PIPELINE DESl6N fOR WATER EN6IMEERS THIRD REVISED AND UPDATED EDITION
DEVELOPMENTSIN WATER SCIENCE, 40
OTHER TITLES IN THIS SERIES VOLUMES 7-3 ARE OUT OIF PRINT 4 J.J. FRIED GROUNDWATER POLLUTION 5 N. RAJARATNAM TURBULENT JETS 6 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS 7 v. HANK AND J. SVEC GROUNDWATER HYDRAULICS 8 J. BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL AFRICA 9 T.A. McMAHON AND R.G. MElN RESERVOIR CAPACITY AND YIELD 10 G. KOVACS SEEPAGE HYDRAULICS 1i w.n. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICSOF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978. LAUSANNE, SWITZERLAND 12 W. BACK AND D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME 13 M.A. MARlfJO AND J.N. LUTHIN SEEPAGE AND GROUNDWATER 14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE 15 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 in the series) 16 W. BACK AND R. LETOLLE (EDITORS) SYMPOSlClM ON GEOCHEMISTRY OF GROUNDWATER 17 A.H. EL-SHAARAWI (EDITOR) IN COLLABORATION WITH S.R. ESTERBY TIME SERIES METHODS IN HYDROSCIENCES 18 J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL REGIONS 19 D. STEPHENSON PIPEFLOW ANALYSIS 20 I.ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS 21 M.M.A. SHAHIN HYDROLOGY OF THE NILE BASIN 22 H.C.RIGGS STREAMFLOW CHARACTERISTICS 23 M. NEGULESCU MUNICIPAL WASTEWATER TREATMENT 24 L.G.EVERETT GROUNDWATER MONITORING HANDBOOK FOR COAL AND OIL SHALE DEVELOPMENT 25 W. KINZELBACH GROUNDWATER MODELLING: AN INTRODUCTION WITH SAMPLE PROGRAMS IN BASIC 26 D. STEPHENSONAND M.E. MEADOWS KINEMATIC HYDROLOGY AND MODELLING 27 A.M. EL-SHAARAWI AND R.E. KWIATKOWSKI (EDITORS) STATISTICAL ASPECTS OF WATER CIUALITY MONITORING - PROCEEDINGS OF THE WORKSHOP HELD AT THE CANADIAN CENTRE FOR INLAND WATERS, OCTOBER 1985 28 M.JERMAR WATER RESOURCES AND WATER MANAGEMENT 29 G.W. ANNANDALE RESERVOIR SEDIMENTATION 30 D.CLARKE MICROCOMPUTER PROGRAMS IN GROUNDWATER 31 R.H. FRENCH HYDRAULIC PROCESSES IN ALLUVIAL FANS 32 L. VOTRUBA, 2. KOS. K. NACHAZEL, A. PATERA ANDV. ZEMAN ANALYSIS OF WATER RESOURC_ESYSTEMS 33 L. VOTRUBA AND V. BROZA WATER MANAGEMENT IN RESERVOIRS 34 D. STEPHENSON WATER AND WASTEWATER SYSTEMS ANALYSIS 35 M.A. CELlA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 1 MODELING SURFACE AND SUB-SURFACE FLOWS. PROCEEDINGS OF THE VII INTERNATIONAL CONFERENCE, MIT. USA, JUNE 1988 36 M.A. CELIA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 2 NUMERICAL METHODS FOR TRANSPORT AND HYDROLOGICAL PROCESSES. PROCEEDINGS OF THE V11 INTERNATIONAL CONFERENCE, MIT, USA, JUNE 1988 37 D.CLARKE GROUNDWATER DISCHARGE TESTS: SIMULATION AND ANALYSIS
THIRD REVISED AND UPDATED EDITION
DAVID STEPHENSON Department of Civil Engineering University of the Witwatersrand Johannesburg, South Africa
ELSEVlER Amsterdam - Oxford - N e w York - Tokyo 1989
ELSEYIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 2 1 1, 1000 A€ Amsterdam, The Netherlands Distributors for the United States and Canada:
ELSEVIER SCIENCE PUBLISHINGCOMPANY INC. 655, Avenue of the Americas New York, NY 10017, U.S.A.
ISBN 0-444-87373-2
0 Elsevier Science Publishers B.V., 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./ Physical Sciences & EngineeringDivision, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred t o the publisher. No responsibility is assumed by the Publisher for any injury and/or damage t o persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Printed in The Netherlands
V
PREFACE TO FIRST EDITION
Pipelines lengths
are
and
being
working
are
essential
for
years
has
recently
to
constructed
pressures.
achieve economic
resorted
to
been
in
and
in
an
and
safe
semi-empirical
done
ever-increasing
Accurate
rational
designs.
design
bases
Engineers
formulae.
to r a t i o n a l i z e
effort
diameters,
design
have
Much
the
work
design
of
pipelines. This as
book
well
as
retaining
presenting
oook
or
hydraulic
subject
is
to
but
field.
a l so of
be
bring
useful
infancy
and
of
the
graphs
in
planning
of
features
manufacture, practice
design
of
which
large
at
the water
in
the It
are
should
stressed
of
may
suitable the
as
and
were of
In
are
and
the
is
techniques
to
the
Pipelines covered
as
and
many
half, book
t h i s book other
be
noted
that
covered pipes,
and v a r i o u s coatings.
opposed
by
will
fluids some
of
not
desk. to
of
The the the
computers.
design
deal
in
and and
detail
i t replace design
Emphasis
industrial
pub1 ications.
on
is
the
and
domestic
Although
directed
be of use to engineers i n v o l v e d as of
patents.
methods
structural
nor should
mind
hydraulics
with
does
Many
research.
the assistance of
in will
in t h e i r
calculators
The
other
students.
are s t i l l
in
engineer's
in
the book
further
concerned
the
to
techniques
background
of
the c i v i l
introduction
advanced
for
aim
bear
l a y i n g a n d operation, from
Although
the
problems
second
discussed.
many
concrete
leads
many
book
data.
post-graduate
prepared with
this
of
be
for
design methods
instances,
an
most
and
provide
computers
engineer,
piping
described
may
pipelines.
piping
is
proposed
book half
ancillary
of
many
the sound theoretical
book
acceptance
with
techniques in
d a t a on
under-graduate
modern
the
rational
such as mathematical optimization,
solution
first
It
contains
to
new
on
the most modern design
i3ecause of
methods
codes
some
material
approaches
engineer. also
the s u b j e c t s ,
The
pub1 ished
conventional
the
the
col lates
well the
as
solids
designs
These
stiffening
and
include pipes
and
techniques
types and
gases.
of
pre-
branches
VI
The S . I .
system of
metric u n i t s i s preferred i n
imperial u n i t s a re g i ve n a n d equations examples work in
text.
summarized general chapter.
at
these The the
for as
many they
The
end
appendix data.
problems a n d
instances.
of
the reader
often elaborate on
algebraic
references a r r a n g e d
other useful
in many
Most g r a p h s
a r e represented i n uni versa1 dimensionless form.
are given
through the
i n brackets
the book although
symbols
that in
gives
used
chapter
together
the order of further
i s advised
ideas not in
the
references
Worked to
highlighted
each
chapter
are
with
specific
and
subject matter i n the and
standards
and
PREFACE TO SECOND EDITION
The
gratifying
in small ations
response
amendments to
to
the f i r s t
the second
e d i t i o n of
impression,
t h i s book
resulted
a n d some major a l t e r -
i n t h i s new edition.
The
chapters
replaced
by
on
data
transport
more
of
relevant
solids
to
and
water
sewers
Thus
chapter on the effects of a i r i n water pipes i s included, chapter
on
pumping
systems
for
water
have
engineers.
new
as well as a
The
pipelines.
been
a
latter
was
reviewed by B i l l Glass who added many of h i s own ideas. There
are
additions and
u p d a t i n g throughout.
There
is additional
information on p i p e l i n e economics and optimum diameters i n Chapter 1 . A
comparison
Chapter and
2.
The
sewer
drainage
of
currently sections
flow
are
engineer
used
on non-circular
omitted.
and
‘Stormwater
Hydrology
introduction
to
water
friction
as
These
such
are
and
Drainage’
hammer
theory
sections
together.
An
on
structural
largely
covered
enlarged
design
section
on
is
now
pipe and p a r t l y
are
of
in
preceeds
the
the
made
full
in
pipes
interest
to
author’s
the book
1981).
A
basic
design
of
water
(Elsevier,
l i n e s i n Chapter 4 .
hammer protection of pumping a n d g r a v i t y
The
formulae
of
flexible
soil-pipe
pipes
are
interaction
brought
and
limit
states of f l e x i b l e pipes preceeds the design of s t i f f e n e d pipes. Although recognised needs
some
that
of
this
refreshing
the
new
edition
is
now
fairly
basic,
it
is
i s d e s i r a b l e for both the p r a c t i c i n g engineer who
and
the
student
p i p e l i n e design f o r the f i r s t time.
who
comes
across
the
problem
of
VIII
PREFACE
TO THIRD E D I T I O N
Recent research i n c a v i t a t i o n a n d flow control h a s prompted a d d i t i o n a l sections on pipes a n d make up
this.
There
secondary this
a r e also new
stress.
edition.
Some
sections on
Additional sections
supports
references
appearing
and
in
a
to
exposed
new
layout
p r e v i o u s editions,
noteably on p i p e network systems a n a l y s i s a n d o p t i m i z a t i o n have been ommitted
as
p a r a l l e l book
they
were
considered
‘Pipeflow A n a l y s i s ’
more
appropriate
in
b y the same p u b l i s h e r .
the
alJthOr’S
IX
ACKNOWLEDGEMENTS
The b a s i s for course of
Engineers although I the
my
01 i v e r ,
and
in
t h i s book was d e r i v e d from my experience a n d i n the
duties
the Hand Water
these
Engineers.
organizations
Board a n d Stewart, S v i r i d o v
The
may
extensive
therefore
be
knowledge reflected
of
herein
I am solely to blame f o r any inaccuracies o r misconceptions.
am g r a t e f u l twins
with
Consulting
during
to my wife Lesley,
many
a
lost
who,
weekend,
i n a d d i t i o n to looking a f t e r assiduously
typed
the
first
d r a f t of t h i s book.
David Stephenson
X
CONTENTS
CHAPTER 1
ECONOMIC PLANNING
.
.
.
lntroduct ion P i p e l i n e Economics B a s i c s of E c o n o m i c s M e t h o d s of Ana I y s i s Uncertainty in Forecasts Balancing Storage
CHA?TER 2
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HYDRAULICS
The F u n d a m e n t a l E q u a t i o n s of F l u i d F l o w F l o w H e a d Loss R e l a t i o n s h i p s . . Empirical Flow Formulae 2 a t i o n a l Flow Formulae C o m p a r i s o n of F r i c t i o n F o r m u l a e M i n o r Losses . . P r e s s u r e and F l o w C o n t r o l i n P i p e s lntroduct ion T y p e s of V a l v e s I so l a t i n g V a Iv e s Control Valves C a v i t a t i o n in C o n t r o l V a l v e s . . I n t e r a c t i o n b e t w e e n C a v i t a t i o n a n d W a t e r Hammer P r e s s u r e s
. . . . . . . . . . . . . . . . . .
CHAPTER 3
1 2 9 10 11 14
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16 18 18 19 24 26 28 28 28 29 29 32 34
P I P E L I N E SYSTEM ANALYSIS AND DESIGN
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Network A n a l y s i s E q u i v a l e n t P i p e s for P i p e s in S e r i e s o r P a r a l l e l Loop Flow Correction Method The Node H e a d C o r r e c t i o n M e t h o d A l t e r n a t i v e M e t h o d s of A n a l y s i s iqetwork A n a l y s i s b y L i n e a r T h e o r y O p t i m i z a t i o n of P i p e l i n e Systems D y n a m i c P r o g r a m m i n g f o r O p t i m i z i n g Compound P i p e s T r a n s p o r t a t i o n P r o g r a m m i n g for L e a s t - c o s t A1 l o c a t i o n o f Resources L i n e a r P r o g r a m m i n g f o r D e s i g n of l e a s t - c o s t Open N e t w o r k s
. . . . . . . . .
37 37 38 40 41 43 44 45
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.
48
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52
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.
XI
CHAPTER 4
WATER HAMMER AND SURGE
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R i g i d Water Column Surge Theory M e c h a n i c s o f W a t e r Hammer E l a s t i c W a t e r Hammer T h e o r y Method o f A n a l y s i s Effect of F r i c t i o n Protection of Pumping Lines Pump I n e r t i a Pump B y p a s s R e f l u x V a l v e Surge Tanks Discharge Tanks A i r Vessels In-Line Reflux Valves Release V a l v e s Choice o f P r o t e c t i v e D e v i c e
.
. . . . . .
CHAPTER 5
AI3
. . . . . . .
. . . . . . . .
IN P I P E L I N E S
Introduction Problems of A i r Entrainment A i r I n t a k e a t Pump Sumps A i r Absorption a t Free Surfaces H y d r a u l i c Removal of A i r H y d r a u l i c Jumps Free F a l l s A i r Valves Head Losses in P i p e l i n e s W a t e r Hammer
. . . . . . . . . . . . . . . . .
CHAPTER 6
58 60 64 64 68 69 73 76 77 79 85 89 91 93
. . . . . . . . . .
97 97 99 101 102 102 104 105 108 109
EXTERNAL LOADS
. . . . . .
. . . .
. . . . .
. . . . . . .
Soil Loads Trench conditions Embankment Conditions Superimposed Loads T r a f f i c Loads Stress Caused b y Point Loads Uniformly Loaded Areas . Effect o f R i g i d Pavements
. . . . . . . . . . . . . . . . .
. . . . . . .
.
113 113 116 120 121 121 122 123
XI1 CHAPTER 7
CONCRETE PIPES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Effect of B e d d i n g Prestressed Concrete Pipes Circumferential Prestressing C i r c u m f e r e n t i a l P r e s t r e s s a f t e r Losses Circumferential Stress u n d e r F i e l d Pressure L o n g i t u d i n a l Prestressing L o n g i t u d i n a l Stresses A f t e r L o s s e s P r o p e r t i e s o f Steel and C o n c r e t e
CHAPTER 8
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160 162 165 172 173 173 174 175 176
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179 179 179 180 180 180
STEEL AND F L E X I B L E P I P E
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
I n t e r n a l Pressures Tension R i n g s to Resist I n t e r n a l Pressures D e f o r m a t i o n of C i r c u l a r P i p e s u n d e r E x t e r n a l L o a d Effect of L a t e r a l Support S t r e s s d u e to C i r c u m f e r e n t i a l B e n d i n g More General Deflection Equations S t i f f e n i n g R i n g s to R e s i s t B u c k l i n g w i t h no side support Tension R i n g s Stiffening Rings
CHAPTER 9
. . . . . . . . . . . . . . . . . . . . . . . . . .
10
. .
142 143 146 149 151 152 156 156 156
SECONDARY STRESSES
Stresses a t Branches Crotch Plates Internal Bracing Stresses a t Bends T h e P i p e a s a Beam Longitudinal Bending Pipe Stress a t Saddles . . Ring Girders Temperature Stresses
CHA?TER
127 129 131 131 133 134 136 136
P I PES.
. . . . . . . . .
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F I TT I NGS AND APPURTENANCES
. . . . . . . . . . . . . .
?ipe M a t e r i a l s Steel P i p e Cast I r o n P i p e Asbestos Cement P i p e Concrete P i p e Plastic Pipe
. . . . . .
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.. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.. . . . . . . . . . . . . . . . . . . .
.. . . . . . . . . . . . . . . . . . . . .
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L i n e Val ves Sluice Valves B u t t e r f l y Valves Globe Valves Needle a n d Control Valves Spherical Valves Reflux Valves A i r Valves A i r Vent Valves A i r Release Valves Thrust Blocks Forces Induced by Supports . L o n g i t u d i n a l Stress Temperature Stresses Forces at Bends L a t e r a l Movement Forces on Supports Unbalanced Forces Flow Measurement Venturi Meters Nozz I es Orifices Bend Meters Mechanical Meters Electromagnetic I n d u c t i o n Mass a n d Volume Measurement Te I erne t ry
CHAPTER 1 1
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182 182 183 184 184 185 186 186 186 188 190 194 195 195 196 196 197 197 198 198 199 1 99 200 200 201 201 201
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205 206 208 208 210 212 21 6 21 7 218 21a 222 223
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.
L A Y I NG AND PROTECTION
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Selecting a Route L a y i n g a n d Trenching Thrust Sores Pipe Bridges Underwater Pipelines Joints a n d Flanges Coatings Linings Cat hod i c Prot ec t ion Galvanic Corrosion Stray Current E l e c t r o l y s i s Thermal I n s u l a t i o n
. . .
.
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XIV
CHAPTER 12
PUMP I NG I NSTALLAT I ON5
I n f l u e n c e of Pumps in P i p e l i n e Design T y p e s of P u m p s P o s i t i v e Displacement Types C e n t r i f u g a l Pumps T e r m s and D e f i n i t i o n s Head Total Head Net P o s i t i v e S u c t i o n Head S p e c i f i c Speed Impeller Dynamics Pump C h a r a c t e r i s t i c C u r v e s ivto t o r s Pumpstat ions
. . . . . . . . . . .
. .
. . . . . . . . . . .
228 228 228 229 231 23 1 231 232 233 234 236 239 240
GENERAL REFE2ENCES AND STANDARDS
. . . . . .
242
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250
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252 253 254 255 256
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258 260
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BOOKS FOR FURTHER READING
.
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APPEND I X
. . . . . . . .
Symbols for p i p e f i t t i n g s Properties of p i p e shapes P r o p e r t i e s of w a t e r P r o p e r t i e s of p i p e m a t e r i a l s Conv ers i o n f a c t o r s
AUTHdR SUBJECT
INDEX INDEX
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. . . . .
1
CHAPTER 1
ECONOMIC PLANNING
I NTRODUCT ION
Pipes
have
been
used
for
many c e n t u r i e s
for
transporting fluids.
The Chinese f i r s t u s e d bamboo p i p e s t h o u s a n d s o f y e a r s ago, p i p e s were
unearthed a t
were
in
England.
that
pressure
used
however, used
extensively
were f i r s t
grade
diameters square
spiral
small
and
3
to
welded
became
available
is
still
and
working
The
Welding
and
for
the
Cast
design
of
pipelines
with
10 Newtons have
Reliable
per been
welded
or
a l s o made
asbestos cement,
this
was pipes
facilitating
techniques
pipelines
iron,
i n c r e a s i n g use o f
P i p e l i n e s a r e now
conditions.
pipes
iron
Steel
circumferentially
p r e - s t r e s s e d concrete, varying
cast
used.
pressure over
manufactured.
suit
of
t h e e n d of t h e l a s t c e n t u r y ,
longitudinally
to
advent
manufactured. and
p i p e s to b e m a n u f a c t u r e d .
claywares,
the
large r o l l i n g m i l l s has enabled
be
enabling
were
Century
c e n t u r i e s wood-stave
with
large bore pipelines.
metres
in r e i n f o r c e d concrete,
and
19th
later
only
pipelines
steels a n d
over
millimetre
perfected
was
introduced towards
c o n s t r u c t i o n of high
It
the
in
In
Pompeii.
and lead
flow
plastics formulae
century,
thereby
a l s o p r o m o t i n g t h e use of p i p e s . Prior fluids
to
this
century
transported
common
means
for
Liquid chemicals
being
pumped
now o v e r world.
by
water
a n d sewage
pipeline.
transporting
and
solids
gases
in slurry
The g l o b a l
kilometres
of
e x p e n d i t u r e on
pipelines
and
oils
form or
t h r o u g h p i p e l i n e s on ever
two m i l l i o n
were p r a c t i c a l l y
Nowadays
over
the o n l y
are long
the
distances.
in containers
i n c r e a s i n g scales.
most
are
also
There a r e
pipelines i n service throughout
the
p i p e l i n e s i n 1974 was p r o b a b l y o v e r
5 5 000 m i l l i o n . There
are
many
advantages
of
pipeline
o t h e r methods s u c h a s r o a d ,
rail,
waterway
(1)
the
most
Pipelines
are
often
( c o n s i d e r i n g e i t h e r c a p i t a l costs,
(2)
Pipelining
costs
are
not
very
transport
compared
with
and air:-
economic
form
of
transport
r u n n i n g costs o r o v e r a l l c o s t s ) . susceptible
to
fluctuations
in
2 prices,
since
the major cost
i s the c a p i t a l o u t l a y and subsequent
o p e r a t i n g costs are r e l a t i v e l y small. Operations
are
not
to
susceptible
attendance i s r e q u i r e d .
labour
disputes
as
little
Many modern systems operate automatical-
lY. Being
hidden
beneath
the
ground
a
pipeline
will
not
mar
the
n a t u r a l environment.
A b u r i e d p i p e l i n e i s reasonably secure against sabotage. A
pipeline
is
independent of
external
influences
such
as
traffic
congestion and the weather. There
is
normally
no
problem of
r e t u r n i n g empty
containers
to
the source.
It
is
relatively
easy
to
increase the c a p a c i t y of
a pipeline by
i n s t a l l i n g a booster pump.
A b u r i e d p i p e l i n e w i l l not d i s t u r b surface t r a f f i c a n d services. ( 1 0 ) Wayleaves
for
pipelines
are
usually
easier
to
obtain
than
for
than
for
roads and r a i l w a y s .
(11)
The
accident
rate
per
- km
ton
is
considerably
lower
other forms of t r a n s p o r t .
(12) A
pipeline
can
cross
rugged
terrain
difficult
for
vehicles
to
cross. There are of course disadvantages associated w i t h p i p e l i n e systems:The
initial
capital
uncertainty
in
expenditure
the
demand
i s often
some
large,
degree
of
involved
in
so i f there i s any
speculation
may
be
necessary. There
is
often
a
high
cost
( e s p e c i a l l y long fuel
lines).
Pipelines
used
(although
cannot
be
there
are
for
more
multi-product
than
filling
a
one m a t e r i a l
pipelines
operating
pipeline
at on
a
time batch
bases).
There solids,
are
operating
problems
associated
with
the
pumping
of
such as blockages on stoppage.
I t i s often d i f f i c u l t
to locate leaks o r blockages.
P I PEL I NE ECONOM I CS
The main cost
of
a p i p e l i n e system i s u s u a l l y that of the p i p e l i n e
3 itself.
The
gravity
pipeline
systems b u t
cost
is
fact
in
practically
as the adverse head
cost
for
increases so the power
the
only
and
pumping s t a t i o n costs increase.
1.1
Table
indicates
some
relative
costs
for
typical
installed
p i p e l i nes. With the
the
time
year,
economic
of
writing
and
particular increase
instability pipeline
relative the
faster
costs
cost
of
than
those
and rates of
costs for
may
different
petro-chemical of
inflation prevailing at
increase
by
materials
materials
concrete
20% o r more per
for
will
such
instance,
vary.
as
PVC
In may
so these f i g u r e s
should be inspected w i t h caution. TABLE 1 . 1
Relative P i p e l i n e Costs Bore mm
Pipe M a t e r i a l
150
6 7
PVC Asbestos cement Reinforced concrete Prestressed concrete M i l d steel High tensile steel Cast i r o n <:,,-s,
1 500
450
-
23 23 23 33 28 25
10 11 25
80
-
90
150
- 180 - 120 -
100
90
75
indicates not r e a d i l y a v a i l a b l e .
1 u n i t = d;/metre
i n 1974 under average conditions
The components m a k i n g up the cost of a p i p e l i n e v a r y widely from situation
to
situation
but
for
water
pipelines
in
Supply of p i p e
- 55%
(may
Excavation
- 20%
open
country
and
t y p i c a l conditions are as follows:reduce
as
new
m a t e r i a l s a r e developed)
may
(depends reduce
excavation
as
on
terrain,
mechanical
techniques
im-
prove)
- 5% (may increase w i t h
L a y i n g and j o i n t i n g
bour costs)
- 5%
F i t t i n g s a n d specials Coating and w r a p p i n g Structures ( v a l v e chambers,
anchors)
- 2% - 2%
la-
4
L
10
a L 0
r
m ._ U
5 Water
- 1%
hammer protection
Land acquisition, protection,
access roads, cathodic
security
structures,
.
- 1%
fences
Engineering and survey costs
- 5%
Admi n i s t r a t i ve costs
- 1%
Interest d u r i n g construction
- 3%
Many factors have to be considered in s i z i n g a p i p e l i n e : pumping
mains the flow
0.7
to
m/s
about
2
1 m/s
for
velocity
depending
m/s,
low pressure
at on
the optimum diameter flow
and
working
of 100 C/s
heads and a flow
for
of water,
and may be even h i g h e r f o r h i g h e r pressures.
factor
and
cost
power
v e l o c i t y o r conversely
000 C / S
1
of
and
structures
for
influence any
from It
is
increasing
about 400 m
pressure heads at
also
the diameter
varies
pressure.
to 2 m/s
a flow
For water
The c a p a c i t y
the
optimum
p a r t i c u l a r flow.
flow
1.1
Fig.
i l l u s t r a t e s the optimum diameter of water mains f o r t y p i c a l conditions. I n planning scale costs.
of
a
p i p e l i n e system i t should be borne i n mind that
operation
By
of
doubling
a
pipeline
the
head remaining constant, hand
the
cost
delivered which to
install
to
1/3
large
considerable
the
doubles
of
multi-product
a
of
pipe,
on
effect
other
factors
the c a p a c i t y increases six-fold.
approximately
decreases
justifies
has
diameter
the
that
original.
lines.
diameter
so
Whether
main
at
It it
the
the is
is
unit
such
as
On the other
cost
this
per
scale
i n fact
outset
the
the
unit effect
economical
depends
on
the
f o l l o w i n g factors as well as scale:Rate of low
growth i n demand ( i t may be uneconomical
capacity
factors
during
initial
years).
to operate a t
(Capacity
factor
is
the r a t i o of a c t u a l average discharge to design c a p a c i t y ) . Operating to
factor
maximum
depend
on
(the ratio
throughput the
rate
i n s t a l l i n g storage a t Reduced
power
costs
of
during
of
average the
draw-off
throughput
same and
at
period), can
be
any
time
which
will
improved
by
the consumer's end. due
to
low
friction
losses
p i p e l i n e i s -not o p e r a t i n g a t f u l l c a p a c i t y . C e r t a i n t y of f u t u r e demands. V a r y i n g costs w i t h time ( b o t h c a p i t a l
and o p e r a t i n g ) .
while
the
(6)
Rates of
(7)
Physical d i ffi cu l ti e s
interest and c a p i t a l in
availability.
the construction of
a
second
pipeline i f
required. The
optimum
factors,
not
rate
cost
of
design
p e r i o d of a p i p e l i n e depends
least b e i n g the r a t e of inflation,
c e r t a i n t y of f u t u r e demands In
waterworks
pipelines
for
throughput size
10
of
demands
it
up
has
10
to
and h i g h growth rates, so
the p i p e l i n e ,
years.
Longer
to
the r a t e of
that
planning
been
30
to
are
economic
to
scale and
economic
years
hence.
to
For
c a p a b i l i t i e s may
supplementation may stages
of
loans and the
growth,
found
technical
number
1973).
(Osborne a n d James,
practice
a
interest on c a p i t a l
addition
in
on
normally
size large
l i m i t the
be r e q u i r e d w i t h i n justified
for
small
bores and low pressures. It
may
Where
not
always
pressures
are
be
high
it
is
lay
economic
a
to
uniform
bore
pipeline.
reduce the diameter
and
consequent1 y the wal I thickness. In there
planning
a
may
a
be
Alternative economic.
trunk
main
number
layouts
with
of
should
progressive
possible
be
decrease
combinations
compared
before
i n diameter
of
deciding
diameters. on
the
most
Systems a n a l y s i s techniques such as l i n e a r programming and
dynamic programming are i d e a l l y suited f o r such studies. Booster pumping high
the
stations
along
pumps a t input
may
the
entire
the design
installed
end,
though
line.
stage
along
lines
instead
of
additional
By
providing
for
intermediate
instead of pumping to a h i g h head
the pressure heads
thicknesses may b e minimized. even
be
high pressure head a t the i n p u t end and m a i n t a i n i n g a
a
pressure
booster at
pump
to
and consequently
the p i p e w a l l
There may be a s a v i n g i n o v e r a l l cost,
pumping
stations
are
The
required.
booster
stations may not be r e q u i r e d f o r some time. The c a p a c i t y booster this
is
increase
pumps not
of
the p i p e l i n e may often be
a
at
later
always
stage
economic.
approximately
with
although The
the
power losses increase considerably The diameter be
selected
pipeline
cost
by
of an
a
square
increases
with
of
should losses the
be
r e a l i s e d that
along flow,
a
pipeline
consequently
f o r h i g h e r flows.
pumping main economic
it
friction
increased b y i n s t a l l i n g
to convey a known discharge can
comparison increasing
of
alternative
diameter,
whereas
sizes.
The
power cost
7
TOTAL COST
5
DIAMETER
1.2
Fig.
O p t i m i z a t i o n of d i a m e t e r of a p u m p i n g p i p e l i n e .
C
COST I N CENTS
P E R m3
Cl c2
C
4 =
01
Fig.
7 -3
Optirriization of
02
Q3
throughput
0,
+
0;
Discharge
0
for certain diaweters
8 overcoming
in
power Thus
costs by
costs,
friction
increase
adding
one
least-cost chapter.
steeply
together
obtains system
There
reduces
a
can
will
as
the p i p e l i n e
pipeline and
curve be
On
correspondingly.
such
selected.
Figure
An
b e a h i g h e r cost
v a l u e of
1.2,
example
other
hand
in d i a m e t e r .
i s reduced
the present
as
the
operating
from
is given
which later
the
in the
the g r e a t e r the design d i s c h a r g e
rate. If
at
some
capacity
of
diagram
such
a
stage
later
pumping as
different
possible
kilolitre
or
it
is
system,
Figure
it
in
1.2
is plotted
to
increase
i s convenient the
throughputs,
similar,
desired
form
the cost,
to
of
the
throughput
replot d a t a from a
Figure
1.3.
Thus
for
now e x p r e s s e d i n c e n t s p e r
a s the ordinate w i t h a l t e r n a t i v e
(real)
pipe diameter a parameter. It any
can
be
demonstrated
pipeline
annual
is
basis)
a
minimum
is
twice
the
that
the
when
cost
the
annual
per
unit
of
p i p e l i n e cost
cost
the
of
throughput
for
(expressed on
power
an
in o v e r c o m i n g
friction. in cents p e r c u b i c metre of water
T h u s t h e cost + C2(d)
C,(P) c =
is
61 wHQ + C 2 ( d )
C, -
(1.1)
Q
= c,w
+
2gdA
Hs)
+
CZ(d)/Q
- C2(d)/Q2
2C1 wHf/Q minimum C i.e. P of
C Z ( d ) = 2 C,(P) i s power
water,
H
friction,
Q
diameter
d,
(1.2)
requirement,
is is
the
total
pumping
C,(P)
is
proportional
to wHQ.
head,
subscript
rate,
C2(d)
t h e cost
of
is
power
s
w
refers
the
cost
i s the u n i t weight to
of
static a
and f
to
pipeline
of
( a l l costs converted
to a u n i t
time b a s e ) . (In a given
similar
diameter
maximum
if
a v a i table).
the
manner penstock friction
it
c a n b e shown supplying
head
loss
a is
that
the
power o u t p u t of a
hydroelectric one
third
of
station the
total
is
a
head
9 R e t u r n i n g to F i g u r e 1.3,
(1)
At
(2)
At
any
particular
the f o l l o w i n g w i l l
throughput
Q,
there
t h i s d i a m e t e r t h e c o s t p e r ton of
at
if
not
throughput
was
t h r o u g h p u t Q2.
some the
same
as
is a
c e r t a i n diameter
b e a m i n i m u m ( i n t h i s case D
w h i c h o v e r a l l costs w i l l
further
be observed:
2
1.
throughput could be reduced
increased.
