162 1.5

259 1.5

rvcight

713

103

162

293

\reights.rre brsed on rverage

49

1.5

7l

32

1.5

98

168 1.5

50

39 1.5

1.5

l3

t23

t

78

205

4.3

1.lr

172 1.5

268

435

4.8

5.2

104

1.5

pounds. Lightf.rce type benerth

is

rveight factor ior

insulrtion.

Insuiation thicknesses

and

condirions and do not constitute

rocommendrtion for specihc of materials. lnsuhtion wcights rre brsed on t5% mrgnc-.ia antl hydrous crlcium rot. The silicatc at 11lbs,/cubic foot. righrs oi listed thickncsses 3nd rreighls

3

thicknesses

combination covering lrre lhe dieof the inner later of dirtomrceous errih rt 2I lbs cubic

-cums

3.3

3.8

3.8

90

t45

ll9

t72

179

304

6.5

0.4

6.4

6.8

7

138

264

150

3r0

7.9

4.3

4.9

455 5.5

Flanged Bonnet Globe or Angle

138

)47

ls5

2t5

515

Flanged Bonnet Check

llE

210

110

7.6

E

4.3

8

is $eight in

1.5

5

1.5

I.5

Boldf&ce type

l

98

density.

2ra

2|rc/..)

66

{ilobc

10.4

1500

E3

Bonnet

10.4

s00

51

Pressure Seal

E.41

600

t2a

Pressure Scal

8.41

400

9l

Bonnet-Cate

6.90

300

1.5

Cet,e

- FdJ JiLII ;hJ

4

Stecl 250

105

Flanged Bonnct

4

3.76

2.34

1.5

Tee

1-{

11,.i

68

45" Elbow

Y

1,t;

Casi,

L.R. 90' Elbow

Et\

3rl

4.08

|

1100,1200

3r/t,

2%

2ra

2

S.R. 90" Elbo*

,an

16 lb cu.

1.86

37

/,$

.7

22

Blind

rc

1%

Ncck

El:::lr$F

E II'

1

125

Lap Joini

/a

1l

.7

00-199 200-20s 300-399 400+s9 500-599 000-699 700,;9c 800-Ec3 900-999 1000-1009

18

3,\

'

Rctiltg

N-l,Ns

0 F | z

Pressure psr

Slip-On

i sli19

ll

In.

Nom. Thick.,In.

5" pge

1.3

t9.E

Fiber-

O.D.

209

xxs

Tee

Tcmpereture ll.enge "F

5.56:J"

Pipe

rl er foot end the outer irl

t23

5.2

165 5

1E5

665

615 6

1340 7

on llenges, !lll\'fs or littings, rnc )r DJ bl th. muitiplt thc \reight fsctor

350 350 3.1

soecial surfxco linishes.

co\,enng 1o hnd tlrc $Lrglrt ol coverlne

950 6

5

Di Dt

415

4

5

ll

lbs/cubic foot. .lurie rlInsulation \\0ighis inclurie lorvances for \\'ire, cement, crnnoi vns, bends xnd p.rint, hut not

350

130

560

6

1150 7

520 3.8

865 4.5

280 4

450 4.5

lng used rveight per foot o[ covering on,str.riqht t,ifo.

x||ro\l\'!ive \\'.rqh is rrc approximrtc. \\-hen possiblc, oblarn

weiglrts fronr the mllnufrcLurerC.rst iron vrlve rvcishis l|re fol \reights fluged end vrlves;steel \reightl for $cLdirrq end vlrlvcs. flanged ,\ ll fianee(l fittiDs, flanged include vol\c .rn.l ILrngc wprgl,tsr includ€ bolts tl,c t,rol,ortionxl \eight of bolt! ll joints up all ioints. or siuds to make up

2'10


6" pr""

6.625, o.D.

WEIGHTS OF PIPING X{TTERIALS

\\'eter-Ils/Irt

z '. z F

u/

AX

w

{T\ LilI t---1

\JJ Tempcraturc Ilange "F

z

Magnesia Calcium

t z

Combinst)on

Fiber* Sodium

Boldface

sq-,$ z

#r|& N-S dISrsS

z

-Xl t#

rA

kL ,N z

/>

lt' '{

l-dl .|

@ ru

1-
rc

type is weight in tleight iactor for

trpe benea,th oounds. Liehtiace ' iveight.

is

Insulation thichnesses and weights are based on average conditions and do not constitute

a

recommendation

for

specific

thicknesses of materials. Insulation weights are based on 85% masnesia and hvd.ous calcium siliate at 11 lbs/cubic foot. The listed thicknesses and weights of

combinstion covering &re the sums of the inner layer of diatomaceous es,rth at 21 lbs/cubic foot and the outer layer at

l1 lbs/cubic foot.

Insulation $eights include aIIowrnces for \aire, cement, can-

vas, bands and paint, but not special surface finishes.

To find the weight of covering flanges, valves or fiLtings, multiplt; the weight fxctor bl the rveight per foot of covering used on straight pipe.

on

Valve ueights xre sppro\imete. When possible, obtrin

weights from ihe mrnuf&cturerClst iron valve ueights are for flenged end valvcs; steel weights for rveidinq end valves.

All

flanged

litting,

flanged

valvc 3nd nlnge Ncrgnts Incluoe tLe DrotJortional $cieht of bolts ot stud" to mrke up all joints.

* 16 lb cu. ft. density.

,qR


WEIGHTS oF PIPING

MATERIALS

8.625.

Pipe

o.D. 8''

211

"T"e

t'-

2

i. z B

r_!j

w {t} E:I ,4\"

A

F--l-r \tJ Temperature Range

'F

Magnesia

2 Calcium F

-

z

Combina,-

tron Nom. Thick.,In.

FiberSodium

ffi$

2 F

a

7

Neight.

is veight

Jactor lor

Insulation thicknesscs cnd \reights are based on average

$\

a

is

conditions and do not constitute

A

recommendation for specific of materiols. Insulation rveights are based on 85% magnesio and hJ'drous calcium silicate at 11lbs/cubic foot. The Iisted thicknesses aod $'eights of combinetion covering are the

/A

foot and the outer la]'er at

A

egilq

thicknesses

sums of the inner layer of diatomaceous earth at 21 lbs/cubic 11 lbs/cubic foot.

Insulation rveights include al,lowances lor wDe, cemenl, c&nvas, bands and paint, but noi soecial surface finishes. '

d

-

j.43

t4r\

+
tlpe js Neiaht in

ffi

d <,fs$

z

Boldfnce

pounds. Lighilirce tvpe bineeth

16 lb cu.

ft. density.

To find the weight of covering

on flanges, valves or frttings,

multiply the weight f&ctor by the Neight.per folt of covering used on slrarghl prpe.

Yalve rveights are approximcte. lYhen possible, obtcin

lleights from thc manufrcturer. Cast ilon valve weiehts are for flanged end valves; sGel \\'eights

Ior seldinq end valvcs.

AII

flcneed fitting, flanged

valvc and llangc rveights include tlrc nroDortioDrl \eiqht of bolts or stu,li to make ut all joints.

212


10"

z (,

z

prpn

lo.zbo, o.D.

IVDIGIITS OF PIPING tr{ATDRIALS

Ih fl\ L:J .4'4^ L:!-l_,

\]J lrmpcr:rturc lirnge'F

z

Magnesia Calaium

F P

z

Combina-

\om. Thick., ln.

iion

FiberSodium

(,

ffi$ qFl

rr$

N-|s ryrTqJr

Ai

z

Boldfece

/AJ

!.

,-11

z

,N />

tHt'{

lN'

@ ff1 +
t{pe is l\'eight in

pounds. Lightface t1'pe benerth

*eight is rveight foctor ior insulation.

Insulation thicknesscs

\Yelding Neck

and

rveights are based on average conditions and do not constit,ute a recommcndetion for specific thicknesscs of materials. Insulation weights are based on 85/o magnesie and hl drous crlcium silicate at 1l lbs/cubic foot. The listed thicknesses and weights of

combination covering are the sums of the inner layer of diatomaceous earth at 2I lbs/cubic foot and ihe outer lsyer at 11

ibs/cubic foot.

Insr-rlation Neights include allowances for vire, cemeni, can-

vas, bands and !B.int, but not

spacirl surfrce 6nishes. To find the weight of covering on ffanges, valves or fittings, multiplt' the $eight frctor b! tLe lieight t'er foot of covering used on streight pipe. \'rlve \rcights ere approri-

matc. \Yhen possiblc, ol)irirr

ciglrts from thc nrnnufrcturcr. (lxst iron vrlYc \\'ciglrts arc for lllngcrl cnd vrlrcs: stcoi teights fol lcldilg cnd vrlves. rr

-\)l

fl.rngcd fitting,

flnngcd

!'rlvc :!nd l]3nge \\'eights include tlru prolroriioDxl scislrt of l)olts or studs to mrkc up:rlL joints.

*

16 lb cu.

ft. derxity.

Appendix C: Propenies oi

rz.lso'o.D.

WEIGHTS OF PIPING MATERIAI,S Schedulc

)io.

|

20

{,)

IJJ

f4

(_!-f

.

2n^ F flIT Eji1 o -: -t i3tr-/>" t-

d_l\

.330

43.8 49.7

L.R. 90' Elbow S.R. 90" Elbow

L.R.

.406

.500

49.6

53.5

65.4

49.0

48.5

47 .O

.375

100

120

12"

.687

.843

1.000

EE.5

t07 .2

r25.5

44.0

4

r.6

39.3

.562 46.0

l-J! 139.7

t58

t51

3

3

80

2

104 2

60

7E

181

167

360

3

1.o

Calcium

silicate

,s| Combina;z iron FiberSodium

,ffi ;+

z

5.4 33

44

30

3E

,|

Reducer

9,1

'|

E9

1.5

900-999 1000-1099 1100-1:to 100-199 200-299 300-399 400-49S 500-5s9 600-699 700-799 800-E99

Nom. Thick., In.

1)4

114

2

2t/4

3

3

3rlt

4

4

4%

Lbs/Ft

6.04

6.04

8.13

10.5

t2.7

12,1

15.r

17.9

17.9

20.4

20.4

3

3%

4

4

414

1)i

17.7

21.9

26.7

26.7

31.1

3l, r

2\/r,

216

4

4

5

c

14.20

14.20

24.&

4.64

32.&

32.40

Nom. Thick.,In.

Lbs/Ft Nom. Thick.,In.

Pressure Rating psr Screwed or

Slip-On

Cast

250

71

r37 1.5

1.5

a4 a lAl

S.R. 90' Elbow

/..4

L.R. 90' Elbow

A,N I /}!

45' Elbow

z@

600

900

1500

| 72 | | 1.5 | 88 I 1.5 I

164 1.5

261

3EE

820

1611

434 1.5

843 1.5

1919 1.5

433

902

1573

1.5 163 1.5

212

164

ta7

286

1.5

1.5

1.5

475

t474

261 1.5

453

345

509

669

El5

5.2

5

5.2

485

624 6.2

6.2

6.2

6.2

235

383

2E2

6E4

6.2 4.7

1124 4.8

5r3

754 7.4

943

1361

r92E

8.3

a.7

s.3

1420 5.5

215s 7

2770 7.2

4650 8

1410

7.2

2600 8

3370 8

1975

2560

45r5

6

7

7.8

1015 5

Fhnqed Bonnet Globi or Angle

808

1200

7t0

1410

9.4

9.5

5

Flanged Bounet

674

ll60

560

Checlc

9..1

9.5

densrty.

6.2

4.5

635 4

Bonnet-Globe

I.D

469

8.5

Pressure SeaI

t.5

1775

159E

720

705

l.c

92E

414

1298

Bonnet-Gate

5.8

2500

1.5

4.3

4.3

6E7

Pressure SeeI

1.5

209

7.8

Flanged Bonnet Gate

r.o

lllE r.5 | 1.5

265 5

Tee

fi.

400

r44

341

177

403

IP '{

300

72 |

96

|

150

1.5 |

Lap Joint

Blind

l1/r,

1r/1,

ffi

125

Welding Neck

{N

* 16 lb cu,

1rt

t%

Lbs/Ft

'$$js

E

l

273

1E0

Lateral

#rils

,

;

2.5

2.5

cap

z 9

3

119

r32

Temperature Range "F

Pwr:

1{0

45" Elbow

Tee

213

XS

sid.

Wall Designation

Thickness-In. | .250 33.3E Pipe-Lbs/Ft 5l .10 Wsier-Lbs/Ft

80

60

40

30

PiPe

214

Mechanical Design of Process System:

14" ,trr.