Costs
would
be a minimum
Thus a p i p e l i n e ' s optimum throughput
the
throughput
at
for
which
it
is
the
is
optimum
diameter.
If Q
(3)
Q4
were
1
increased
+
Q1
=
pipeline
Q3
(with
so t h a t
total
throughput
a
not
to
install
D3 )
but
to
increase
optimum
the p i p e w i t h
through
a m o u n t Q3
an
by
i t m a y b e economic diameter
D2,
diameter
Q4C4
i.e.
second
the
flow
i s l e s s t h a n QIC1
+ Q3C3. (4)
a
At
later
pipeline
stage
the
when
justified
is
it
throughput
through
the
to
construct
overloaded
second
a
line
could
be
reduced. The
power
increasing most
cost
pipe
per
unit
diameter
economic
to
of the
so
increase
increases w i t h size (White,
additional
throughput
corresponding
throughput
decreases
likelihood
through
an
of
it
with being
existing
line
1969).
B A S I C S OF ECONOMICS
Economics designs. some
is
used a s a b a s t s f o r c o m p a r i n g a l t e r n a t i v e schemes o r
Different
rational
comparison interest
schemes m a y
form of
is
the
rate
discount
on
loans
r e q u i r e a discount reflect
a
b e more
time
The cash compared basis.
For
( i t s present
rate
which
redemption from
preference,
may
be
funds.
the
in
National
form
of
projects
the may
the p r e v a i l i n g interest r a t e ,
whereas
private
in the a c t u a l c a s h flows,
organizations
a n d consequently
to
will
use the
interest rate. i.e.
those
Thus a l l
instance
of
flows,
with
or
cash flows necessitating
The c r u x o f a l l methods o f economic
r a t e different
rate
interested
real borrowing
have different
comparison.
one
of
cash
flows
pound
value)
payments another
this
may
received year
if
and
by
returns,
bringing
be discounted next it
year
of
them
is
could earn
one scheme may b e to
a
common
to t h e i r p r e s e n t the
same
5% i n t e r e s t
as
if
time
value.
fl/l.05 invested
10 this a
year.
It
definite
annual
to a71
r i s the
t o meet
paying
into a
from a
expenditure
interest
repayments
rate.
Provision
loan over
i s made f o r
s i n k i n g fund w h i c h a l s o c o l l e c t s
at
the
e n d of
each
year
required
in n y e a r s i s
i n t e r e s t r a t e on t h e p a y m e n t s i n t o t h e s i n k i n g f u n d . i s R,
t h e i n t e r e s t r a t e o n t h e toan
R(l+r)"+
capital
a certain
load by
The
to amount
where
usual
period at
r e p a y i n g the interest.
is
If
then the t o t a l a n n u a l payment i s
r-R (1.4)
( 1 + r )n-t Normally
the
interest
rate
on
the
loan
i s equal
to
the
interest rate
e a r n e d b y t h e s i n k i n g fund so t h e a n n u a l p a y m e n t on a l o a n of
El
is
(1.5)
Conversely
the
present
year over n years
v a l u e of
a
p a y m e n t of
S1 a t
t h e e n d o f each
IS
The p r e s e n t v a l u e of a s i n g l e amount of f l i n n y e a r s i s
Interest on
loans,
various
tables
and
are
available
the present
interest
rates and
for
determining
v a l u e s of
annual
redemption
the a n n u a l
payments o r
periods
(lnstn.
of
payments
returns, Civil
for
Engs.,
1962)
Methods of A n a l y s i s
Different engineering may
b e compared
and
incomes
value
for
schemes r e q u i r e d
economically
associated
comparison,
with
the
a
in a
to meet
n u m b e r of
t h e same o b j e c t i v e s
If a l l
ways.
scheme a r e d i s c o u n t e d
analysis
is
termed
a
to
payments
t h e i r present
present
value
or
11 discounted
cash
flow
incomes of d i f f e r e n t return
method.
o r g a n i s a t ions
analysis.
On
The
where
latter tax
is
Present
most
returns
such cases i t i s suggested that i s obtained.
the
other
schemes a r e compared,
value
and
hand
this
frequently profits
if
annual
i s termed used
feature
net
the r a t e of by
private
priminently.
In
the assistance of q u a l i f i e d accountants
comparisons
are
most
common
for
public
u t i I i t ies.
A
form
benefit/cost of
a
water
of
economic
analysis.
scheme,
for
supplies,
instance
a
popular
certain
although t h i s
domestic supplies. a r e attached
analysis
An economic benefit
economic
is difficult
Those schemes w i t h
highest
priority.
the
in
States
to a l l
value
is
attached
in
the
schemes
mutually
to
case of
benefit/cost
are
is
products
to e v a l u a t e
the highest
Where
United
i s attached
values
exclusive
such as i s u s u a l l y the case w i t h p u b l i c u n t i l i t i e s the scheme w i t h largest
present
requirements of
value a
of
net
town f o r
benefit
is
adopted.
instance were f i x e d ,
It the
the
total
least-cost
the
water supply
scheme would be selected f o r construction.
Uncertainty i n Forecasts Forecasts of
demands,
i n v a r i a b l y clouded w i t h
whether
they
uncertainty
be f o r water,
and
risk.
a n a l y s i s i s r e q u i r e d f o r each possible scheme, a n y p a r t i c u l a r scheme w i l l by
their
probability
for
be the sum of a
number
uncertain
forecasts,
but
his
analysis
a
are
probability
the net
the net
b y 5 to
(1971) recommends under-designing for
i.e.
possible
of
o i l o r gas,
Strictly
benefit of
benefits mul t i pl i ed demands.
Berthouex
10% f o r p i p e l i n e s to a l l o w does
not
account
for
cost
inflation. An a l t e r n a t i v e method of a l l o w i n g f o r or
interest
c a p i t a l cost
discount
scheme,
rate:
increasing
uncertainty
the
rate
i s to a d j u s t
will
which would be p r e f e r a b l e i f
the
favour future
the
a
low
demand
were uncertain.
Example
A consumer r e q u i r e s 300 P/s of increase
his
economic
l i f e of h i s f a c t o r y ) .
consumption
to
600
water P/s
for
for
a
5
years further
then
25
plans
years
to
(the
12 He
draws
75% of
for
the
time
every
day.
Determine
the
economic diameter and the number of p i p e l i n e s r e q u i r e d . i s s u p p l i e d b y a p u b l i c body p a y i n g no t a x .
Power
0.5
for
p/kWhr,
which
includes
an
allowance
on a s i n k i n g f u n d i s 10% p e r annum, of
The water
costs
a
flat
operating
and
The interest r a t e on loans ( t a k e n over 20 y e a r s ) a n d
maintenance.
cost
most
pipelines,
pumps
and
a n d the
power
6%
is
to 5300 p e r
pumpstations costs amount
rate of
inflation in
p.a.
incremental
Pump
kW,
and
(including
a n allowance f o r standby p l a n t ) a n d pump e f f i c i e n c y i s 70%. The effective discount r a t e may be taken the r a t e of i n f l a t i o n , x
+
1.10/1.06
The s u p p l y
O/s,
one
be made t h r o u g h one
P/s,
installed
Similarly
d e l i v e r i n g 300 P / s . for
two
or
five
a l t e r n a t i v e diameters pipeline.
since E l
interest
rate
less
f l
t h i s year i s worth
51 x 1.04 next year.
could
h a n d l i n g 600
4% p.a.,
i.e.
as the
years
i s made
large
pipeline
pipelines
after
the
each
was
capable
comparison
table for
made f o r
of
300
delivering
A
other.
i n the f o l l o w i n g
an a n a l y s i s
two
a
of
single
pipelines
each
i n d i c a t e d an optimum diameter of 600 mm
This
each p i p e l i n e a n d a
5 7 500 p e r 100 m.
smaller
total
present
Thus one p i p e l i n e ,
value for
both p i p e l i n e s of
800 mm diameter,
w i l l be the
most economic solution.
Note
that
pipeline,
the
although
analysis it
was
is
independent
assumed
that
of
the
pressure
length
was
continuous low-pressure p i p e was a l l t h a t was r e q u i r e d . protection
costs a r e assumed
a n a l y s i s i s also
incorporated
independent o f
the p i p e
in
the c a p i t a l
such Water
cost
loan period,
the
of that
a
hammer
here.
The
a l t h o u g h the
r e s u l t s would be s e n s i t i v e to change i n the interest o r i n f l a t i o n rates. Discount
5,
25
factors
and
30
were obtained years
periods.
from
present
v a l u e tables
Uncertainty
was
not
4% over
for
allowed
for
but
would f a v o u r the two smaller p i p e l i n e s . Another
i n t e r e s t i n g p o i n t emerged from
p i p e l i n e was demand increase,
installed
increasing it
would
from
initially,
300
to
due
600
be more economic
to
a
P/s, to
the a n a l y s i s : high then
boost
the
I f a 600 mm
uncertainty if
the
of
the
demand
did
pumping
head
and
13 Sol u t i o n : 1.
I n s i d e D i a .mm
2.
FIOW
3.
e/s
5.
7.
e.
loss kw/100 m = (3.)xQ/70
0.14
0.55
0.06
0.24
0.03
0.12
0.02
0.07
0.60
4.,72
0.26
2.06
0.13
1.03
0.09
0.60
3900
31000
1700
13500
Annual cost
850
6600
590
3900
pumping
silo0 m
20
155
Equiv.Capita1 c o s t of p u m p i n g over 5 years = (6Jx4.452
90
--
Equiv .capital c o s t of p u m p i n g o v e r 25 y e a r s .
( 6 . )x15.622
-
24-30
e
67
40
-
-
1060
4
33
20
-
520
-
3
20
10
-
-
310
P r e s e n t v a l u e of p u m p i n g cost
2 070
= (8.)/1.170
10.
600
600
Energy requirem e n t s kW h r / y r / 100 m
=
9.
900 300
300
Power
= (4.1~8760 x 0.75
6.
800 300 600
600
H e a d loss
m/100 m 4.
700
600_ _ ~ _ _
N O
900
260
440
Cost of p u m p s etc.
f/100 11.
12.
13.
m : = ( 4 . ) x300
Present v a l u e of pump cost = (10.,)/1.170 for second s t a g e P i p e l i n e cost f/100 m TOTAL
180
1410
80
620
40
310
30
180
180
1200
80
530
40
260
30
150
3600
4200
7140
5750
4800
5400
5560 ::
5850
COST
f / 1 0 0 m f o r 300 G 600 e / s 7. '9. + 1 1 . t i 2
(least cost)
14
_ - -
-
Rate
m’ls
Reservoir empty
cumulative demand =/Qdt
Reservoir f u l l = c a p a c i t y required
24h I
1.4
Fig.
pump
Graphical c a l c u l a t i o n of r e s e r v o i r capacity
total
flow
rather
than
the
pipeline indicated
by
600 mm
one
a
through provide
comparison
the a
of
the
(57 140/100 m )
line
one
second present with
through two 600 mm lines ( 5 7 500/100
600
existing
600
mm
value
the
diameter
mm
pipeline. of
present
This
is
pumping through value
of
pumping
m).
BALANCING STORAGE
An
aspect
system
is
reservoir
industrial time mean may
of
water
day.
annual be
provide
which
six
deserves
close a t t e n t i o n
storage.
Demands such as those f o r
fluctuate
Peak-day
the season,
the day
demands a r e sometimes
demand whereas
peak draw-off
times
for
pipeline
the
mean
capacity
b a l a n c i n g r e s e r v o i r s are the head of
with
in p l a n n i n g the p i p e l i n e
to
a
day.
meet
the
of
domestic the
i n excess of
week
and and
twice
the
from r e t i c u l a t i o n systems
It
would
peak
be
uneconomic
draw-off
rates,
to
and
n o r m a l l y constructed at the consumer end ( a t
the r e t i c u l a t i o n
system)
to meet
these peaks.
The storage
c a p a c i t y r e q u i r e d v a r i e s i n v e r s e l y w i t h the p i p e l i n e c a p a c i t y . The b a l a n c i n g storage and
pipeline
capacity
requirement
may
for
be determined
any
known draw-off
w i t h a mass flow
pattern diagram:
15 Plot
cumulative
curve
plot
pipeline. period.
a
line
Move Then
draw-off with
this
the
over slope
line
period
a
equal
down
till
maximum o r d i n a t e
just
touches
between
the
the b a l a n c i n g storage r e q u i r e d (see F i g . An
economic
storage
comparison
capacity
for
is
time,
and a b o v e t h i s
the discharge capacity
to
it
versus
of
the
the mass draw-off
two
lines represents
1.4).
necessary
to
determine
a n y p a r t i c u l a r system (Abramov,
the
optimum
1969) b y adding
t h e cost o f r e s e r v o i r s and p i p e l i n e s and c a p i t a l i z i n g running c o s t s f o r different cost
is
c o m b i n a t i o n s and c o m p a r i n g them, selected.
It
is found
that
the system w i t h
t h e most economic
least total
storage capacity
v a r i e s f r o m one d a y ' s s u p p l y b a s e d o n t h e mean a n n u a l r a t e f o r s h o r t pipelines
to
Slightly than
more
450
reserve
mm
two
supply
day's
storage
may
diameter).
storage
should
be
long
for
b e economic
In a d d i t i o n
a
provided;
up
for
pipelines
(over
60
km).
small-bore
pipelines
(less
certain to
amount
of
emergency
12 h o u r s d e p e n d i n g u p o n
the a v a i l a b i l i t y of maintenance f a c i l i t i e s .
REFERENCES A b r a m o v , N., 1969. M e t h o d s o f r e d u c i n g p o w e r c o n s u m p t i o n in p u m p i n g w a t e r . I n t . W a t e r S u p p l y Assn. C o n g r e s s , V i e n n a . Berthouex, P.M., 1971. Accommodating u n c e r t a i n forecasts. J. Am. W a t e r Works Assn., 66 ( 1 ) 14. I n s t n . o f C i v i l Engs., 1962. A n I n t r o d u c t i o n t o E n g i n e e r i n g Economics, London. and James, L.D., 1973. M a r g i n a l economics a p p l i e d t o Osborne, J.M. p i p e l i n e d e s i g n . P r o c . Am. SOC. C i v i l E n g s . , 99 ( T E 3 ) 637. W h i t e , J.E., 1969. Economics o f l a r g e d i a m e t e r l i q u i d p i p e l i n e s . P i p e l i n e News, N.J.
L I S T OF SYMBOLS
C
-
cost p e r u n i t o f t h r o u g h p u t
D
-
diameter
n
-
number of y e a r s
Q
-
throughput
r
-
i n t e r e s t r a t e o n s i n k i n g fund
R
-
i n t e r e s t r a t e on
loan
CHAPTER 2
HYDRAULICS
THE FUNDAMENTAL EQUATIONS OF FLUID FLOW
The
three
continuity For
most
steady, is
simply
the
flow
rate
is
with
meant
time.
stream
tube
The
that
there
there
states
that
one-dimensional
on
the
is
variation
no
lateral
stems in
forces
on
from
rate at
the
across
the
any
is
an
element in
energy of
energy.
the equation.
tion
and
for
this.
to
'steady point
along
a
boundaries
of
Newton's
fluid
basic
law
between
causing
of
two
the
motion sections
change.
For
flow t h i s i s
p i s the f l u i d
i s velocity
basic
equa-
section By
at
flow
the
i s irrotational.
momentum f l u x the
any
tube.
velocity
that
flow
the flow
the c o n t i n u i t y
stream in
implies
are
equation.
(2.1
i s the force,
The
from
no
flow
the
mechanics
t h e energy
pQAVx
flow r a t e , V
change
of
fluid
the flow
along
flow
change
steady,
F
sum
the
the
where
is
equation
equals
=
equating
section
I t also implies that
momentum
AFx
by
another
and
in
one-dimensional
'One-dimensional'
stream tubes.
and
obtained at
equations
the momentum equation a n d
incompressible,
tion
flow'
important
equation,
mass density,
Q
a n d s u b s c r i p t x r e f e r s to the
equation
fluid
by
is
i s the volumetric 'x'
direction.
d e r i v e d b y e q u a t i n g the work
gravitational
Mechanical
and
a n d heat energy
pressure transfer
In most systems there i s energy
1
forces
to
done the
a r e excluded
loss due to f r i c -
turbulence and a t e r m i s included i n the equation to account The
resulting
equation
for
steady
flow
of
incompressible
f l u i d s i s termed the B e r n o u l l i equation and i s conveniently w r i t t e n a s :
where V
=
mean velocity
V2/2g
=
velocity
at a section
9
=
g r a v i t a t iona I acce I e r a t ion
P
=
pressure
head ( u n i t s of
length)
17 p/y
=
Y
= u n i t weight of f l u i d
pressure head ( u n i t s of
Z
= e l e v a t i o n above an a r b i t r a r y datum
he
=
head
loss
due
to
length)
friction
or
turbulence
between
pressure
head p l u s e l e v a t i o n
sections 1 G 2 The
sum
the
of
velocity
head
plus
is
termed the total head. Strictly
the v e l o c i t y head should be m u l t i p l i e d b y a coefficient to
account f o r the v a r i a t i o n in v e l o c i t y across the section of the conduit. The average v a l u e of the coefficient f o r t u r b u l e n t flow laminar
flow
uniform
or
variation
it
2.0.
is
non-uniform in
the
Flow
through
depending
on
cross-sectional
a
conduit
whether
velocity
i s 1.06 and f o r termed
is
or
not
either
there
distribution
a
is
along
the
conduit. For i.e.
the
there
The flow should
Bernoulli should
be
equation
to
no change
apply in
i s assumed to be one-dimensional
be
incompressible,
although
the
gases w i t h reservations (Albertson et a l . , The tical
the
velocity
respective
heads
are
illustrated
flow at
should
any
be
and i r r o t a t i o n a l .
equation
steady,
p o i n t w i t h time.
may
be
The f l u i d applied
1960). i n Fig.
2.1.
For most p r a c -
cases the v e l o c i t y head i s small compared w i t h the other heads,
and i t may be neglected.
ENERGY LINE ENTRANCE LOSS FRICTION L O S S COtiTRACTION L O S S
FRICTION LOSS
I
PRESSURE H E A D P/ x
E L E \ A T ION
Fig.
to
2.1
Energy heads along a p i p e l i n e
18 F L O W HEAD LOSS RELAT I ONSH I PS
Empirical Flow Formulae The throughput
o r c a p a c i t y of
on the t o t a l head difference
a p i p e of
f i x e d dimensions depends
between the ends.
T h i s head
i s consumed
b y f r i c t i o n and other ( m i n o r ) losses. The
first
friction
f i e l d observations. waterworks developed.
head
These e m p i r i c a l
practice The
conventional
loss/flow
although
head
relationships
rational
formulae
,+-
formulae a n d a r e u s u a l l y
derived
stil I
relationships are
more
loss/flow
were
formulae
established
thus
i n an exponential
from
popular have are form
in
been termed of
the
type
v
= K
where V the
sY
R~
m
radius
perimeter,
q u a r t e r of per
= K*Q"/D~
i s the mean v e l o c i t y of flow,
hydraulic
wetted
s
or
and
of
K' a r e coefficients, R i s
area
for
pipe flowing
a
circular
the diameter) a n d S
length
K and
(cross-sectional
pipe).
Some of
of
flow
divided full,
i s the head g r a d i e n t
by
the
equals
one
( i n m head loss
the equations more f r e q u e n t l y a p p l i e d
a r e l i s t e d below:
SI units
Basic Equation Hazen -Wi I I iams Manning Chezy Darcy
S=K1 ( V / C w )
1.85
/D
1.33
1
units
K =3.03
(2.3)
K2=2.86
(2.4)
K =4.00
(2.5)
1
S=K2(nV)2/D
K2= 6.32
s=K~(v/c~)~/D
K 3=13.13
S= X V /~2 g ~
f.p.s.
= 6.84
1.167
3
DimensionI ess
(2.6)
Except f o r the Darcy formula the above equations a r e not u n i v e r s a l a n d the form of the equation depends on the u n i t s .
I t should be borne
i n m i n d t h a t the formulae were d e r i v e d f o r normal waterworks p r a c t i c e a n d take no account liquid. friction of p i p e .
of
variations
They a r e f o r t u r b u l e n t flow coefficients
vary
in gravity,
temperature o r type of
i n pipes over 50 mm diameter.
w i t h p i p e diameter,
type of
The
f i n i s h a n d age
19 The conventional do
not
involve
formulae a r e comparatively
fluid
viscosity.
They
simple to use as they
may be solved d i r e c t l y as they
do not r e q u i r e an i n i t i a l estimate of Reynolds number to determine the friction solved
factor
diameter rule,
or
for
friction
calculator,
paper. pipe
(see next
directly
The
The
Solution
head g r a d i e n t
computer,
equations
networks
section).
flow.
of
the
the
equations
formulae
i s simple w i t h
nomograph
are
where
rational
of
or
particular
flow/head
graphs use
for
loss
cannot
for
be
velocity,
the a i d of
a slide
p l o t t e d on
log-log
analysing
equations
flows
in
have
to
be
practice
is
the
i t e r a t i v e l y solved many times. The
most
popular
Hazen-Williams
flow
formula.
are tabulated
i n Table 2.1. the
waterworks
aid
in
of
organizations
for
I f the formula chart
a use
is
graphs
of
C decreases w i t h age,
type of
use in t h i s equation
i s to be used f r e q u e n t l y ,
the
a g a i n s t flow f o r v a r i o u s p i p e diameters, v a l u e of
waterworks
F r i c t i o n coefficients
solution
with
formula
most
efficient
loss
head
way.
gradient
a n d v a r i o u s C values.
Many plotted As the
p i p e a n d p r o p e r t i e s of water,
f i e l d tests a r e d e s i r a b l e f o r an accurate assessment of C.
TABLE 2.1
c
Hazen-Williams f r i c t i o n coefficients
New
Cond i t ion 25 years 50 years old old
150 150
140 130
140 120
130 100
150 130
130 110
100
60
90
50
120
100
80
Type of Pipe
PVC: Smooth concrete, AC: Steel, bitumen I ined, ga I vanized : Cast i r o n : Riveted steel, v i t r i f i e d woodstave:
For diameters less than 1 000 mm,
subtract 0.1
Badly corroded
45 ( 1 - Dmm
) C
1 000
Rational F l o w Formulae Although use
for
acceptance fic
the
many
conventional
years,
more
flow
amongst engineers.
b a s i s backed b y
formulae
rational
are
formulae
likely
are
to
remain
gradually
in
gaining
The new formulae have a sound scienti-
numerous measurements a n d they
are uni v ers al l y
20 applicable.
Any
consistent
units
of
measurements
may
be
used
and
I i q u i d s of v a r i o u s viscosities a n d temperatures conform to the proposed formulae. The for inal of
rational
flow
past
research
d a t a on
flow
formulae
bodies o r over was on
for
flat
smal I-bore
roughness f o r
flow
i n pipes a r e s i m i l a r
plates
to those
( S c h l i c h t i n g 1960). The o r i g -
pipes w i t h a r t i f i c i a l
roughness. Lack
l a r g e pipes has been one deterrent to use of
the r e l a t i o n s h i p s i n waterworks practice. The v e l o c i t y maximum
in
a boundary a
shear
in a full
the centre. layer
force
resistance
to
viscosity,
and
p i p e v a r i e s from zero on the boundary to a
Shear forces on the w a l l s oppose the flow and
i s established
onto
an
relative in
inner
w i t h each a n n u l u s of f l u i d i m p a r t i n g
neighbouring
motion
turbulent
of
flow
it
concentric
is
the
fluid
is
imparted
annulus.
termed
by
The
kinematic
turbulent
mixing
w i t h t r a n s f e r of p a r t i c l e s of d i f f e r e n t momentum between one l a y e r and the next. A this point
boundary
layer
layer gradually the f l o w
i s established expands
becomes uniform.
established flow
i s g i v e n by
at
until
it
The
the entrance to
a conduit and
reaches the centre.
length of
Beyond t h i s
pipe required for f u l l y
S c h l i c h t i n g , (1966).
X
D
= 0.7
The
Re'"for Reynolds
Re
number
i n c o r p o r a t i n g the f l u i d viscosity flow
formulae.
and becomes t u r b u i e n t
for
equation
shear
head
force
loss
over
a
=
f
nD2/4
L vz XE 29
v
is
of
is
a
dimensionless
which i s absent
higher Re
length
m u l t i p l i e d by the a r e a :
TnDL = v h
VD/V
=
Flow i n a p i p e i s l a m i n a r f o r
The
basic
(2.7)
t u r b u l e n t flow.
pipe
i n t h e conventional
low R e !less
( n o r m a l l y the case
derived equal
number
by
setting
to
the
loss
than
2 000)
i n practice!. the in
boundary pressure
Fig.
2.2
Moody r e s i s t a n c e d i a g r a m for u n i f o r m f l o w
i n conduits
21
22 where X is
the
=
( 4 7 / y ) ( V Z / 2 s ) ( r e f e r r e d to
shear
D
stress,
loss over
head
is
the
length L .
a
pipe
diameter
and
engineering
turbulent
ivterest
and
complex
hf
Re
is
the
friction
and
!he
relative
The and
X
transition
zone
undefined
but
= 64/Re
will
L a m i n a r flow
between
is
also
i.e. X
not occur laminar of
little
i n practice.
Turbulenr rough
practice.
is
flow
friction factor),
Poiseuille found that
i s independent of the r e l a t i v e roughness. i n normal
Darcy
the
X i s a f u n c t i o n of
F o r l a m l n a r flow,
roughness e/D.
as
flow
conditions
boundary.
conditions
are
distribution
The
derived
in
a
may
occur for
from
general
turbulent
the
boundary
either
with
equations
the
a
friction equation
layer,
smooth
factor for
which
is
or
for
the
a
both
velocity
from
derived
m i x i n g l e n g t h theory:
Integrating,
w i t h k = 0.4
where
the
v
is
velocity
hydrodynamical l y
/+=
a
distance
y‘= v / m s o
5.75
log Y
m
y is
from a
the
laminar
/%=V
+
= e/30
log
fl
-
where e i s the boundary roughness.
a n d 2.11
(2.11) and expressing v
D
~
2 log -
+
0.8 layer,
i n terms of
vdA w e get
(2.12) smooth b o u n d a r y ) a n d
1.14
(turbulent boundary layer,
i s affected and
+ 8.5
equations 2.10
( t u r b u l e n t boundary
Jf
and
(2.10)
5.5
i s r o u g h the l a m i n a r sub-layer
y’
5.75
Re-arranging
= 210g Re
sub-layer,
that
the average v e l o c i t y V b y means of the equation Q = 1
For a
was found e x p e r i m e n t a l l y .
the boundary
Nikuradse found that
J-T
boundary.
V
The constant 5.5
Thus
at
smooth b o u n d a r y there
Nikuradse found that
Where
a n d c o n v e r t i n g logs to base 10,
(2.13) rough boundary)
23 Notice tive
that
for
a
r o u g h n e s s e/D
smooth
A
boundary,
and for
a
very
is
independent of
rough boundary
it
is
the r e l a -
independent
o f t h e R e y n o l d s n u m b e r Re f o r a l l p r a c t i c a l p u r p o s e s .
Colebrook
and
White
combined
E q u a t i o n s 2.12
a n d 2.13
to p r o d u c e
a n e q u a t i o n c o v e r i n g b o t h smooth a n d r o u g h b o u n d a r i e s a s w e l l a s t h e t r a n s i t i o n zone;
(D e +Rx 9.35)
1 = 1.14 - 2 l o g
Their Equation
equation
reduces
2.13
rough
satisfactory
for
results
radse's original ness.
h!atural
roughness. TABLE
2.2
for
(2.14)
to E q u a t i o n 2.12 pipes.
This
various
experiments
for
smooth
semi-empirical
commercially
pipes,
and
equation
available
used s a n d as a r t i f i c i a l
to
yields
pipes.
Niku-
boundary
rough-
r o u g h n e s s i s e v a l u a t e d a c c o r d i n g to t h e e q u i v a l e n t s a n d
T a b l e 2.2
g i v e s v a l u e s of e f o r v a r i o u s s u r f a c e s .
Roughness of p i p e m a t e r i a l s
V a l u e o f e ~n mm f o r n e w ,
( H y d r a u l i c s Research station,
c l e a n surface
Finish:
1969)
unles? otherwise stated
Smooth
Rough
Average
_-__.
Glas?, d r a w n metals S t e r l , DVC or AC
0 0.015 Coat?(( strel 0.03 GaIvnr>cze-d, v i t r i f i e d c l a y 0.06 Cast i r c r o r cement l i n e d 0.15 Spun concrete or wood s t a v e 0 . 3 R i v e t e d steel 1.5 F o u l sewers, t u b e r c u l a t e d 6 water mains Ur,Iinrd rock, e a r t h 60
_____ 0.006
0.003 0.03 0.06 0.15 0.3 0.6
0.06 0.15 0.3 0.6 I .5
3
6
15
30
150
300
__-
Fortunately A increases constant
i s not v e r y
linearly
with
d e p e n d i n g on
sensitive
age
local
to t h e v a l u e o f e assumed.
water
for
conditions.
pipes, There
the
may
e
proportionality
also
be
reduction
i n c r o s s s e c t i o n w i t h age. The v a r i o u s r a t i o n a l f o m u l a e f o r ::J
Moody
this
and
viscosities
graph
water
of
at
is
were
A
presented
various
p l o t t e d on a Fig.
as
temperatures
2.2. are
single The
graph
kinematic
listed
the
in
Apprndix. The Moody d i a g r a m pipe
velocity
to d i r e c t
amenable head
loss,
velocity
to
and
i s useful for calculating manually
head
rate
is
flow
or
a
is
solution for trial
calculate
r e c a l c u l s t e v e l o city etc.
and
known. the
error
Reynolds
Unfortunately
convrse,
i.e.
approach
is
number,
Convergence
then
for
it
veloc:ity,
necessary read
loss
not
given
i.e.
off
i s f a i r l y r a p i d however.
A
if
very
guess
,
then
24 The Colebrook W h i t e e q u a t i o n i s e a s i e r to use i f h e a d loss i s g i v e n and velocity loss
Station
i s to b e c a l c u l a t e d .
given
X
or
at
equation
It
flow
Wallingford
Cclebrook-White graphs
or
velocity
i s not
so e a s y
however.
re-arranged produce
to
( H y d r s u l i c Research S t a t i o n ,
The the
simple
solve f o r
to
Hydraulics
in
variables explicit
head
Research the
flow/head
1055
1969): i n t h e form-
E q u a t i o n 2.14 may b e a r r a n g e d
(2.15) Thus e,
a
for
g r a p h may
graph for
has
any
water
plotted
f l u i d at a certain
b e p l o t t e d in terms of V,D at
step
15OC a n d e = 0.06.
similar
also a v a i l a b l e for a
graphs
further,
and
to
V,
the
R a n d S,
gravity.
for
non-circular
Colebrook-Whi te e q u a t i o n tional
Using
and S.
various sections,
conditions.
Research
dimensionless
but
including factors
this
form
resistance diagram
was
published
with
d e r i v e d on a s i m i l a r b a s i s
of
2.3
The
the
Station
charts.
(VVatson,
graphs
for
viscosity,
equation
they
Fig.
2.3
as
are
Going
re-wrote
parameters
the
propor-
roughness
produced
in dimensionless parameters.
their
i s such a
b y r e p l a c i n g D b y 4R.
in
terms o f
Fig.
The H y d r a u l i c Research S t a t i o n
Hydraulics
universal also
temperature a n d defined roughness
an
This
a
graph
example
is
1979).
Comparison of F r i c t i o n F o r m u l a e Diskin
(1960) p r e s e n t e d
a
useful
comparison of
the f r i c t i o n f a c t o r s
f r o m t h e Hazen-Will iams a n d D a r c y e q u a t i o n s : The D a r c y e q u a t i o n may b e w r i t t e n a s
or
v v
=JTprn
(2.16)
c Z &R
=
(2.17)
w h i c h i s termed t h e Chezy e q u a t i o n a n d t h e Chezy c o e f f i c i e n t i s
cz The
=
&p
(2.18)
Hazen-Wi I I iams
equation
may
be
rewritten
for
al I
practical
purposes in the f o l l o w i n g dimensionless form: S
=
5 1 5 ( V / C W ) * (Cw/Re)
By c o m p a r i n g be deduced t h a t
this with
0.15
(2.19)
/gD
t h e Darcy-Weisbach
equation
(2.16)
i t may
26 The
Hazen-Williams
Re
and 2.2).
and
It
values
will
be
Cw
coefficient
may
be
observed
from
Fig.
Hazen-Wi I I iams coefficient coincide
with
in the t r a n s i t i o n zone.
pipes
the
with
therefore
a
Moody
2.2
that
a
functionof
diagram lines
for
(see
X
Fig.
constant
the Colebrook-Whi te I ines o n l y
I n the completely t u r b u l e n t zone f o r non-smooth wi II
coefficient
i .e.
number
is
p l o t t e d on
actual l y
reduce
the
greater
the
Reynolds
cannot associate a c e r t a i n Hazen-Wil I iams coefficient
one
a p a r t i c u l a r p i p e as
i t v a r i e s depending on the flow
rate.
The
Hazen-Will iams equation should therefore be used w i t h c a u t i o n f o r h i g h Reynolds numbers and r o u g h pipes. of C w above approximately practice ( R The
It will
also be noted that values
155 a r e impossible to a t t a i n in water-works
6
around 10 ) .
Manning
p a r t f u l l pipes.
equation
is
widely
used
for
open
channel
flow
and
The equation i s
(2.21 where
K
is
1.00
in SI
P the wetted perimeter. for non-circular
TABLE 2.3
1.486
u n i t s and
where A
h y d r a u l i c r a d i u s A/P
R
One
is D/4
for
i s the
a c i r c u l a r p i p e , a n d i n general
Values of M a n n i n g ' s ' n '
method of
ventional
KV2/2g
and R
area of flow and
0.010
0.01 1 0.01 2 0.013 0.015 0.017
LOSSES
i n section
press
I b units,
sections, 4R may be substituted f o r D.
Smooth glass, p l a s t i c Concrete, steel ( b i tumen I i n e d ) galvanized Cast i r o n Slimy or greasy sewers Rivetted steel, v i t r i f i e d wood-stave Rough concrete
MINOR
in ft
i s the cross-sectional
expressing
i s the e q u i v a l e n t friction
loss
formulae
losses through f i t t i n g s where
K
is
the
head
loss
loss through f i t t i n g s and changes
l e n g t h method, are
used.
in terms of
coefficient.
often Modern
used when
the con-
p r a c t i c e i s to ex-
the v e l o c i t y head i.e. Table 2.4
gives typical
he = loss
27 coefficients plementary
although data
and
valve
loss
The v e l o c i t y V
opening.
to
manufacturers coefficients
K
may
which
also
will
provide vary
sup-
with
gate
use i s n o r m a l l y the mean t h r o u g h the f u l l
bore of the p i p e o r f i t t i n g .
TABLE 2.4
Loss coefficients f o r p i p e f i t t i n g s
Bends hBKBV2/ 2 g Bend a n g l e
Sharp
30" 45" 60 O 90 1 80° 90" w i t h g u i d e vanes r
=
2
6
0.07 0.10 0.12 0.13
0.06 0.08 0.08 0.08
if
the r a d i u s i s
r/D=l
0.16
0.07 0.13 0.18
0.32
0.68 1.27 2.2
0.22
0.2
r a d i u s of bend to centre of p i p e
A significant
reduction
in
bend
loss
i s possible
f l a t t e n e d i n the p l a n e o f the bend. Valves
hv = KvV2/2g
Type:
Opening:
SLuice Butterf I y Globe Needle Ref I u x
1/ 4
1 /2
3/4
Ful I
24 120
5.6 7.5
1 .o 1.2
0.2
0.6
0.5 1-2.5
0.3 10
4
1
Contractions a n d expansions in cross-section
Wal I-Wal I Angle ___
0 -
Contract ions :
Expansions
hc= KcVJ29
h = K V 2/2g c c l
A 2 4 0.2 0.4 0.6 0.8 1.0 - __ __
7.5" 150 30 O
180"
.5
.37
.25
.15
.07 0
Al/A2
0 .13 .32 .78 1 .O
0.2 0.4 0.6 0.8 1.0 .08 .24 .45 .64
.05 .15 .27 .36
.02 .08 .13 .17
0 0 .02 0 .03 0 -04 0
28 Entrance and e x i t
he = KeV2/2g
losses:
Protruding Sharp Bevel l e d Rounded
PRESSURE AND F L O W CONTROL
Entrance
Exit
0.8 0.5 0.25 0.05
1 .o 1 .o
0.5 0.2
IN PIPES
I ntroduct ion Valves the
and other
cause of
is
reduced
water
giving
rise
Knapp
et
upstream
fittings
vapour
to
vaporizes.
cavitation
1961).
al, and
in pipes
bubble formation The
bubbles
damage
The
downstream
fluid.
The
geometry
conditions
referred
to
velocity
increases
as
to
pressure,
r a t e affec? the c a v i t a t i o n p o t e n t i a l the
critical.
as
may
the
pipe
of
the
as
well
ratio
the
h e a d may
When
be
the
pressure
subsequently
collapse
or
valve
valve
the
damage
well
closure
vapour
cavitation
1970,
(Ball;
as
valve
as
which
cavitation
the
reduce
degree of
under
The
and
which
downstream.
as and
p r e s s u r e of
commences
increases
of
upstream
for
identifying
the flow
are
as
flow
downstream
to
p r e s s u r e increases. A of
number
operation
The
of
of
popular
reduction
empirical control
measure
ratio,
commercially
i.e.
to
work
of
the
potential
r a t i o of
valve types
influences of
s a f e zone
less
valves
the for
problem
is
the
pressure
u p s t r e a m to d o w n s t r e a m p r e s s u r e s .
valves
ratios
cavitation
are
than
said
3 or 4.
critical
operate
to
w i t h a c a v i t a t i o n index a s indicated
various
the
v a l v e s h a v e been p r o p o s e d b y v a l v e s u p p l i e r s . of
available
pressure reducing
relationships
It
for
i s h o w e v e r more l o g i c a l
Jater.
conditions,
pressure
Many
efficiently
reducing
Since t h e geometry the or
application
flow
control
of is
described.
TYPES OF VALVES
Valves
are
used
for
i s o l a t i n g o r flow control.
two
aistinct
purposes
in
pipelines,
namely
29 I s o l a t i n g Valves Isolating
valves
They
should
only.
They
be
are
and
there
damage not
close
off
in
the
fully
open
operated
the o b s t r u c t i o n to
is
to
the
flow
or
through
fully
a
closed
pipe.
position
h a v e poor flow c h a r a c t e r i s t i c s i n the p a r t l y open position.
i.e.
gate
used
is
often
shut.
the seat
to
to
i s l a r g e l y the exposed area of a gate
l i t t l e pressure reduction o r
practically
designed
the flow
and
At
that
stage
flow
control
cavitation
v a l v e body may r e s u l t .
is
until
the
possible
and
T h i s type of v a l v e i s
reduce the pressure a p p r e c i a b l y .
i.e.
it
i s designed
to pass the f u l l flow when f u l l y open w i t h minimal head loss. Such
valves
spherical
include
valves.
designed
to
These
close
operated b y
gate
as
valves,
valves
rapidly
spindles
with
are
as
screw
butterfly generally
possible. threads,
valves
and
operated
by
Although butterfly
gate
r o t a r y or hand
and
valves
are
valves and rot ary
v a l v e s can be operated b y t u r n i n g a h a n d l e t h r o u g h 90" to f u l l y close the
valve
seating these
from
the
fully
open
position.
I n order
pressures however a n d sometimes to control
valves
spindle
may
have
indirectly
from
reduction the
gear
boxes
handwheel.
in
to
overcome
high
the r a t e of closure order
Alternatively
to
drive
electrical
the and
pneumatic control systems can be used to operate these valves. Typical i!lustrated open
sl(iice in
bore area
non l i n e a r , area
valves,
10.1,
Figs.
a n d degree of
reduces
rapidly
i s reduced r a p i d l y rise
to
10.2
valves
and
10.4,
The
and
t u r n i n g of
the
I t can be observed i n the case of
in
u n f a v o u r a b l e w i t h respect
higher
reduction
butterfly
in
the to
final
water
d u r i n g the f i n a l
water
velocity
hammer in
the
pressures pipe.
handwheel
The
of
than
as
the
closure
and
tne
uniform
problems
of
are
between generally
is
valve
closure.
pressures
stages of
valves
relationship
the gate
stages
hammer
spherical
that
the
This
is
velocity
this
gives
rate
cavitation
of
are
g e n e r a l l y avoided w i t h such \ ~ a l \ / e sas they a r e not operated i n p a r t l y closed c o v d i t i o n s except i n emergencies.
Control Valves Various water
types of
v a l v e s h a v e been designed to control
i n pipelines b y
linearly
the flow of
r e d u c i n g the open a r e a a n d to c o n t a i n
the c a v i t a t i o n effect due to reduction of pressure through the v a l v e .
A
30 typical
valve
valve).
Diaphram type valves,
2.4)
in
common
and plunger
a v a r i a t i o n of slots.
any
( a needle
which
valves even
is
has a piston covering the
and
more
basket
type
appropriate
r e l y on a s i n g l e
high
for
duty
pressure
increase i n velocity
and
head d i s s i p a t i o n due to expansion whereas the l a t t e r types which
have
variable
pressure
resistance
trim
i n a number of
damage
as
a
result.
r a t i o i s l i m i t e d at It
10.3
Fig.
r a d i a l flow sleeve v a l v e s ( F i g .
valve
are
types
in
v a l v e s a r e also employed a n d there
type
2.5)
(Fig.
The former
illustrated
slotted
type control
expansion
valves
reducing.
is
the r a d i a l flow
Multiple
control
use
rings
or
layered
baskets
reduce
the
stages a n d a r e s a i d to s u f f e r less c a v i t a t i o n
This
is
largely
because
each stage b u t o v e r a l l
i s a l s o recognised that
pressure
reducing
may be r e l a t i v e l y h i g h .
it
these v a l v e s a r e
the
less noisy
when
reducing
h i g h pressures. The
needle v a l v e
was
as
it
at
a l l stages of opening.
or
the
COI
was
initial
valve) (e.g.
or
quality the
by
materials
pistons o r
1981).
Dvir,
water
as
workings.
valve
i s however expensive owing
i s now replaced to a
sophisticated
the
such
latter
type
of
elastometers
valve
other
hand
the
( t h e sleeve
its
diaphram
type
low pressure valves
i s not sensitive
f l e x i b l e d i a p h r a m prevents
the
to
l a r g e extent by simpler valves
as
diaphrams i n the case of
The
On
i n power s t a t i o n p r a c t i c e
v a l v e which could control flow
I t often h a d a p i l o t needle f o r f i n a l seating
The
opening.
struction and
using
once used widely
recognised as a streamlined
ingress of cannot
to
poor
dirt
into
accommodate
h i g h pressure d i f f e r e n t i a l s and s u f f e r s wear a f t e r prolonged operation. It
may
also
be
subject
to
vibration
and
instability
as
a
venturi
action i s caused d u r i n g the l a s t stages of closing. Piston is
type v a l v e s can b e accurately
towards
downstream or
the atmosphere
stream on
the
face of
system
and
of
of
the
i s supported
that
is off
also
be
operated
off
to
In
to
system.
some
types
the downstream
by a spring.
the
pressure
I n others the down-
f l u i d pressure depending Such p i l o t systems can be
the water
a r e often r e q u i r e d to prevent
can
piston.
i s exposed
a p i l o t control
hydraulically,
strainers
face
the p i s t o n
the p i s t o n can be subject
the operation
operated
exposed
face of
c o n t r o l l e d p r o v i d e d the flow
pressure.
the p i l o t
electrical
tubes
I n t h i s case blocking.
solenoids
or
The
from
a
31
Fig.
~
2.4
i 2 . 5~
F l e x f l o Sleeve v a l v e f o r f l o w control
, .i i g h d u t y control reduction
v a l v e n i t n t r i p l e aasi(ets
foi'
heao
p n e u m a t i c s u p p o r t system. The sure
control
to
system c a n
a n d t h e sensor a
be designed
a c e r t a i n maximum f i g u r e .
pilot
d o w n s t r e a m senses
valve held b y
means o f
to
limit
t h e downstream
pres-
As t h e u p s t r e a m p r e s s u r e b u i l d s UP an
i n c r e a s i n g p r e s s u r e i t w i l l open
in
a spring and this pilot valve will
t u r n p e r m i t a b i g g e r p r e s s u r e f r o m u p s t r e a m t o come b e h i n d t h e p i s t o n and
partly
close
control
flow
orifice
or
controls get
the
ports.
Alternatively
in
which
case
rate venturi
is
the
measured.
the
valve
p r e s s u r e on
The
pressure
may
b e u s e d to
either
side
of
in
difference
an turn
p i l o t v a l v e w h i c h w i l l e i t h e r p e r m i t a g r e a t e r p r e s s u r e to
the
behind
the
piston
to
close
the
valve
or
exhaust
the
pressure
b e h i n d t h e p i s t o n to open t h e v a l v e d e p e n d i n g on w h i c h i s r e q u i r e d .
CAVITATION
The
IN CONTROL VALVES
mechanism
control high
valve
is
velocity
turbulence from
by
jet
as
statical
whereby
flow
converting and
it
is
then
emerges
reduced o r the
the
into
pressure energy
p r e s s u r e i s reduced
pressure energy velocity
the
open
energy
pipe
upstream is
again.
to v e l o c i t y e n e r g y
in a
into a
dissipated The
in
conversion
i s obtained from
the
Bernoul I i e q u a t i o n ;
(2.22) Here
P
that
P/W
is
the is
datum a n d V velocity be V
upstream the
pressure,
pressure
i s the w a t e r
head,
w h e r e H = P/W.
This
replacing
h
by
ah.
coefficient
is
often
introduced
v = c where the the
d
i s often given
the the
Thus
if
unit
weight
elevation
2
of
is
the
To
affects
so
fixed
however n e g l e c t s u p s t r e a m v e l o c i t y the
account in
latter can for
the
be accounted f o r b y
upstream
equation
velocity
and
in
fact
head
a
the p i p e
in t h e f o l l o w i n g f o r m
(2.23) discharge
v a l v e opening. valve
a
i s a c o n s t a n t then t h e
JzsnF; Cd
water
above
t h e p r e s s u r e h e a d i s r e d u c e d to z e r o w o u l d
a n d downstream p r e s s u r e a l t h o u g h
velocity
is is
velocity.
p o s s i b l e assuming
=
W
Z
Apart the
coefficient
from
the f a c t
discharge
which that
coefficient,
may
vary
depending
on
t h e d e g r e e of o p e n i n g o f even
if
the
discharge
33 coefficient to v a r y
was separated from the degree of opening i t would be found
owing
to the d i f f e r e n t contraction r a t i o as a d i f f e r e n t area i s
open. The only
actual
be
found
incipient
i.e.
valve
is
and a
from the
a n d choking
stream.
stage of
throttling
experiment.
p o i n t at
i.e.
at
appreciably
Cavitation
which
the stage a t
vapour
which
affected
which c a v i t a t i o n
by
has
commences can
been
classified
bubbles commenced to
as
form,
the d i s c h a r g e coefficient o f
vaporization
of
the
water
the
down-
The v a p o r i z a t i o n occurs because the pressure head i s reduced
the energy
low
i s transformed i n t o k i n e t i c energy which impinges i n t o
pressure
A
downstream.
cavitation
have
significant
factor
been
proposed
the
in
number
of
(Winn
indication
of
parameters and
for
Johnson,
cavitation
is
assessing
1970). the
The
cavitation
index.
(2.24) where
P
is
the
pressure a n d s u b s c r i p t d r e f e r s to downstream,
u to
upstream a n d v to vapour pressure.
For
streamlined
tation
index
cavitation
drops as
often
case i t w i l l
valves low
occurs
it
0.1
a
then
the the
index
occur
until
the
cavi-
p o o r l y designed v a l v e s
i.e.
nearer
1.0.
at normal o p e r a t i n g pressure r a t i o s .
pressure
can
pressure
v a l v e s i s much lower. pressure
not
whereas f o r
higher
i s seen from the c a v i t a t i o n
whereas
the
as 0.1
at
may
In
any
be found on inspection that most control v a l v e s experience
a degree of c a v i t a t i o n Pv
cavitation
be
index
if
the c r i t i c a l
by
a
factor
reduced
reduction
ratio
possible
with
For an average c r i t i c a l c a v i t a t i o n
reducing
ratio
Neglecting
that
i s from 2.24
neglecting
of
index nearly
is 10
unstreaml ined index of 0.33
vapour
pressure,
4.0. Various forms of 1970).
Very
little
the c a v i t a t i o n is
however
c a v i t a t i o n index and much work T h e method of Various velocity
index
known
about
owing
quantitatively
to
the
photographic
the
scaling
down
of
the
has to be done i n t h i s f i e l d yet. assessing c a v i t a t i o n i s a l s o d i f f i c u l t .
methods have been attempted i.e.
format ion,
have been proposed ( T u l l i s ,
increase
in
methods,
bulk
estimation of the increase of volume
pressure
caused
by
measurements
bubble due
to
collapse
of
the
bubbles
and
sonic- methods.
2.6
Fig.
shows
the
v a r i a t i o n i n noise measured on a r a d i a l flow sleeve v a l v e at d i f f e r e n t c a v i t a t i o n indices f o r a f i x e d degree of opening.
I n t e r a c t i o n between C a v i t a t i o n and Water Hammer Pressures
It
is
recognised
that
pressure subsequently the
accompanying
the
collapse
of
vapour
bubbles
when
increases may cause erosion of steel.
noise a r e often
the
symptoms
of
a
the
T h i s and
poorly
selected
valve. There hammer
is
however
wave the
closed so
an
celerity
interesting
and
the
b u b b l e formation
relationship
cavitation increases
between
potential.
As
the a
water
valve
is
a n d t h i s reduces the water
hammer wave c e l e r i t y downstream (Ch. 4 a n d 5 ) . If
the
which
free
in
turn
then
it
the
valve
gas is
fraction
a
can
f u n c t i o n of
discharge
with
the
equation
equation
and
wave c e l e r i t y . the
when
cavity the
It
in
pressure.
The
bubbles
are
solved
pressure
to
pressure This
increases.
bubbles
downstream
may
as
release
they
which r a p i d l y
are
therefore
released
not then
initially
turns
q u a n t i t i e s of due
collapse it
drop
will
be
rapidly
water hammer deceleration effect.
the
wave c e l e r i t y
promise f o r
reduces r a p i d l y
i s reduced so that
neglects
wave
the p o t e n t i a l of
equation index,
the flow
reflections
and
cavitation
to effect
so
to
into l i q u i d gas
may
the
drop
completely.
the
lowering
index
cavitation
to
to
study
index
however b y the fact that p a r t
Small
(iteratively) would
cavitation
form
closed due begin
the
cavitation
downstream pressure
downstream pressure a n d water ham-
i s made d i f f i c u l t
again
contained
equations
gas
i s not gas b u t vapour
pressure
the
to
the water hammer equation,
the
relating
f o r free gas volume downstream,
of
related
i s possible to solve sirnuttaneously
together
mer
be
the upstream or
found
as
the
be in
If
the
that
the
valve
is
Then as bubbles
and the consequent
reduces more s t e a d i l y . on
but
it
does
hold
better control of flow
as a v a l v e closes especially
d u r i n g the i n i t i a l stages of closure where
this
flow
theory
indicates
that
previous1 y considered the case.
reduction
is
more
rapid
than
was
35 REFERENCES
1960. F l u i d M e c h a n i c s A l b e r t s o n , M.L., B a r t o n , J.R. a n d Simons, D.B., f o r E n g i n e e r s . P r e n t i c e H a l l , N.J. B a l l , J.W., 1970. C a v i t a t i o n d e s i g n c r i t e r i a . I n T u l l i s (1970). Proc. I n s t . Colorado State Univ. D i s k i n , M.H., Nov. 1960. The l i m i t s o f a p p l i c a b i l i t y o f t h e HazenW i l l i a m s f o r m u l a e . L a H o u i l l e B l a n c h e , 6. D v i r , Y., 1981. P r e s s u r e r e g u l a t o r s in w a t e r s u p p l y systems. Water a n d I r r i g a t i o n Review, Water Works A s s o c i a t i o n o f I s r a e l . H y d r a u l i c s Research S t a t i o n , 1969. C h a r t s f o r t h e H y d r a u l i c Designs o f C h a n n e l s a n d PiDes. 3 r d E d n . . H.M.S.O., London. K n a p p , R., D a i l y , 'J.W. a n d Hammitt, F.G.',1961. C a v i t a t i o n . McGrawHill. S c h l i c h t i n g , H., 1960. B o u n d a r y L a y e r T h e o r y . 4 t h E d n . , McGraw-Hill N.Y. T u l l i s , J.P., 1970. Control o f f l o w i n c l o s e d c o n d u i t s . Proc. I n s t . Colorado State U n i v e r s i t y . Watson, M.D., J u l y 1979. A s i m p l i f i e d a p p r o a c h t o t h e s o l u t i o n o f p i p e f l o w p r o b l e m s u s i n g t h e Colebrook-White method. C i v i l Eng. in S.A., 2 1 ( 7 ) , p p 169-171. Winn, W.P. a n d Johnson, D.E. December 1970. C a v i t a t i o n p a r a m e t e r s f o r o u t l e t v a l v e s . Proc. ASCE, HY12. LIST O F SYMBOLS
A
-
cross-sectional
C
-
Hazen-Will iams f r i c t i o n f a c t o r
C'
friction factor
Cz
-
d
-
d e p t h o f water
D
-
diameter
e
N i k u r a d s e roughness
force
he
-
hf
-
f r i c t i o n h e a d loss
K
-
loss c o e f f i c i e n t
L
length of c o n d u i t
n
-
Manning friction factor
P
-
wetted p e r i m e t e r
p
-
pressure
f Fx g
a r e a of flow
Chezy f r i c t i o n f a c t o r
Darcy f r i c t i o n factor
gravitational
( e q u i v a l e n t to A )
acceleration
h e a d loss
36
Q
-
R
-
Re S
flow rate hydraulic radius Reynolds number h y d r a u l i c gradient
v
mean velocity
V
velocity a t a point
X
distance along conduit
Y
distance from boundary
across a section
2
elevation
Y
specific
P
mass density
T
shear stress
V
k i n e m a t i c viscosity
x
Darcy f r i c t i o n f a c t o r - ( f i n USA)
F i g . 2.6
weight
Noise output from a control
valve
37
CHAPTER 3
PIPELINE SYSTEM ANALYSIS AND DESIGN NETWORK ANALYSIS
The
flows
controlled points
through
by
and
steady-state
the the
a
system
of
interlinked
difference between residual
flow
pressure
pattern
will
pipes or
networks a r e
the pressure heads a t heads
at
the
be established
the
input
A
drawoff
points.
network
such that
in a
the f o l l o w i n g two c r i t e r i a a r e satisfied:-
(1)
The net
(2)
The
flow
towards
must equal outflow, net
j u n c t i o n or
node
i.e.,
i s zero,
inflow
and
loss
head
any
around
any
closed
loop
is
zero,
i.e.,
only
one head can e x i s t at any point a t any time. The
l i n e head losses a r e u s u a l l y
and
most
loss
relationships
h
methods
= K?Qn/Dm
of
analysis
for
where
pipes
h
is
are
are
the
the o n l y based
usually
loss,
head
significant
on
this
assumed
P
head Losses
assumption. to
be
i s the p i p e
of
the
length,
Head form €Ithe
flow and D the i n t e r n a l diameter of the pipe. The
calculations
are
simplified
if
the
friction
K
factor
can
be
assumed t h e same f o r a l l p i p e s i n the network.
E q u i v a l e n t Pipes f o r Pipes i n Series o r P a r a l l e l
It the in of
i s often
same series
or
to
loss
and
parallel.
know
the
e q u i v a l e n t p i p e which
flow
as
a
The
number
equivalent
pipe
of
would g i v e
interconnected pipes
may
be
used
in
place
the compound pipes to perform f u r t h e r flow c a l c u l a t i o n s .
The of
head
useful
equivalent
different
equating
diameter
diameters total
the
and
head
the e q u i v a l e n t p i p e of
of
a
compound
lengths
loss
for
length equal
in
any
p i p e composed of
series flow
to
may
be
sections
calculated
the head
loss
by
through
to the l e n g t h of compound pipe:-
z
K ( Z P ) Q ~ / D= ~ K~P Q " / D ~
..
De
=
(3.1)
38 ( m i s 5 i n the Darcy f o r m u l a a n d 4.85
Similarly,
in the Hazen-Williams f o r m u l a ) .
the e q u i v a l e n t diameter of a system of pipes i n p a r a l l e l
i s derived by equating the
total
flow through the equivalent
pipe ' e '
to the sum of the flows through the i n d i v i d u a l pipes ' i ' i n p a r a l l e l : Now h = h.
KP Q " / D ~ =~ K P ~ Q ~ ~ / D ~ ~ e
i.e.
Q.
So
=
and Q = So cance l i n g out Q , a n d b r i n g i n g D
and
P
e
to the
l e f t h a n d side,
P i s the same,
and i f each
De = [ C ( D i m / n ) ] n / m The
equivalent
loss c h a r t .
read
off
(3.2)
diameter
For pipes
the
flow
could
also
in parallel,
through
each
be d e r i v e d u s i n g a flow/head
assume a reasonable head loss and pipe
from
the
chart.
Read o f f
the
e q u i v a l e n t diameter which would g i v e the total flow a t the same head loss.
For p i p e s i n series,
assume a reasonable flow a n d c a l c u l a t e the
loss w i t h assistance of
the c h a r t .
total
head
pipe
diameter which would discharge
Read off
the equivalent
the assumed flow
with
the total
head loss across i t s length.
I t often speeds network analyses to s i m p l i f y p i p e networks as much as
possible
parallel. could this
using equivalent
Of
always is
in
course be
fact
the
used the
diameters
methods of to
for
network
a n a l y s e flows
minor
through
p r e f e r r e d method f o r
pipes
in
series or
a n a l y s i s described below compound
more complex
pipes and
systems
than
those discussed above.
Loop F l o w Correction Method
The both
loop
involve
method
and
successive
the node method of approximations
a n a l y s i n g p i p e networks
speeded
technique developed b y Hardy C r o s s (1936).
by
a
mathematical
39 The steps
i n ba ancing
the flows
i n a network b y the loop method
are: Draw all
the
pipe
inputs,
network
drawoffs,
schematically fixed
heads
to
a clear
and
booster
scale. pumps
Indicate (if
pres-
connect
pairs
ent). If
there
is
more
than
one
constant
head
node,
of constant head nodes or r e s e r v o i r s b y dummy pipes represented by
dashed
the
flow
lines.
Assume
corresponding
corrections,
omit
a
to
this
diameter
fixed
pipe
and
but
length
loss.
head
include
In
it
n
and
calculate
subsequent
flow
calculating
head
I osses. Imagine the network
To
speed
may
be
as a
convergence assumed
assuming
a
loops
are
as
to
series
pattern of
of
the
form
large
loops
of
needed
to
closed
solution
of
superimposed
side
ensure
loops
some
by
side.
that
each
i n any
the loops
Use
is
pipes
instead
only
pipe
order.
major
of
as
many
at
least
in
one loop. Starting
with
containing tracting flows
as
time,
many
and
on
assume
a
calculating
loops
other
a
pipe
pipe,
drawoffs
to
one a t
any
the
flows
if
flow.
to
other
unknown.
as
there
around
i n each
loops
Proceed
a s i m i l a r basis.
assumptions
Proceed
the flow
at
to
a
loop
pipe by
sub-
nodes.
Assume
n e i g h b o u r i n g loops
I t w i l l be necessary to make
are
loops.
The
more
accurate
each assumption the speedier w i l l be the solution. Calculate formula
the
such
head
loss
h =
as
( p r e f e r a b l e i f the a n a l y s i s Calculate around
the
the
arriving the
loop
ing
the
at
net
loop,
head
starting
i s not zero, following
pipe
or
in
use
a
any
loop
flow/head
using loss
a
chart
i s to be done b y h a n d ) .
loss
add head
the
each
in
Kk'Qn/Dm
around t h e
loop,
i.e.,
proceeding
losses and s u b t r a c t head g a i n s u n t i l point.
correct
increment
If
the
net
head
the flows
arol;nd
flow
the
in
in
the
same
loss
around
loop b y adddirection
that
head losses were c a l c u l a t e d :
(3.3) T h i s equation
i s the f i r s t
o r d e r approximation
to
the differen-
t i a l of the head loss equation and i s d e r i v e d as follows:-
40
h = KEQn/Dm
Since
dh
KtnQn-'dQ/Dm
=
(hn/Q)dQ
=
Now t h e t o t a l head loss around each loop should be zero,
i.e.,
c ( h + dh) = 0
x
C h +
(hn/Q)dQ = 0
The v a l u e of h/Q i s a l w a y s p o s i t i v e ( o r zero i f h a n d Q a r e z e r o ) .