14'o.D.

WEIGHTS OF PIPING ]IATERIALS

{.f z |.

z

t

/)

fl\

fJJ

t -t c---r---l

\L"J

Tcmpcrature Range

z

Alagnesia Calcium

'F

Nom.

Thick.,In.

Nom.

Thick.,In.

F

t Conlbination

z

1

l\'pc is Ncight in *eight is lYcight lactor for Boldlace

ffi

pounds. Lightface tl pc l)eneath

S{r-rM

$eights are based on lverage

insulation.

N]s {N z

/.4 --ll /,4

z

,N i>


and

conditions and do not constitutc a recommendation for spccific

thicknesses of rnaterials. Insulation $eights are ba-sed on E5% magnesia and hvdrous cak.ium silicate at 11lbs/cubic fool. The

listed thicknesses and lreights of combination covering Lire the sums of the inner l&\'er of diatomaceous

e:irlh at 21 lbs/'cubic la] er at

foot and the outer 11 lbs/cubic foot.

.{l

Insulation \reights include alfor lvire, cement, canvas, bands and ptint, but not

ru

To find the leight of covering on flanges, valves or fittings, multiplt the weight fcclor b]'the MeiAht pcr foot of covering used on strnight pipe.

0,

@ 0

+
FSO

lorvances special

su

ace finishes.

Valve s eights are spnro\imate. When possible, obtain

weights from the mrnufscturer. Csst ilon velve Neights are for flanged end valves: steel weights for rveldine end valves.

All

flaneed fitting,

flanged

valve cnd flonge $eights include the nroDortiorrrl \\'cigl,t of holts or sludi to mrkc up all joints, * 16 lb cu. ft. density

il -

Appendix C: Prop€rties of


re"

o.o.

Pipe

16t'

215

plpu

tl

A.

vz z

;

lJj i\

w

{T\ 1-5:I J,1 E=_:ir t

fl\ \iJ .+r

Temperature Ra.nge

z

'F

l 100-1200

I\Iagnesia Calcium

F Combina-

z

tion

!'ih.rSodium

z

Boldfxce tvDe

stjjs

Insulrtiod thicknesses and weiqhts are bascd on averase

conditions and do not constituie & recommend&tiol for spccific thicknesses of materials- Irrsuhtion weights ere bosed on 85% magnesir and hydaous cnlcium silicate &t ll lbs/cubic foot. The listed thicknesses &nd \yeights oi

A

combiortion covering are the

sums oI the inner layer oI diatomaceous earth at 2l lbs/cubic

.A 1

Lighifirc tt pe benesth is rveight factor for

insulation.

$$l.M

z

rveielrt in

teight

qr\ssF z

is

S$

pounds.

foot and the outer layer at rr rDs/cuDLc ioot.

A

Instrlati<.rn weights irclude al,low&nces Io! $alrc, cement, ca!!

4!B

vas, bands and pcint, but

Dot,

specilll surlace fi nishes. To find the weight of coverbg

on flanges, v&Ives or fittings,

@ t i[I

multiply the weight frctor by the r eight per foot of covering used on str&ight pipe. Flenged Bonnet

@

t4


Valve Neights are approximatc. When possible, obtrin

weights from the m.nuf&ciurer. Cllst iron v.rlvc \reights:rre for flanged end valves: steel $eigh6 Ior rvelding end valves.

All

flcnged fitting,

flanged

vclve and flangc wcights include the prot)ortionul Neighi of lrclr,s or studs to make up 3ll ioinis.

216

Mechanical Design of Process Sy:,rems

18" plpr 18" o.D.

WEIGI{TS OF PIPING MATERIALS

LLl

z F

z E

f^

('4r

fl\

H' UL, c.=-=I

IA \JJ

'fcnpcnturc ll

z

Magnesia Calcium

tCombin.r.-

Dgc

'I,'

Il,s / Iit

\om. Thir,k., In.

tion

Fiber-

\om. Thitk., In.

Sodium

ffi

z

ffi

Nl$

si)\r'|\s Z F

/'a IA

rA ,N

z

/$ 4444

is lcicht in t5 pe b-enerth reiglrt. is \cjght fschor for Boltlface tvne

pounds. Lig)rifrce

Instrlation thicknesses

aod

rvciglrts flrc l,rsr:d on r,vcrrge conditions ltnrl do not (oustituta a r-ccommcndrtion for specific thicknesscs of matcricls. Insulation \reights ore bascd on 85/o magncsia and h-Ydrous calcium silicrte at 11 lbs/cubic foot. The listcd thickncsses and rveights of combination coveljng are the sums oI the inncl hver of diatomaceous eorth at 21 lbs/cubic

foot and the outet laver at 11 lbs/cubic foot.

Insulation s'cights include alIolanr:cs for \rirc, cemcnt, conves, b:rnds and print, but not spccial sur'Iace finishcs. To find ihc \lcight of covering

on flanges, valvcs oa fittings,

multit)l]'the xe;ght factor by the

a

@ iln +
rc

\eight pcr foot of covering

used

on stroight pipe,

Vrlvc \rriqhts rre aptrroxi-dt,tain mate. \l'hen possil,le,

lscights from the m$nufacturer. Cast iron valve \yciqhts are for flanged end velves; st-eel \\eights Ior welding end valves.

All

flanged

fitting,

flanged

valve and flange scights include thc proDortionrl \\ci(lrt of bolts or si,udi to meke up all joints. * 16 lb cu. ft. deDsity.

::

Appendix C: Propen:*

1VEIGIITS OF ]'IPING }I.\TDRI,\LS

20,,o.D

l-

21

20"

e-,rz

l{t) Pip€'-Lbs./I,t

\\'at.r

3;9

Lbs/ I,t

Ll

9

'17

&Jj z F i:

z

Ih

\-.1-_t

{l\ -'t

r'-: F4

,!^

!*J----!

'Icmpcraturc Renge "F

z

300-3c3 100+cc i00-;9u 1000-6e0

I{agnesia

o Calcium

2a.l

F Combina-

z

4l.:

tion

43.r

Fiber-

{-1-

1

\om. Thick.,In.

Sodium 1-1.03

Pressure

ffi z

psr

Rnting

sm$ N+s gr(\i.x$

z F

(,

z

g J

/A /41

/,+ A\ />

€4!4

@ fln

l'langed tsonnet Globe or Anglc

J-
rc

* 16 lb cu. ft. deDsity,

(last.Ir('n

| ll25 l2s

is r..r: : .: rir)f I :..,: \l{ttglrL. ls \\etglll Iri-: : ::: Illsulrtion thi|krrts... :: vc;ghts uc brsc(l 0r ,,. :. ::corrditiols urrtl iIr rror ,,.:.-:.:::r! rccommrr{lxti(,n a,)r .-- l tlti< kncsscs of mritli,.l: I: --.-tiorr rveiehts rLn' 1,,,.t i :. :i I nNgncsil rLnd lrr,ir ru. -:-sili(rtc lri 11 lLs r ui,:. : - . listc(l tLi( knciscs ,t:. i , :: , ::conrl)in$tion co\'!f:r:: .. :: sums of t))r inncr -.:.,: : ,tolnxceous rtLrtlr :,i l: .: i - : fooL oniL tl)c a';:.: - . : -: ll Ibs r:ulric fooi IusulLtion r, r::.:. :: -loNrurccs ior r|ir,. vrLs, blnrls:i'l:,1 :.:.: - : : sp( ( lrLL :Llr 1t1.. :.: :, . . Roldfrrce tYpe

poun(ls. Lighthcc

\lrgllt l)ff iL_'r: .: ' I : _. onstfrLigi,:r: f. \_rtlvc Li,:::.:. .:. .. nlrtr'. \\ '.1: \fi{)its ir,r:r :].- r.. , (,Lst ir,:r'. .... : -- .- :.fl:LrLgcrl i r:

i

iot $r:Lli:-ir::- .. : .. .\ll :l:,r..r. : : :: : _'

:

vrh-c rrri i ::.,::r': r. ::r -. tlrc prorl:l:,:.1- .:: : ::

or studi i1r ::r:i:

.:

; ,.- .:

218


24"

prpr.

24" o.D.

\T UIGI I1'S OF

I'IPI\G

}IATEITIALS

\Y.ltcr-Lbs/It

ui Z F

z e

f><

w

{T\ trJ-t -/A

J]\

t___-l____-!

Icnrpcrlturc llongc 'F Magnesia

z Calciun F

p Combinction

z

FiberSodium

ffi z qN

trs

Njs EN,fr\l z ::

d ,N

z

/D

Boldfsce troe is weicht in pounds. Liehifl.ce tvDe b;neath -

rreight'iactor for Insulation thicknesses and $'eights are based on averaqe ireight.

is

conditions and do not, constitule

a

recommendation lor specific of materials. lnsuhtion ucights are bused on.85/e m3gnesla ano nyorous cstclum silicate at ll lbs/cubic foot. The listed thicknesses and lr'eiqhts of combinotion covering arl the sums of the inner layer of diatomaceous earth at 2l lbs/cubic thicknesses

foot and the outer lsyer at

ll

lbs,/cubic foot.

tt, .rl IH

l=<[J

@ e

++J

rc * 16 lb cu. ft. density.

{:

I}zAppendix C: Properties of

WEI(IHTS OF PIPING MATERIALS

z F

F a

za"

o.o

Pipe

26t'

219

prps

Llj /\

Iit

{1\

E--I t J'\

z

-:I !-I_'

\"J Temperature Range

'F

Ilagnesia

z Calcium brUcate o

F

3 combina3 tion

3;m::;FiberSodium

Boldface type is weight in pounds. LiEhtface type beneath weight is weight factor

ffi z

for insulation.

Insulation thicknesses and weights are based on average conditions and do not constitute a recommendation for specifrc thicknesses of mat€rials. Iosulation weishts ate based on 85% magndsia and hvdrous calcium silicate at 11 l6s/cubic foot.The listed thicknesses and weights of combination covering are the sums of the inner layer of diatomaceous earth at 21 lbs/cubic

s.{-n$

N-is fFq.s | z F

,41

AI

foot and the outer layer at

/r+

11 lbs/cubic foot.

Insulation weights include

,N

allowances

&"f n' !l u:-Ji

ing on flanges,

t
rc

ft.

v-alves

or fit-

covetlngused on siralghl plpe. Valve weights are approxi-

mate. When possible, obtain weights from manufacturer, Cast ilon valYe weights are

for flansed end valve€i steel weishts Ior weldineend valves. A'il flane€d fitting, flanged

+
cement,

tings, multiply ihe weight factor by the weight per.foot of

@ fi)

*

fo! wire.

canvas, bands and iaint, but not special surface ffnishes. To-find the weiqht of cover-

valve and flange weiRhts in-

clude the propo-rtionaf weight of bolts or studs to make up deDsitt'.

all joints.

220

Mechanical Design of Process Syslems

28"

prpn

28- o.D.


W /4

{.J-f F

Ih

t-+J

{1}

trJ:I B

\IJ Tempelature Range "F nlagnesia Calcium

Combina-

tion

FiberSodium

ffi$

ffi

ds]-s iN z F F

z

,-a

A tr' .{ B---Jl

t=<3

@ 0

+
rc

* 16 lb cu. ft. derBity.

Boldface type is weight in pounds. Lightface type beneath weight is weight factor

for insulation.

Insulation thicknesses and weights are based on average conditions and do not co[stitute a recommendation for sDecific thicknesses

of

mate-

rials. Insulation weights are

based on 857, magnesia and lrydrous cjrlciuJn silicat€.at 11 lDs/cuorc root. I ne lrsteo [nlcknesses and weights of combination covering are the sums of the inner laver of diatomaceous earth ai 21 lbs/cubic

foot and the outer layer at 11 lbs/cubic foot,

Insulation weights in€lude for wire, cement,

allowances

canvas, bands and paint, but not special surface finishes, To find the weight of cover-

ing on flanges, valves or ffttings, multiply the weight factor by the weight per foot of covering usedon straight pipe. Valve weights are approxi-

mat€. When possible, obtain

\reights from manufacturer.

Cast iron valve weights are steel weishts forweldinsend valves. A-ll flanged fftting, flanged

for flanged end vslves;

valve and flahge weights in-

clude the proportional weight of bolts or studs to make up

all joints.


WEIGHTS

0I' PIPIN(} MATERIALS

Bo"

o.D.

Pipe

30"

221

prpe

u-f

Ih fl\ E-I

F

z

4',q E::l

'

L--r-----U

\L/ Temperature Range

'F

Ilagnesia Oalcium

t tlon Fiber SodiLtm

ffi z

E

lr-'$

Nls CI-]-\}


for insulation.