(7)
I f there
is a
head from
booster pump
i n any
loop,
Ch before m a k i n g the flow
subtract
correction
the generated
u s i n g the above
equations.
(8)
The flow around each
(9)
Steps 5-8
(steps 5-71.
loop i n t u r n i s corrected thus
a r e repeated u n t i l the head arourld each
loop
balances
to a s a t i s f a c t o r y amount.
The Node Head Correction Method With loops,
the
node
initial
corrected b y flows
were
method,
heads
are
of
instead
assumed
at
assuming each
successive approximation
corrected
for
the
loop
initial
node.
flows
Heads a t
around
nodes a r e
i n a s i m i l a r manner to the way
The
method.
steps
in
an a n a l y s i s
a r e as follows:-
(1)
Draw all
(2)
the
pipe
inputs,
Assume at
network
drawoffs,
initial
that
arbitrary
node
assignments,
schematically
is
the
to
a clear
scale.
Indicate
f i x e d heads a n d booster pumps. heads at
fixed).
speedier
The
will
be
each node more the
(except i f the head
accurate
the
convergence of
initial
the
solu-
tion.
(3)
Calculate head
the
using
flow
the
in
each
formula
Q
pipe
=
to
any
(hDm/Kt)'/"
node or
with
using
a a
variable flow/head
loss c h a r t .
(4)
Calculate zero,
*"
the
net
inflow
to
the specific
node a n d
if
this
i s not
correct the head b y a d d i n g the am'ount
-Q
=
C(Q/nh)
(3.4)
41 T h i s equation i s d e r i v e d as follows:-
dQ = Qdh/nh
c ( Q + dQ)
We r e q u i r e
But
= 0
dH = -dh
so F l o w Q a n d head loss h a r e
considered
H i s the head a t the node.
node.
positive
if
towards
the
i n p u t s ( p o s i t i v e ) a n d drawoffs
( n e g a t i v e ) a t the node should be i n c l u d e d i n E Q .
(5)
Correct
(6)
the head a t
each variable-head
node in s i m i l a r manner,
repeat steps 3 a n d 4 f o r each node.
i.e.
Repeat
ends
of
degree of a
pipe
to 5 )
(steps 3
the procedure
sufficient
accuracy.
i s zero
at
until
a l l flows balance to a
I f the head difference between the any
stage,
omit
the
pipe
from
the
p a r t i c u l a r b a l a n c i n g operation.
A l t e r n a t i v e Methods of A n a l y s i s Both
the
loop
method
and
the
node method of
networks can
be done m a n u a l l y b u t
networks.
done
If
tables
or
space.
Fig.
even
manually,
on the pipework
3.1
a computer
calculations
b a l a n c i n g flows
i s preferred for
should
layout drawing
be if
set
there
out
in
large
well
in
i s sufficient
i s an example analysed m a n u a l l y b y the node method.
There a r e s t a n d a r d computer programs a v a i l a b l e f o r network a n a l y s i s , most of which use the loop method. The main advantage of the node method i s that more i t e r a t i o n s a r e required
than
especially
if
for
the
loop
the
system
method is
very
to
achieve
the same convergence,
unbalanced
to
start
with.
It
is
n o r m a l l y necessary f o r a l l pipes to h a v e the same o r d e r of head loss. There
are
include
a
number of
overcorrection
methods in
some
for
speeding
cases,
or
the convergence. using
a
second
These order
approximation to the d i f f e r e n t i a l s f o r ca I cu I at i n g correct ions. The node head correction
method
i s slow
to converge on account of
42 the fact
that
Also
time.
corrections
the
d i s s i p a t e through
head correction
equation
the network one p i p e a t a has
an
amplification
factor
( n ) a p p l i e d to the correction which causes overshoot.
3Oomm
60m h *26
!a
x
2OOOm
-
lQIh
1140 1 7
s/h 0.7
0,7 0.7 97
0 0
0.7
N
+
+5s 80 1.5 + 5 4 80 1.5 tS2.7 80 1,s 0 .1.7 *0,7
0
0
0
5,3 9
6
NOTES Heads i n metres, flows i n l i t r e s per second, diameters i n millimetres, lengths i n metres. Arrows i n d i c a t e p o s i t i v e d i r e c t i o n of h C Q ( a r b i t r a r y assumption). Blackened c i r c l e s i n d i c a t e nodes w i t h f i x e d heads, numbers in circles indicate order i n which nodes were corrected. Head losses evaluated from F i g . 2.3. H =
Fig.
3.1
1.85
Q in Q/ h
Example of node method of network flow a n a l y s i s
43 The
loop
flow
preparation. defined data
Flows must
indirectly
preparation
gence.
data
in
be
the
and
method
assembly.
has
assumed
assumed
Trial
disadvantage
loops,
flows.
in
data
and drawoffs
The
often offsets
relatively and
the
around pipe
interpretation
i s so because of
This
with
correction
are
added e f f o r t
in
the q u i c k e r conver-
low computing costs compared
error
design
is
also
cumbersome
if
loop flows h a v e to b e changed each time a new p i p e i s added.
Network A n a l y s i s b y L i n e a r Theory The ual in
Hardy
Cross methods of
methods of comparison
involve
the
solution
but
network
suffer
simul taneous
head
balance.
solution
and
very
few
iterations are required
with
the
number of
simul taneous
of
Simultaneous
iterations
head correction methods. of
drawbacks
in
w i t h computer o r i e n t a t e d numerical
flow
ber
a n a l y s i s a r e s u i t e d to man-
sets
of
the
effort required
methods.
The
equations
solution
has
the
latter
describing effect
that
to balance a network when compared
for
the
loop
flow
correction a n d node
O n the other h a n d solution of
equations,
even
if
rendered
a
l a r g e num-
linear,
requires
a l a r g e computer memory a n d many i t e r a t i o n s . Newton-Raphson linear
equations
problem
becomes
techniques
for
successive
a r e mathematically subordinate
to
approximation
sophisticated b u t
the
mathematics.
Charles (1972)
l i n e a r i z e d the head loss equation,
approximation
at
each
step
and
establishing
of
non-
the engineering Thus
Wood
and
i m p r o v i n g the l i n e a r equations
for
head
balance around loops. Isaac and M i l l s
(1980) s i m i l a r l y
l i n e a r i z e d the head loss equation
as follows f o r flow between nodes i and j :
8..
= C..+(H.-H.) IJ I J
//m
where
the
the
IJ
term
each i t e r a t i o n .
Substitute node :
in
square
(3.5)
root
sign
is
assumed
a
constant
for
If the Darcy f r i c t i o n equation is employed,
equation
3.5
into
the
equation
for
flow
balance
at
each
EQ..
= Q.
J
i IJ
Q.
where
i
is
J
node
to
the
drawoff
negative
j,
at
if
node j
from
and
i.
to
j
Q.. i s the flow from node iJ There i s one such equation
f o r each node. If has
each
a
be
set
of
solved
each
is
Q.. 'J
by
simultaneous
H
for
node
replaced
at
then
node.
i n 3.5,
l i n e a r i z e d expression
equations
each
initially,
the
(one for
The
new H ' s .
solve f o r
each
procedure
node)
is
to
one
which can
H
estimate
at
The procedure i s repeat-
ed u n t i l s a t i s f a c t o r y convergence i s obtained.
OPTIMIZATION O F PIPELINE
The in
pipe to
previous
pipe
network
fixed
be
to
demands
for
layout
a
and If
and
at
is
repeated
for
so d e r i v e d
the
various
at
of
would
be
This
another
would
flows
could
flows
trial
A
the to
layout.
Each
would
to
meet
would
be accep-
alternative
diameters
process of
have to b e costed a n d
calculated.
sufficient
layout
error
corresponding be
i t would be neces-
just
try
flows
particular
proposed layout
i s repeated u n t i l
and
the
any
pattern
were
necessary
possible
then
For
flow
possibilities.
corresponding
hand.
calculating
nodes
pressures were s a t i s f a c t o r y , it
for
loops.
to meet c e r t a i n drawoffs,
sizes a n d a n a l y s i s of
solution
closed
diameters,
number
if
methods
without
inputs
network a
not,
pipe
described or
and
or
new
compare
analysed
table.
with
drawoffs
To design sary
section
networks
SYSTEMS
the
that
a satisfactory would final
then
be
networks
network w i t h
least
cost selected. A out
technique recourse
positive with
closed
trial
techniques and
error,
possible
head
losses
can
number of be
described
used
least-cost would
for
be
general
i s that
and
optimization
There a r e a
discussed
the
T h e problem
loops. flows,
and
is
mathematical
ships. tion
to
determining
technique
diameters, tine
of
costs
network desirable.
directly, No
optimization
with-
direct of
and
networks
the r e l a t i o n s h i p between p i p e i s not
techniques
linear
require
and most rou-
linear
relation-
s i t u a t i o n s where mathematical optirnizato optimize
below.
The
l a y o u t s a n d these cases a r e
cases
are
normally
confined
to
45 single mains or is
known.
To
tree-like
networks
optimize
for
network
a
which
with
the
closed
flow
in each b r a n c h
loops,
random
search
t e c h n i q u e s o r s u c c e s s i v e a p p r o x i m a t i o n t e c h n i q u e s a r e needed. Mathematical analysis design
techniques
techniques
techniques
techniques
(which not
(again
mathematical
a
optimization
techniques
is
analysis
a
not
also
as
as as
will
be
steepest
systems they
operations
or
retained
are
research
descriptive).
( o r mathematical
such
known
nomenclature
really
techniques
include simulation technique
are
incorrect
techniques),
name
optimization
selection
an
The
name
here.
Such
modelling) coupled with
path
ascent
or
random
searching. The which
direct
optimization
is useful for optimizing
ation
programming,
and
methods
linear
Dantzig,
Linear
dynamic
programming,
a series of events o r things,
for
transport-
for a l l o c a t i n g s o u r c e s to d e m a n d s
is u s e f u l
programming,
1963).
computer,
which
include
inequalities
programming
(van
usually
der
Veen,1967
requires
the
use
and of
a
b u t there a r e standard optimization programs available.
D y n a m i c P r o g r a m m i n g f o r O p t i m i z i n g Compound P i p e s One o f can
the simplest optimization
normally
gramming.
be used without
the
an optimum
technique
mathematics.
The
diameters
a
length trunk
of
main
along
the
line.
a
trunk The
indeed one which i s dynamic pro-
may
be
used
pipe which
and
number main
problem
way of selecting
s e r i e s of e v e n t s a n d does n o t
pressures
supplying
of
the
on
techniques,
i n fact o n l y a systematic
a
technique
compound
depending
diameters
is
program from
and
recourse to computers,
of
may is
may
to
select
vary
consumers
t h e most economic
in diameter
For
flows.
instance,
from
a
select
along
its
consider
reservoir.
be reduced as drawoff
to
involve any
a
The
takes place
t h e most economic d i a m e t e r
f o r each section of p i p e . A
simple
example
and
the
should point.
head at the
demonstrates
3.2.
the p i p e l i n e in Fig.
the
each d r a w o f f p o i n t
hydraulic
The e l e v a t i o n s
pipe are indicated.
grade of
u s e of
the
technique.
Consider
Two c o n s u m e r s d r a w w a t e r f r o m t h e p i p e l i n e ,
line
i s n o t to d r o p b e l o w 5 m,
drop
below
neither
the p i p e p r o f i l e a t
any
each p o i n t a n d the l e n g t h s of each section of
T h e c o s t o f p i p e i s EO.l
p e r mm d i a m e t e r
per m of
46 pipe.
(In
pressure
this head,
variation). pipe
case
although
it
is is
The a n a l y s i s w i l l
(point A ) .
residual
cost
the
assumed simple
5 m,
take
to
account
arrangement w i l l
point A.
at
independent
The head,
will
we
only
the
such
a
consider
three
be w i t h minimum at p o i n t B may be
H,
a n y t h i n g between 13 m a n d 31 m above the datum, analysis,
of
of
be s t a r t e d at the downstream end of the
The most economic
head i.e.
be
to
b u t to s i m p l i f y the
possible
5
m
corresponding
to
heads
with
increments between them a t p o i n t s B a n d C.
Fig.
3.2
The
P r o f i l e of p i p e l i n e optimized b y dynamic programming
diameter
each o f
D
of
the
pipe
A
between
B,
and
the three allowed heads may be determined from a head loss
c h a r t such as F i g .
2.3
and
i s i n d i c a t e d i n Table 3.1
along w i t h
(1)
the corresponding cost. We
also
will
number
of
3 =
but
9,
regarded. possible
one
In
HC =
the
diameter
Now B,
19
then
this
cost
only
three
hydraulic these 3.1
is
the
possible
grade
lines
heads
between
at B
at
an
adverse g r a d i e n t
(I I) a
set
of
grade
required
The cost of to
of
Table
hydraulic
and
2.3).
consider
possible
line
between
hydraulic for
a
flow
figures
is
6 and
C.
gradient of
from
110 P / s x
must
the
be
added the cost of
(I)).
x
may be dis-
Thus to B
if
H
B
i s 0.006
310 rnm
(from
310 x 1 000
t h i s p i p e l i n e w o u l d be 0.1
i n t h i s case f60 000 (from Table 3.1
so
The
is 3
C
presented f o r each
C
is
point C.
and
=
=
13 and
Fig.
f31000.
p i p e between A a n d
For each possible head
47 TABLE 3.1
I
D y n a m i c p r o g r a m m i n g o p t i m i z a t i o n of
1 1: 1 1 I 23
.004
300 1 6 0 0 0 0
.0065
260
52000
.009
250
50000
111
19
1
-006
I
310
62000
- ._
L
24
29
.0035
.001
340
430
68000
8 3000 __I. 5 1000:'f
86000 79000 165000
I --i
a compound p i p e
48
HC
there
with
an
which
In
i s one
minimum
asterisk.
need
this
be
total
cost
In
example,
the
when
next
pipe
and
for
proceeding
section
the
least
260,
total
cost cost
340
and
tively.
It
which
case
may
section
as
sections;
with
are This
added
000
mm
for
to
one w i t h
proceed the
next
course many would
increased
each s e c t i o n .
The cost o f
booster
station
pump
i t s cost
by
B
to
each
last
and
level.
t h e c o s t s of
optimum
Thus
pipe
at C,
and
the minimum diameters
C and C
-
pipe.
corresponding
economic
standard
could
-
are
D respecin
diameters
b e selected
length could
for
each
be made up
l a r g e r s t a n d a r d diameter
a n d one
b u t w i t h t h e same t o t a l
head
p i p e c o u l d b e c o n s i d e r e d and t h e
considering
more
possible
heads
at
the p i p e s c o u l d be v a r i e d w i t h presssures.
could
be considered a t a n y
a n d c a p i t a l i z e d p o w e r cost
c o m p u t e r may
the
To
the
(I1 I).
of
result.
more s e c t i o n s o f
be
is
and
of
most
pipes
or
D
p o s s i b l e head
3.1
- B,
t h e n e x t smal l e r s t a n d a r d d i a m e t e r ,
Of
costs
the
keep
and
indicated.
s t a n d a r d diameter
the c a l c u l a t i o n s
loss a s the theoretical
accuracy
marked
section
the r e s e r v o i r
each
Table
A
next
gradients
the
and
Sections
desirable
nearest
C
D are
i s done f o r
S151
the
namely
-
selected from is
be
the
of
two
C.
to
C
to
between
D,
hydraulic
Section
section
up
total
310
the
costs f o r
this
arrangement
possible
(It I)
3.1
Table
a n d C,
I t i s t h i s cost a n d t h e c o r r e s p o n d i n g d i a m e t e r s o n l y
recalled
t h e r e i s o n l y one p o s s i b l e h e a d a t
diameters
p i p e between A
of
p r ove useful
if
many
should
point.
be added
in
A
i n w h i c h case the tables.
A
p o s s i b i l i t i e s a r e to b e c o n s i d e r e d ,
and there a r e s t a n d a r d dynamic programming programs a v a i lable. It the
will
b e seen t h a t
at
each step.
describe a p p l i c a t i o n s of
Transportation not
required
programming the
use
of
is a
computer.
technique The
such the
a
resource
least-cost along
system each
is
route
which
technique
of
delivering
t h e least-cost
(1969)
a l l o c a t i o n of resources
another
a l l o c a t i n g t h e y i e l d o f a n u m b e r of that
reduces
t h e t e c h n i q u e to s i m i l a r a n d o t h e r p r o b l e m s .
p r i m a r i l y for consumers
programming
(1969) a n d B u r a s a n d Schweig
Kaliy
T r a n s p o r t a t i o n programming f o r least-cost
does
dynamic
p o s s i b i l i t i e s to be c o n s i d e r e d b y s e l e c t i n g
n u m b e r of
arrangement
t h e t e c h n i q u e of
sources
achieved. should
normally is
to
a
The be
of
use
number cost
of
linearly
49 proportional the
to
technique
the is
throughput
probably
of
along no
that
use
in
route
and
selecting
I t i s of use, however, i n selecting a least-cost
sizes.
through head
an
is
existing
small
in
pipe
distribution
comparison
with
system,
static
for
the
t h i s reason
optimum
pumping p a t t e r n
provided
head,
or
pipe
for
the
friction
obtaining
a
p l a n n i n g g u i d e before demands a r e accurately known.
CONSUMER REQUIREMENT
M
N
10 L l S
15 L I S
SOURCE
Fi9.
An
3.3
YIELD
12 L I S
Least-cost example
a l l o c a t i o n p a t t e r n f o r t r a n s p o r t a t i o n programming
example serves
to
a r e two sources o f
i l l u s t r a t e the
water,
and €3 could d e l i v e r
A and B,
1 2 a n d 20 e / s
10 a n d 15 4 / s respectively. of
pumping along
technique.
I n t h i s example,
a n d two consumers,
and N.
i s a s u r p l u s of water.
routes A - M, A - N,
I3
-
M
A
a n d M and N r e q u i r e
respectively
thus t h e r e
M
there
The cost
and B - N a r e 5,
7, 6
a n d 9 p/1 000 l i t r e s respectively. The
data
(I).
Each
unit
cost
corner
of
are
row of
the
set
out
represents
delivery
in a
along
corresponding
tabular source
form
and
each
route
block
in
for
each
solution column
a
i s indicated i n
the table.
in
Tabel
demand. the
The f i r s t
3.2 The
top
right
step
i s to
50 make
an
that
each
block
arbitrary yield
of
the
satisfies bottom
the f i r s t first
the
d e m a n d of
is
i s 2,
maximum
column
i s completed,
of
M
Starting
possible the
and
resources
the top
allocation is
left
10.
is
written
This in
P r o c e e d i n g to t h e n e x t c o l u m n ,
the
since
in the
the maximum possible a l l o c a t i o n
which satisfies the y i e l d of
So t h e n e x t b l o c k
r o w A.
Proceed
through the
the maximum possible assignment a t each stage u n t i l a l l
a r e allocated
allocation
with
amount
t o b e c o n s i d e r e d i s i n r o w 0 , n a m e l y c o l u m n N. table making
in such a manner
resources
satisfied.
c o r n e r o f b l o c k AM.
column
row
assignment
demand
table,
the
left
initial
and
the
is
13
i f to
(even in
the
the slack
second
row,
column).
then
t,he
Thus
7
the next the
in
third
column.
mi
T r a n s p o r t a t i o n p r o g r a m m i n g o p t i m i z a t i o n o f an a l l o c a i o n
TABLE 3.2
( 1 )
CONSUMER : M
SOURCE Y I E L D
REQUIREMENT 5 :
12
A
10
N
SURPLUS
EVALUAT ON
15
7
NUMBER : 0
2
---J
20
B
7 13
5
EVALUATION NUMBER:
-2
7
( 1 1 ) 0 A
12
B
20
~~
2 10
7
7
-2
the
figures
4 Once
initial
an
methodically would
be
until
the
allocation a
most
least-cost
is
made
d i s t r i b u t i o n emerges.
p r o f i t a b l e arrangement,
assign
a
are
re-arranged
To d e c i d e w h i c h relative evalua-
t i o n n u m b e r t o e a c h r o w and c o l u m n a s f o l l o w s : Assign numbers
the
such
evaluation
value that
number
0
to
row
t h e sum o f is
equal
to
1
and
work
out
the
the row evaluation the
cost
coefficient
other
evaluation
number a n d column for
any
occupied
51 block.
2,
The v a l u e f o r
and
numbers sum
on.
so
if
beneath bigger
is 5,
column M
Now
write
the cost coefficient
than
the cost
sum
and
BM.
The
determined b y
BN,
the
added
allocation
BM,
it
If
this
would p a y to
T h i s i s not easy to see
The
would b e to
amount
which
biggest
and
introduce
can
be
i n fact
an amount
put
in
block
in into
BM
is
( I ) ) . Now f o r each u n i t which i s
i n Table 3.2
AN
is
BM
T h e biggest possible
a closed loop u s i n g occupied blocks as corners
would
and
requirements
to
coefficient.
one u n i t
block
to
and
cost
maximum drawing
to block
yields
the block,
i n t o t h e block.
improvement
(see the dotted c i r c u i t added
of
unoccupied block
i s i n d i c a t e d b y the biggest difference between the
case the o n l y ,
Block
each
f o r row B i s
stems from the method of determining each e v a l u a t i o n
improvement
evaluation our
of
N i s 7,
and column e v a l u a t i o n
the cost coefficients of occupied blocks.
sum from r a t e of
but
column
the row
coefficient
introduce a resource a l l o c a t i o n immediately,
for
sum of
the
subtracted
consistent.
10,
maximum r e - d i s t r i b u t i o n
have to be subtracted
since
this
AM
block
this
would
10 i s made,
i.e.
from
In
case
from block to
keep
the
evacuate
AM.
block
and the amount
the
maximum The
i n the block
a t each corner of the closed loop adjusted by 10 to s a t i s f y y i e l d s a n d requirements.
Only one r e - d i s t r i b u t i o n
of
resources should
be done at
a time. After making number to
and
the
until the
most
fact
is
that in
best
new
sums
no
distribution
in
in
and
further
there
any
allocation, as
p r o f i t a b l e block
there
ficient
the
evaluation
repeat
possible
two
In
our
steps,
more
the e v a l u a t i o n
Allocate
improvement,
sum g r e a t e r
example
but
(11).
the r e - d i s t r i b u t i o n
cost
i s no e v a l u a t i o n
block.
re-calculate
Table 3.2
we
than
arrived
compl icated
resource procedure
indicated the cost
at
the
patterns
by
coef-
optimum involving
more sources and consumers may need many more attempts. The example can o n l y serve to introduce the subject of t r a n s p o r t a tion
programming.
with
in
niques
textbooks such
as
There on
the
subject
der
Veen
serves
in
happened
table
as
an to
blocks could
be allocated
Computat ions
then
at the end.
many
Van
example o n l y the
are
of
other
a
proceed as
and
evacuated
very
which
are
dealt
mathematical optimization
(1967)
introduction. be
conditions
small
before and
Dantzig
For
(1963)
instance,
if
simultaneously,
quantity
two one
denoted by
the q u a n t i t y
'e'
techn-
and
this
blocks of
'e'
the say.
disregarded
52 L i n e a r Programming f o r Design of Least-Cost Open Networks
i s one of
L i n e a r programming niques.
The
systems,
use
of
although
a
the
computer simple
The technique may o n l y is
linear,
cannot
so
be
closed
loops to
design
each
branch
loss,
diameter
used
in the
to
resort
known.
render
the
of
p i p e of
different
or
Since
cost
are
system
pre-selected
given
design
pipe
relationships the
is
tech-
complex
by
hand.
programming
networks
For each
where
with
can
be
the flow
in
It
between
following
flow,
head
technique
the
treated as the v a r i a b l e .
length of
will
indicate
that
some
thereby
i n effect e l i m i n a t i n g them.
can
treated
be
pressure
at
in
the
certain
I inear
inequality
certain
range.
points
of
The
analysis. in
diameter
pipes
The head losses
h a v e zero
Any other type of I t may
length o f
lengths,
linear constraint
above a f i x e d
the greater-than-or-equal-to-type)
total
The
be r e q u i r e d to m a i n t a i n
the network
p i p e of
a
each
and costs a r e l i n e a r l y p r o p o r t i o n a l to the respective p i p e lengths. program
is
b r a n c h o r main p i p e ,
diameters a r e allowed and
diameter
for
done
Linear
of
networks
non-l inear,
linear:
is
approximations.
tree-like the
essential here
application.
successive
to
mains
normally
optimization
the r e l a t i o n s h i p between v a r i a b l e s
restricted
and
number
if
optimizing
trunk
is
be used
is
without
used
is
example
for
it
used
the most powerful
minimum
or
within
the (a a
a c e r t a i n diameter may be
r e s t r i c t e d because there i s i n s u f f i c i e n t p i p e a v a i l a b l e .
DIAMETER m m UNKNOWN L E N t T H m OPTIMUM L E N G T H m HEAD LOSS m
Fig.
3.4
Least-cost
250
200
2 OD
150
X,
x3
50
x2 I50
XL L 00
012
3.2
t r u n k main b y
The example concerns
a
trunk
0 0
1 - 6 6 TOTAL 5 . 0
l i n e a r programming
main w i t h
two
drawoff
points
(Fig.
53 3.4). and
The p e r m i s s i b l e diameters of of
the
second
v a r i a b I es , X,, ferent
X2,
diameters.
comparison but
loss,
linear
200
and
and X4
This
the
of
leg,
X3
simple
costs
of
the f i r s t 150
leg a r e 250 a n d 200 mm,
alternatives
is
used
here
are
lengths of
example could
all
programming
There
mm.
which are the
thus
be optimized b y giving to
four
pipe of
the
manual
correct
demonstrate
dif-
the
head tech-
nique. losses per 100 m of p i p e a n d costs p e r m for the v a r i o u s
The head
pipes a r e i n d i c a t e d below:-
Head loss @ 40 e / ’ s m/1OO m
D iameter mm
250 200 150 linear
below
5
(I).
Table 3.3
0.1 0.42
constraints
and
the
on
the
coefficients
system
are
the
of
4 3 expressed
equations
x1
Objective Function: The computations
a, at
b
x4
= 4
+ 0.71X2 + 0.1X3 + 0.42X4 5x1 + 4x2 + 4x3 + 3xq
= 5
proceed
i s necessary to
and
very
to
satisfy c
in
the
Table
by
introduce
setting
indicate
the by
u n i t o f X, To
amount
of
introducing
real
slack
i n the program b y
to zero,
variables variables
into
each
The slack
v a r i a b l e s a r e designated
and
cost
(I),
particular the one
To
whether
it
is
are
set
the slack
4 and 5 respective-
(I)),
l i n e of
of
coefficients
i n i t i a t e the solution,
the values 5,
program unit
their
the
variable the
worthwhile
any other v a r i a b l e ,
main body of the t a b l e which
column
would displace 1 u n i t of a and 0.25
determine
= m i n i mum
equality.
l y (see the t h i r d column of Table 3.3
placed
+
3.3
b a n d c a r e assigned
The numbers i n any
all
artificial
h i g h values designated m.
variables a,
in
5
X2
+
x3
equation
equation
tabulated
0.25X1
Head L o s s :
it
are
in
Lengths a r e expressed i n h u n d r e d metres.
Lengths
so
cost i~100/100 m
m/1OO m
0.25 0.71
The form
@ 14 e/s
would
variable.
be Thus
disone
u n i t s of c. replacing
any
variable
a number known as the oppor-
54 T A B L E 3.3
P-qg.
L i n e a r P r o g r a m m i n g S o l u t i o n of P i p e P r o b l e m s
co>t
V c r able _ C o e_ ff.
Avo unt _ _
a
m
5
b
m
4
C
m
5
OPPORTUNI T Y
:l
x2 4
x3 4
x4 3
0.25
0.71
0.10
0.42
2
x3 4
x4 3
a
b
c
Red.
m
m
m
s
1
5/.71
5
b
m
4
C
m
1.45
i
x1
a
5
4
1
1
I l l
x2 b
4
5
2
m
0.55
x4
3
3.45
5
4
1
1
1
0.1
0.42-
x3 4
I
l 4
1 1 .71m-4
0
0
a
b
c
m
m
m
x4 3
j
1
0 3.28-0.76m
1.69 1
-1.69
0
1.1-0.69m
0.5"
-2.38 2.38 3.38-8.2
IV
x4
4
4.5
5
0.5
3
-0.69
0
2.16
1.52
0.69
1
4
0
1
1
0.31
0
( N o f u r t h e r improvement posc iD l e 1
-2.16 I
m-
3.45'
5
1
0.24
-1.1
b
-0.71
0.76
1.I
11-1.lm
1
4 - 1 . l m 3-1.42m
0
x1
a
1
-0.46 lt0.46
x2 x1
,
dALUE:
4
x2
!-
rn-
m-
55 tunity
number
i s calculated
introduced,
then
-
x
m
)
(0.25
the
cost
m)),
the
opportunity
value
entries
that
of
the
total
program
thus
for
from
column.
each
column
by
in
the
the
the
(5 -
column
coefficient
coefficients
subtracting
the column
introduce would be X2, unit
X2
The is
column
that
is
which
may
per
the
lowest
since i t shows
( o r negative o p p o r t u n i t y
designated
the
key
opportunity
The
column. value
the
variable.
value).
key
column
( i n the cost
mini-
Only one v a r i a b l e may be introduced a t a time.
determine
which
now
shows
mization case). To
reduction
i.e.
multiplying
the
cost
(0 x
value,
by
and
of
1
-
m)
cost
The most p r o f i t a b l e v a r i a b l e t o greatest
x
calculated
corresponding
second
cost
(1
the o p p o r t u n i t y
is
X
I f one u n i t of
increase b y
i s designated
column
variable
formed
each
would
which
the
in
for
be
the
maximum
introduced,
amount
calculate
the
of
the
key
column
replacement
ratios
variable for
each
row as follows:Divide
the
corresponding ment be
ratio
is
amount number
lowest
the
number
selected
positive at
the
program
variable
i n the key column.
introduced without
the
the
of
as
that
is
the
v i o l a t i n g any
replacement
ratio of
each
maximum amount
is
the
designated
key
row
by
the
lowest p o s i t i v e replace-
the constraints.
of
intersection
The
for
column
which
could
The row
the key and key
with
row a n d the
row,
key number. After
introducing
( T a b l e 3.3
(11))
so
a
new
variable,
that
the
replacement
program v a r i a b l e and by
the
new
the
and
its
cost
ratios
is
remain
rearranged correct.
The
in the key row a r e replaced
i t s cost coefficient
variable
matrix
coefficient.
The
amount
column
as well as the body of t h e t a b l e a r e r e v i s e d as follows:Each number i n the key row i s d i v i d e d b y the key number. From each
number
number
i n the key
in
key
the
The ratios
procedure and
negative all
a
non-key
row,
row m u l t i p l i e d b y
column
g i v e n as T a b l e 3.3
in
divided
by
the
the
key
subtract
the
corresponding
r a t i o of the o l d row number number.
new
The
tableau
is
(11).
of
revising
opportunity
studying the
table
value.
positive opportunity
opportunity is
In
values
repeated the
so
values until
example
the
there
Table
least-cost
and is
3.3
solution
replacement no
further
(IV)
i s at
shows hand
56 (indicated
by
the
current
program v a r i a b l e s
and
t h e i r corresponding
values). The ming
reader
(e.9.
cription
should
Van
of
der
the
r e f e r to a s t a n d a r d textbook on
(1967) a n d D a n t z i g
Veen,
technique.