Insulation thicknesses and weights ale based on average conditions and do not constitute a recommendation for specilic thicknesses of mate-

rials. Insulation weights

are

based on 859t magnesia and hydrous caicium silicate at 1l 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 11 lbs/cubic foot.

Insulation rveights include allorvances for wire, cement, canvas, banCs and paint, but not sDecial surface finishes. To_lind the u'eight of covering on flanges, valves or fit-

z

tinss. multiDl\.the weieht factoibl the rieight per-foot of covering used on straight piPe. Valve weights are approxF

G

@ CD+ * 16 lb cu. ft. density.

rrt

mate. When possible, obtxin weiqhts from manufacturer. Cist iron valve weights are for ffanged end valves; steei

weights lor weldingend valves. All flanged fitting, flanged

valve and flange weights include the proportional weight of bolts or studs to make up

all joints.

222


32"

prcn sz, o.D.


tu?

tg

z

f\

l_p

{T\

7

!

LJJ-

4',4 {-r-, lr-f-r

\L/ Temperature Range .F

Magnesia Calcium

z Silicate

{ uomDlna5 llon

FiberSodium


,@$ 3*

for insulation, Insulation thicknesses and

3

tute a

euls

weights are based on average conditions and do not consti-

fsls

speciflc thicknesses

!J:!i.\\! ,-11

z F

tr

z

/A

.A

A

of materials. Insulation weights are based on 857. magnesia and

hydrous calcium silicat€ at 11 lbs/cubic foot.The listed thicknesses and weights of eombination covering are the sums of the inner laye! of diatomaceous earth at 21 lbs/cubic

foot and the outer layer at 11 lbs/cubic foot.

Insulation weiEhts include

t"{3

allowances for w-ire. cement. eanvas, bands and paint, but not special surface finishes. To find the weieht of covering on flanges, valves or fittings, multiply the weight factot by the weight per foot of

m

weights from- manufacturer. Cast iron valve weiehts are for flanged end vatves; steel

t€

valve and flange weights include the orooortional weieht

4!4

@

lt

lecommendation for

+
covering used,on straight pipe. v alve wergn!s are approxlmate. When Dossible. obtain

\

eights f or .!rrelding end valves. All flanged fitting, flanged

of bolts oi all joints.

stluds to make-up

\



s4"

o.D.

Pipe

223

34" *trc

G /.^ u-/

b /-i\

z F

I

z

rT

F

2,1 c_=_=r

-r

"t\ {---t-r \IJ

Temperature Range "F

2

Magnesia Calcium

{ tion z

FiberSodium

ffi

z

{

ffi

Njis N

z

3

a"

z

-l) /A AI

// N

/>

@

m

+
rc


r-

for insulation.

Insulation thicknesses and weishts are based on average conditions and do not constitute a recommendation for sDecific thicknesses of mate_

rials. Insulation weights arq based on 857, magnesis altd hvdrous calcium silicat€ at

11

l5s/cubic f oot. The listed thicknesses and weights of combi-

+.{ 3

Boldface type is weight in pounds. Lightface tYPe beireath weight is weight factor

nation covering ale the sums of the inner layer of diatoma-

at 21 lbs/cubic foot and the outer layel at ceous earth

11 lbs/cubic foot.

Insulation weights include for v/ire, cetnent,

allowances

canvas, bands and paint, but not special surface frnishes' To find the weisht of coverine on ffanees, v-aives or fittinles. multi6lv the weiqht fac-

tor"bi the iveight per-foot of coverrng usecl on slralghl plpe. Valve weights are approxi-

mat€. When possible, obtain weights from manufacturer.

Cast ilon valve weights are

for flanged end valves; steel weiehts forweldinsendvalves. A'il flanged fitting, flanged

valve and flange weights include the proportional weight

of bolts or studs to make up all joints.

224


36" "t"u s6" o.D.

z F

EI

3


W uj f\ w {T\ t=l _/A F--i

A \iJ

Temperature Range'F I\{agnesia

Ctllcitm, Nom. Thick., In.

Fiber-

Nom. Thick,, In.

Sodirm

ffi z

6{fliN$

N-S {raT,s ,tA z F

4t /A

z

/t\ l|' tl p6l

.lk{ l-
+q]

@

* 16 ]b cu. ft. derNity.

Boldface type is weight in pounds. Lightface type beneath weight is weight faetor

for insulation. Insuiation thicknesses

and

['eights are based on averag:e conditiods and do not consti-

recommendation lor specific thicknesses of mate-

tute a

rials. Insulation weights

aae

based on 85% magnesia and

hydrous calcium silicate at

11

lbs/cubic foot. The listed thicknesses and weights of combi-

nation covering are the sums of the inner layer of diatoma-

at 21 lbs/cubic foot and the outer layer at ceous earth

11 lbs/cubic foot.

Insulation weights include

allowances

for urife,

cement,

canvas, bands and paint, but not sDecial surface finishes. To-find the weight of cover-

ins on flanees. valves or fittirigs, multiply the weig-ht factor by the welgrr! per lool or covering used on straight pipe. Valve weights are approxi-

mate. When possible, obtain

weiahts from manufacturet. Cast iron valve weights are

for flanqed end valves; steel weichts iorweldineend valves, A-ll flanged fitting, flanged

valve and flange weights include the proportional weight

of bolts or studs to make up all joints.

D Appendix D Conversion Factors

225

226


Alphabetical Conversion Factors TO CONVERT

INTO

MULTIPLY BY

A

Abcoulomb

Statcoulombs Sq. chain (Gunters)

sq feet

acres acres actes acres acre-feet acre-feet cm cm in. In.

meler

meter ampere-hours arnpere-hours ampere-turns

ampere-turns/cm ampere-turn5/cm

ampere-tutns/cm ampere-turn5/in. ampere-turns/in. ampere-turns/ In.

ampere-turns/meter ampere-turns/meter ampere-turns/meter Angstrom

An8stron

un un

it it

Angstrom unit

amps/sq amps/sq amps/sq amps/sq amps/sq amps/sq

Btu/min Btu/sq ftlmin

.4047

10-:

3.259 x

cm meter cm In.

coulombs faradays

gilberts

1Cl'

6.452 10.

0.1550 6.452 x 10-. 3,600.0 0.03731

2.540 r00.0

amp-turns/cm amp-turns/meter grlberts/cm

39.37

0.4950

amp-turns/ in.

0.0254 3937 x 10-'

Acre (US)

.0247

ft of water (at 4'C)

1x 10-ro 1x 10-.

|

I19.60

o.o247 | 100.0 1.495 x 101

.007348 76.0 33.90 29.92 1.0333

In. of mercury (at 0"C) kgs/sq cn kgs/sq meter l0,332. pounds/sq jn. t4.70 tons/sq ft 1.058

B

Barrels (U.S., dry) Barrels (U.S., dry) Barrels (U.S., liquid) barrels (oil) oars bars

cu. tnches quarts (dry) 8al tons

gallons (oil)

bars

arrnospnetes dynes/sq cm kgs/sq meter

bars bals Baryl Eolt (US Cloth)

pounoS/sq In. Dyne/sq. cm. Meters

BTU

Liter-Atmosphere

8tu

ergs

Btu Btu Bttr Btu t'(U Btu

graln-caloneS horsepoweahrs ioules kjlogram,calories

8tu Btu/hr

foot-lbs

krlografi-meters kilowatt-hrs foot,pounds/sec

horsepower

kilowatts waIls watts/sq in. Cubic Cm, cu

ft

0.0700 3.929 x 0.2931 12.96 0.02356 0.01757

l0 '

t7.57

o.r22r 1.818 x 10'

1.2445

cu In.

2,150.4

cu meters

o.03524

laters

pecks

pints (dry) quarts (dry)

4.0 64.0 32.0

105.0 31.5 42.0

0.9869 105

!..020 x lcr. 2,089. 14.50 1.000 10.409 1.0550 x 10'o 778.3 252.0 3.931 x l0-l 1,054.8

0.2520 107.5 2.928 x

o.2t62

c Candle/sq. inch centares {centiares)

Lamberts sq meters Fahrenheit glams Ounce fluid (US)

centiliters

0.01257

ncn Meter l\4 icron or (i.,lu)

Kilometers Ton/sq. inch cms of mercury

toot-lbs/sec

B.T.U. {mean) Lambeats

centiglams Centiliter Centiliter Centiliter

0.3937 0.01

Astronomical LJnit Atnospheres

norsepower-hrs watts

Calories, gram (mean) Candle/sq. cm Centigrade

t.257

amp/turn5/cm

sq. yards acres sq meters

gram-cal/sec

MULTIPLY BY

I0 I

amp{urns/in. amp{urns/neter gilberts/cm

I

Bucket (Br. dry) bushels bushels bushels bushe,s bushels bushels bushels

tNt0

1,550.0

|.257

gilberts/cm

/hr

Btu/man

43,560.0

neler

Btu

8tu/min

1.562 x 4,840. In.

Btu /hr Btu/hr

Btu/min

I x 1Cl'

4,O47.

Ares ares

atmospneres atmospheres atmospneres atmospheres atmospneres atmospheres atmospheres

10

43,560.0

sq mete6 sq mrles sq yards cu feet gaflons

amperes/sq amperes/sq amperes/sq amperes/sq amperes/sq arnperes/sq

10ro

160

Rods

Square links (Gunters) Hectare or sq. hectometer

Acre

2.998 x

TO CONVERT

10-'

centimeters centimeters

Cubic inch

m

meters es

mallimete6 m ils

yards centrmeters centimeter-dynes cm-grams centimeter-dynes meter-xgs po!nd.feet centimeter-dynes centimeter-grams cm-dynes centimeter-grams rneter-kgs poundJeet centimeter-grams centimeters of mercury atmospheres centimeters of mercury feet of water centimeters of mercury kgs/sq meter centirneters of mercury pounds/sq tt centimeters of rnercury pounds/sq in.

centimeters/s?c

feet / min

centameters/sec centameters/sec

feet/sec kilometers/hr

centimeters/sec centimeters/sec centlmeters/sec centimeters/sec centimeters/sec/sec centimeters/sec/sec

xnotS

l0-' lO-.

1,094 x 10-I 1.020 x 10-! 1.020 x 10-l 7.376 x 10-r 980.7 10-5 7.233 x 10-5 0.01316 0.4461 136.0 27.85

0.1934 1.1969 0.03281

0.036 0.1943

mete6/min miles/ hr miles / rn in

centarneters/s€c/sec

feet/sec/sec kms/hr/sec meters/sec/sec

centimeters/sec/sec

miles/hrlsec

Chain Chain Chains (surveyors' or Gunter's)

Inches meters

Cords Cord feet Coulomb coutomos

.6103 0.01 3-281 x 0.3937 10- 5 0.01 6.214 x 10.0

centimeters centimeters centimeters

Circumference

0.01

liters feet kilometers

circular mils

1.0

(C'x9/5)+32

2.705

inches

10

3.142 .4870

drams

centrmeters cent,meters

circular mils circular Inils

3.9685 x

o.02237

3.728 x l0-r 0.03281 0.036 0.01

o.02237 792.00 20.12

yards sq clns sq mils Radians sq Incnes

22.O0

cord feet cu. teet

8

Statcoulombs faradays

5.057

r 10-.

0.7854 6.283 7.854 x

10-'

l6

2.998 x 10' 1.036 x 10-'

I

Appendix D: Conversion Factors

227

(Continued). Alphabetical Conversion Factors TO CONVERT coulombs/sq cm coulombs/sq cm coulombs/sq in. cou,ombs/sq in, coulombs/sq meter coulombs/sq meter cubic centimeterc cubic centirneters cubic centimeters cubic centimete6 cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic feet cubic feet

cubic feet cubic cubic cubic cubic cubic cubic

feet feet feet feet teet feet

cubic feet/min cubic teet/min cubic teet/min cubic teet/min cubic feet/sec cubic teet/sec

cubic cubic cubic cubic cubic cubic cubic ctibic cubic cubic cubic

inches inches inches inches inches inches inches inches inches meters rneters cub,c meters cubic meters cubic meters cubac mete6 cubic meters cubic meters cuDrc meters cubic yards cubic yards cubrc yards cubic yards cubic yards cubic yards cuorc yards cubic yards

cubrc yards/min cubic yards/fiin cubic yards/min

I

INTO

coulombs/sq in, coulombs/sq meter coulombs/sq cm

64.52 10.

coulornbs/sq meter coulombs/sq cm coulombs/sq in. cu feet cu inches cu mete6 cu yards Sallons (U. S. liq.)

1,550.

l0-.

6.452 x t0-l 3.531 x 10-' 0.06102

10-.

liters pints (U.S. liq.)

quarts (U.S. liq.) bushels (dry) cu cms cu inches cu meters cu yards gallons (tJ.S. iiq.)

liters pints (U.S.liq.) quarts (U.S. liq.) cu cms/sec gailons/sec liters/sec pounds of water/min million gals/day gallons/ min cu cms cu feet cu meters cu yards

ga

onS

liters mil-feet pints (U.S. liq.) quarts (U.S. liq.)

bushels (dry) cu cms cu feet cu tnches cu yards gallons (U.S. liq.)

liters pints (U.S. liq.) quarts (U.S. liq.) cu cms cu feet cu rncnes cu meters gallons {U.S. liq.)

liters pints {U.S. quarts (u.s.'iq.) liq.) cubic ftlsec Sallons/sec liters/sec

ULTIPLY 8Y

1.308 x

10-'

2.542 x 0.001 2.113 x 1.057 x

l0-!

lO-' 10-!

0.8035

-

2A32O.O

Gram

days

decrgrams

seconds grams

deciliters

tlers

oecrmelers degrees (angle) degrees (angle) degrees {angle)

meters quadrants radrans seconds

oramS oramS

otams Dyne/cm

oyne/sq. cm. Dyne/sq. cm. Dyne/sq. cm.

t,72A.O

o.02832 0.03704 7.4a0s2

dynes dynes dynes dynes dynes dynes

2432 59.84 472.0

0.t247 0.4720

IN?O

MULTIPLY 8Y

fadians/sec

0.01745

revolutaons/min

0.1667 2.778 x

revolltions/sec gtams

r0.0

liters

10.0 10.0

meters

10

ounces (avoidupois)

0.r371429

ounces (troy)

0.125

cubic cm.

3.6967 1.7714

Srams

grains ounces

27.3437 0.0625

Erglsq. millimeter Atmospheres Inch of Mercury at 0'C Inch of Water at 4'C grams

.01

9.869 x 10-' 2.953 x l0-'

4.015 x 10-' 1.020 x 10 I

10-'

JOUTeS/Cm

joules/meter (newtons) kilograms poundals pounds

oynes/sq cm

bars

EII Etl

Cm.

1

'

101.020 x 10 6 7.233 r 10-5 2.248 x 10-' 10-6

62.43 0.646317 448.831 5.787 x 10-. 1.639 x 10-' 2.143 x 10-5 4.329 x l0-3 0.01639

1.061x

105

0.03463 0.01732 106

5C.lt 61,023.0 1.308 264.2 1,000.0

Em, Pica Ern, Pica

2,1r3.0 1,057. 7.646 x IO' 27.O

Dyne

ergs ergs

Btu dyne-centimeters foot'pounds

erSs ergs ergs ergs

Srarn-calo es

erg5/sec

cm/sec

t2.74

l0-1.

kilowatFhrs

O.277ax

watt-houts

Btu/min

farads Faraday/sec faradays faradays Fathom Iathoms

microfarads Ampere {absolute} ampere-hours coulombs

feet leet

centimeters

teet feet leet feet ol water feet of water leet of water

l0-rr

1.0

Joules Kg-carofles Kg-melers

Sram-cm5

ft-lbs/sec

feet feet

1.000 9.480 x

7.367 x 10-l 0.2389 x 10 1.020 x 10 ! 3.7250 x 10-r' 102.389 x l0 -rl 1,020 x 10-'

kg-calories/min kilowatts

202.0 764.6 1,615,9 807.9 0.45 3.367

0.01111 0.01745 3,600.0

-

ft-lbs/min

0.7646

0.1 0.1 0.1

.4233

Crn.

ergs/sec

46,656.0

1.650 x 86,400.0

114.30 45

Inches Inch

*glsec

ergs ergs ergs

0 Dalton

CONVERI degrees/sec degrees/sec degrees/sec oeKa8rams dekaliters dekamete6 Drams (apothecaries' or troy) Drams (apothecarieS' or troy) Drams (U,S., fluid or apoth.) TO

l{eter feet krlometers meters rniles (naut.) miles (stat.)

millimeters

'

'

I0

t3

0.2778 x 10 -ro 5,688 x 10-, 4.427 x lO-' 7.3756 x 10-l 1.341 x l0-ro 1.433 x l0-' 10-,0

10 9.6500 x 26.4O

lcr

l0

9.649 x 1.828804 6.0 30.48 3.048 x 10

'

0.3048 1.645 x l0-. 1.894 x 10 . 304.8

lg

mr ls

1.2 x

armospnere5 an. of mercury Kgs/sq cm

0.02950 0.8826 0.03048

228


(Continued). Alphabetical Conversion Factors TO CONVERT teet of water feet of water feet of water teet/m in feet/ min

INTO

kgs/sq meter pounds/sq ft Pounds/sq in.

feet/ min feet/ min

cms/sec teet/sec kms/hr meters/min

feet/min

miles/hr

feet/sec feet/sec feet/sec feet/sec feet/sec feet/sec teet/sec/sec feet/sec/sec feet/sec/sec feet/sec/sec feet/ 100 feet

crns/sec

Foot

-

candle

kms/hr knots

meters/min

miles/hr males/

rn

in

cms/ sec/sec

kms/hr/sec meters/sec/sec miles/ hrlsec per cenl graoe Lumen/sq. meter

MULTIPLY BY 304.8 62.43 0.4335

grains (troy) grains (troy) Srains (troy) giains (troy) Srains/U.S. gal grains/U,S. 8al

0.5080 0.01667 0.01829 0.3048 0.01136 30.48 1.097 0.5921 18.29 0.6818 0.01136 30.48 1.097 0.3048 0.6818 10.764 1.286 x 10-3 1.356 x 10' 0.3238 5.050 x l0-' 1.356 3.24 x 1.0 .

foo!pounds

Btu

foot-pounds loot.pounds foot-pounds foot-pounds foot-pounds foot-pounds

ergs

foo!pounds foot-pounds/min foot-pounds/min loot-pounds/mjn loot-pounds/m,n foot-pounds/min toot-pounds/sec foot-pounds/sec foot-pounds/sec toot-pounds/sec foot-pounds/sec

kilowatt-hrs

3.766 x

Btu/min

1.286 x

foot-pounds/sec hotsepowel


0.01667 3.030 x 10 -5 3.24 x lO-. 2.260 x l0-5

Btu/hr Btu/min

o.o77 17

grarl1-calofles np-nrs JOules

kg'calories kg-meters

horsepower

Furlongs

kg-calories/min kilowatts miles (u.S.)

turlongs

rooS

furlonBs

feet

Sallons garrons

galrons Sallons gallons gallons gallons (liq. Br. lmP,)

gallons (U.S.) gallons of watef gallons/min gallons/min gallons/min gausses Sausses Sausses gausses

gilberts

gilberts/cm gilberts/cm

gilberts/cm

cills (British) gills

cu cms cu feet cu Inches cu meters cu yards

liters gallons (U.S. liq.) eallons (lmp.) pounds of water

cu ftlsec liters/sec

cu ft/hr lanes/sq in. weDers/sq cm webers/sq in. webers/sq meter ampere-turns

amp-turns/cm amp-turns/in amp-turns/meter cubic cm.

liters

Sills

pints (liq.)

Grade

Radian drarns (avoirdupois)

Grains

0.r383

parts/rnillion

l0-' l0-3

l0-'

1.818 x 0.01945 1.356 x 10-'

grams/cm Slams/cu cm

gr-arns/cu cm Srams/cu cm grams/ liter grams/ liter

10-t

0.04167 17.118 142.56 14.286

980.7

joules/cm joules/meter (newtons) kilograms

milligrams ounces {avdp) ouhces (troy) pounoals pounds

pounds/inch pounds/cu ft pounds/cu in pounds/mil-toot grains/gal pounds/ gal

grams/liter grams/liter

parts/nillion

grams/sq cm

pounds/sq

gram-calones gram-calories Sram-catones Stam-catofles Sram-calories gram-calones gram-caloraes/sec gram-centimeters gram-centimeters gram-centrmeters gram'centametels

6tu

grafi-centimeters

2.0833 x

parts/million oynes Slarns

grams grams grams grams g,ams

1.0

0.06480

pounds/million gal

Srams Srams Srams Srams

MULTIPLY 8Y

grains (avdp) grams ounces (avdp) pennyweight (troy)

grains/lmp.8al Sralns

1.0

INTO

TO CONVERT

pounds/cu

ft

ft

foot-pounds horsepowet-hrs

kilowatt-hrs watt-hr9

Btu/hr Btu ergs

joules kg-cal xg-meters

15.43 9.807 x lo-t 9.807 x 10-! 0.001 1,000. 0.03527

0.03215 0.07093 2.205 x l0-' 5.600 x l0-r 0.03613 3.405 x l0-t 58.417 8.345 o.062427 1,000.0 2.0481 3-9683 x 10-t 4.1868 x l0'

3.0880

1.5596 x l0-. 1.1630 x l0-. 1.1630 x 10-3 14.286 9,297 x lO-. 980.7 9.807 x l0-5 2,343 x 10-3 10

o.125

-'

40.0 660.0 Hand nectares nectares neclograms

3,785.0

23i.0

3.785 x 10-' 4.951 x 10-t 3.785 1.20095 o.83267 8.3453 2.22a x

l'-t

0.06308 8.0208 6.452

l0-l

6.452 x

10-,

10-. 0.7958 0.7958

2.02r 79.58 142.O7

0.1183 0.25 .01571

0.03557143

10.15

Cm.

acres sq feet grams

hectoliters

liters

hectometers hectowatts henries Hogsheads (British) Hogsheads (U.S.) Hogsheads (U.S.)

meters watts

millihenries cubac

ft.

hoasepower

Btu/min foot-lbs/min foot-lbs/sec

horsepower

kg.calories/min kilowatts

ho15epower

horsepower horsepower (boiler) horsepo',ver (boiler) horsepower-hrs horsepower-hrs horsepower-hrs horsepower-hts norsepower-nrs

1.076 x 100.0 100.0 100.0 100.0 1,000.0 10.114

horsepowet (550 ft lb/sec) horsepower (metric) (542.5 ft lb/sec) watts

Btu/hr kilowatts Btu ergs

footl bs gram.calol|es JOU

leS

103

8.42184

cubic ft. gallons (U.S.)

holsepower horsepower horsepower (met.ic) (542.5 ft lb/sec) horsepower

(550it lb/sec)

2.471

42.44 33,000. 550.0 0.9863 1.014 10.68 0.7 457 7

45.7

33.479 9.803

2,547. 2.6845 x 10u 1.98 x l0' 641,190. 2.684 r l0'


229

(Continued), Alphabetical Conversion Factors TO COI{VERT

tt{To

ho.sepower-hrs horsepower-hrs horsepower-hrs nours houls HundredweiShts Hundredweights Hundredweights Hundredweights Hundredweights Hundredweights

kg.calories l(g-meters

ilIULTIPLY BY 641.1

kilowatt-hrs qays

2.7X7 x

lU

o.7457 4.167 x 5.952 x

10-r

t12

(long) pounds (long) tons (long) (short) ounces (avoirdupois) (shortl pounos (short) tons (metric) (short) tons (long)

l0-r

0.0s

t600

100 0.0453592

o.0446429

I inches inches inches inches Inches inches inches inches inches inches inches inches inches inches inches inches inches inches

centimeters meIels miles millimeters mils

mercury mercury mercury mercury mercury of mercury

of of of of ot

of water (at of watet (at of water (at of water (at of water (at of water (at

International

4'C)

yaros atmospheres feet of water kgs/sq cm kgs/sq meter

2.540

2.540x 10-t 1.578 x 10-5 25.40 1,000.0 2.77a x rO-' 0.03342

pounds/sq tt pounds/sq an.

atmospheres

4'C) inches of mercury 4'C) kgs/sq cm 4'C) ounces/sq in. 4'C) pounds/sq ft 4'C) pounds/sq in. Ampere Ampere(absolute)

InternationalVolt Inte.nationalvolt lniernational volt JOUIeS

joules joules ioules joules joules joules/cm ioules/cm joules/cm .loules/cm

ioules/cm

volts(absolut€) Joules(absolute) Joules

Btu ergs footpounds kg-calories kg-meters watlhrs grams dynes joules/meter(newtons) poundals pounds

0.03453 345.3 70.73

5.204 0.03613 .9998 1.0003

l-593 x 10-'' 9.654 x l0'

10-'

107

l0-' lO-'

1.020 x 10.