There
are
l i n e a r program-
(1963)) f o r
many
other
a
cases
full
des-
which
can
type
and
be mentioned below:the
If
constraints
not
just
are
introduced
are
equations,
equations.
into
The
the 5 (less-than-or-equal-to)
of
slack the
variables
1.h.s.
artificial
of
slack
with
each
zero
cost
constraint
variables
with
coefficients
to make
high
them
cost
coef-
f i c i e n t s a r e then omitted.
If
the
constraints
of
are
introduce
artificial
slack
into
the
1.h.s.
the
with
zero
of
cost
the 2
(greater-than-or-equal-to)
variables
constraint
coefficients
from
high
with
and
cost
subtract
each
slack
inequality
type,
coefficients variables
to
make
them
equations. If
the
objective
value
with
function
function
the to
is
highest be
is
to
be
negative
maximized,
minimized,
value
the
is
the
opportunity
selected,
opportunity
if
the
with
the
but
value
h i g h e s t p o s i t i v e v a l u e i s selected. The
opportunity
ponding
variables
one u n i t of If
two
the when very
the
that
i.e.
amount the
of
represent they
shadow
indicate
the
values
of
the
corres-
value
of
introducing
row
i s selected,
v a r i a b l e i n t o the program.
replacement
ratios
program
matrix
is
a r e equal,
variable
in
rearranged.
whichever the
other
Merely
row
will
assume
it
to
first
the
be
zero
have
a
s m a l l v a l u e a n d proceed as before.
example then
values
of
pipe
programming
two
stage
diameters
and
search
optimization, is
given
methods
in are
namely
Stephenson also
Lam (1973) described a g r a d i e n t o p t i m i z a t i o n
(1964).
discussed. method.
layout
and
Non-linear
For
instance
57 REFERENCES Buras, N. and S c h w e i g , Z., 1969. A q u e d u c t r o u t e o p t i m i z a t i o n b y d y n a m i c p r o g r a m m i n g . Proc. Am. SOC. C i v i l E n g r s . 95 ( H Y 5 ) . Cross, H., 1936. A n a l y s i s o f f l o w i n n e t w o r k s of c o n d u i t s o r c o n d u c t o r s . U n i v e r s i t y of I I I i n o i s B u l l e t in 286. D a n t z i g , G.B., 1963. L i n e a r P r o g r a m m i n g and E x t e n s i o n s , P r i n c e t o n U n i v e r s i t y Press, Princeton. Isaacs, L.T. a n d M i l l s , K.G., 1980. L i n e a r t h e o r y m e t h o d s f o r p i p e n e t w o r k s a n a l y s i s . P r o c . Am. SOC. C i v i l E n g r s . 106 ( H Y 7 ) . Kal l y , E., 1969. P i p e l i n e p l a n n i n g b y d y n a m i c computer programm i n g . J . Am. W a t e r W o r k s Assn., (3). Lam, C.F., 1973. D i s c r e t e g r a d i e n t o p t i m i z a t i o n of w a t e r systems. P r o c . Am. SOC. C i v i l E n g r s . , 99 ( H Y 6 ) . S t e p h e n s o n , D., 1984. P i p e f l o w A n a l y s i s , E l s e v i e r , 204 pp. V a n d e r Veen, B., 1967. I n t r o d u c t i o n t o t h e T h e o r y of O p e r a t i o n a l R e s e a r c h . C l e a v e r Hurne, L o n d o n . Wood, D.J. and C h a r l e s , O.A., 1972. N e t w o r k a n a l y s i s u s i n g l i n e a r t h e o r y . ? r o c . A X E , 98 (HY7) p 1157 - 1170.
L I S T O F SYMBOLS
C
-
cost
D
-
diameter
h
-
head loss
H
-
head
K
-
const a n t
e
-
Iengt h
Q
-
flow
58
CHAPTER 4
AND SURGE
WATER HAMMER
R I G I D WATER COLUMN SURGE THEORY
Transient are
often
pressures
the
cause
caused
by
bursts.
of
a
change of
The
r a t e in conduits
flow
pressure fluctuations
associated
w i t h s u d d e n f l o w s t o p p a g e c a n b e s e v e r a l h u n d r e d metres head. Transients
in
gories:
Slow
surge,
whereas
of
the
or
fluid
small
closed
motion
rapid
and
conduits are normally
mass
in
change
conduit
changes
is
flow
in
of
oscillation flow
referred
rate
or
the
classed
into
two cate-
fluid
is
referred
accompanied
by
elastic
to
as w a t e r
pressure
hammer.
the
two
to
a
strain
For
slow
theories
yield
t h e same r e s u l ts. It
i s normally
(whenever
the
r i g i d column pressible the
easier
theory
theory
mass.
column
relating
A
umq
in
the
an
head
system b y
applicable)
than
difference
instantaneous
conduit
i s d e r i v e d from Newton's b a s i c
to
r i g i d column elastic
applied
the
theory
theory.
With
i s t r e a t e d a s a n incomacross
acceleration.
d i f f e r e n c e between
bore
by
in the c o n d u i t
pressure
uniform
a
is
the w a t e r
produces
tion
to a n a l y s e a
t h e e n d s of rate
the
The
the
in
of
equa-
water
change
of
ends
basic
col-
velocity
a n d is
l a w o f motion,
(4.1 where
is
h
conduit
tion and t The with
a
may
the
is
head
in
flow
useful
deceleration
the
or
is
between
velocity,
g
ends,
L i s the
gravitational
accelera-
the is
two
i s time.
water
starting
hydro-electric
tion
difference v
equation
slow
lating trip
the
length,
be
graphical ly.
of
level up
in
for
a
in
column.
in
variations a
pumping
installation
solved
calculating
water
steps
The f o l l o w i n g
of s o l u t i o n o f t h e e q u a t i o n : -
fed
by
of
At
the
a
surge
line,
or
a
head
I t may
shaft power
pressure
associated
in
calcu-
following load
pipeline.
b y computer,
e x a m p l e demonstrates
rise
be used f o r
power
changes The
tabular
the numerical
in
equa-
form o r method
59 Example
A
100 m l o n g penstock w i t h a c r o s s s e c t i o n a l a r e a ,
is protected against bine,
with
a
water
cross
unrestricted orifice. and
there
Calculate
is
a
the
hammer b y
sectional The
sudden
rise
load water
of
2
and
m2
an
i n t h e c o n d u i t i s 1 m/s
velocity
in
o f 1 m2
surge s h a f t a t the tur-
A2,
area,
initial complete
maximum
a
A,,
rejection
at
level
the
in
the t u r b i n e . surge
shaft
neglecting friction. Take -0.098h.
At
=
1 sec.
Then from Equ.
By c o n t i n u i t y ,
0.1 1-2 2-3 3-4 4-5 5-6 6-7
h
0.5 0.476 0.428 0.359 0.272 0.172 0.064
or
method
Av
Another water
column
the
and
of
a
cause
be the
Following
pumping
line,
vaporization
column
r i g i d column
may
stop
water
4.16,
o f 2.26
m.
taking
The a c c u r a c y o f t h e
smaller
time
intervals A h
include
a p p l i c a t i o n of t h e r i g i d w a t e r column e q u a t i o n i s w i t h
water
distance
pumps the
to
the
4.1
0.951 0.855 0.717 0.544 0.345 0.129 0.094
The method c a n r e a d i i y b e e x t e n d e d to
separation.
end
sufficiently
slowly
V
a n d i s calculator-orientated.
useful
upstream
cases
= 0.5~.
w h i c h may b e compared w i t h t h e a n a l y -
c o u l d be i m p r o v e d b y
respectively.
h e a d losses,
Equ.
m,
100 =
t h e mean v a n d h o v e r t h e t i m e i n t e r v a l s to c a l c u l a t e
taking
and
= -9.8h/
-0.049 -0.096 -0.138 -0.173 -0.199 -0.216 -0.223
s o l u t i o n o b t a i n e d from Equ.
numerical
= -ghAt/L
A v = -0.098h
0.5 0.976 1.404 1.763 2.035 2.207 2.271"
The maximum r i s e i s 2.27 tical
Av
A h = A1vAt/A2 = l v / 2
Ah = 0 . 5 ~
t
4.1,
beyond theory
water
column
column o f
i n i t i a l flow velocity.
the
stopping
of
the
pressure
frequently
peaks
along
vapour
the
with
will
length t w i l l
of
the
pump
time
before the 0
the
In
such
decelerate analysis.
to d e t e r m i n e
stopping.
vapour
be Q = A t v * / 2 9 h
t
at
drops
line. will
accurate for
r e s p e c t to
travel
volume
a
pocket
is s u f f i c i e n t l y
integrated twice
instantaneously
at
the
If
the
pocket
behind
where v
i s the
0
60 MECHAN I CS O F WATER HAMMER Water
hammer
occurs,
as
would
indicate an
name
implies,
(or accelerated).
water i s r a p i d l y decelerated theory
the
infinitely
The
a
column
r i g i d water
l a r g e head r i s e
p i p e l i n e c a r r y i n g l i q u i d were slammed s h u t however,
when
if
a
a c e r t a i n amount o f r e l i e f u n d e r these c o n d i t i o n s ,
e l a s t i c i t y of the f l u i d a n d of
the p i p e
d i s c h a r g e end of
is
a
pipeline
will
pack
against
the
will
rise
sufficiently
gate, to
The amount o f
the
water
of
the
causing
stop
momentum l a w . amount
shut
the
itself.
a
fluid
in
rise.
stopped p e r u n i t
to
the
required
replace
There
a is,
due
to
the
at
the
of
the
The
accordance
water
in
valve
upstream
pressure
liquid
if a
Thus
column
valve
instantaneously.
of
gate
pressure with
the
time depends o n
volume
by
created
the
compression of w a t e r a n d e x p a n s i o n o f t h e p i p e . I t can thus
be shown
that
the r e d u c t i o n in v e l o c i t y
Ah,
front
the
relationship
between
the
head r i s e
a n d the r a t e of p r o g r e s s of
A V
the
i s A h = -CAV/g
(4.2a)
where c i s t h e w a v e c e l e r i t y a n d g i s g r a v i t a t i o n a l
acceleration.
equation
It
is
often
wave
referred
to a s J o u k o w s k y ’ s
law.
can
This
further
be
p r o v e d from a mass b a l a n c e t h a t
c
=
1/ If
y,)
3 .iw
kd EY the p i p e h a s a
(4.3a) rigid
and r i g i d side f i l l
( e l a s t i c m o d u l u s E2 a n d
lining
( m o d u l u s Es)
thickness
t h e e q u a t i o n to use i s
(4.3b)
where w
i s the u n i t
p i p e diameter, k
a
factor
about 0.9).
w e i g h t of
or
a s ZOO
which
depends
on
the
y the p i p e w a l l
end
fixity
when
for
free a i r
thin wall i s present
of
for
steel p i p e s .
the
a
d
pipe
51,
the
(normally
r i g i d walled
I n t h e case o f
(see C h a p t e r
is
thickness a n d
c may
tunnel plastic
be a s
low
m/s.
The earlier,
pressure thus
illustrated reservoir the
i s i t s b u l k modulus,
K
c may b e a s h i g h a s 1370 m/s
o r as low a s 850 m/s
pipe,
liquid,
E i s i t s e l a s t i c modulus,
in
end,
reservoir,
wave
travels Fig. the so
caused
upstream, 4.1(1).
pressure that
the
by
valve
closure
superimposed on
When in
the
the
wave
the
front
the
pipe
forces
velocity
now
reverses
b a c k to s t a t i c ( r e s e r v o i r ) p r e s s u r e a g a i n .
referred
static
reaches
water and
head, the
backwards
to as
open into
pressure drops
61 PRE5WRE NAVE
4.1
Fig.
A
negative
That in
wave
the
The
entire
sucks
up
the
water
+v
and
(2)
wave
front
negative
back
to
Water hammer wave at d i f f e r e n t stages
will
in
thus
is
pipeline
-v
wave
of
head
pipe
to
the
into the
the head
w i l l repeat i t s e l f
travels
t u r n reach
pipe,
downstream from
the closed end.
where
0
v
amplitude
reservoir.
so
reverts
that to
was
0
Cv,/g Upon
the
static
the
below
velocity
the velocity
original
reaching
head.
the r e s e r v o i r .
Now
velocity.
static, the
travels
reservoir
in the p i p e r e v e r t s
The sequence of
i n d e f i n i t e l y unless damped b y f r i c t i o n .
---+---1
Hz g
‘with
0
no
friction
2 L/c
I
Fig. 4.2
Head f l u c t u a t i o n s at v a l v e end.
3 L/c
it
4L7c
I
t
waves
62 The 4.2.
variation
In
the
case
in
head
of
pumping
conditions
i s normally
stream
the
of
reduction charge wave
in
pump
(Fig.
returns
the v a l v e lines,
associated is
pressure.
end
at
The
4.3),
towards
be as
decelerated,
the
pumps.
wave
trip.
change
resulting
in
a
towards
reverses
pressure
i n flow
The water
travels
velocity
The
indicated i n Fig.
most violent
a pump
negative
where
the
the
with
suddenly
will
at
and
the
downsudden
the
a
dis-
positive
pump
alter-
nates from a pressure drop to a pressure r i s e .
Wave front
snit i d l y
Vapour pressure Initial V
F i g . 4.3
The tion,
Water hammer head drop a f t e r pump t r i p
wave
via
in
stages
in
air
valves
be
seen it
water
line friction, flow
will
Fig. up
behind
4.4
which
wave
are
Thus
and
air
in
cross
if
there
will
be
is
f r i c t i o n can
illustrates
wave
a
a rapidly
not
quite
shut
at
seca
drawn
The effect of
the p i p e l i n e from the
changes
variation. vaporize
and from solution.
travels
heads
by
gradual
the
from
most
different
valve.
horizontal,
due
The to
' p a c k i n g ' effect causing some flow across the wave f r o n t . The
effect of
one
equation.
tion
changes i n section The
2Ah'A./c. I
= A1/c,
2
wave
or b r a n c h pipes can be
head change
Ah'
i s r e l a t e d to the o r i g i n a l head change Ah'
Ah'
I
or
pressure,
as
pressure the
i s complicated
vaporization,
negative
readily
= Vo
Ah
/(1
+
after
r e a c h i n g a junc-
by the equation
I
A 2'=2
+
A3/C3 +
+ A 2 / A 1 + A3/A1
+
included
i4.4a)
...
.. .
where A . i s the cross sectional area of p i p e i and c
(4.4b) 1
. c2
c3-
63
~
1
3 "Distance from valve" 2
Xz- F 'x
cvo 9
F i g . 4.4
Head a t p o i n t s a l o n g along p i p e l i n e w i t h f r i c t i o n , instantaneous stoppage
When a
valve
i n a g r a v i t y main i s closed g r a d u a l l y ,
analogous to a series of system
could
form
of
be
analysed
analysis
simultaneous
to
the
is
solution
hammer equation. lar
minute waves emanating
of
the
In fact
so-called
numerical ly
useful
for
or
graphically.
the sines
discharge
the effect i s
from the v a l v e .
demonstrating
valve
for
The
The g r a p h i c a l
the
principles
equation
and
of
the water
d r a w n on a g r a p h a r e v e r y simi-
characteristic
lines
adopted
in
numerical
a
pipeline
solu-
t ions.
4.5
Fig. valve at to
4
illustrates
a
L/c
and
degrees of
the
valve
analysis
The v a l v e
discharge
compute
closure
one
a n d S.
Thus
the
applies
head the
of
i s closed over
characteristics
closure a r e p l o t t e d on the g r a p h .
head loss to p i p e velocity
To
graphical
the discharge end.
for
with
a
a p e r i o d equal four
different
The l i n e r e l a t i n g f r i c t i o n
i s also indicated. at water
the
valve
hammer
at
time
equation
L/c 4.2
after
initiating
between p o i n t s R
64 Av - A h
-(c/g)
A h
where
i s t h e d i f f e r e n c e i n f r c t i o n h e a d b e t w e e n R a n d S.
Ahf
Computations
at
+
+ (c/g) Av
the
Similarly
t h e w a t e r hammer e q u a t i o n f r o m S t o R ,
applying A h
(4.2b)
f
waves point
thus
hf
(4.2~)
proceed a l o n g
peak a n d
S occurs
then
at
t
l i n e s of
die out
4
=
L/c
slope
+
or
d u e to f r i c t i o n . and
is
- c/g.
Ultimately
The m a x i m u m h e a d
182 m e t r e s a c c o r d i n g
to t h e
4.5.
computations on F i g .
ELAST I C WATER HAMMER THEORY
The
fundamental
velocity
a
in
differential
conduit
may
wave
equations
b e d e r i v e d from
relating
pressure
consideration of
l a w o f m o t i o n a n d t h e c o n s e r v a t i o n of mass r e s p e c t i v e l y ,
to
Newton's
and are:
(4.5) ah + -c 2 - =a vo at
ax
g
The
last
t o obey tion
term
of
a
strictly
steady-state
correct.
are higher normal
Tests
accounts for
with
friction
which
a constant f r i c t i o n factor.
friction indicate
factor that
for
head
transient
i s assumed The assump-
conditions
i s not
losses d u r i n g t r a n s i e n t
flow
t h a n those p r e d i c t e d u s i n g t h e f r i c t i o n f a c t o r a p p l i c a b l e to
flow
reversals
4.5
in Equ.
Darcy's equation
conditions.
Energy
when t h e v e l o c i t y
is
probably
absorbed
during
flow
i s low and t h e f r i c t i o n f a c t o r c o n s e q u e n t l y
relatively high.
Methods of A n a l y s i s
A
common
pressures a chart for zero
no
method
used for
over
analysis
of
pipe
(Lupton,
systems
1953).
for
water
hammer
4.6
i s such
Fig.
the maximum a n d minimum heads a t the downstream v a l v e
line friction.
constant.
of
to be g r a p h i c a l l y
time
T
The v a l v e and
the
To u s e t h e c h a r t
area
valve
i s assumed discharge
to r e d u c e
coefficient
linearly is
to
assumed
c a l c u l a t e t h e v a l v e c l o s u r e p a r a m e t e r cT/L
65
H ( m 1 20c
6'
- 200
::m 55
R 5
S'cVALVE
SHUT
_/--
-. /---
R 2
RI
55 23
t'
51
t d t = L/c
_/-_ / - -
R, -R
F i g . 4.5
Graphical
x -t
CHART
water hammer a n a l y s i s f o r
closure with f r i c t i o n
S
' 0
slow valve
66 and
valve
axis
head
parameter
loss
the maximum
head parameter -h/(cvo/g) answers
are
the
below s t a t i c
of
lines).
Multiply
head.
Note t h a t
the c h a r t
is for
sluice
water
and
hammer
butterfly
valves
the e n d of heads
T h e most economical for
usually
are
the
are
such
the
graphical
in
intervals. set
than
to
in
finite
pipeline at
time
form
The x
By
expressing
of
the
flow
the result t h a t
by
A
the c h a r t .
important I ines.
computer.
(Streeter
Solution
and Lai,
is
1963 a n d
water and
hammer
solved
for
equations
are
successive
time
i n t e r v a l s a n d At
is
- t g r i d on which s o l u t i o n takes p l a c e i s
Starting
from
known
conditions
along
the
one proceeds to c a l c u l a t e the h e a d a n d velocity a t
each p o i n t a l o n g the l i n e at time t
adding,
most
with
i s d i v i d e d i n t o a number of
4.7. t,
in a r e a
t h e w a t e r hammer e q u a -
digital
differential
difference
ax/c. Fig.
by
a n d the
above a n d
The c h a r a c t e r i s -
predicted
solution of
is
characteristics
The
The c o n d u i t
equal
cvo/g
1950) w h i c h d i f f e r s l i t t l e i n p r i n c i p l e f r o m t h e o l d
method.
expressed
systems
method o f
Streeter a n d Wylie,
depicted
by
that
valve stroke,
higher
method of
particular
by
the vertical
linear reduction
more a c c u r a t e a n a l y s i s i s t h e r e f o r e n e c e s s a r y f o r
tions
off on
( f u l l lines) a n d minimum
maximum a n d minimum heads respectively
reduction occurs a t the
(dashed
Read
/g)
a c o n d i t i o n r a r e l y encountered in p r a c t i c e .
w i t h time, tics
he/(cvo/g).
head parameter h ' / ( c v
equations
4.5
+
and
At. 4.6
as
one gets two simultaneous equations
total
differentials
and
i n v o l v i n g dh a n d d v :
(4.7b) Equs. time
4.7a
t
+
At
and
4.7b
may
i n t e r m s of
be
known
and v ' at point p at P P h a n d v a t two other points q a n d r
solved
for
h'
at time t : (4.8a)
(4.8b)
67 Valve closure factor C T/L
F i g . 4.6
At
Maximum a n d minimum head a t downstream v a l v e f o r l i n e a r c Io s u r e
the terminal
either
h
speed.
The
is
fixed, correct
the known condition computat ions
points, v
or
Equ.
a n additional condition i s usually
imposed;
is
or
4.7a
a
function or
4.7b
of
t o e v a l u a t e t h e new
commence
at
known
a
gate
solved
is
opening
simultaneously
h a n d v at time t
conditions
and
are
pump with
+ A t . The
terminated
when
the pressure f l u c t u a t i o n s a r e s u f f i c i e n t l y damped b y f r i c t i o n . Where t h e n Equs.
a
branch 4.8a
pipe
a n d 4.8b
s occurs or
there
is a
change
snoulci b e r e p l a c e d b y E q u s . 4.9
i n diameter,
a n o 4.10:
68
TIME
A
/ Fig.
x - t G r i d for water method.
4.7
hammer a n a l y s i s b y c h a r a c t e r i s t i c
Effect of F r i c t i o n Fluid along
friction
the
gradually
damps
If
conduit. die
away
the
there
and
water is
the
no
hammer
exciting
waves
as
influence
pressure along
they
the
the conduit
travel
waves will
will
tend
to
s t a t i c pressure. The
characteristic
dicts
the
wave.
At
method the
of
wave
water
sharp
friction
wave
provided
pumping
over-pressures friction
head
there
computer accurately is
no discontinuity
i s necessary an analytical
(1950)
demonstrated
travelling stoppage
xxv
cates
it
by
back is
solution
along
in
the
t o r e s o r t to some o t h e r
that
indicated
pre-
a by
is feasible
at
t h e a m p l i t u d e of line the
with
a
friction
hyperbolic func-
4.4): tanh
-
In
solution
Fortunately
Ludwig
instantaneous
(see F i g .
of
wave front,
analysis. front.
hammer
fol lowing tion
of
effect a
method
lines at
is
minimum
following
the greater
and
cv
--./p)] 4
( 4gd '
pump than
maximum
sudden
will
(4.11) pump
exceed
the
approximately head
stopping
0.7cv / g .
envelopes
the
pumping 0
along
maximum
head
Fig.
if
4.8
pipelines
the indiwith
69 various stream plot
friction end.
heads
To
use
following
the
multiply
the maximum a n d minimum
factor
0
when
chart
stoppage
ordinates
is
should
only
valid
provided
at
no
point
fall
It
has,
however,
heads
with
column separation
profile.
at
by
the
up-
cv / g
and
head envelopes f o r the correct f r i c t i o n
there
is
no
column
the negative wave t r a v e l s up the p i p e l i n e i.e.
envelope
mum
the
above o r below s t a t i c on a p i p e p r o f i l e d r a w i n g .
hf/(cv / g ) ,
The
instantaneous
chart,
10
below
the minimum head below
m
separation
the
been found from experience that a r e often s i m i l a r
to
pipeline
the maxi-
those without
separation.
4.8 may also be used to determine the maximum and minimum
Fig.
heads along the
pipelines w i th fri cti o n
downstream
end b y
following
a closing valve.
sudden flow
Turn
the c h a r t
stoppage a t upside down
a n d r e a d o f f maximum envelope instead of minimum a n d vice-
versa.
PROTECT I ON OF PUMP I NG L I NES (Stephenson, 1972)
The
pressure
transients
fol lowing
power
failure
to
electric
motor
d r i v e n pumps a r e u s u a l l y the most extreme t h a t a pumping system w i l l experience. should often
Nevertheless,
also
be
the over-pressures
checked.
caused b y s t a r t i n g pumps
Pumps
with
steep
induce h i g h over-pressures
when
t h e power i s switched on.
i s because the flow so
a wave
By
partly
with
a
i s small
( o r zero)
head equal
closing
the
to
pump
when
head/flow
the pump
the closed v a l v e
delivery
characteristics
valves
This
i s switched on
head i s generated.
during
starting,
the
over-pressures can be reduced. The
over-pressures
caused b y
closing
l i ne valves or
scour
valves
should also be considered. the
If
denly,
pumps
the
flow
close
to
the
water
column
atmospheric
i s vapour thus
occur
supplying will
pressure.
at
r e t u r n e d as a
peaks
If
the
grade
line,
the
pressure
cause
pressure.
unprotected p i p e l i n e a r e stopped sud-
a l s o stop.
hydraulic may
an
The
lowest
pipeline
the
value
to
profile is relatively
sudden drop
deceleration
to
to which
a
value
of
the
less than
pressure could drop
Vaporization or even water column separation may along
p o s i t i v e wave
the
pipeline.
When
the
the water columns w i l l
to water hammer over-pressures.
pressure wave
is
rejoin g i v i n g rise
70
Fig.
4.8
M a x i m u m and m i n i m u m h e a d e n v e l o p e s f o l l o w i n g instantaneous pump stopping in pipelines w i t h friction
71 Unless pumping
some
method
pipeline
of
system
water will
hammer
normally
water hammer overhead equal to cv /g.
comparison
most
lines
with
where
the
economic
pumping
solution,
i n s t a l l e d i t may
water
hammer
head.
and
have
to
I n fact
0
high-pressure
protection be
is
designed
for
a a
t h i s i s often done w i t h
heads
may
be
small
this m a y
For
short
lines
if
water
hammer
even
installed,
in
be the
protection
is
be prudent to check that the u l t i m a t e s t r e n g t h of t h e
p i p e l i n e i s s u f f i c i e n t should the p r o t e c t i v e device f a i l . The
philosophy
against
water
reduce The
the
surge
is
is
the
design
similar.
of
The
most
methods of
object
in
downsurge i n the p i p e l i n e caused b y
upsurge
entirely
behind
hammer
will
then
eliminated. to
feed
be correspondingly
The
water
most into
common
the
pipe
most
stopping
reduced,
method
of
or
protection
cases
to
the pumps.
may
limiting
is
even
the
be
down-
as soon as the pressure tends
to drop.
Fig.
Pipeline p ro fi l e i I lustrat ing suitable devices f o r water hammer protection.
4.9
Suitable i n Fig.
4.9.
locations Most of
for
various
the systems
protective
locat ions f o r
devices
are
various
i I lustrated
i n v o l v e feeding water i n t o the pipe.
Observe
that
column
beyond
phenomenon of
the
gather pump
If
to
flux
in
the
The
valve
of
would
and
flow
then
allow
the
into
stopped
no
by
would
the
the
water
energy,
energy,
the entrance
between
against
however,
potential
kinetic
be
Part
column
impact
consequently
may
device a t
heads
in
water
If,
maximum
and
hammer
The w a t e r c o l u m n g r a d u a l -
direction
minimum
water
water
i s converted
difference the
of
the
phenomenon.
column
decelerate
which
there
will
water
hammer
installing
be
a
re-
the discharge t a n k
to
A small o r i f i c e b y p a s s to the re-
the pipeline.
in
water
the
elastic
surge
over-pressures.
point
reverse
or
to
momentum
throttling
vessel,
of
reverse
its
point
the
e l a s t i c energy.
hammer
in
so
motion
the
effect
the
at
change
of
allowed
water
with
v a l v e or
air
the
was
slow
energy
instead of
it
over-pressure.
or
a
arrested
sudden
flux
prevented
to
under
cause is
coincides no
is
momentum
column
momentum c h a n g e of
sudden
tank
energy
ends.
the
converted kinetic
decelerates
the
cases
the
is
original
potential ly
all
in
pressures on
e i t h e r s i d e to g r a d u a l -
l y equalize. Fortunately and
for
hammer theory
analysis may
be
i n some cases,
If
the
pump
of
bypass
is
of
similar
a
or
bypass In
the
design
effects,
necessary.
analysis
of
elastic may
reflux these
water
be
systems
protective by
incorporates
of
so
air
vessels
a
that
Rigid
surge
hammer
done are
in-line
water
water
tank
trial
device and
envisaged,
valves
may
instances
method of
oped,
by
a
solution,
varying
the
such
error.
column
action,
and
as
a
a
analysis
a
or,
or
a
is
usually
a
number
if
computer
discharge
location
similarly
design
valves
program
s i z e and d i s c h a r g e c h a r a c -
as
The
computer
reflux
graphically
Normal ly the location,
economical and
the
for
inertia
normally
an
analysis
of
determined
pump
for
system
b e developed.
teristics
not
valve,
be
available the
of d i s c h a r g e tanks.
The
solutions
trial.
are of
employed
pipeline
necessary.
could
charts
investigation
to
have
program
general
and
is
be
tank size
methodically,
to
in-line
determined
usually
program could
parameters
have
of
the
by most
be develan
opti-
reducing
water
mum s o l u t i o n a r r i v e d a t . The
following
sections
hammer in p u m p i n g l i n e s ,
describe various
methods o f
a n d offer design aids.
73 Pump Inertia If to
the r o t a t i o n a l
rotate
pressure
the
pump
the
of
for
transients
e n t r a i n e d water on
i n e r t i a of
may
will
delivery
a
while
be
side,
after
reduced.
continue
the water column.
a centrifugal
thereby
power
The
feed
to
pump and motor continue
rotating
water
water
pump,
hammer
motor
and
i n t o the p o t e n t i a l vacuum
a1 l e v i a t i n g
The effect
failure,
the
sudden
deceleration
i s most noticeable on low-head,
short
pipelines. After
the
gradually the
power
slow
delivery
higher pump
in
delivery gather
turbine
the
the
the
a
until
it
can
no
suction
at
side
direction,
of
the
these
will
it
with
there pump.
in
the
no
The
reverse
conditions.