10' 100.0 723.3 22,44

K kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms

kilograms/cu meter kilograms/cu meter kilograms/cu fieter kilograms/cu meter kilograms/meter Kilogram/sq. cm. kilograrns/sq cm kilograms/sq crn

cm cm cm rneter meter meter meter meter kalograms/sq meter

inches of mercury

kilograrns/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq kilograms/sq

kilograms/sq mm kilogram-calories kilogram-calories kilogram-calories kilogram-caloraes kilogram.caloaies kilogram-calories kilogram-calories kilogram meter9 kilogram meters kilogram meters kilogram meters kilogram meters kilogram meters

kiloliters

0.07355 2.540 x l0-1 0.5781

0.7376 2.389 x 0.1020 2.77Ax

INTO

HULTIPLY BY 24.

pounds/sq lt pounos/sq In.

2,O44. 14.22

9.678 x 10-' 98.07 x l0-. 3.281 x l0-: 2.896 x 10-l 0.2044 1.422 x 10.

atmospheres oars

teet ot water inches ot mercury

pounds/sq ft pounds/sq in. kgs/sq meter

l0-'

Btu foot-pounds hp-h.s

3,088. 1.560 x 10-1 4,186. 426.9 4.186 1.153 x l0-3 9.294 x 10-r 9.804 x 10'

joules

kg-meters

kilojoules kilowatt-hrs Btu

foo!pounds 9.804 2.342 x lO'' 2.723 \ 1O-' 1,000.0 1,000.0 10, 3,281. 3.937 x lO 1,000.0

JOUIeS

kg-calories

kilowatt-hrs

kilolines

o.4912 2.458 x 10-!

9.480 x

TO CONVERT

dynes 980,665. grams 1,000.0 joules/cm 0.09807 joules/meter(newtons) 9.807 poundals 70.93 pounds 2205 9,842 x 10-' tons (lond tons (short) 1.102 x 10-r grams/cu cm 0.001 pounds/cu tt 0.06243 pounds/cu in, 3,613 x 10-5 pounds/mil-foot 3.405 x 10-'o pounds/ft 0,6720 980,665 oynes 0.9678 atmospheres feet of water 32.81

kilometers kilometers kilometers

liters centimetels {eet inches

kilometers

meterS

kilometers

miles millimeters

kilometers kilometers kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr

kilometers/hrlsec kilometers/hrlsec kilometers/hrlsec kilometers/hrlsec kilowatts kilowatts kilowatts kilowatts kilowatts kilowatts kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kiiowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs kilowatt-hrs

0.6214 lCl' 1,094. 27.74 54.68

yards

cms/sec

feet/min teet/sec

0.9113

knots

meters/nin miles/hr

0.6214 27.74

cms/sec/sec ft /sec/sec meters/sec/sec

0.9113 0.2774

miles/hrlsec Btu/min

0.6214

foot-lbs/min foot-lbs/sec

4.426 737.6

norsepower

kg-calories/min Btu

foot-lbs

1.341

14.34 1,000.0 3,413. 3.600 x 10r' 2.655 x 10. 859,850.

gram-calories horsepower-hrc joules xg.carofles k8-meters

knots knots l(nots knots

1,341

3.6 x lcl. 5bu.5 3.671 x 10'

pounds ot water evaporated from and

at212'F. kilowatt-hrs

\W

3.53

pounds ot water raised

frcm62" to 212" F. feet/hr kilometers/hr nautical miles/hr statute miles/hr

22.75 6,080. 1.8532 1.0 1.151

230


(Continued). Alphebetical Conversion Factors TO CONVERT knols knots

INTO

yards/hr feet/5ec

MULTIPLY BY 2,027. 1.589

L leaSue Light year

Light Year lines/sq cm lines/sq in. lines/sq in. lines/sq in. lines/sq in. links (engineer's) links {surveyor's) liters liters liters liters liters liters liters liters liters

liters/min liters/min

lumens/sq ft Lumen Lumen

Lumen/sq. ft. tux

miles (approx.) Miles Kilometers

9.46091 x 10"

gausses Sausses

0.1550

5.U

5.9 x 10rr 1.0

weDers/sq cm w€bers/sq in. webers/5q meter inches inches bushels (U.S. dry) cu cm

cu feet cu tnches cu mete6 cu yards eallons (u.S. liq.)

pints (U.S. liq.) quads (U.S.liq.)

cu ft/sec gars/sec foot-candles Spherical candle power Watt Lumen/sq. meter foot-candles

1.550 x

l0-l

l0-'

1.550 x 10-r

t2.o 0.02838 1,000.0 0.03531 61.02 0.001 1.308 x 10-r

0.2642

2.r13 1.057 5.886 x l0-' 4.403 x 10-' 1.0

.07958 .001496 10.75

0.0929

tl maxwells

kilolines

0.001

megohms megohms

fieters

centimeters

meters metets meters metels meters meters meters metets

leet

meters/m,n

cms/sec

meters/man

feet/min

39.37 0.001 5.396 ! 10-1 6.214 x 10-' 1,000.0 1.094 1.179 1.567 3.281

meters/mrn meters/min metels/min meters/min meters/sec

teet /sec

0.05458

kms/hr

0.06

knots

0.03238 0.03728

mete6/sec

feet/sec

meters/sec meters/sec mere6/sec metels/sec meters/sec/sec meters/sec/sec

kilomete15/hr

5,O

kilometers/min

0.06

miles/hr miles/min

0.03728

mete6/sec/sec mete6/sec/sec meterkilograms meteFkilograms meteFkilograms microfarad micrcgrams micrchms

anches

kilometers miles (naut.) miles (stat.)

millimeters yards

miles/hr feet/

m

in

1Cl.

10u 10. 100.0

3.281

kms/hrlsec rniles/hrlsec cm-dynes cm-grams pound-feet farads glams megohIns

9.807 x

liters

Microns miles (naut.) miles (naut.) miles (naut.) miles (naut.) miles (naut.) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute)

mererc

19

I x 10-'

feet kilometers

6,04O.27

meters miles (statute) yards centametels

1,853. 1.1516 2,027. 1.509 )( 5,280. 6.336 x

feet inches kilometers meterc miles (naut.) yards

cms/sec leet/man

mil-feet

cu inches

milliers

kiloSrams meters

feet/sec kms/ht meters/min

miles/min sec/sec feet / sec /sec /

kms/hr/sec

10

r.609 1,509.

0.8684 1,760.

M.70 8& t,467

26.42

0.1667 44.70 L.467 1.509

meters/sec/sec cms/sec teet/sec kms/min knots/min

0.4470 2,642. 88.

miles/hr

60.0 9.425 x 1,000.

g|a Ins

grams

parts/million

millihenrie5

henries

milliliters

liters centimetels feet inches kilometers meters

millimete6

miles

millimeters millimelers million gals/day mils

mrls yards cu ftlsec

0.8584

0.001 1.0 0.001 0.001 0.1

3.281 x

10-.

10-'

1.094 x

l0-'

1.54723

anches

mils mils

kilorneters yaros

2.77Ax

cu ft/min

cubic cm. cubac cm. oeSrees

quadrants radians seconds kilograms

kilometers kilowatts

10-t

0.001 6.214 x

mils

centimeters feet

10-'

I x lo-t 0.01543235

2.540 x 8.333 x 0.001 2.540 x

myriagrams myriameters myriawatts

1Cl'

o.o26a2 0.8684

knots

cms

1..'J5

1.609

kms/min

milliSrams/litet millimeters millimeters millimeters millimeters millimeters

IT.IULTIPLY BY

10-. 10-.

miles/hr rniles/h. miles/hr miles/hr miles/hr miles/hr miles/hr miles/h. miles/hr/sec miles/hrlsec miles/hrlsec miles/hr/sec miles/min miles/min miles/min miles/min miles/min

miner's incheg Minims (British) Minims (U.S., flu;d) minutes (angles) minutes (angles) minutes (angles) minutes (angles)

r00.0 ft/sec /sec

ohms

micrcliters

mils

195.8 3.281

INTO

microhms

Millimicrons Milligrams milligrams

10-l

webels maxwells microhms ohms

megaltnes

TO COI{VERT

t.5

10-t 10-!

10-'

lO-'

0.059192

0.0516r2 0.01667 1.852 x 10-' 2.909 x l0-. 60.0 10.0 10.0 10.0

lCr'

l0-.

N

10-.

decibels

10-rl

Dynes

8.686

1x105


231

(Continued). Alphabetical Conversion Factors TO CONVERT

INTO

MULTIPLY BY

0 OHlvl (lnternational) ohms ohms ounces ounces ounces 0unces ounces ounces ounces ounces (fluid) ounces (fluid) ounces (troy) ounces (troy) ounces (koyJ ounces (troyj Ounce/sq. Inch

ounces/sq In,

OHIV (absolute) megohms

mtcrohms drams grains grams pounds ounces (troy) tons (long) tons (metric)

cu rnches liters grains grams ounces (avdp.) pennyweights (troy) pounds (troy) Dynes/sq. crn.

pounds/sq rn.

1.0005

10 . 1@

16,0 437.5

2a349527 0.0625 0.9115 2.790 x 10-5 2.835 x 10-5 1.805 o.02957

480.0 31.103481 1.09714 20.0 0.08333

4309 0.0625

P

parts/mil!ron

lViles Kilometers grains/U.S. gal grains/lmp. gal

parts/mjllion

pounds/million gal

Pecks (British) Pecks (British) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) Pecks (U.S.) pennyweights {troy) pennyweights {troy) pennyweights (troy) pennyweights (troy) pints (dry) pints 0iq.) pints (liq.) pints (lrq.) pints (liq.) pints (l'q.) pints (liq.) pints (liq.) pints (riq.) Planck's quantum

cubic inches Iters

Parsec Parsec

parts/ftillion

Poase

Pounds (avoirdupois) poundats pounoars pounoars pounoats poundats pounoars pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds p0unds pounds (troy) pounds (troy)

bushels cubic inches

liters quarts (dry) grarns

ounces (troy) grams po!nds (troy) cu lncnes

l9 x 10rl 3.084 x 10r3 0.0584 0.07016 8.345 554.6 9.091901 0.25

n.'

Erg

-

second Gram /cm, sec,

/

ft tt

in. R^"n.i
8.809582 8 24.O

lo(/
MULTIPLY BY 13.1657

t2.0 240.0 o.a22457 3.6735 x 10 ' 3.7324 x 10-l 4.1143 x 10-' 0.01602 27.68 0.1198 2.670 x 10-' 1.356 x 10'

r3,825. 0.1383 0.01602

t6.o2 5.787 x 5.456 x 27.64 2.768 x 1,724. 9.425 x 1.488

10-' 10 ' 10

L0-'

178.6

2.306 x 1Cr' 4.125 x lO 0.01602 0.01414

'

4.882

6.944 x t0-l 0.06804 2.307 2.036 703.1

144.0

0.05 4.1667 x

0.01671 24.87 4.732 x l0 6.189 x 10-' 0.125 o.4732 0.5 6.624 x 1O 1'

'

1.00

14.5833 oynes 13,826. 14.10 Srams joures/cm 1.383 x joules/rneter (newtons) 0.1383 kilograms 0.01410 pounds 0.03108 drams 44,4423 r. dynes grarns 7,000. grams 453.5924 joules/cm 0.04448 joules/meter (newtons) 4.448 0.4536 kilograms 16.0 ounces 14.5833 ounces (troy) pounoals pounds (troy) t.21528 0.0005 tons (short)

l0

5,760. 373.24177

o

10-l

33.60

ounces (troy)

grarns grams

'n,lc

^^"nd
473.2

cu feet cu lncnes cu meters cu yards gallons Irters quarts (liq.)

INTO CONVERT pounds (troy) ounces (avdp.) pounds (troy) ounces (troy) pounds (troy) pennyweights (troy) pounds (troy) pounds {avdp.) pounds (troy) tons {long) pounds (troy) tons (metf ic) pounds (troy) tons (short) pounds of water cu feet pounds of water cu inches pounds of water gallons pounds of water/min cu {t/sec poundjeet cm-clynes pound-feet cm-grams poundjeet meter-kgs pounds/cu ft grams/cu cm pounds/cu {t kgs/cu meter pounds/cu tt pounds /cu in. pounds/cu ft pounds/mrlJoot pounds/cu in. grns /c! cm pounds/cu in. kgs /c! meter pounds/cLr in. pounds/cu ft pounds/cu in. pounds/mri foot pounds/ft kgs'meter pounds/ in. grns/ cm pounds/mil-foot gmslcu cm pounds/sq ft atmospheres pounds/sq ft feet of water pounds/sq ft inches of mercury (n

TO

quadrants (angie) quadrants (angle) quadrants (angle)

oegrees rad ra ns

q!adrants (angJe) quarts (dryj

1.571

seconds cu tncnes cu cms cu teet cu inches cu meters cu yalds gallons

3.24 x

quarts lliq.) quarts (liq.) quarts (liq.) quarts (liq.l quarts (liq.) quarts (liq.) quarts (1,q.)