If
The
of
the
off,
the
deliver
force
pump
still
reflux
pump
or
will
reverse
against
through
spinning
rapidly
of
will
head is s t i l l
control
and
speed
pump
water
water
direction,
i t reaches r u n a w a y speed.
deceleration
cut
the d e l i v e r y
then
the
is
is
longer
the time.
head,
provided
momentum
under
rapid
motor
reverse
increase u n t i l is
the
down
direction,
and
to
head e x i s t i n g
than
forward
supply
in
the the
valve
on
decelerate
will
act
as
the
pump
a
will
Under these conditions there
reverse flow
a n d water
hammer over-
pressures w i I I resu I t. I f there i s a r e f l u x v a l v e reverse still
wi II
flow
The
occur.
be
on
arrested,
pressure
the
but
changes
delivery water
at
ing
the
work
done
after
the wil I
1963) o r b y computer.
a time increment A t
i n decelerating
the pump,
overpressures
t h e pump f o l l o w i n g power f a i l -
u r e may be c a l c u l a t e d g r a p h i c a l l y (Parmakian, The pump speed N
side of
hammer
i s obtained b y equat-
the pump to the energy
transferred
to the water:
Solving f o r N
1
- N2
= L N we get
900wHQ A t A N = n' MNFN where
M
is
(4.12) the
N
is the speed
of
the time
head
above
moment of in
rprn,
interval, suction
w
inertia
of
the
pump
impeller
and
motor,
FN i s the pump e f f i c i e n c y a t the b e g i n n i n g i s the u n i t weight of f l u i d ,
head a n d
q
i s the discharge.
H i s the pumping As
an approxima-
74 tion,
FN = (N/No)Fo where s u b s c r i p t o r e f e r s to i n i t i a l conditions.
The
head/discharge
accurately
characteristics
of
the
pump
can
be
fairly
represented b y the equation
t i = aN2 + bNQ - cQ2 a,
b
and
c
on
the
points
are
(4.13)
constants
which
can
head/discharge/speed
be
evaluated
characteristics
provided
of
the
three
pump
are
known. Substituting pipe,
and
q
vA
=
A
where
4.8,
u s i n g Equ.
is
the
cross
two equations
sectional
result
area
involving
of
the
two
un-
knowns which may be solved f o r h and v at the pump. Fortunately summarized
the
in
r e s u l t s of
chart
form.
pipeline
P.
The
times
of
parameter and
the
various
for
presented
upsurge at
values
charts flow
l a r g e number of
Charts
the maximum downsurge and the
a
also
of
by
Parmakian
indicate
the pumps and midway
pump
indicate
reversal,
analyses have been
zero
inertia
the
and
maximum
pump
speed
the
pipeline
reverse
and
along
speed
maximum
re-
verse speed. Kinno
and
which
include
speed
of
ing
the effect
the pump
maximum
Kinno
flow
of
have
prepared
that
through
if
comprehensive
charts
l i n e f r i c t i o n and pump e f f i c i e n c y ; specific
i s also discussed.
upsurge
suggests
reverse
(1965)
Kennedy
reverse
Of
rotation
of
could
be
the
upsurge
the
pump was
i s a chart
interest the
pump
reduced
permitted,
but
is
indicat-
prevented.
considerably
with
if
reverse r o t a -
tion prevented.
4.10
Fig. will
occur
ues
for
the
maximum
summarizes
in
various minimum
head
the
head
values
around 85 p e r cent.
t
wave
will
of
the
subsequen
mitted,
are
also presented
ues
the
magnitude
prevented maximum
with
of
the
are
and
systems
from
to cover
be observed r e t u r n s to
upsurge in
at
the pump
upsurge which
reflux
valve.
headrise
above
operating
equal to the lowest head-drop
that
If
Kinno's
paper,
and
Valthe
pump efficiencies
( t = 2L/c).
if
flow
reversal
These values
would occur reversal
head
Ho
.
which
the minimum head often
flow
below H
pressures
power f a i l u r e .
typical
the pump
the c h a r t .
a
minimum
following
taken
a r e adjusted
occurs when
the f i r s t
maximum
pumping
if
would
The v a l i s per-
are lower than
reverse flow
was be
prevented
was the
approximately
75 The the
author
pump
inertia
pressures. the pump
has
If
a
simple
will
the
have
inertia
r u l e of an
thumb
effect
parameter
in
I
=
Here M
i s the moment of
i s the volume of water i n the pipe.
from
Fig.
4.10,
and
i n e r t i a of
it
was
the water
MNZ/wALHoZ
the pump,
assumed
a s c e r t a i n i n g whether
reducing
i n e r t i a may reduce the downsurge b y
and AL ed
for
at
least
hammer
exceeds
0.01,
10 per cent.
N i s the speed
i n rpm
The expression was d e r i v that
c/g
is
approximately
e q u a l to 100.
F i g . 4.10
M a x i m u m and rninimiJm h e a d s at p u m p a f t e r power f a i l u r e
76 Some i n s t a l l a t i o n s have a fly-wheel the
moment
of
inertia.
impractically
be
In
heavy,
most
also
f i t t e d to the pump to increase
cases
flywheel
the
would
have
i t should be borne i n mind that
to
start-
i n g c u r r e n t s may thereby be increased.
In
subsequent
sections
the
effect
and the pumps a r e assumed to stop
of
pump
inertia
is
neglected
instantaneously.
Pump Bypass Reflux V a l v e
One
the
the
of
against
water
pump
(Fig.
charge o n l y ing
in
conditions
head
and
the
simples hammer 4.11).
arrangements is
a
reflux
of
through to
the the
the
line
parallel
with
non-return
pumping
pressure
head
would
difference
bypass
be
would
head,
valve.
pressure
in The
less
the
suction
reflux
valve
The head may water
would
friction
than the
the head i n the d e l i v e r y
case
pressure
any
dis-
Under normal pump-
higher
cvo/g.
which
v a l v e would
maintain
On stopping the pumps,
suction
suction
pumping
in
the pumps.
i n a closed position.
below
a
installed
or
Pipe would tend to drop b y the amount to
protecting
valve
the same d i r e c t i o n as the
The
reflux
loss
would
be
drop drawn
therefore o n l y in
the
bypass.
drop The
r e t u r n wave overpressure would be reduced a c c o r d i n g l y . REFLJX VALUE
J S U C T I O N PIPE
F i g . 4.11
This cases, tion er
Pump w i t h bypass r e f l u x valve.
method
as
pressure. hammer
sure).
of
water
the d e l i v e r y
The
hammer
I n other cases
overpressure method
protection
pressure w i l l
be
used
below
in
all
the suc-
there may s t i l l b e an a p p r e c i a b l e wat-
(equal
really
cannot
often never drop
has
i n v a l u e to use
only
the
when
initial the
drop
pumping
i n preshead
is
77 considerably
less
sure
along
the
tion
reservoir
than
entire level
cv /g.
should
s t i l l be column separation Normally reservoir. fairly
the
and
also
pipes
there
water
length be
draw
may
be
above,
prevent
initial
be
the
suction
drop
i n pres-
tolerable.
relatively
high
or
The
suc-
there
may
line.
directly cases
from
where
a
in a similar
pressure
constant
the
intake
hammer could be a problem i n
cases a bypass r e f l u x v a l v e would, ed
the
should
i n the d e l i v e r y
intake
However,
long
I n addition,
pipeline
it
way
exceeding
head
pipe
too.
is
I n these
to that describ-
the d e l i v e r y
pres-
sure.
It
should
be
noted
pump
during
the
period
head,
if
especially
speeds,
as
is
bypass r e f l u x
the
that
water
that
the
case
the
may
machine
with
also
delivery was
drawn
In
the
the suction
high
for
pumps.
be omitted,
through
i s below
designed
through-flow
v a l v e could even
be
head
specific
some cases
the
a l t h o u g h there i s normal-
l y a f a i r l y h i g h head loss through a s t a t i o n a r y pump.
Surge Tanks The
water
pressure, tank
in
as
of
of
a
grade
in
l i n e of
to be used. in
the
surge end
tank
of
treated
is
the
in
case
rise.
the
of
a pumping
tank tank
for
a
Surge
line
is
i s open
the
flow
head
drop are
although
there
It
profile
and water
relatively
the
i t could
pipeline
surge
the
and
tank
between
other
be treated
independent p i p e l i n e shorter
or
this
filling the
they
can
hydraulic
at the
means.
as
may
at
to enable an open a
some
length,
pipe,
principally
that
The
which
a r e cases where
pipeline
by
atmospheric
the p i p e l i n e .
the
seldom
is
hammer
large,
in
low enough
protect
to
to
variations
used
be possible to construct
against
exposed
is
tanks
systems.
intermediate
as an
surge
tank
penstocks,
I t may
tank
a
bottom of
pumping
pipeline
the
in
balancing
head
turbine
applied
and
the
a
discharging
case
head be
while
acts
occur,
surface
tank
a peak pumps If
the
the discharge
section
could
be
in
length than the o r i g i n -
The f l u c t u a t i o n s of the water surface level
i n a surge tank follow-
a l pipeline.
ing ween
power the
failure pumps
may and
be
studied
surge
tank
analytically. are
The
high-frequency
transients water
bet-
hammer
78 phenomena ably.
which
The
will
analysis
not
affect
concerns
the
the
water
slow
level
motion
in
column between the surge tank and d e l i v e r y end of R i g i d water column water
hammer
will
not
pass
the
h
surge very
is
the
tank end.
height
P
and The
the
of
open
delivery
head
h
gradually
since e l a s t i c
tank.
The
rate
of
(4.14)
above
increases as
water
the line.
i s the p i p e l i n e length between
head
notice-
the
= -gh/P
deceleration of the water column i s d v / d t where
of
may b e used in the s t u d y ,
theory
waves
the tank
surges
the
level
the tank
the
level
in
of
the
and delithe tank
drops (see F i g . 4 . 9 ) . Another equation r e l a t i n g h a n d v
may be d e r i v e d b y considering
c o n t i n u i t y of flow a t the tank o u t l e t :
(4.15)
A v = Atdh/t P
Ap
where
and At
respectively.
are
the cross sectional
Note that
the flow
from
areas of
the p i p e a n d tank
the pump side
i s assumed to be
zero. Solving
Equs.
0 and v = v
4.14
and 4.15
that at t = 0,
a n d u s i n g the fact
to e v a l u a t e the constants o f
integration,
h =
one o b t a i n s an
express ion f o r h :
(4.16) From surge
in
t h i s equation
it
is
v
the
tank
i s apparent ,
-
surge
is
(II
/ 2 ) J AtP/A
P
g:
m r
that
and
the amplitude of the down-
the
time
till
down-
the f i r s t
-
Time zero
i s assumed
be that
to
i n s t a n t at
which the water hammer wave reaches the surge t a n k . If pump the
there
i s a g r a d u a l deceleration of the water column between the
a n d surge t a n k , correct
deceleration
then
the above expressions w i l l
continuity
equation
will
to
have
be
and
solved
the
rigid
not
column
numerically
for
hold, and
equation
successive
for time
i n t e r v a I s. The
fluctuations
in
tank
level
may
damped
be
orifice,
I n t h i s case the pressure v a r i a t i o n s
extreme
than
for
the
unrestricted orifice.
in
with
a
throttling
the l i n e may be more
Parmakian
( 1 9 6 3 ) presents
c h a r t s i n d i c a t i n g the maximum upsurge f o r v a r i o u s t h r o t t l i n g losses. A have
number of been
sophisticated
proposed
(Rich,
variations
1963).
The
in
the design of surge tanks
differential
surge
tank
for
79 instance The
includes
tank
may
variations systems,
a
small-diameter
have a
are
more
as they
varying
riser
in
the
cross section o r
applicable
to
a r e useful f o r
hydro
m i d d l e of
the
tank.
m u l t i p l e shafts.
power
plant
than
Such
pumping
damping t h e surges i n cases o f r a p i d
load v a r i a t i o n on turbines. Discharge Tanks I n s i t u a t i o n s where the h y d r a u l i c g r a d e one
which
pipeline.
under
The
pressure b u t
the p i p e l i n e p r o f i l e i s considerably
l i n e i t may s t i l l be possible to use a
normal
tank
operating
water
would
lower than
surface
be below
conditions
is
tank,
but
from
the
isolated
be subjected to atmostpheric
would
the h y d r a u l i c g r a d e
line,
as opposed to
that of a surge tank.
Fig. 4.12
A
Discharge tank
discharge
tank
would
normally
be
situated
along
the p i p e l i n e a n d possibly on subsequent
rises.
The tank
the
nearer
should
be
discharge
will
the
level
connected from
below
the
valve
would
water be
the
should
be
Fig.
4.12
the the
surface held
bypass to
tank,
in to
the tank
small-bore
discharged.
b e more e f f i c i e n t
tank
is
pipeline
to
the h y d r a u l i c g r a d e
via
a
reflux
elevation
tank.
the
in
the
pressure
the r e f l u x v a l v e , installed depicts
to
a
first
rise
a n d successively h i g h e r
if
by
the
i n r e d u c i n g pressure v a r i a t i o n s
i n t o the p i p e l i n e
shut
on
fill
typical
valve
line.
It
i n s t a l l e d to
the p i p e l i n e head drops
in
Normally the
connected
to
the
slowly
tank
discharge
the
pumping a float
tank
reflux line.
A
valve
in
after
it
has
arrangement.
80 The
use
of
discharge
tanks
was
reported
in
detail
by
Stephenson
(1972). The f u n c t i o n of caused The
by
pump
water
pipeline action
a discharge stoppage,
column a
(or
of
subsequent head
the
necessary
between
i s to f i l l
any
low pressure zone separation.
the
end
tank
tank)
difference
prevent
to
cause water
tank
thus p r e v e n t i n g water column and
will
discharge
g r a d u a l l y decelerate
between
reverse motion of
hammer overpressures
the
the
two
ends.
the water
of
the
under
the
may
be
It
column which could
t h i s could be achieved by
-
instal-
l i n g a r e f l u x v a l v e i n the line.
A
discharge
the
lowest
following
first
tank
tank
will
only
to
which
the
level
drop
tanks
tank
head
pump stopping.
along
should
operate
a
line
be successively
i s considerably
in
Thus
should
the
the
water
surface
i s above
pipeline
would
otherwise
the normal o p e r a t i n g head on the
be
less
higher.
less than
if
than
c v /g,
I n cases
cv /g,
and
0
where
r i g i d water
subsequent
the head on the
column
theory
may
be used to c a l c u l a t e the discharge from the t a n k : Integrating expression f o r Multiplying yields the
twice
discharge
distance
sectional tank
respect
by
area
of
and
h
is
time,
to
column
travels
the cross sectional by the
the
the
P
obtains
the
the
the
pipeline
where A
0
is
an
before stopping.
area of
is
distance between the
the p i p e l i n e ,
head on
one
Q = APv 2/2gh,
tank;
pipe,
a n d the open end of
one,
is
with
the distance the water
this
the volume discharged
cross
there
4.1
Equ.
tank
or the next tank measured
below
if the
h y d r a u l i c g r a d e l i n e ( o r level of the next t a n k ) . Fig. a
4.13
fraction
depicts the
of
The coordinates using elastic the
head,
discharge
discharge
at
the
overpressures theory
tank
never
tank
accurately
hammer
a
indicated by
the g r a p h
column
overpressures
discharged from a
increase. exceeds
is
are
low. less
than by
r i g i d column equation. a computer
approximately
r i g i d column successively
For
applicable
I t appears, that
tank expressed as
analysis
I t i s i n t e r e s t i n g to note that when
less
predicted
becomes
the
were obtained from
water hammer theory.
h, is
of
the volume
and
however,
indicated
by
rigid
higher the
that
0.5
theory,
cvo/g,
water
heads
rigid
water
hammer
the discharge
water
column
p r o v i d e d the conditions discussed below a r e compl ied w i t h .
the
and
from
theory,
81 4.13
Fig. tank
i s only
i s assumed
should be an side)
of
a p p l i c a b l e f o r a s i n g l e tank along the line.
be a t
in-line
the
r e t u r n from
to
tank.
reflux valve
Without
the tank
immediately
this reflux
towards
upstream
valve,
the pumps.
would
I n a d d i t i o n to water hammer the discharge from the
would exceed that f o r the assumed case where i t o n l y discharged
downstream. along h'
(on the pump
a p o s i t i v e wave
overpressures which would r e s u l t a t the pumps, tank
The
the pump end of the p i p e l i n e , o r else there
The
maximum overpressures
the p i p e l i n e on
is
measured
fraction
above
the
If
cv / g .
of
indicated by
the c h a r t
the d i s c h a r g e side of the tank.
the
discharge
head,
upstream r e f l u x
and
occur
The overpessure
is
expressed
as
i s omitted F i g .
valve
a
4.14
should be used. For peaks, line.
very
long
pipelines
more
than
one
The
tanks
separation
is
should be likeliest.
p o i n t beyond a tank
with
a
discharge
lowest
of
may
i n s t a l l e d at
The
as
number
tank
successively
be
installed
peaks where
the
head
will
which
the downsurge t r a v e l s along
higher
along
the
water column occur
the
at
line
any
i s that
of the water surface elevation of the preceding t a n k .
4.15
Fig. along first
a tank
valve
is
be
tank
the
The
located
should
second of
indicates
pipeline.
at
the
installed
should
discharge
is
chart
also
from
also o n l y
pump end of immediately
have
a
two
the
line,
upstream
reflux
tanks
appiicable
valve
or
of
installed
provided else
the
the
a reflux
tank.
immediately
The
upstream
it.
4.15
Fig.
is
between
the
and
open
the
for
really
tanks
different
end
only
is
equal
of
the
length
applicable to
the
and
cases where
distance between
pipeline;
ratios
for
however,
4.15
Fig.
the distance
the second
the c h a r t s
could
be
tank
hardly vary
used a s a g u i d e
f o r other cases. in and
4.15
Fig.
second
second
tank
corresponding is
that
line.
and
is
and the
pipe
between
The
h,
tank,
the
and
the
relevant
discharge h
difference
head at
length
discharge
The
the
h2 i s
the
tank
that
from
e
the are
between
i n elevation
between
the
second
tank
is
tank
substituted i n
is
the
first
between
the p i p e l i n e . two
a n d the discharge
from the f i r s t
and
elevation
the discharge end of
t 1 is
second
in
difference
tanks
end of
2
the pipe-
broken
indicated
full
by
The
and J?
indicated by
the v a l u e
the
lines lines.
i n d i c a t e d on
the
82
tc
08
06
O L
9 h' c vo 0 2
0 10
08
Q ?gh __ A
LV,' 06
OL
0.2
0
0
Fig.
4.13
D i s c h a r g e f r o m t a n k a n d m a x i m u m head r i s e w i t h i n - l i n e r e f l u x v a l v e u p s t r e a m of t a n k .
83
F i g . 4.14
Discharge from tank a n d maximum head r i s e (no in-line r e f l u x v a l v e ) .
F i g . 4.15
Discharge from two t a n k s a n d maximum head r i s e ( e l = @ a n d r e f l u x v a l v e upstream of each tank).
2
85 v e r t i c a l scale to o b t a i n the respective discharge Q from each t a n k . The maximum overpressures i n d i c a t e d b y F i g . 4.15 I t is,
i n the downstream side of the second tank. limit
the
further the
lateral
reflux
pipeline.
water from
In
hammer the
water
extent of
valve
may
then
tank
hammer
the
last
tank
and
t h i s case the r e f l u x v a l v e on could
analysis
however, possible to
the overpressure b y j u d i c i o u s
between
tank
i n v a r i a b l y occur
possibly exceed
should
be
with.
indicated b y
carried
location of a
delivery
end of
the pump s i d e of
dispensed
that be
the
out
the
The discharge
the
chart,
based
on
and a
the
theory
out1 ined e a r l i e r i n the chapter. The best p o s i t i o n f o r selected
by
trial
and
discharge error
c h a r t s presented may suffice, or
major
pipelines
with
should
be c a r r i e d out,
cular,
a final
check
tanks
and
and i n - l i n e
experience.
For
b u t f o r complex
large
either
friction
ref l ux valves i s simple
cases
the
cases w i t h many peaks
heads,
graphically o r
a
complete
analysis
b y computer.
should be done f o r flows
In parti-
less than the maximum
design c a p a c i t y o f the p i p e l i n e . Even though a number of tanks may be i n s t a l l e d along a p i p e l i n e , vaporization
is
tanks.
Provided
steeply
between
water on
always there
possible
are
tanks,
no
this
hammer overpressures.
all
rising
vapour
sections.
along
local
rising
peaks,
sections
and
the
I imited v a p o r i z a t i o n However,
Cases
are
air
the
l i ne rises f a i r l y
should
not
lead
to
vessels should be i n s t a l led
known
bubbles t r a v e l l i n g along g e n t l y
between
where
vaporization
and
r i s i n g mains have r e s u l t e d i n
severe c a v i t a t i o n of a l i n e a l o n g the top of the pipe.
A i r Vessels If
the
p r o f i l e of discharge
tank
or
force
water
into
compressed
air
illustrated
in
the in
in
the
will
vessel
should
tend be
to
is
not
protect
vessel
4.16).
(a
The
to
line.
reverse.
the
air
to
may
it
use
be
a
surge
possible
to
wave b y means of
vessel
arrangement
i n the vessel
will
is
gradually
the pressure i n the vessel equals
this
However,
unrestricted,
enough
line,
low-pressure
pressure
At
high
the
typical
i s released u n t i l
adjacent
column
pipeline
p i p e b e h i n d the a
Fig.
decrease as water that
a tank
stage
the
whereas inlet
decelerating the outlet
should
be
of
water the a i r
throttled.
A
86 suitable reflux
arrangement valve,
smaf I - o r i f i c e
4.16
Fig.
2.5
pirical
vessel
the
the
design
ratio
of
2.5.
The
the
when
( 1 9 6 3 ) suggests that outlet
a n d recent of
have
water the
discharge
water
bypass would a l l o w the vessel
times
effect
to
shuts
out
column
through
a
A
reverses.
to r e f i l I slowly.
A i r vessel
Parrnakian be
is
which
inlet
author
the a i r
loss.
vessel
However,
inlet
head
loss should
t hi s relationship
i s em-
research w i t h the a i d of computers has enabled the
loss
head
charts
reverse
head
to
reproduced
flow has
head
loss
compiled
be by to
i n v e s t i g a t e d thoroughly. parrnakian forward
design
were compiled f o r
flow
charts
The a i r
head
loss
covering
an
the
equal
to
extended
i n l e t t h r o t t l i n g ( F i g s . 4.17
r a n g e of
p i p e l i n e s a n d v a r i o u s degrees of
to 4.19).
The c h a r t s a r e s u i t a b l e f o r checking water column separation
a l o n g the e n t i r e p i p e l i n e length, volume
and
degree of
inlet
l i m i t to the overpressures. The c a l c u l a t i o n s for er; lies
it
was
assumed that
between
adiabatic
a n d f o r r e a d i n g off the r e q u i r e d a i r
throttling
corresponding
to any
specified
Outflow t h r o t t l i n g i s neglected.
p l o t t i n g the c h a r t s were performed b y computthe expansion
(HS
1.4
-
law f o r
constant)
and
the a i r the
i n the vessel
isothermal
(HS
=
Fig.
4.17
Maximum a n d minimum pressure envelopes w i t h a i r vessel. 2 = 0.5.
F i g . 4.18
M a x i m u m and m i n i m u m p r e s s u r e e n v e l o p e s w i t h a i r vessel. P = 1.
88 constant).
The
relationship
adopted
further
assumed t h a t t h e a i r vessel
pumps,
t h a t the pumps would stop
flow
was
HS1'3
It
constant.
=
was i m m e d i a t e l y
was
d o w n s t r e a m of t h e
instantaneously and that no reverse
t h r o u g h the pumps was permitted.
The
dimensionless
parameters
associated
with
the
charts
are
as
fol l o w s :
Pipeline parameter
P = c v /gH
A i r vessel parameter
B = v 0'AL/gHoS
Throttling parameter
C = Z/Ho
where S
i s the
loss t h r o u g h
The
outlet
0
initial
air
t h e a i r vessel
head
loss
was
volume
in the
0
vessel,
and 2
i s the
head
i n l e t c o r r e s p o n d i n g to a l i n e v e l o c i t y -v assumed
to
be
negligible.
the absolute head ( i n c l u d i n g atmospheric head)
Note t h a t
0-
Ho i s
i n t h i s case.
0.2 I
Fig.
4.19
Maximum a n d minimum pressure envelopes P = 2.
with
a i r vessel.
The c h a r t s a r e u s e d a s f o l l o w s to d e s i g n a n a i r v e s s e l : line parameter,
P,
i s c a l c u l a t e d from the maximum l i k e l y
The p i p e -
line velocity
89 and
pumping
head,
4.17
to 4.19.
T h e p i p e l i n e p r o f i l e is p l o t t e d on the a p p l i c a b l e set of
minimum-head it
does
not
fall
to
below
The
inlet
the The
throttling
to
10 ( o r more). pumping
works
necessary
at
any
to
the
C.
a
of
of
l/lOth
thus
of
still
smaller
S,
air,
design
suppress
diameter
vortices
cause line
is
procedure
i s to
m,
the
main
the
cannot
value
of
2 m/s a n d
corresponding
pipe diameter).
be
equal
tolerated,
it
inlet I f the
will
B (corresponding to a
be
larger
i s known.
to ensure no a i r escapes volume.
is
usually
designed
to
The vessel
i n t o the pipe-
This
i s the volume
1/1.3
be about one-half
the
The outlet should be designed w i t h a bellmouth to
and
the water
in
to
the degree of
approximately
of
200
i s c a l c u l a t e d once B
be s u f f i c i e n t
main p i p e diameter.
dissolve
point selected
depend on
The normal
a n d should exceed the maximum a i r
outlet
such that
envelope a l o n g the p i p e l i n e from actually
d u r i n g minimum pressure conditions a n d i s S ( H /Hmin) The
Figs.
achieved b y s e t t i n g C approximately
order
be
from
than i n d i c a t e d b y the minimum pressure requirement.
volume
c a p a c i t y should line,
to
indicated
volume of a i r ) The
the
out
select
to
profile
maximum-head
of
selected
envelope selected
( F o r a p i p e l i n e velocity
head
chart
corresponding
overpressures
represented b y
a
overpressures
pipeline
B
of
minimize the overpressures,
diameter
corresponding
the
value
read off
same c h a r t .
the
the
curves a n d a minimum-head
vaporization. used
and
air
entrainment.
to some extent
The
air
and w i l l
in
the
vessel
will
h a v e to replenished b y
means of a compressor.
In-L ine R e f Iux V a Ives Normally not al
a
reflux
reduce water extent
of
positioning
the
of
shock.
reflux
hammer pressures. led
upstream of
the
effect
of
valve
i n s t a l l e d on
hammer pressures,
For the
the
In
valves
fact,
i t s own
although in
some
in
a
i t may
pipeline w i l l
limit
situations
the
later-
indiscriminate
in
a
l i n e could
instance
if
a pressure r e l i e f v a l v e was i n s t a l -
reflux
other
valve
valve.
It
the may
be detrimental
reflux
valve
also
amplify
would
to
water
counteract
reflections
from
b r a n c h pipes o r collapse of vapour pockets. In-line surge down, side
reflux
tanks, the of
tank
the
valves
discharge or
reflux
would tanks
vessel valve.
n o r m a l l y be used or
would This
air
vessels.
discharge would
water
alleviate
i n conjunction
Following into the
pump
with
shut-
the p i p e e i t h e r violent
pressure
90 drop
The reflux
a n d convert the phenomenon i n t o a slow motion effect.
valve
would
then
arrest
the
water
column
at
the
time
of
reversal,
which coincides w i t h the p o i n t of m i n i m u m k i n e t i c energy and maximum potential
energy
of
momentum change
the water
in
column.
There
would
therefore be
little
the water column when the r e f l u x v a l v e shut and
consequently n e g l i g i b l e water hammer pressure r i s e . There a r e s i t u a t i o n s where water column separation and the format i o n of
vapour
be
tolerable,
in
water
vapour at
the
would
pockets
i n the p i p e l i n e f o l l o w i n g
provided
the
vapour
hammer pressures.
pocket could
arrested
not collapse
the water
at
of
the
i t s p o i n t of
vapour
resulting
column beyond the
i n fact be prevented w i t h an i n - l i n e
downstream extremity be
pockets d i d
Reversal of
pump stoppage would
pocket.
reflux valve
the water
minimum momentum,
column
there would
so
be l i t t l e head rise. Vaporization water If
hammer
the
first
peaks,
the
of
extent theory.
along
vapour
peaks
wouJd
the
last
be
and
the
was
confined
could
head on
peak
in
the vapour
pipeline
pocket
The decelerating
rigid
water
column
be
pipeline
where
pressure of
the decelerating head,
In
the water.
than
subsequent
to
first
peak.
the
estimated
using
rigid
the
dispersion
the water column between two peaks
with
a vapour
would
be the d i f f e r -
respect pocket,
to
t,
Integrating
one o b t a i n s
an
k?AvoZ/2gh, where h i s
C i s the water column l e n g t h a n d A i s the p i p e
ensure
reflux
valve,
allowance should be made f o r
of the vapour pocket.
suitable dip to
The
column
area.
locating
lateral
the
higher
the discharge end
equation
the volume of
cross sect iona I
a
the
vaporization
expression f o r
at
at
in e l e v a t i o n p l u s the intermediate f r i c t i o n head loss.
ence
and
occur
pressure dropped to rise
the
o r between
the
would
i n the p i p e l i n e
proper
functioning
i n order
of
some
The v a l v e should be i n s t a l l e d to
trap
the vapour pocket
the v a l v e doors when
the water
column r e t u r n s .
A small-diameter permit
slow
occur on of
the
bypass
r e f i l l i n g of
restarting
order
of
to
the r e f l u x v a l v e should be i n s t a l l e d to
the vapour
the pumps.
one-tenth
of
pocket,
or
else overpressures may
The diameter of the bypass the
pipeline
diameter.
An
should be air
release
91 valve
be i n s t a l l e d in the p i p e l i n e a t
should
the peak
which would come out of solution d u r i n g the p e r i o d of
to release a i r
low pressure.
i s a common p r a c t i c e to i n s t a l l r e f l u x v a l v e s immediately down-
It
stream
of
the
pumps.
Such
hammer
pressures
in
through
the
and
pump
the
reflux
valves
pipeline.
prevent
They
water
would
not
merely
hammer
prevent
prevent
pressures
water
r e t u r n flow r e a c h i n g the
pumps. In
some pump
installations,
instead of r e f l u x valves,
(1968)
Kinno delivery to
be
valve.
the
Assuming he
closing
control
valves,
a r e i n s t a l l e d on the pump d e l i v e r y side.
studied
tolerable,
automatically
effect
a
of
limited
describes
how
c o n t r o l l e d closure return
water
flow
of
through
hammer
a
pump
the
pump
overpressures
can
be s l i g h t l y reduced b y c o n t r o l l i n g the r a t e of closure of the v a l v e .
Release Valves There
are
a
number of
sophisticated water
(often r e f e r r e d to as surge r e l i e f a b l e commercial l y . matically
open
The
valves
pipe
leading
in
the
effect are
suction
the
gradually
normally
the
v a l v e s o r surge suppressors) a v a i l -
close
the
needle
reservoir.
The
complete
range
the
valve
type, or
discharge
velocities
pump
valves,
have a gradual
closure.
Needle a n d
which
tripping.
discharge
else sleeve
v a l v e s must of
after
which
designed to minimize c a v i t a t i o n
high
release v a l v e s
have h y d r a u l i c actuators which auto-
to the suction r e s e r v o i r ,
suitably
with
then
are
over
These valves
hammer
into
a
mounted throttling
sleeve
valves
a n d corrosion associated
occur
d u r i n g the t h r o t t l i n g
process. The v a l v e s a r e u s u a l l y reflux
valves
should
not
and
i n s t a l l e d on
discharge
discharge
a i r through the throat,
into
directly
the
The returns on
should
the
the top of
maintaining
suction as
they
reservoir.