90.0 5,400.0

minutes

liters

1O5

67.20 946.4 0.03342 57 .7

5

9.464 x 1.238 x 0.25

l0-. 10-l

0.9463

1

R

ians radians radrans radians rad

W

radians/sec radians/sec radians/sec radians/sec /sec €dians/sec /sec raorans/ sec/sec revolutions

revoru!ons tevotutons revolutions/min revolutions/min revolutions/min

rninutes quaorants seconds degrees/sec revolr.rtions/min revolutrons/sec revs/min /min

revs/nrn/5ec revs/sec /sec quadrants radrans oegrees/sec

fadians/sec revs/ sec

57.30 3,438. 2.063 x 10r 57.30 9.549 0.1592 573.0 9.549 0.1592 360.0 4.0

6.243 6.0 0.1047 0.01667

232


(Continued). Alphabetical Conversion Factors TO CONVERT revolutions/min/min revolutions/min/min

INTO

radians/sec/sec

revolutions/min/min

revs/sec/sec

revolutions/sec revolutions/sec revolutions/sec revo,utions/sec/sec revolutions/sec /sec revolutions/sec/sec

oegrees/sec

Rod

Chaan (Gunters)

xoo

Meters

radians/sec

MUI.TIPLY BY 1.745 x 10-r 0.01667 2.778 x 10-.

360.0 6.283 50.0

radians/sec /sec

revs/min/min revs/man/sec

3,600.0 60.0 .25 5.029

INTO

TO COI{VERT square squate square square square square square square square

mrls !nrl5 yards yards yards yards yards yards yards

sq

cns

gra,ns

minutes quaoranls radians Kilogram

tempemture

("c) +273

Pounds

20

2,778\ lO . 0.01667 3.087 x 10-6 4.848 x l0-l 14.59 32.17

Steradians

circular lnils sq feet sq rnches sq miles sq millimeters sq yards acres

circular mils sq cms sq inches

1.973 x 10' 1.076 x l0-3

0.1550 0.0001 3.861 x 10-'r

r00.0 1.196 x 10-. 2.296 x 10-, 1.833 x l0o 929.O

144.0

0.09290

square Inches square square square square square square square square square square square square square square square square square square square square square square square square square square square

Inches Inches Inches inches

k'lometers

kilofleters kilometers kilorneters kilometers kilometers kalometers

meters meters melers meters meters meters meters

miles miles miles mrles

millimeters millimeters millimeters millimeters rn ils

sq mrles sq millimeters sq yaros circu lar mils sq cms sq teet sq millimeters sq mils sq yards acreS sq cm5 sq ft

0.8361 3.228 x 1O-, 8.361 x l0'

sq males

sq millimeters

3.587 x l0-r 9.290 x lCr 0.1111 1,273 x 106

6.452 6.944 x

l0-3

tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons tons

(long) (long) {long) (metric) (metric) (short) (short) (short) (short) (short) (short) (short) (short)/sq ft (short)/sq ft of water/24 hrs of water/24 hrs of water/24 hrs

cns

sq feet sq miles

sq feet sq xms

sq meters sq yards

circular mils sq cms sq feet

sq inches

circular mils

3.861 x

1,973.

0.01 1.076 x 10-r 1.550 x 10-! 1.273

5/9

foot-lbs/min

3.4129 0.05688 107.

44.27

0.7374

watts


1.341 x l0-1 1.360 x 10-! 0.0t 433 0.001

Watts (Abs.) Watts (Abs.) watt'hours

B.T,U. (mean)/man.

0.056884

joules/sec. Btu

3.413 3.60 x 10'o

walls watts

1.196 640.0 27.88 x 10. 2.590 2.590 x 10d 3.098 x 106

1.0

.003336

toot'lbs/sec

106

10-'

('F)

.39370

Volt/cm. Statvolts

eags/sec

1Cp

1.8

kilog€ms 1,016. pounds 2,240. tons (short) 1,120 kilograms 1,000. pounds 2,205. kilograms 907.1848 ounces 32,000. ounces (troy) 29,166.65 pounds 2,000. pounds (troy) 2,430.56 tons (long) 0.89287 tons (metric) 0.9078 kgs/sq meter 9,765. pounds/sq in. 2,000, pounds of water/hr 83.333 gallons/min 0.16643 cu ltlhr 1.3349

Btu/hr Btu/min

1,550.

sq millimeters sq yards actes

1.0

w

watts

lO-.

('C)

v Volt/ inch Volt (absolute)

10. 7.716 x 10-. 247.1 10x 10.76 x 106 1.550 x 10' 0.3861 1.196 x 2.471 x 10. 10.76

absolute temperature

temperature ('F) temperature ('c) + r7.78 temperalure absolute temperature ("F) +460 temperature ("F)-32 temperature ('C)

106

sq mrles sq yards sq

9.0 ,296.

T

s

square feet

't

sq inches sq meters

feet

Scruples seconds {angle) seconds (angle) seconds (angle) seconds (angle) Slug Slug Sphere square centimeters square cent|melerS square centimeters square centrmeters square cen!melers square centimeters square centimeters

6.452 x 10-6 10-6 2.066 x 10-. 8,361.

sq Inches acres sq cms

Rods (Surveyors' meas.) yards

rods

MULTIPLY BY

horsepower horsepower (metric)

watt-hours watt-hours

erSs

watt'hours

gram-caloneS horsepolver-hrs kilogram-calories

watt-hours watt-hours watt-hou.5 watt-hours

Watt (lnternational)

foofpounds

I

2,656. 859.85 1.341 x

0.8605

kalogram-meters

kilowatt-hrs Watt (absolute)

0.001 1.0002 1Cp

kilolines

10,

l0-1

-----Appendix D: Conversion

Factors

Synchronous Speeds syncnronou3

sPc.o

Frcqusncy

r

120

- T;;Ei;;FIEQUEiICY

60.ycle

50

.y.lc

3600

3000

r800

t

6 8

50 Gycl. 12

171.1

142.9

500

11

|

63.6

136.4

1200

1000

a6

|

56.5

130.4

900

750

375

18

l50

r25

600

300

111

t20

500

250

t38.5

124.6

214.3

133.3

||t.l

375

187.5

128.6

t

l0 l2

600

II

5r

t6

150

t8

400

4.3

|

500

56

166.7

5.a

o7.l

t21.1

103.5

360

300

t50

60

120

100

327 .2

272.7

136.4

62

rr6.t

96.8

2l

300

250

61

2.5

93.7

26

276.9

230.8

lt5.a

66

t0t.

28

257 .1

211.3

t

07. t

58

r

30

210

200

100

32

225

187.5

93.7

72

31

2n.8

175.5

88.2

71

97 .3

8r.l

36

200

166.7

83.3

76

91.7

78 -9

38

t89.5

157 -9

78,9

92.3

76.9

10

r80

150

75

?0

75

Courtely Ingersoll-Rand Co.

80

I

90.9

05.9

88.2

102 -9

85.7

t00

83.3

2Sg

234


Temperature Conversion NOTA Thc G.nter .oluh'l of nu|'b.t! in boldfo.. .efeB to the teDperotur. in desreei, either Cenrig.odc or Fohrenh.ir, whidr it ir d.!ir.d to conv.rt inlo lh. olh.rtol.. lf.o.v.rtins kom fohr€nhcil lo Ccntis.ode degr€e!. the equivolent tempe.oiure will bc found in lh.lefi col'r6n, whileil convc.li.s lron d.s.c€i Ccnrigrodc to

d.gr..r fobr.nhi.t,

thc oniy€r

Cenlisrod.

-20.6

-16.7

-t6.1

- .l

-159.1 -151 -136

-4t8

-2oO

328

-100 -361

-316

-tlo -tto

-292 -271 -256

-t50 -lao -r30

-238 -220 -202

-120

-181

-t66

-18.3 -15.6

-50

-67 .0 -58 .0

a5

-49.0

-/2.9 -,40.0

-!l

-40 -35

-31.1 -3t .7 -28 .9 26.1

t7 .2 .8

u

5r.8

-8 .9 -8 .3

l4 l5

220 225

t2a

I

l0

163.4 165.2

I

t6

230 235 240

116 155 461

167 .O

I

l8

7.45

173

25 27

80.6

2.4

8? .,{

a9

3l

81.2 86.0 82.8

32

89.6

7a 75 76 7a

,9 !o

152

168.8 170.6

l2l

t72.1

127 129

121

171.2 't76.O

27 .2 27 .S

8l

177 .8

a2

t79.6

28.3 28.9 29 .1 30.0 30.6

83

3t.l

ll3

l8l

132

135 138

t{

3f

98.6

3l

100.,{

39 40

102.2 104 .0

8.9

/t8

118.,(

-4.0

9.1

105.8 to7 .6 109.1

.7 32.2 32.8 33.3 33.9 31.1 35.0

31

35.6 36.7

114.8

37 .2

| 16.6

536 545 554

E5

185 .0

86

186.8

l,a9 154

|

88.6

t60

|

90 .,4

t66

300 310 320 330

t71

3:10

626 611

a, E8

s72 590 608

89 90

192.2 194.0

177

350

662

9l

|

95.8

182

t88

360 370

680

.6

99.4

r93

3t0

,16

201 .2

t99

731

203.0 204.8

201

390 a0o

210 216

at0 420

206,6 208.4 21o.2 212 .0

221

r30

805

L0 aso 150 170 {r0 ago 500

gza 812

92 93 9a 95 95

9A

99

197 r

227

40 .6

t05

221

238

43.3

0

213 219

a9 50

120.2

,(6.l

||5

122.O

5l

t20 t25

218

251

t23.9

18.9 5t .7

257

260

| et-r'r Degreca KeMn,'K:'C + 273.2

518

290 495

.,a

230 239

=

500 509

lt6

100

cent,'.=|et + ,ot -ro

280

2t5

ta2 191

143

9f

113.0

250 233 260 255 270 215

137

I83.2

!4

95.0

-22.0

Desr€e'

26.1

26.7

8.3

10.0 l0 .6

23.9 21.1 25.0

25.6

l]1.2

(ony€rling Ceotigrcdc or foh.enhcil i.lo thc othcr 3cal.r.

119

77 .O

14 15 a6 17

formulor ol lh. .isht hoy oho bc ured

215

25

6.7

.4.0

ttt

t02 t04 t07

-3 .9

12

-t0

212

-1.1

5-6 6.1

-t3.0

110

100.0

23 24

10.0

392 ,a0r

,3

{3

383

200

371

210

22.8

96.8

195

t5.4

205

d8.0 69.8 71.6 73.1 75.2

36

t90

I

317 356

93.9

20

93.2

85.0 82.8

l15

117.2

t

338

96.1

72

9t.,(

!65 t70 t75 ta0

329

13.6

73.9 76.7 79.1 s2.2

.6 154.4 | 56.2 158.0 159.8 161 .5

fl

34 35

38.2

l{0.0 l4r.8

t20

50.8

2t .7 22.2

LI

71.1

I55 t50

3ll

34.6 | 36.4

150

t

2t.r

0.6

65.6 68.3

55 57

62.6 61.1 66.2

0.0

32.8

r

l8 .9

t7 t8 t9

30

293

2e1

149.0

59 70

1.7

l,l5

55

20.6

2l

.0

266

8.3

60 .8

6.7 -6.1

r3l

t30 t35 ta0

90.6 93.3

t5

/tt

-31.0

l, |

5.0

-25 -20

-ll

18.2

50.0

5l

3.9 4.1

-50

9

52 53 61

20.0

-t 03.0 -65.0 -75,0

t6.7

6l

59.0

-75 -55

16. r

I9..{

-t l2 .0

-53 .9 -51 .l

|

5t

57 .2

-90

91.0

59 60

l5 .6

t0 t3

1.7 2.2

-ro

16.4

60.0 62.8

|

t2.a

I

12r.2

57

14.1 15.0

lt.6

5t.t

13.3

t3.9

al.0

125.6 127.1

52 53 5a 55 55

39 .2

-10.6 -10.0

-148.0 -t 30.0

-r0

11.7 12.2

3

7

-t2.8 -t2.2

-382

-I00

.l

32.0

1

-13.t -r3.3

-230 -220 -210

-ll0

23 -O

35.6 37.1

5

C.ntlgrod.

Centigrode

I2.8

2

-15.0 -14.1

-116 -f10 -t34 -129 -123 -I8 -l 12 -107 -tot -96 -90 -8{ -79 -73.3 -67 -S -62.2

-r50

-5 I

-rao

-r90

Fohrenhcil

0

-tsf

-56.7

fo'rnd in the column on thc right.

C.ntigrodc

-273.17 -a59.f -268 -r50 -262 -aao -{30 -257 -25t -420 -216 -aro -,100 -210 -231 -390 -3r0 -229 -370 -223 -2t8 -360 -350 -212 -3{0 -207 -330 -20t -310 -t96 -190 -3ro -300 -t81 -290 -179 -2t0 -173 -2f3 -f69 -168 -rro -260 -t62 -250 -157

-59.r

$ll b.

Dcqree' Fohr.,

'F = ! 9

fc + .ot -.0 c +32

Degrccr Rcrftlne, ol :oF+459.7

69S

v0

748

860 678

896 914

932

3*. Aooendix D: Conversion Factors

Altitude and Atmospheric Pressures

Kelrq Hs Ab3. -1526 -1373

-5000

,{500 ,{000

77 75 73

21

35.58 35.00

H9 Abr.

PSIA

.7

17.15

.229 .209

903

t7.t9

889.0

23

s{.12

87t.3

16.t0

.188

-3500 -3000

t068

71

22

859.5

16.62

.t69

-915

70

2l

33.84 33.27

8,(5.l

t

6.34

.r19

2500

-763

68

20

-610

830.6 816 .4

16.06 15.78

l8

3t .58

802.1

-305

65 61 63

32.70 32.11

.129

-2000 -1500 -1000

17

3l .02

757

6l

t6

30.17

773.9

59

29 .92

760.O

29.38

716.3

28 .46

733

28.33

719.6 706.6

-1220

15S

0

0

500 1000

t53

I500

.158

2000

6t0

?500

763

3000

915

l8

3500

1068

17

t000

1220 1373

t4 55

,4500

12

ll 50

0.95

6000 7000

1.1

l83l

1.3

2136 2111 2716

3,(

3050

23

20,000

1.9 2.4 3.8

25,000 30,000

1.7 5.7

7628

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1.7

7.6 8.5 9.5

40,000 15,000 50,000 55,000

10.1

60p00

ll.,4

20.000 80,000 90,ooo t00,000

t3.3 t5.2

120,000 160,000 180,000

22.8 26.6 30.4 31.2

200p00

37 .9

t,(0,000

't7.1

r8.9

1 5 | t,( 't2 | 21 6

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9153

-66 -70 -70 -70 -70

12,201 13.730

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t6/81

27.159 30,5t 0 36,612

67,t22

,(00,000

75.9 94.8

t22,010

-11

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500,000 600,000

It4

900,000

132

244,080

tp0o,ooo

189

305,100

1.200,000 1,400,000 1,600,000

228 266

l,8oo,ooo

312 379

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23.99 23.10

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319.5 282.1

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235

236

Mechanical Design of Process Systems l!

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Index

American Society of Mechanical Engineers.

mass flow in, 1, 3-4, 6, 8, 11 piping,3 angle of internal friction, 3-4, 6-7 angle of friction, effective, 6*7 critical flow factor for, 7

See

ASME. API, degrees for hydrometer, conversions, tables of, 92 defined,8T-88 ASME Section VIII Division I joint reliability factor, l13-l14 joint types for tubesheets. I l5 maximum tube joint force, ll3, 157 tube joint load criteria, 113 vessel code, 99, 101 Axial flow compressors aircraft, for, 59 airfoil blades for pitch, 58 size,58 applications of, 44, 58-59 characteristic curve for, 59 operating range of, 49 surge

piping factor, 304 pneumatic gases in, 7 pressure vessels, differences

stresses

13- 14

wall friction angle, 4-5 Blowers and fans, 59 Bulk solid properties bins, in, 1, 6 bulk density, 3, 6

Beams, boundary conditions for, continuous beams, 142 Bins

arching (rathole, l-2, 6) critical dimension for, 3, 12 critical flow factor for, 4 critical hooper dimensions, 6 dead storage, 1-2

critical dimensions of, 3 pressure of, consolidating, 4, 6-7 stresses,

hooper wall, on, 3 solids, in, 3

typical values oi 7 yield strength, solid material,

1

flow, erratic, I flushing of, 1 funnel flow in, 1, 6, 8 hoop pressure in, rnaximum, 6 hooper angle,

in,

truss design, 18-20

limit of, 59

degradation flow condition, 1 design of, reasons for inefficiency,

from,

1

segregation, 1 shear stress, 1 solid flow, pressure distribution for, 8 steady flow, consolidating pressure for, 3 structural design, conical portions, rectangular, 17 frame detail, 20 stiffener design, 14-16 hoop force, 16

Centrifu gal compressors

actual, or inlet, flow rate, 80 advantages of, 43-44 affinity laws, 50

3

237

3


anti-surge devices for, 52 diagram of, 53 applications of, 49 compressibility curves for, 81 compressibility factor, significance of, 83 compression process, diagram of, 50 compression ratio of, 50, 80-81 discharge temperature

average,80 dependence on ratio of specific heats, 83 frame data, typical, 80 gas, cyclic vibration of, 50-51 noise induced by, 50-51 gas inlet conditions, 50

impeller, 49 types of, 52, 52

inlet parameters, effect of varying. 52 intercoolers, sizing of, 50 mechanical losses of, 82 percentage of power required, 83 mixtures compressibility factors for, 79-81 specific heats for, 79 nncratinc 'arlo" 44 performance curves, typical, 51 polytropic head, 81 maximum per stage, 82-83 significance of, 83 polytropic relations for, 46-50 pressure versus capacity for constant speed compressor, 52

rpm, required, 82 selection of, 79-83 shaft power, required, expression for, 82

single stage, 49-50 specific heat ratio significance of, 83 stages, required number of, 82 standard cubic feet, use of, 52

surge,50 control of, 52 surge limits, 50, 52 temperature, discharge, 49-50 temperature ratio for, 81 volumetric flow, expression for, 80 Centrifugal pumps advantages of, 31 API hydrometer,

conversion factors, table of, 92 defined, ST-88 bearings, 34 outboard type, 34 brake horsepower, 34, 36, 70, 9l

required,96 shut-off, at, 36 by-pass for, 34, 36 casrngs,

horizontally split, 32 vertically split, 32 advantages of, 32 components of, 33 efficiency of, 70 head, total, 36 heat dissipation in, 34, 36

intercooler for, 37 Hydraulic Institute, 68, 71-72 hydraulic requirements of, 34, 36-37 impeller, axial flow pump, for, 32 mixed flow pump, for, 32 vanes of, 32 radial type, 32 volute of, 32 net positive suction head (NPSH) definition of, 34 pressure pads for, 91 Newtonian fluids, 68 non-Newtonian fluids, 68, 79 packtng, 32 performance curves for, 34 typical, 69, 75, 95 pressure drop discharge line, for, 67 -68, 9l, 95-96 friction factor for, 66-67 , 89-91, 93, 95-96 suction line for, 65-66, 90-91,93,95,97 viscosity, effects of, 68, 70-72 seals,32 double seals criteria for use, 32 types of, 35 seal flush, 34

single seals types of, 35 versus double seals, 32 selection of, 70 total dynamic head, application of, 70, 74 types of, 31, 34-35 vaporization of pumped liquid, causes of, 34 viscous liquids, pumping of, 37

correction-factor curves, 37, 38-39

criteria for, 37 equivalent water-performance of, 37 water horsepower, 34, 36 defined, 36 Compression, ideal gas compressibility factor discharge, at, 45

Heat transfer, convection of, air normal to cylindeq 126

mean, 45

suction, at, 45 isentropic (reversible adiabatic), 46-49 adiabatic efficiencY, 46 energy, isentroPic, 46 polytropic efficiencY, 46

principles of, ff 44-48 real gas. compressibility factor. 44 Compressors

acfm,59-60 advantages of, 59-60 conversion to, standard volumetric

flow, 60

actual volumetric flow. See acfm' flow conditions, sPecifYing, 59 actual, or inlet flow, 59 mass

flow,

59

flow, 59-60 flow, conversion to standard volumetric flow,

standard volumetric mass

60

principles of comPression, 44-48

scfm, 59-60

specifing flow conditions, 59 acfm, exPression for, 60 actual, or inlet flow, 59 mass flow, 59 specific volume, exPression for, 60 standard volumetric f1ow, 59-60 standard volumetric

flow

compressibilitY factor, 59 conversion to actual or mass flow, 60 disadvantages

of, 60

specific volume, exPression for, 59 'ttandard" condition, defined, 59-60 comparisons of various forms, 60 volume flow, equation for, 59 types of, 43 volume flow, exPression for, 59

External loading on shell structures applications of , l7Q-17 5 "critical value," 170 shell thickness, 170

Hydraulic Institute, 37 Hydraulics API hydrometer conversion factors, table of, 92 defined,8T-88 Internal pressure, stress concentration factor, 169 lsentropic comPression brake horsepower, 48 discharge temperatue, 48 head, adiabatic, 46 heat, mechanical equivalent of, 45 horsepower, ratio of isentroPic, 45 horsepower input for single stage, 45 ideal eas, 45 adia--batic efficiencY, 45 horsepower, isentropic, 45 mechanical efficiencY, 45 overall adiabatic efficiencY, 45 multistage,46 perfect gas, formulations for, 44 real gas, formulations for, 45 isentropic exPonent for, 45-46 relations, basic versus polytropic compression, 47 reversible,48 Jenike and Johanson method, 1-8

Lifting lug design, 170-175 choker angle for, 175 standard designs for, 171 L'Hospital's rule, 165 Ingarithmic mean temperature difference. See LMTD. LMTD, application of, 148-149, 154, 160, 162' t65 correction factot F, 117 -l2l multipass exchangers, variance in, 117 variance in shell and tube heat exchangers, 117 zero LMTD exchanger, 165

Multi-stage reciprocating compressors, 58

Flow of solids, problems of, 1-3

Non-Newtonian fluids, 162 Nozzle reinforcing pads disadvantage of pads, 170

Gas

pad width, maximum, 170 Nusselt number, 125-126, 156

Fans and blowers, 59

compressibility tactor, 44 general gas law, 44 specific heat ratio for, 44 universal gas constant, 44, 59 Gear pumps, 37, 40

Petroleum fractions

API hydrometer for, 87-88 Plate-fin heat exchangers advantages

of,

147

24O


applications of, 99 disadvantages

of,

147

illustrated, 149 Kays and London coefficients, 148 thermal shock and fatigue, 148

of, 147- 148 vacuum brazing of, 148 Polytropic compression uses

efficiency

overall polytropic, 48 polytropic vs. isentropic, 46-47 gas horsepower, 47

head, adiabatic, 47 horsepower, compressor (polytropic head), 48 perfect gas, for, 47 polytropic exponent, 46 polytropic head (compressor horsepower), 48 real gas, for, 47 relations, basic versus isothermal compression, 47 Positive-displacement pumps

applications of, 31 brake horsepower, 77

definition of, 31 efficiency of, 77 pump selection, use in, 77 gear pumps, 37 , 40, 78 heat dissipation in, 43 intercooler, 43 temperature switch, 43 net positive suction head. See Pumps. performance curves for rotary gear pumps, 79 pressure drop suction line, 74 velocity heads, 74 pressure protection for, 42-43 priming of, 79 reciprocating pumps diaphragm pumps, 3l piston pumps, 31 nlrrnocr nrrmnc 1l rotary pumps cam pumps, 31 gear pumps, 31 lobe pumps, 31 screw pumps,31 types of, 37 vane pumps, 31

screw pumps, 40-41 vane pumps, 37 Prandtl number, 125,152, 156, 164 Pulsation response spectra compression bottles, 64, 65

typical,65 methods of predicting, 64

orifice plates, application of, 65 piping system excited by, 65 pulsation bottles. See Compressor bottles. pulsation dampener. See Compressor bottles. reciprocating equipment, induced by, 62, &-65 Southwest Research Institute, 64 Structural Dynamics Research Corporation,