They
i n v a r i a b l y draw
by
an e l e c t r i c a l
fault or
b y a pres-
(as Fig. 4.20).
valve to
the
pipe
and t h i s could reach the pumps.
The v a l v e s may be actuated sure sensor
suction
the d e l i v e r y side of the pump
to
pumps
open as
the piston
the
pressure
a
fully
before
the
p o s i t i v e pressure
increases a g a i n within
negative wave.
pressure
As
wave
the pressure
the v a l v e g r a d u a l l y closes,
desired
limits.
The
closing
may be a d j u s t e d b y a p i l o t v a l v e i n t h e h y d r a u l i c c i r c u i t .
rate
92
Reflux Pump valve
Acc u mu lot or
Suction
reservoir 4.20
Fig.
The returns on
Water hammer release h y d r a u l i c actuator
valve to
should
the
open
pumps
as
a
the top of t h e p i s t o n
maintaining
the
fully
valve
arrangement
before
positive
the
pressure
within
negative
pressure
increases a g a i n
simp1 i f i e d
pressure
As
wave.
the v a l v e
wave
the pressure
g r a d u a l l y closes,
I i m i ts.
desired
with
The
closing
rate
may be a d j u s t e d by a p i l o t v a l v e i n the h y d r a u l i c c i r c u i t . If
no
the v a l v e to
the
water of
overpressure
operating hammer
the
llel.
higher
would be sized
pumps, They
head.
could
Where
likely
is
t w o or
be
than
the
to discharge
to
operating the f u l l
reliability
be
a
is
problem
more release valves set
operate
to
at
head
flow of
at
tolerable, head equal
importance,
during may
is a
be
and
if
partial
shutdown
installed
i n para-
successively
lower
delivery
throttled
delivery
heads. In
the
valves,
event
of
normal
pump
shutdown a g a i n s t
the release v a l v e s could be disengaged to prevent
t h e i r oper-
at ion. The types of ing
lines
use
is
This
control
v a l v e s a v a i l a b l e as release valves f o r pump-
n o r m a l l y cannot open
therefore
method
of
limited water
to
in
less than
pipelines
hammer
over
protection
is
about f i v e seconds. Their
two
kilometers
normally
most
in
length.
economical
93 for
cases
when
the
pumping
l a r g e r the pumping head, Since
there
hammer
is
analysis
no
head
greatly
exceeds
cv /g,
since
the
the smaller the v a l v e needed. protection
should
be
against
performed
underpressures, check
to
that
a
water
water column
separation i s not a problem.
A
less
above,
sophisticated
which
has
valve
been
used
spring-loaded
release v a l v e .
sure
a
reaches
prefixed
than on
the
small
The v a l v e
maximum.
control pump
i s set
valves
described
installations,
to open when
Some overpressure
is
the
the pres-
i s necessary to
open the v a l v e a n d to force water out.
Choice of Protective Device The will
best
method
depend
system.
on
The
of
the
water
hammer
hydraulic
and
accompanying
table
protection physical
for
a
pumping
characteristics
summarizes
the
ranges
line
of
over
the
which
v a r i o u s devices a r e s u i t a b l e .
The most i n f l u e n t i a l parameter i n selec-
ting
i s the p i p e l i n e parameter P = cvo/gHo.
the
When
bypassing
values
P
of
it
the pumping head Ho,
i s g r e a t e r than
the
pumps
may
becomes necessary
For
suffice. use
to
The protective
approximate
suitable
order
device,
of
a surge t a n k ,
a
smaller
discharge
a n a i r vessel, o r a
devices l i s t e d i n the t a b l e a r e a r r a n g e d
increasing
one checks
a reflux
successively
i n combination w i t h an i n - l i n e r e f l u x v a l v e ,
release v a l v e . in
protection
the head cvo/g
valve
tank
method of
down
cost,
the
thus,
table
to
until
select
the
the
most
variables
are
o r more p r o t e c t i v e devices on
the
w i t h i n the r e q u i r e d range. It
same omical In
may line.
be
to
in
use
two
p o s s i b i l i t y should
arrangement often
particular
effect
possible
This
the
reducing
the
be ignored as the most econ-
i n v o l v e s more than one method of protection.
rotational
comprehensive water
not
i n e r t i a of
required
hammer
the
capacity
analysis
of
pump a
often
tank
has
or a i r vessel.
would be necessary
of protection devices i n combination i s envisaged.
a slight A
i f a series
94 TABLE 4.1 Summary of methods of water hammer protection
Method of Protection ( i n approximate order of increasi n g cost)
I n e r t i a of pump
Required r a n g e of v a r i a b I es
MN*
Remarks
Approxi mate on I y
wALHo2 > 0 * 0 1 Some water may a l s o be d r a w n through pump
Pump bypass reflux valve
In-line reflux va I ve
__
cv
Surge tank
h small
> 1
0
gh
P i p e l i n e should be n e a r h y d r a u l ic g r a d e l i n e so height of tank i s Dractical P i p e l i n e p r o f i l e should be convex downwards. Water column separation l i k e l y .
Automatic release valve
D i scharge tanks
cv
0
>
h = pressure head a t t a n k , p i p e l i n e prof i l e should be convex upwards
'
gh
A i r vessel
Normally used i n conj u n c t i o n w i t h some other method of protection. Water column separation possible
cv
o < __ gHO
l
P i p e i ine p r o f i l e p r e f e r a b l y convex downwards
95 REFERENCES Kinno, H. and Kennedy, J.F., 1965. Water hammer charts for c e n t r i f u g a l p u m p systems, P r o c . Am. SOC. C i v i l E n g s . , 91 (HY3) 247-270. Kinno, H. ,1968 W a t e r h a m m e r c o n t r o l i n c e n t r i f u g a l p u m p s y s t e m s , P r o c . Am. SOC. C i v i l E n g s . , 94 (HY3) pp 619-639. L u d w i g , M. and Johnson, S.P., 1950 Prediction of surge pressures i n l o n g o i l t r a n s m i s s i o n l i n e s , P r o c . Am. P e t r o l e u m I n s t . , N.Y. 30
.
(5).
.
L u p t o n , H.R., 1953 G r a p h i c a l a n a l y s i s o f p r e s s u r e surges in pumpi n g s y s t e m s , J . ~ n s t . W a t e r E n g s . , 7. P a r m a k i a n , J . , 1963. W a t e r Hammer A n a l y s i s , D o v e r P u b l i c . I n c . , N.Y. R i c h , G.R., 1963. H y d r a u l i c t r a n s i e n t s , D o v e r p u b l i c s . I n c . , N.Y. and L a i , C., 1963. W a t e r h a m m e r a n a l y s i s i n c l u d i n g Streeter, V.L. f l u i d f r i c t i o n . P r o c . Am. SOC. C i v i l E n g s . , 88 (HY3) pp 79-112. Streeter, V.L. and Wyl ie, E.B., 1967. H y d r a u l i c T r a n s i e n t s , McGrawHill. D., 1966. W a t e r h a m m e r c h a r t s i n c l u d i n g f l u i d f r i c t i o n , Stephenson, P r o c . Am. SOC. C i v i l e n g s . , 92 (HY5) pp 71-94. Stephenson, D., 1972. D i s c h a r g e t a n k s f o r s u p p r e s s i n g w a t e r h a m m e r i n p u m p i n g l i n e s . P r o c . I n t n l . Conf. o n p r e s s u r e surges,B.H.R.A., C r a n f ie l d. Stephenson, D., 1972. Water hammer p r o t e c t i o n o f p u m p i n g l i n e s , t r a n s . S.A. I n s t n . C i v i l E n g s . , 14 ( 1 2 ) .
L I S T O F SYMBOLS
A
-
p i p e cross sectional area
B
-
a i r vessel
p a r a m e t e r v 'AL/(gHoS)
c
-
t h r o t t l i n g p a r a m e t e r Z/H
d
-
p i p e l i n e diameter
0
E
-
modulus of e l a s t i c i t y of p i p e w a l l m a t e r i a l
F
-
pump rated efficiency
f
-
Darcy friction factor
( e x p r e s s e d as a f r a c t i o n )
-
g r a v i t a t i o n a l acceleration
h
-
p r e s s u r e h e a d a t an i n t e r m e d i a t e s e c t i o n o f t h e p i p e l i n e
h'
-
water hammer h e a d r i s e measured above the d e l i v e r y h e a d
hf
-
f r i c t i o n h e a d loss
9
he -
h e a d loss t h r o u g h d o w n s t r e a m v a l v e f u l l y o p e n
H
head
-
(in
in
p i p e l i n e measured
c a s e of
air
vessel
above
design,
pump suction reservoir
take
H
as absolute,
atmospheric head) p u m p i n g head above suction r e s e r v o i r level
Ho I -
p u m p i n e r t i a p a r a m e t e r MN'/WALH
J
p u m p p a r a m e t e r F M N Z c / l 80wALv gH
-
0
0
'
0
i.e.
level plus
K
-
b u l k modulus of water
e
-
length of an intermediate p a r t of p i p e l i n e
L
-
pipeline length
M
-
moment
N
-
pump speed i n rpm
P
-
p i p e l i n e parameter cv /gh
Q
-
volume of water discharged from discharge tank
s
-
volume of a i r i n i t i a l l y
t
-
time
T
-
l i n e a r v a l v e closure time
v
-
water v e l o c i t y i n p i p e l i n e
v
-
i n i t i a l water velocity
of
inertia
t r a i n e d water
of
rotating
p a r t s of
motor
and
( = mass x r a d i u s of g y r a t i o n ' )
0
0
i n a i r vessel
in pipeline
w
-
weight of water per u n i t volume
x
-
distance a l o n g p i p e l i n e from pump
Y
-
wal I thickness o f p i p e
z -
pump,
head loss through a i r vessel Darcy f r i c t i o n factor
i n l e t f o r p i p e l i n e velocity
=
en-
97
CHAPTER 5
A I R IN PIPELINES
INTRODUCTION
It The flow or
is
recognised
that
air
a i r may be absorbed at at
the
entrance
i n free form
tively
large
they
will
the
air,
of
remain
in
The
in
likely
air
water
entrained
may
An
to
many
or
air
pockets.
The pockets may
either
present
line.
i n bubbles or
volume
section.
cross
to
is
free surfaces,
thus
pipelines.
in
be
pocket
turbulent
in
accumulate on top of
travel
along
equilibrium,
the
solution
implies a r e l a the pipe
l i n e to peaks.
be e n t r a i n e d by
There
the f l o w i n g
water or be released through a i r valves.
Air It
i n solution
i s only
air
losses the to
when
form
to
i s not
increase. to
form
those
in
partly
on
the
problems
bubbles
large full
drain
the system,
of
used
the to
pipe. release
l i n e a n d to draw
arise.
may
pockets.
coalesce
Flow pipes,
Air
valves
of
the
top
and
rise
to
conditions
then
become s i m i l a r
except
a
quantities
i n from
dissolved
b u l k s a n d head
that
in
slightly
pipeline
it
which collects
different
air
of
a
of
w i l l be pressurized.
used to e l i m i n a t e the a i r
large air
to permit
The water
i n c l u d i n g the free a i r ,
valves are frequently
top
also
that
The
pipe
Air
to present many engineering problems
the pressure reduces s u f f i c i e n t l y
bubbles
i s l i k e l y that
likely
during
design
the
are
filling
of
the atmosphere d u r i n g vacuum con-
d i t i o n s i n the line.
PROBLEMS O F A I R ENTRAINMENT
Air fects.
drawn
in
through
Minute a i r
bubbles o r
- the formation of lapse and erode lers
in
Air
vacuous
air
supply in
due
drawn
flow to be unsteady.
to in
the in
which
have can
a number of
ef-
promote c a v i t a t i o n
subsequently
rapidly
col-
T h i s effect occurs i n pump impel-
high
gulps
can
solution
cavities
the pump o r pipe.
particular
pressures.
pump
a
peripheral
can
cause
speed
which
vibration
by
lowers causing
98
Large quantities intermittent1
-
-
-__
a.
Low level sump
I-
i
I
Air e n t r a i n e d by a falling jet
o
* 1
+
'
To pump
Air enters intake b. Free fall into sump
__1-
____
Surface dimple barely detectable
-=-+
---+
Well define surface dimple
-.
Air drawn intermittent ly from bottom of vortex into intake
Air core extends into intake (fully developed entraining vortex)
c . Vortex formation
FIG.
5.1
Inlet arrangements conducive
to a i r
entrainment.
4
99 Air
i n a r i s i n g main,
emerge
Air
from
solution
if
whether ambient
in free form w i l l collect a t
pipes o r pocket
the
acceleration
in the pipe.
of
The
dispersed
pipeline w i l l
increase.
include surging,
by
latter
the water
b u b b l e form,
may
the top of
be washed along
air
or
temperature
may
i s reduced.
the p i p e l i n e and then r u n
Here i t w i l l e i t h e r escape through a i r v a l v e s o r
u p to h i g h e r points. vent
i n s o l u t i o n o r i n b u b b l e form, pressure
past
the velocity will
result
the a i r
i n the water,
of
the water past the
i n a head loss due to
pocket.
Even
if
air
is in
the f r i c t i o n head loss a l o n g the
Other problems caused b y a i r present i n pipes corrosion,
reduced pump e f f i c i e n c y , malfunction-
i n g o f v a l v e s or v i b r a t i o n s .
Air
may
water, size
in
present
bubbles,
1
from
velocity
be
is
mm/s)
that
rising
to
to
slow
they
the
concentration
micro
5 mm.
so
in
the
bubbles
Micro
in
surface.
or
pockets
in
bubble,
mm
suspension
I n fact
on
solution.
the
90 rnm/s,
for
a
top
Bubbles
be smaller,
turbulence
p r o f i l e i n the same way
sion i n f l o w i n g water.
of
bubbles may
1
(e.g.
stay
form
of
the
0.1
mm
considerable
bubble,
time
4
before
may create a n e q u i l i b r i u m
that
sediment
s t a y s i n suspen-
The r i s e velocity of small a i r bubbles i s
w = dgZ/18 v
(5.1
where the kinematic
in
range
and t hei r r i s e
v of water a t 20 C i s 1.1
viscosity
1
x 10-6m2/s, d
i s b u b b l e diameter a n d g i s g r a v i t a t i o n a l acceleration. For
air
bubbles
to
form
should be present.
Then
be
solution.
released
from
depends
on
the
2% a i r
by
volume
readily
temperature
nucleus
capacity
of
and pressure.
The
At
measured a t
f i g u r e v a r i e s from 3.2% at O°C
AIR
a
or
uneven
when conditions a r e correct,
standard
water
to
dissolve
air
20 C water may absorb
atmospheric
down to 1.2% a t
surface
air will rapidly
pressure.
This
looo.
INTAKE A T PUMP SUMPS
The major source of a i r i n pumping lines i s from the i n l e t sump o r forebay.
Here the water exposed to the a i r
depending the water.
on
its
temperature,
will
pressure a n d
absorb a i r a t a r a t e
degree
of
saturation
of
100
a.
Air
b.
Air
c.
pocket w i t h s u b c r i t i c a l
flow past.
pocket w i t h super-critical
A i r pocket
F i g . 5 .2
Air
flow past.
in e q u i l i b r i u m position. pockets in pipelines.
101 Air
in
flowing
form
free
water.
may
The
also
suction p i p e entrance w i l l entrance likely
velocity
to
be
partially carried
and
drawn
when
be
formation
dragged a
greater
This
free
in
vortex
entice a i r
the
in.
of
the conduit
to
or
drawdown
i n t o the conduit. the
turbulence,
air
may
later
the
conduit.
As
pressures
again
the the
The h i g h e r the
the
more
dissolve
air
is
wholy
or
I n any case i t i s
pressures increase beyond the pump.
along
by
outside
reduce,
it
may
be
released from solution. The the
configuration
tendency
draw
to
(1957), Prosser to
in air.
intake.
approaches
be1 lmouthed
the pump sump has an
and
important
b e a r i n g on
Extensive studies b y Denny a n d Young
(1977) and others have
minimize a i r
concentric
of
i n d i c a t e d how to design sumps
C i r c u l a t i o n i n the sump should be avoided b y and
preferably
straight facing
inflow.
The
downwards
inlet
should
be
Hoods ( s o l i d
upstream.
or p e r f o r a t e d ) above the i n t a k e minimize a i r intake. The
degree
entraining
of
submergence
drops . o r
hydraulic
should
be
jumps
are
as
great be
to
as
possible.
avoided.
Fig.
Air 5.1
indicates some i n l e t arrangements to be avoided.
AIR ABSORPTION AT FREE SURFACES
The
rate
of
diffusion
of
gas
across
a
liquid
interface
can
be
expressed i n the form
-dM_ dt
-
AK
(Cs-
C)
(5.2)
where M i s the mass r a t e of exposed, Cs
K
is a
transfer
l i q u i d f i l m constant,
is the concentration a t
v i s c o s i t y a n d turbulence.
saturation.
per
C
u n i t time
t,
A
i s the area
i s the gas concentration a n d
K is a f u n c t i o n of temperature,
T h i s equation i s often w r i t t e n i n the form
(5.3) where r i s the d e f i c i t r a t i o , Co i s the concentration a t time 0, i s the volume of water per surface area A ( V / A
= depth of water).
and V
102 HYDRAULIC REMOVAL OF A I R
Air
trapped
increase
the
in
air
a p i p e and allowed to pocket
The
size.
accumulate,
water
cross
some o r a l l of
the
Alternatively
water.
entraining
air
and
gradually
sectional
therefore d i m i n i s h a n d the velocity of the water w i l l some stage,
will
area
will
increase u n t i l at
the a i r w i l l be dragged along the l i n e b y a
hydraulic
carrying
i t away
jump
may
form
i n b u b b l e form,
in
as
the
pipe
depicted
in
F i g . 5.2 The pipe
relationship
diameter
between
has
been
a i r pocket volume,
investigated
by
a
washout
number of
these r e s u l t s a r e summarized by Wisner et a l
velocity
and
workers,
and
(1975).
Kal inske a n d B l i s s (1943) produced the f o l l o w i n g equation f o r r a t e of water flow Q at which removal commences:
Q2
5
gD
= 0.707
where D
e
tan
e
(5.4)
i s the p i p e slope angle.
equation energy
i s g r a v i a ional acceleration and
i s the p i p e diameter and g
is s i m i l a r diagrams
possibility critical.
that
The term on the l e f t h a n d side of K a l i n s k e ' s the
to
5.3
(Figs. the
air
in
parameter
is
the
specific
momentum a n d
In
fact
points
5.4).
and removed
if
the
water
it
depth
to
drops
the
below
Then a h y d r a u l i c jump forms downstream which could e n t r a i n
air. Wisner air
et
al
(1975) produced d a t a from which
pockets may be deduced.
independent of
slope and
r e l a t i v e volume of (see F i g .
Hydraulic A
air
They
is a
function
i s practically
of Reynolds number
vD/v
and
pocket 4U/71D3 where U i s the a i r pocket volume
5.5)
Jumps
hydraulic
jump
draws
in
air
in
the
bubbles e x h i b i t a s u r p r i s i n g l y low tendency free form f o r the water,
the r i s e velocity of
i n d i c a t e r i s e velocity
a
long time.
form
of
bubbles.
These
to coalesce a n d remain i n
A i r may be absorbed from
the bubbles by
b u t t h i s takes a long time a n d many of the bubbles r i s e to
the surface before they a r e absorbed.
103
104
1
>
1o2
Fig.
5.5
= VD/v
E q u i l i b r i u m velocity of water f o r at l o 0 to 70° to the h o r i z o n t a l .
Kalinske
and
Robertson
rate
air
entrainment
of
(1943) at
air
pockets
in
a
pipe
found from model experiments that a
hydraulic
jump
was
given
the
by
the
equation Qd/Q
where
= 0.0066(F1
Qd
is
the
- 1)le4
(5.5)
volumetric
r a t e of
air
entrainment,
Q i s the water I
flow
rate
F1
and
is
the
upstream
r e l a t i o n s h i p was d e r i v e d f o r free
surface
considerably
downstream. greater
air
a jump
Froude
vl//gyl.
That
i n a r e c t a n g u l a r channel w i t h a
Experiments entrainment
number
by
rate
the
author
i n closed
pipes
indicate
a
(see Fig.
5.6)
Free F a l l s
A
jet
falling
free
into
a
pool
of
water has a s i m i l a r
air
intake
105 effect was
to
a
low
jump.
Avery they
head
the
represents
found
aeration the
this
r a t e of
higher was
expended
air,
the base of
For an
a
for
efficiency
energy in
i n t a k e at
(1978).
a e r a t i o n at
decreasing
21% oxygen
Assuming
Oxygen
a n d Novak
losses,
loss
head
term
by
50%,
ciency of for m
hydraulic
studied
lost
or
1
free f a l l s
oxygen defi-
to 1.6
up
head
only
would
initial
k g 0 /kWh
2
losses,
e.g.
k g 02/kWh.
in
the
indicate
The
or
jump
aeration
1
at
kW
fall.
rates
for
a i r u p to 8 kg/kWh. Water
flowing
amount
inlets
with
a
fall
free
e.g.
morning
glory
o r even siphon s p i l l w a y s w i l l a l s o e n t r a i n a consider-
type s p i l l w a y s , able
into
of
air
1976).
(Ervine,
Gravity
pipelines
are
therefore
as much of a problem as pumping lines.
0
2
F:
6
4
~
v
J3A/B Fig.
5.6
A i r removal a t h y d r a u l i c jumps
in c i r c u l a r conduits.
A I R VALVES
Air valves. fices air
accumulating These
are is
up
are to
3
accumulated
in
a
pocket
normally mm
in
of
in
the
i n diameter). a
chamber
a
pipe
'small
may
be released b y
orifice'
type
(typical ori-
The v a l v e opens when to
permit
a
ball
to
air
sufficient
be
released
from a seat around the o r i f i c e . On
the other
hand a i r discharge
d u r i n g f i l l i n g operations
(before
106
This sectio parallel t o hydraulir gradient constitutes1 peak Section Of pipeline running parallel t o hydraulic gradient and constitutes peak
Section of pipeline forming peak with respect t o horizontal and 0150 t o hydraulic gradient and peok with respect t o hydraulic gradient only
No peok Horizontal Section Of Pipeline having d w n w a r d grade and point of increaseof downward grade
Datum
Section of pipeline having upward grade and point of decrease of upward grade
Scour
Horizontal Long descending section of pipeline
FIG.
5.7
P o s i t ~ o no f
Datum
Long ascending section of pipeline
a i r valves along pipelines
107 pressurization) may
be
leased pipe
and
through from
is
air
the
seat
Fig.
low.
i n t a k e d u r i n g vacuum conditions
'large orifice' around
10.6
a i r valves, the
orifice
illustrates a
the b a l l of when
double
in
pressure
air
valve
the p i p e
which
i s re-
inside
with
the
both
a
small and a l a r g e o r i f i c e . The sures
size a n d spacing of outside
the
pipe
a i r valves w i l l
and
permissible
depend on ambient pres-
pressures
inside,
the
size
of p i p e a n d water flow rates. The equations
for
the
discharge r a t e
the c o m p r e s s i b i l i t y of
air
and
are
as
through
follows
pressure beyond the o r i f i c e p 2 i s g r e a t e r absolute i.e.
orifice
(Marks,
than
gauge p l u s atmosphere a n d p,
an
involve
1951).
0 . 5 3 ~ ~( a l l
If
the
pressures
i s i n i t i a l p r e s s u r e ) , then
(5.6) For p 2 ' 0 . 5 3 ~ ~ then
the flow
becomes c r i t i c a l
a n d flow
r a t e i s inde-
pendent of p2. Then
(5.7) where W a
is
i s the mass r a t e of flow of a i r ,
the o r i f i c e area,
rn
is
the
mass
C i s a discharge coefficient,
density
of
air
and
letting
air
into
k
is
the
a d i a b a t i c constant. Normally or
out
of
whether it,
p2
for a i r a n d C = 0.5 Qa = 0.34 a
where second a
the
is
air
less
valve
than
is for
0 . 5 3 ~ ~ Then .
i n t o the last equation,
substituting
the
k
is
if
SI
pipe 1.405
i t s i m p l i f i e s to
/-
Qa
=
(5.8)
tne
volumetric
units are
i s the area of
of
water a n d S a Since a i r density
r a t e of
employed)
the o r i f i c e , is
the
h
air
measured
at
( i n c u b i c metres p e r the
initial
pressure,
i s the i n i t i a l absolute head i n metres
relative
i s proportional
flow of
density to
of
air
at
initial
the absolute head,
pressure.
t h i s simp i f i e s
f u r t h e r to
( 5 9)
Qa = lOOa where
Qa
is
the
air
volume
flow
absolute) in m 3 / s a n d a i s in m'.
r a t e at
initial
pressure
(+
O m
Thus
t o r e l e a s e 1% a i r f r o m a p i p e f l o w i n g a t a v e l o c i t y of 1 m/s,
a n d under
low
t h e n (5.8)
head (10 m absolute being the minimum f o r no vacuum)
r e d u c e s to ~ . _ _ _
~
1 m/s x A = 0 . 3 4 a J 9 . 8
0.01
x
i.e.
d = 0.006D
thus
10/1.15
x
lo-’
x
(5.10)
the o r i f i c e diameter should
1% o f
be about
the
p i p e diameter
to
r e l e a s e 1% a i r b y v o l u m e i n t h e p i p e . The
theory
of
(1950)
to
cavity
formed b y
derive
metres
of
d
is
the
velocity
h2
C
the
orifice flow
water for
the
is is a
was
through
used air
If initial
head
column
a
Parmakian
valves
to f i l l
a in
the
is
beyond
orifice,
g
discharge coefficient f o r the valve,
each
a i r and S
by
head (absolute)
D i s the p i p e diameter,
diameter,
a d i a b a t i c constant f o r h2 > 0 . 5 3
hl,
is
acceleration,
the
for
an
p a r t i n g water columns.
orifice of
through
equations
water
gravitational
flow
s i d e of
the
air
V
i s the r e l a t i v e
k
valve,
is
i s t h e r e l a t i v e d e n s i t y of a i r ,
the then
hl,
(5.11) a n d f o r H
2-
(5.12) air
For
at
300
m
above
sea
level
and
air
temperatures
of
24OC
3
t h e n Sa
p l u s 20% h u m i d i t y equivalent
t o hl
=
9.97
i s 1.15
m of
x 10-
water.
k
a n d atmospheric pressure i s
i s 1.405.
For a i r valves
C
is
a b o u t 0.5.
HEAD LOSSES I N P I P E L I N E S
Air
suspended
increase
in b u b b l e form o r
t h e s p e c i f i c volume.
in p o c k e t s i n f l o w i n g
T h e mean v e l o c i t y
water
will
i s consequently h i g h e r
109 to convey
a c e r t a i n volume of water per u n i t time.
increase i n accordance w i t h an equation such
The head loss w i l l
as the Darcy- Weisbach
equation (5.13) v to use w i l l be v = ( 1
The velocity where v
W
i s the velocity
of
+
f)v
(5.14)
W
p u r e water f l o w i n g and f
i s the volumet-
r i c concentration o f free a i r i n the pipe. The head loss around a s t a t i o n a r y a
of
loss
velocity
head.
If
h y d r a u l i c jump
forms,
I f the velocity
i s subcritical
difference
in
velocity
the
the head
head
a i r pocket
size of
air
i s due p r i m a r i l y to
pocket
is
such
that
loss may be e v a l u a t e d from F i g .
throughout, is
lost.
a
5.4.
i t may be assumed t h a t the could
It
be
established
more
closely u s i n g momentum p r i n c i p l e s though.
WATER HAMMER
The water
presence of hammer
free
air
considerably.
in
pipelines
Fox
(1977)
can
reduce the s e v e r i t y of
indicates
that
the
celerity
(speed) of an e l a s t i c wave w i t h free a i r i s
c =
/*
(5.15) (5.16)
For l a r g e a i r contents t h i s reduces to c =where pipe
p i s the mass density
diameter,
b
i t s thickness,
absolute pressure and f c
2% o f
of water,
K i s i t s b u l k modulus, D i s the
E i t s modulus of e l a s t i c i t y ,
p
i s the
i s the free gas f r a c t i o n b y volume.
i s reduced r e m a r k a b l y f o r even r e l a t i v e l y low gas contents. air
at
a
pressure
head of
50 m of
water
Thus
reduces the c e l e r i t y
from about 1100 m/s f o r a t y p i c a l p i p e l i n e to 160 m/s. The Joukowsky water hammer head i s A h = SAv
(5.17)
9
where
Av
reduction
is in
the Ah.
change
in
velocity
of
flow.
There
i s thus
a
large
I f the a i r collects a t the top of the p i p e there i s no
110 reason on
to see why
the other
partly full
the same equation
cannot a p p l y .
Stephenson (1967)
h a n d d e r i v e d a n equation f o r the c e l e r i t y of a bore i n a The c e l e r i t y d e r i v e d from momentum p r i n c i p l e s i s for
pipe.
smal I a i r proportions J gAh/f
c =
where
Ah
(5.18)
i s the head r i s e b e h i n d the bore.
of 158 m/s f o r f = 0.02 There valves
a n d Ah = 50m.
i s a school of
in
pipelines
pressures.
The
cessively
large
reduction
in
thought
as
a
intention
p r o a c h i n g columns.
head.
of
The
hammer
which f a v o u r s the i n s t a l l a t i o n of a i r
means
is
air idea
in
of
reducing
primarily
to
wi II ,
Calculations
volume
a l l e v i a t e water
This indicates a celerity
water
cushion
however,
the
hammer
over-
impact of
indicate that
ap-
an ex-
i s r e q u i r e d to produce any
significant
stems
vessels
from
pipelines.
the
I t will
use of
air
be r e a l i s e d that
air
to in
vessels i s under h i g h pressure i n i t i a l l y a n d therefore occupies a
air
smal I
relatively trip,
volume.
Upon
pressure
reduction
following
puk = constant where
U
pump
(5.19)
i s the volume of
necessary
volume
of
air.
air at
a n a l y s i s to be excessive f o r An
a
the a i r from an a i r vessel expands according to the equation
unusual
low
The size of
air
v a l v e s to draw i n the
(vacuum) pressures w i l l
be found on
l a r g e diameter pipelines.
problem due possibly
to a i r coming out of
solution
in
a r i s i n g main was reported b y Glass (1980). Here a t h i n stream of a i r along after
the a
top
pump
of
the
trip.
line
After
a
supposedly number of
collapsed on years
the
a
pressure
rise
p i p e b u r s t along a
l i n e a l o n g the s o f f i t .