(scRc),

64

surge drums. See Compressor bottles. Pumps API degrees, defined, 87-88

calculation sheet for, 36, 70, 77

flow capacities of, 34 head, friction, 40 static discharge, 40 static suction, 40 total discharge, 40 total dynamic, 34, 40 total static, 40 total suction, 40 Hydraulic Institute, 68, 7 | -72 inline, nozzle loadings for, 61

lift static suction, 40, 42 for water maximum recommended, 43, 77 theoretical, 43, 77 total suction, 40, 42 motors, NEMA frame dimensions, 73 NPSH

definition of, 34 pressure pads for, 91 priming of, 79 pump Hydraulic Design, calculation sheet, 36, 70,77, 93,95-96 pump selection guide, 32

of, 3l of, 31

types uses

velocity heads, effect on pumps, 40 Reciprocating compressors adiabatic compression, work required for, 58 adiabatic exponent, 53 adiabatic expressions for, 44-46, 53 adiabatic process, 57

applications of, 43, 84-86 clearance capacity, effect of, 55 clearance pockets, 43 stop valve, 53

volumetric efficiency, effects on, 56 compressibility factors discharge, 58

inlet, 58

fr lnder compressor horsepower, factors affecting, 53 compression ratio, 58, 84 compressor bottles. See Pulsation response spectra. cylinders, size of, 86 cylinder displacement, 86 diatomic gases, 57 discharge temperature, 85

efficiency, volumetric, 86 Neerken equation for, 86 gas temperature, exPression for, 58 horsepower, theoretical, 58 parameters affecting, 58 horsepower per million curves, 85 correction factors for, 85 intercoolers for, 84 multiple staging of, 58 advantages of, 58 compression ratio for, 84 cylinder size, 58

cylinders, number of, flywheei, effect on, 58 torque, effect on, 58 operating range, 44 piston rod diameter, 86 polytropic exponent, 57 Chlumsky recommendations for, 57 pressure-volume diagram, 56 ratios of clearance volume to volume swept by piston,57 reciprocating compressor cycle, 53, 55 58

re-expansion process, 57 schematic of, 87

volumetric efficiency curves for determining, 57 expression for, 53, 57 for a perfect gas, 57 parameters that affect, 53, 57 theoretical,53 Regenerated gas exchanger design of, 148- 153 vibration check, 153- 154 Reinforcing pads (external loadings) pad width, maximum, 170 disadvantage of pads, 170 Reynolds number, 9, 66-67, 7 4, 89 -91, 93, 95 -96,

t25-127, 140, 141, l5l-152, 156-157, 1U non-Newtonian fluid, Metzner-Reed, 162-163 versus drag coefficients for long circular cylinders, r42

Rotating equipment

APr 611,61 APr 612, 61 API 617, 61

API 618, 61 API criteria, 61-62 NEMA. See Nozzle Loadings. nozzle loadings on, 61-62 allowable, defined, 61-62 NEMA,61_62 applications for, 61 options to, basic, 62 steam turbines, ideal expansion joint, 64 turbo-expanders, reasonable values for, 63 typical for in-line pumPs, 61 piping systems for, 60-65 pulsation bottles. Se? Pulsation response spectra. steam turbines, piping

to, 62

surge drums. 'gee Pulsation response spectra Rotary pumps, types of, 37

Screw pumps, 40-41 Shell-and-tube heat exchangers advantages of, 99 ASME Section VIII Division I Code, 99, 101 ASME tube joint load criteria, 1 13- 1 15 joint reliability factor. I l3-l14 maximum tube joint force, 113 tube joint load, 113

baffle cuts, 111 baffle details, 111 baffle lanes, channel and head, 128 baffle plates, 99 baffle windows, 139 various schemes, 139 baffles annular orifices, 110 doughnut and disc tYPes, 110 flow direction, used for, 107 horizontally cut, 107, 109 longitudinal, 109 structural supports, as, 107 verticaliy cut, 107 vibration dampers, as, 107 baffle windows, Ill basic components of, 107 -112 caloric temperature, 117 , 122-123, 158 Kern relationships for, I22 caloric versus arithmetic rnean, 122 chlorine superheater design, 154- 160 chiller, 101 condenser, 101

deflexion or ligament efficiency, 158 design classifications of, 101 final condenser, 101 fixed tubesheet, 102-1O4 fixed tubesheet design, 100 floating heat exchangers

211

242


internal floating head design, 103-104 advantages of, 104 outside-packed floating head design, 103-104

operating range, 104 packed latern ring design, 103-1M operating range, 1M pull-through bundle design, 103- 104

limitations of, 104 types

of,

regenerated gas exchanger design, 148-153 sensible heat, 116- 117 shell-side, defined, 99 shell-side equivalent, tube diameter, 129, 152, 156, 164 shell-side pressure drop, \39, 152-153,157,

164-165

103- 104

forced circulation reboiler,

101

fouling resistances, recommended minimum, 125 friction factors for, shell-side surfaces, 140 heat transfer bulk temperature of fluid, 125 continuity equation, 128 convection, basic expressions for, 115 factor jH, 129,138, 152, 157 film coefficients, shell-side, 128 Kern correlation, 128 fouling factors, 124 bare tubes versus finned tubes, 124 definition of, 124 versus thermal conductance, 124 fouling resistance, 124 Fourier's law of heat conduction, 116 Grimson equation, for film coefficient, 126 inside film coefficient, 122, 151 laminar, 125 turbuient, 125 laminar boundary layer. 125 modes

reboiler, 99, l0l kettle type, 99

of,

115

McAdams correlation, 125

film coefficient, lZZ, 126, 1,29 overall heat transfer coefficient, 152 caloric, 117, 122, 152, 157, 158 parameter jH, 129, 138 effective diameters for, 129 versus Reynolds number, 138 shell-side film coefficient, 151-152, 156, 163-t64 tube-side film coefficient, 151, i54-156 tube wall resistance, 124 turbulent boundary layer, 125 impingement baffles, i28 latent heat, I 16- 117 ligament or deflexion efficiency, 158 outside

LMTD correction factor R 117- 121 multipass exchangers, variance in, 117 variance of, 117 overall heat transfer coefficient, 122

caloric, 117, 122, 152 partial condenser, 101 process evaluation of, 115-140

expression for, 139, 152 shell-side mass density, 151 shell-side mass flow rate, G,, 139, 152-154, 156, I O-l

Sieder-Thte correlation,

laminar flow, for, 125, 162 turbulent flow, for, 125 steam generator, 101 TEMA class B exchanger, 99, lO4 class C exchanger, 99, 104 class R exchanger, 99, 104 comparisons of types, 105 mode constants for tubes, 112 natural frequencies of straight tubes, I 12- I l3 natural frequencies of U-tubes, 113 nomenclature

of,

102

TEMA specification sheet, 150, i55 tubes, stress, allowable compressive, l12 tubesheets, compressive stress induced OD,

lll

thermosyphon reboiler,

101

tie rods TEMA recommendations for, 110 uses

of,

110

tube arrangements, pros and cons tube bundle, 99, 126, 128

flow area of,

of,

152

Keys and London constants foq 129 tube bundle cross-flow arca, 128 staggered

inline, for,

128

triangular layouts, for, 128 tube count tables, 130- 137 tube geometry angtlar pitch, 126-127 diamond-square pitch, 126 - 127 inJine square pitch, 126-127

inJine triangular pitch, 126-127 tubes

bare, 107 bend radii, minimum, 109 boundary layer, 125 laminar, 125 turbulent, 125 buckling of

129

{ 2rl:t

Euler columl formula, 114 exchanger tubes, 113 Johnson short column equation, 1i4 finned, 107 foreign deposits, 124 inside film coefficient, 122 outside film coefficient, 122 pitch, nominal, 114 stress factors for, 159- 160 tabulated properties of, 108 tubesheets, 99 double tubesheets, 110 uses

of,

110

maximum radial stresses in, 159 single tubesheets, 110 tubesheet-tube connections, typical, I 1 1 tubesheet layouts staggered in{ine, for, 128

triangular layouts, for, 128 typical, 128 tube-side defined, 99 tube-side mass flow rate, 151, 162 tube vibrations. See Tube vibrations. tube wall temperature, 117,122, 124 U-tube exchangers kettle type reboiler, 100 tubesheet

vaporizer,

fot

103

101

vapor-liquid equilibrium calculations, I 17 vertical gas-gas exchanger, 151 Silos. See Bins. Specific diameter, 48 versus specific speed, 49 Specific speed, 48 versus specific diameter, 49 Stack design anchor bolt torque, 26-27 base support detail for, 27

carbon precipitation in,

8

buckling stress allowable, 22 deflection, dynamic, 26 deflection, static, 26 excitation, flexural, 9 flexural frequency, 9 lining of, 8 effect of, 8 gunite,8 modulus of elasticity of, 8 Michell and Love equation, 9, 28

ovaling,8-9 flexural modes of, 9 in-plane, 9 out-of-plane,9

modes of, 9

ovaling frequency. See Flexural frequencl ovaling rings, 9, 26 natural frequency of, 9, 26 reasons for, 9 section modulus of, required, 9 pressure vessels, vertical differences bef$'een. 8 seismic response spectra, 8

vibration, cantilev er, 25 -26 vortex shedding frequency, 9, 26 vortex strakes, 9-11, 27 -28 clearances for, 11 critical wind velocities for, 10 fabrication detail of, 11 fabrication, method of, 11 helix angle of, 10 length of, 10 Morgan equation, 10, 28 radius of curvature of, l0 strake height, 10 range for, 10 wind design anchor bolt design for, 23 bearing pressure for, 23 base plate, Brownell and Young method, 24 chair design, Brownell and Young method, 24-25 compression rings, gusset plate thickness, required,25 effective diameters for, 20 weld, skirt-to-base ring, 25 wind load, 2l-22 wind moment, 21-22 wind pressure, 21 wind response spectra, 8 Steam turbines piping of, 62 Strouhal number, 9 Suction lift, IOr WAIe\

+5, I I

TEMA class B exchanger, 99, 104 class C exchanger, 99, 104 class R exchanger, 99, 104 heat exchanger specification sheet, 150-161 mode constants for tubes, 112 natural frequencies of, straight tubes, 112- 113

U-tubes, 113 nomenclature for shell-and+ube heat exchangers. 102 standard, TEMA, 99, 104

TEMA types, composition of, 105 tie rods,

244


recommendations uses

of,

for,

1

10

110

tube joint load formulations, 113 tubes, minimum bend radii, 109 stress, allowable compressive, I 12 tubesheets,

compressive stress induced on, 111 Tube vibration

baffle damage, modified damage number, 143, 153 baffle plate, illustrated, 143 displacements, inducing excessive, 143-144, t53-154 drag coefficients versus Reynolds number, 142 flow-induced vibration, 144 fluid vortices, force exerted on tubes, l4i jetting, or jet switching, 144 compared to turbulence, 146 cornpared to vortex shedding, 146 shear force on tube, l4l, 143, 153 shell-side fluid, velocity of, 141 maximum recommended, 148 Thorngren, John T., maximum velocity method, 139 tubes

boundary conditions of continuous beams, 142 circle of contact, diameter of, 143

colliding of, 139 deflection oI, 141, 154 effective tube wall, 141 fatiguing of, 139 fluid force causing baffle impingement, 143 force coefficient, 146 fundamental natural frequency of, 146 natural frequency of, (Blevins formulation), 146, 154 shear of against baffles, 143

turbulence

deflection, root-mean-square, 145

joint efficiency,

145

pressure distribution for, 144- 145 response spectra, 145 Wambsganss and Chen relation, 146

Venturi effect, 144 von Karman equation, 141 vortex shedding, 139, 144 compared to turbulence, 146 compared to whirling, 146 resonant frequency of, 141

vortex street, limits of, 141 vortices, breaking-up of, 141 whirling, 144 compared to turbulence, 146 compared to vortex shedding, 146 critical velocity, cxiteria of, 147 whirling parameter, for tube arrays, 148 Tubular Exchanger Manufacturing Association. TEMA. Vane pumps, 37 Velocity heads (K-values), 66-68,

See

7 4, 88-89, 90-9 Vibration ovaling. Se€ Stack design. Rayleigh method for, 8. Also see Volume l. Viscosity absolute viscosity, 68 conversion to kinematic, 68 centrifugal pumps, effect on, 68, 70-72 converting centipose to SSU units, 74 kinematic,68 Vortex shedding, 8-9, 139, l4l,144, 146

Welding Research Council. See WRC. WRC 107 Standard, 169 WRC 297 Standard, 169

1

Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe

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