REFERENCES
Avery, S.T. and Novak, P, 1978. Oxygen t r a n s f e r at h y d r a u l i c structures. Proc. ASCE, HY11, 14190, pp 1521-1540. 1957. The prevention o f vortices i n Denny, D.F. a n d Young, G.A.J., intakes. Proc., 7th Con. I n t . Ass. Hydr. Res., Lisbon E r v i n e , D.A., 1976. The entrainment of a i r i n water. Water Power and Dam Construction. pp 27-30. 1977. H y d r a u l i c A n a l y s i s o f Unsteady Flow i n Pipe NetFox, J . A . , works. Macmillan, London. Glass, W.L., 1980. C a v i t a t i o n of a pump p i p e l i n e . Proc. I n t . Conf. Pressure surges. BHRA, Canterbury.
111 K a l i n s k e , A.A. and B l i s s , P.H., 1943. Removal o f a i r f r o m p i p e l i n e s b y f l o w i n g w a t e r , C i v i l E n g i n e e r i n g , ASCE, 13, 10. p 480. K a l i n s k e , A.A. and R o b e r t s o n , J.M., 1943. C l o s e d c o n d u i t f l o w , T r a n s . ASCE. 108, 2205, pp 1453-1516. M a r k s , L.S., 1951. M e c h a n i c a l E n g i n e e r s H a n d b o o k , 5 t h Ed. McGraw H i l l , N.Y. 2235 pp. P a r m a k i a n , J., 1950. A i r i n l e t v a l v e s f o r s t e e l p i p e l i n e s . T r a n s . , ASCE, 1 1 5 , 2404., pp 438-444. P r o s s e r , M.J., 1977. T h e H y d r a u l i c D e s i g n of Pump Sumps and Int a k e s , BHRA, and C I R I A , L o n d o n . 48 pp. Stephenson, 1967. P r e v e n t i o n o f v a p o u r p o c k e t s c o l l a p s e i n a p u m p i n g l i n e . T r a n s . , S o u t h A f r i c a n I n s t . C i v i l E n g s . 9 , ( l o ) , pp 255-261. W i s n e r , P . , Mohsen, F.M. and Kouwen, N., 1975. Removal o f a i r f r o m w a t e r l i n e s b y h y d r a u l i c means. Proc., ASCE. 101, HY2, 11142, pp
243-257. LIST
OF SYMBOLS
a
-
orifice area
A
-
area
b
-
wal I thickness
c
-
wave celerity
c
-
d i s c h a r g e coef f i c i e n t
c
-
gas concent r a t ion
co -
i n i t i a l concentration c o n c e n t r a t i o n at s a t u r a t i o n
d
-
D
-
p i p e internal diameter
cs
b u b b l e diameter
E
-
modulus of e l a s t i c i t y
f
-
volumetric concentration of a i r
F
-
Froude number
9
-
g r a v i t a t i o n a l acceleration
h
-
head
k
-
a d i a b a t i c constant
k
-
I i q u i d f i Im c o n s t a n t
K
-
bulk m o d u l u s
m
-
mass d e n s i t y o f a i r
M
-
m a s s r a t e o f t r a n s f e r o r s p e c i f i c momentum
P
-
pressure
Q
-
water discharge r a t e
‘d
-
r
-
volumetric r a t e of air entrainment gas d e f i c i t
ratio
112
s
-
t
-
time
u
-
a i r pocket volume
r e l a t i v e density o r s p e c i f i c g r a v i t y
v
-
water v e l o c i t y
v
-
volume of water p e r surface area
w
-
r i s e velocity
w
o f bubbles
-
mass r a t e of flow of a i r
Y
-
depth of flow
x
-
Darcy f r i c t i o n factor
e
-
p i p e slope a n g l e
v
-
k i n e m a t i c viscosity
P
-
mass density of water
113
CHAPTER 6
EXTERNAL LOADS
Low large as
pressure
diameter
well
tion
as
with
pipes,
especially
pumping
internal vacuum
mains
loads.
sewers,
should
or
even
be designed f o r e x t e r n a l
loads
The v e r t i c a l
pressure
inside
the
gravity
soil
mains
load a c t i n g
p i p e could
in combina-
cause
the
pipe
to
collapse unless the p i p e i s adequately supported o r stiffened.
S O I L LOADS
The
load
transmitted
to
a
pipe
from
the
external
surroundings
depends on a number of factors: Rigidity sidefill
of
pipe:
The
more r i g i d
the more load i t w i l l
causing a
l a r g e p a r t of
a
take.
pipe
is
relative
The s i d e f i l l
the b a c k f i l l
to
tends to settle,
to rest on the pipe.
w i t h f l e x i b l e p i p e too to some extent,
the trench thus
T h i s occurs
as a p i p e i s supported l a t e r a l l y
b y the f i l l a n d w i l l not y i e l d as much as a free s t a n d i n g pipe. Type
trench o r f i l l :
of
lation
conditions
w i t h the w i d t h
for
Fig.
pipes.
a n d depth of
trench affects the r e s u l t a n t different
loads
to
a
pipe,
6.1
The
i l l u s t r a t e s v a r i o u s possible i n s t a l load
transmitted
to
the p i p e v a r i e s
trench since f r i c t i o n on the sides of the load.
Embankment f i l l s may
depending
on
the
relative
also t r a n s m i t settlement
of
s i d e f i l l and topfi I I . Young sive
and
equations
various
trench
Trott and and
(1984), a n d C l a r k e charts
for
evaluating
soil
embankment
conditions.
Although
assumptions a r e subject yet
no other
(1968) have developed
to question,
loads
on
many
exten-
pipes of
in
their
the f a c t remains t h a t there i s as
theory w i t h which to c a l c u l a t e s o i l loads on pipes so the
engineer must use t h i s theory w i t h d i s c r e t i o n
(ref.
Spangler,
1956).
Trench Conditions
The s o i l
load transmitted
t h e w i d t h a n d depth of
For
a
normal
to a
r i g i d pipe
in a
trench depends on
trench a n d the s o i l b a c k f i l l properties.
vertical-sided
trench
(Fig.
6.la),
fill
at
the sides of
114 the p i p e w i l l
settle more than
be neglected.
On
the sides of trench
fill
developed
and is
the
sides
of
the
pressure
the
trench
the downward forces,
load.
trench
is
to
the
the trench,
the
to
Equating to
vertical
the
proportional
a n d the sides of
horizontal
a n d the s i d e f i l l support can
h a n d the f r i c t i o n of
takes some of
therefore
between the f i l l active
the other
the trench
the pipe,
vertical
u p w a r d forces
on
any
the b a c k f i l l a g a i n s t The cohesion between
neglected.
The
friction
of
friction
coefficient
a n d the r a t i o K of pressure horizontal
in
the
slice
Marston e v a l u a t e d the total
the
soil. in
the
load on a
p i p e at depth H ( 1 9 1 3 ) : Upward
load
per
unit
length
depth h + ah below ground
Pipe a t
of
s u r f ace : W + dW = W
+
yBdh
2K t a d
-
Wdh/B
Solution g i v e s
W = CdyBZ -2K(tane )H/B where t h e load coefficient C
K
@
d
=
2Ktan6
=
r a t i o of
l a t e r a l s o i l pressure to v e r t i c a l
-
1 - s i n 9 f o r a c t i v e s o i l conditions 1 + sin 0
=
a n g l e of
load.
a n d cohesionless soil
i n t e r n a l f r i c t i o n of b a c k f i l l
e
=
a n g l e of f r i c t i o n between b a c k f i l l a n d sides of trench
H
=
h e i g h t of f i l l above p i p e
B
=
trench w i d t h
Y
=
u n i t w e i g h t of b a c k f i l l m a t e r i a l
Ktane
n o r m a l l y ranges from 0.11
coarse crushed stone. Ktan8.
l o ) , Cd
Note
that
For
approximately
i s given
f o r deep
approaches a
the s i d e f r i c t i o n trench.
Cd
soft c l a y s to 0.16
i n Fig.
trenches,
(H/B
6.2
for
greater
v a r i o u s values for than
shallow
equal to H/B,
takes more of or
wide
the
most of
approximately
load the deeper t h e
trenches
(H/B < l ) ,
Cd
is
so
W = yHB
i.e.
for sands and
l i m i t i n g v a l u e of 1/(2 K t a n e ) . T h i s implies that
i n the trench
very
for
(6.2)
the b a c k f i l l
load i s taken b y the pipe.
The trench equa-
115
ALTERNATIVE /-FORM
SIDE
b : WIDE TRENCH SHALLOW EMBANKMENT
o S R R O W TRENCH
dSHALLOW EMBANKMELT PLSlTlVE PROJECTION
c :
DEEP
EMBANKMENT PROJECTION
POSITIVE -__
TA2r - - - - - -- - - - --- --
g SHALLOW E M B A N K M E N T
N E GAT1VE PROJECT1 ON
h:
DEEP EMBANKMENT N E GAT IVE P R O JE CT ION
1 TUNNEL OR H E A D I N G OR THRUST BORE
Fig.
6.1
A l t e r n a t i v e backf i I I s
c
W I D E TRENCH D E E P EMBANKMENT
_-
f : EMBANKMENT NEUTRAL PROJECTION
NORMAL DENSITY FILL
----
__-_.__ ---/
i
EMBANKMENT INDUCED _ T R-E N C H
116 tion
indicates
the
trench
that
width
the
increases.
the equation
width
load on a r i g i d p i p e increases i n d e f i n i t e l y as
no
next section)
then
apply
evaluate
the
load
trying
and
embankment
the
This
i s not
the case and a t
some trench
longer a p p l i e s a n d embankment conditions (see F i g . both
6.lb
the
criterion
and 6 . 1 ~ ) . I t i s necessary to
trench
(using
(see
criterion
6 . 3 ) , and
Fig.
6.2)
(using Fig. select
to
that
load which i s least. In
the
case
the crown of
of
'V'
a
trench,
i s used since the shear
of
the
trench.
If
the
flexible
width
to
I n t h i s case @ instead of 0
the pipe.
Cd
relatively
the trench
plane
is
side-fill
then
the
is
load
use
i s that
i n the formula f o r
i n the f i l l not against well
on
compacted pipe
the
at
and
the sides
the
depends
on
pipe the
is
pipe
diameter a n d not to the same extent on the trench w i d t h : W
C YBD (flexible pipe) d
=
Note that f o r small H, W
(6.3)
C d = H/B
and i n t h i s case
YHD
=
Embankment Conditions
A p i p e bedded on a f i r m surface w i t h a wide embankment f i l l over it
is
pipe
said
to
be
projects
projection positive natural
under
above
(Figs.
6.ld)
projection
if
ground
the p i p e crown projection
or
embankment
the
level,
and
pipe
and
the
conditions. ground
6.le).
the
i s below
trench
original
It
is
is
rigid
embankment
(Figs.
6.lg
the it
referred and
the n a t u r a l ground
condition
If
level
is
to
lies
crown
the
a
positive
as
a
complete
completely
relatively
level
of
is
above
shallow.
If
one has a negative
and 6 . l h ) .
For very
deep
trenches u n d e r embankments t h e conditions may be the same as f o r the trench
condition
( r e f e r r e d to
If
crown
level
the
projection For tends to
drag
=
with
the n a t u r a l
complete
positive
projection
s e t t l e more than downwards
on
the load on the pipe. W
as the complete trench c o n d i t i o n ) . ground
level
it
i s a neutral
(Fig. 6.lf).
the to
is
here
CcyD2
the
directly fill
case the f i l l
above the pipe.
directly
above
beside the p i p e
The s i d e f i l l
the p i p e and
tends
increase
The r e s u l t i n g load per u n i t l e n g t h of p i p e i s
117 where the load coefficient
e cc =
2K
[email protected] / D
-1
2Ktan@
LOAD COEFICIENT C,
F i g . 6.2
Load coefficient C d f o r trench conditions.
The l i n e
l a b e l l e d complete p r o j e c t i o n condition
v a l u e of
C
condition
.
for
Ktan@
= 0.19,
in F i g .
For deep embankments,
only
u
=
of
g i v e s the
a c e r t a i n h e i g h t of f i l l
the p i p e w i l l s e t t l e at a d i f f e r e n t r a t e to the s i d e f i l l . depends on the product He, settlement r a t i o s where
6.3
which i s the minimum adverse f r i c t i o n
the
pipe
projection
above
This height, ratio
projection of p i p e crown above o r i g i n a l ground level diameter of p i p e
u
and
the
118 s
settlement of adjacent f i l l o r i g i n a l l y at crown levelsettlement of p i p e crown reduction i n thickness of adjacent f i l l below crown level
=
The settlement ground
of
adjacent
fill
includes
level a n d the compaction of
p i p e crown
includes settlement of
the settlement of
the s i d e f i l l .
the bottom of
the o r i g i n a l
The settlement of the p i p e and v e r t i c a l
the
deflection of the pipe. The v a l u e of tion
soil
to
i s 0.7
value well
s n o r m a l l y v a r i e s from 0.3
1.0
for
compacted.
resulting
rock
b u t 0.5 The
product
soil
A
foundation.
common
is
su
for
used i n F i g .
6.3
to e v a l u a t e the
v a r i o u s embankment conditions.
I t i s not
.
necessary to e v a l u a t e H for
unyielding
soft y i e l d i n g founda-
i s recommended i f the foundation a n d s i d e f i l l a r e
load coefficient
The equation
or
for
for
C
deep embankments a n d
incomplete p o s i t i v e
projection conditions
i s more compl icated than f o r the shal low embank-
ment
condition,
it
(i.e.
minimum
but
was e v a l u a t e d by Spangler f o r
adverse
friction)
condition,
and
Ktan4
these
=
0.19
values
are
g i v e n i n F i g . 6.3. Fig. the
6.3
pipe
also
settles
Spangler
gives more
C
evaluated
friction)
for
label led
complete
this
values
than for
case, and
the
C
of
Ktanb
and
for
adjacent =
0.13
the
case
backfill (i.e.
when
(i.e.
minimum
the
values
are
incomplete
trench
conditions
the
top
negative
indicated
of 5).
favourable
in
since
6.3,
Fig. the
mech-
anics a r e s i m i l a r to those f o r trench conditions. For Fig.
w
the
6.19 =
where
negative
and 6 . l h )
projection
=
Cn
=
trench)
condition
(see
(6.6)
i s the same as C
i n Fig.
6.3 f o r
negative su b u t
with
I n t h i s case the projection r a t i o i s
depth of p i p e crown below n a t u r a l ground level w i d t h of trench
a n d the settlement
s
incomplete
CnYB2
replaced b y 6 i n a l l expressions. u
(or
w i t h the p i p e i n a trench under an embankment,
ratio i s
settlement of n a t u r a l ground level-settlement of level of top f i l l i n trench reduction in thickness of s o i l in trench above crown
D
119 1
Load coefficient C
F i g . 6.3
(Spangler,
f o r embankment conditions
1956).
The settlement of the level of the top of the f i l l i n c l u d e the settlement of the bottom of the pipe, a n d compaction
the f i l l
of
s may r a n g e from - 0.1
It
a
certain
replacing
negative
it
by
projection
r a n g e from -0.5 The
The
=
f o r u = 0.5,
load
amount
of
lightly
to - 1.0 f o r u = 2.0.
f o r u = 0.5 per
unit
compacted
compacted
condition
an embankment whether W
deflection o f the p i p e
i n the trench above the crown of the pipe.
i s possible to reduce the load on pipes under a n embankment b y
removing and
i n the trench may
(Fig.
to -2.0
l e n g t h on
fill
fill
6.li).
d i r e c t l y above the p i p e
directly, For
this
i.e.
inducing a
condition
may
f o r u = 2.0. a completely f l e x i b l e p i p e under
i n p o s i t i v e o r negative projection condition
YHD load on a
s
is
(6.7) r i g i d pipe i n a
p r o j e c t i o n c o n d i t i o n ) i s a l s o yHD.
trench up to
i t s crown
level
(neutral
120 C l a r k e suggests
lar
to
for
that
on a
that pipe
the
l o a d on
a
in a
trench,
w th
t h e cohesion of t h e m a t e r i a l above.
this
conclusion
are
not
or
tunnel a
thrust bore i s simi-
reduction
factor
allowing
The a s s u m p t i o n s i n a r r i v i n g a t
and
convincing
further
theory
would
be
extent
be
we1 come. Clarke
also
suggests
that
t r e a t e d a s embankments a n d preferable take
to
place
using
between
uniform
surcharges
the equivalen t
pure elastic
theory,
soil
different
fills
at
depth
as
of
large
determined.
some
load
densities
This
transfer
and
soil
is
must
masses
which settle differently. The pipe
soil
is
conditions the
density
the
are
water
which
saturated normally
pressure
would
(but
not
less
would
in
result
the
submerged)
severe
than
produce
a
for
the
uniform
l i k e l y to c r a c k a p i p e t h a n a p u r e v e r t i c a l
maximum
density.
load
The
saturated
radial
on
a
submerged case,
pressure
as less
load.
Example - N e g a t i v e p r o j e c t i o n case The
top
ground
of
a
pipe
level
trench.
and
in
2 m wide
a
there
is
7
a
trench
m
high
1
is
m below
embankment
natural
above
the
E v a l u a t e the load on the p i p e .
Projection r a t i o u =
1 2
- =
0.5
Settlement r a t i o s = -0.4 s a y .
H/B = 8 / 2 = 4 . From F i g .
6.3,
C
load coefficient
= 3.1
L o a d p e r m o f p i p e = CnyB2 = 3.1
x
18000 x 2*/1000 = 220KN/m
SUPER IMPOSED LOADS
It
is
customary
transmitted infinite,
the
surface
homogeneous,
The f a c t in
by
to
that
theory
transmitted
use
elastic
loads
to a
isotropic,
theory
to
evaluate
buried pipe and elastic
material
the
pressures
to assume a semi-
surrounds
the p i p e .
t h e s i d e f i l l may s e t t l e d i f f e r e n t l y to t h e p i p e i s i g n o r e d and suitable factors
load
if
the p i p e
s h o u l d be a p p l i e d
is flexible.
to
decrease
the
U n f o r t u n a t e l y no such f a c t o r s
a r e a v a i l a b l e yet. If the
t h e l o a d a p p l i e d o n t h e s u r f a c e i s of l i m i t e d l a t e r a l e x t e n t then induced
pressure
on
any
horizontal
plane
below
the
surface
121 decreases w i t h depth. consequently
the
The deeper
the p i p e ,
the w i d e r the spread and
lower the maximum pressure.
On the other
h a n d the
total v e r t i c a l force must remain equal to the superimposed load. Formulde point
load,
for or
evdluating
the
sections
The
impact factor
below
2.0
the
safe
varies
but
adopt
depth
the type of
from
full
due
a
to
surface
are given
in
1.3
load a n d depth of p i p e
for
slow
moving vehicles
i f the p i p e i s shallow.
greater
the amount of
the
loads
i n f i n i t e extent,
impact f a c t o r should a l s o be a p p l i e d .
with
moving vehicles cover
loads, to
vary
and
transmitted
limited or
suitable
will
surface,
reduces f o r point
A
below.
f o r fast
the
a pressure of
than
of
The impact factor
the p i p e diameter
reduction
value
the
and
i s debatable and
impact
to
factor
isolated
i t may be
until
conclusive
f i g u r e s a r e a v a i l a b l e (see also Compstan et a1 1978).
T r a f f i c Loads The
following
loads
Concrete Pipe Assn. (1)
I n fields
(2)
Under
are
useful
for
design
purposes
(see a l s o
1969).
: two wheel
loads each 30 kN spaced 0.9 m a p a r t .
light
roads
:
two
main
roads
and
wheel
loads each 73 kN spaced 0.9m
apart. (3)
Under eight
wheel
of four
heavy
traffic
153 type HB
(BS
load)
:
loads each 112 kN comprising two rows 1.8 m a p a r t
wheels each 0.9 m a p a r t
l a t e r a l l y , measured from i n n e r
a x l e to inner axle.
(4)
Airport
runways:
four
210
k N wheel
loads
spaced
at
1.67m x
0.66 m.
Pipelines
would n o r m a l l y be designed f o r f i e l d
ened under h e a v i e r t r a f f i c . design
loads e x t r a t o p f i l l
I f construction
should b e placed to spread the load d u r i n g
construct ion (Kennedy, 1971 )
Stress Caused by
Boussinesque's below p o i n t as
l o a d i n g a n d strength-
loads a r e l i k e l y to exceed
.
Point Loads
e l a s t i c theory
g i v e s the v e r t i c a l
load a n d a distance X
stress a t
depth H
h o r i z o n t a l l y from the p o i n t load P
122
w
3P H 3
=
27r(HZ + X ' ) The stress at the
stresses
occur
any due
(6.8)
5/2 point to
due to two o r
the
individual
d i r e c t l y under e i t h e r
load o r
more loads w i l l be the sum of
loads.
The
maximum stress could
somewhere between them,
and
the
worst case should be selected b y p l o t t i n g the stress between them. For the
large
pipe
Concrete for
pipe
diameter,
diameter Pipe
and
(l),
loads
average
value
a p p r e c i a b l y across
should
(1969) l i s t s the total
Association
surface wheel
stress w i I I v a r y
the
some
be
taken.
load i n kg/m
The
of
pipe
( 2 ) a n d (3) i n the p r e v i o u s section,
and
v a r i o u s p i p e diameters and depths.
Line Loads The v e r t i c a l
stress at
q per u n i t l e n g t h is,
w
depth H
any
below
a
l i n e load of i n t e n s i t y
b y e l a s t i c theory,
2q~3 n ( X Z + H 2) 2
=
Uniformly Loaded Areas The
stress
surface
could
intensity
load.
any
depth
beneath
be e v a l u a t e d b y assuming
p r i s e a number of
ma1
at
point
loads,
a
distributed
the
load to com-
i n f i n i tesi-
F o r t u n a t e l y Newmark has performed the i n t e g r a t i o n of point
loads
to
give
the
vertical
under
loaded
i n Table 6.1. To e v a l u a t e the v e r t i c a l
under
a
surface
with
one
rectangle
table.
the
particular rectangle. loaded
and
area
load
and
the
the
corner
influence
of
a
coefficients
stress at
loaded area
the p o i n t
any
point
into rectangles
i n question.
Calculate
a n d Y a r e the l e n g t h and b r e a d t h of
corresponding due
intensity
the p o i n t assume
the
stress
rectangle, If
above
where L
read the
Newmark's
d i v i d e the
directly
a n d Y/H
Evaluate
multiplying
loaded area,
corner
the r a t i o s L / H
area.
stress
uniformly
each
rectangular
the
a n d summating the stress due to each
are given
the
loaded area on
by
to the
summate
influence
each
the
factor
rectangle
influence stress
of
coefficient due
to
from
the
load
by
for
the
each
such
i n question f a l l s outside the boundaries of the loaded
area
extends
to above
s u b t r a c t the stress due to the i m a g i n a r y extensions.
the p o i n t and
123 TADLE 6.1
Influence factors f o r v e r t i c a l pressure under the corner of a uniformly loaded r e c t a n g u l a r area (Capper a n d Cassie, 1969).
o 0222 00435
Similar loaded
influence
circles
into
rectangles
also
influence
and
coefficients strips,
or
small
charts
but point
a r e available for
normally loads
available for
any
without
can
be
much e r r o r .
evaluation
shape loaded area (Capper a n d Cassie,
the stresses under
shape
the
intensity
dispersion.
of
the
surface
There
are
of stresses under any
1969).
The stress a t any depth under a uniform load of v e r y is
resolved
load
since
there
l a r g e extent
is
T h i s could also be deduced from Table 6.1
no
lateral
for large L and
Y.
Effect of R i g i d Pavements
A load
rigid
surface
load.
thickness h,
where
pavement
laterally
and The
above a p i p e has the effect of therefore
stress
at
reducing
the
a
H
depth
stress below
a
distributing
intensity rigid
due
the to
pavement
a of
is C_P/R2
(6.10)
W
=
R
-
E
=
modulus of e l a s t i c i t y
h
=
pavement thickness
= r a d i u s of
f o r concrete)
stiffness
(28 000 N/mrnz
or
4 000 000 p s i
124 U
=
Poisson's r a t i o (0.15 f o r concrete)
k
=
modulus
of
0.028N/mm3
subgrade for
reaction,
poor support
R
is
normally
function
of
H/R
s i n g l e point
A
concrete
and
three
X/R
times
and
the
slab
normally
Pressure
has
the
effect
of
coefficients
for
a
point
1970)
Pipe Assn.,
W
Pressure on p i p e = CrP/R2 Depth of Top of Pipe Below Pavement
P
Point Load
R
Radius o f Stiffness
X
Horizontal Distance from Point Load
-
-
20
24
020
054
032 03 1 03? 032
062 051
047
010
022
l!d2
026
o:?
24
043
036
llib
021
28
037
03 I
073
019
32 36
012
025
40 41
02%
013 0XJ 018
O? I 019 018
OIR
027
015
014
48
52 56
018 015 014
Olh 014
012 01 I
60
012
Ol!
013 012 cil? on9
63
011 010
ni;
00s
008
009
nux
uni
12 75
009
ons
007
037
OOR
'I-;
00-
[I!)&
gn
007
007
OOh
00'
n
08
1 2
l!3 101
ObX
061
12
089 076
16 ?0
03
08
68
020
~.
Cr
is
a
i n Table 6.2
for
a
thickness.
i s tabulated
__
(1
slab
H
00 ___
A typical
N/mm3
about
five
times
its
i n a t t e n u a t i n g a p o i n t load.
(Amer. Con.
H R
from
load P on the surface.
thickness of s o i l f i l l
TABLE 6.2
about
varies
to 0.14 N/mm'.
i s 0.084
v a i u e f o r good support
which
(Ifil
01:
-~~
-
U? i
02: 017
016 015
010 or19
28
load
on
a
pavement
125 REFERENCES
American Concrete Pipe Assn., 1970. Design Manual-Concrete Pipe, Arlington. Capper, P.L. a n d Cassie, W.E., 1969. The Mechanics of Engineering Soils, 5th Ed., Spon., London. 1968. B u r i e d p i p e l i n e s , MacLaren, London. Clarke, N.W.B., Concrete Pipe Assn., 1969. Loads on B u r i e d Concrete Pipes, Tech. B u l l . No. 2, Tonbridge. Cray, P., Schofield, A.N. a n d Shann, C.D., lc7C. Compston, D . G . , Design a n d Construction of B u r i e d T h i n Wall Pipes. CIRIA. Kennedy, H., 1971. E x t e r n a l loads and foundations f o r pipes, J . Arc!. Water Works Assn. March. Marston, A . and Anderson, A . O . , 1913. Theory of loads on pipes i n ditches and tests o f cement a n d c l a y d r a i n t i l e s a n d sewer p i p e . Iowa State Univ., Engg. Res. I n s t . B u l l . Spangler, M.G., 1956. Stresses i n pressure p i p e l i n e s a n d p r o t e c t i v e c a s i n g pipes, Proc. Am. SOC. C i v i l Engrs., 82 ( S T 5 ) , pp 1054-1115. Young, D.C. and Trott, J.J., 1984. B u r i e d R i g i d Pipes. Elsevier Applied Science, London. p p 230.
L I S T O F SYMBOLS
trench w i d t h load coefficient,
embankment
condj tion,
positive projection
case load coefficient,
trench condition
load coefficient,
embankment condition,
negative projection
case load coefficient,
r i g i d pavemerot
d i ameter effective modulus of e l a s t i c i t y of s o i l modulus of e l a s t i c i t y pavement thickness or v a r i a b l e depth depth of
cover
depth of f i l l below p l a n e of equal settlement momen t of
inert ia
modulus of subgrade reaction modulus of subgrade reaction r a t i o of
l a t e r a l to v e r t i c a l s o i l pressure
l e n g t h of
loaded area
bending moment bending and
y
or
refer
deflection to
top,
coefficient bottom
and
(subscripts side
t,
b,
moments a n d
zon t al and v e r t i ca I d i stort ions respective I y )
s,
x
hori-
126 pressure p o i n t load l i n e load per u n i t length radius r a d i u s of stiffness settlement r a t i o wal I thickness project ion r a t i o v e r t i c a l pressure W
l a t e r a l soil pressure
W
permissible r i n g load
W
permi ssi b l e v e r t i c a I load
w
vertical
load per u n i t length
horizon t a I distance w i d t h of
load area
a n g l e of bottom support def I ect ion u n i t weight of soil a n g l e of trench
friction
between
backfill
a n g l e of f r i c t i o n of b a c k f i l l m a t e r i a l Poisson's r a t i o
and
sides
of
127
CHAPTER 7
CONCRETE PIPES BEDDING
THE EFFECT OF
Non-pressure external the
design
pipes
are
external
load
per
drain
for main
self
at
are
the
crown,
weight
and
by
the
live
weight
of
a
pipe
to
a
bed.
The
load
loaded
thus
is
called
strength
practical
factors
determination
of
withstand
rigid
laboratory
of
water
the
and
vertical
concrete
per
the very
is
and
to
the
vertical
haunches
and
the
the
haunches.
The
and
horizontal
soil
pressure a n d
pipes).
supported
on
length r e q u i r e d to f r a c t u r e
the
strength.
load
reliable.
and
while
Although
theoretically,
theoretical
more
uncertain
load
laboratory
calculated the
load
line
unit
the
be
specify
r i g i d non-pressure pipes a r e normal-
vertical
influence
of is
could
due
( i n t e r n a l water
pressures a r e neglected f o r non-pressure
designed flat
bottom
loads,
withstand
classes
stresses at
to
standards
different
compressive stress
caused
designed
Various
The
the
run
Concrete pipes a n d the other ly
are
pipe
are
unit
pipes
pressures. of
stresses
transient
or
internal
reinforced accordingly.
stresses
loads,
not
loads
bending main
sewer
loads,
and
(The
effect
the
a
of
number
the of
experimental
tensile lateral
strength constraint
the supports may be a p p r e c i a b l e ) . Alternative
ed
in
that
Fig.
standard
7.1.
The
load which
inforced pipes,
will
concrete
or
testing
is
defined
produce a c r a c k
pipes
90% of
arrangements f o r
strength
the
60% of
or
1/10000
inch
(0.25
mm) f o r unre-
ultimate
load
for
1/100
the
(0.025
inch
i I lustrat-
pipes a r e
B r i t i s h Standard 556 as
in
mm)
wide
reinforced
crack
load
for
prestressed c y l inder type concrete pipes. The strength u s i n g the 3-edge in
excess
of
b e a r i n g test
that was
for
the
bearing
2-edge
standardized
and
test
bearing
is
test.
usually
Recently
5 the
to
10%
3-edge
t h i s i s now defined as the labora-
t o r y strength. Pipes wide higher
laid
length than
in
of the
trenches arc
by
are
the
laboratory
usually
bedding. strength
supported The
as
over
strength
the
bending
is
a
relatively
consequently moments
are
128 less.
F i g . 8.2
summarizes
the
theoretical
b e n d i n g moment c o e f f i c i e n t s
for pipes supported over various angles (defined i n Fig.
8 . 4 ) (CPA, 1962).
0 mm
15&brmm rubber
2 -EDGE
3-EDGE
3-EDGE FOR ANY OIA UP TO l8OOrnrn
Fig.
7.1
The the
S t a n d a r d c r u s h i n g test b e a r i n g s f o r r i g i d p i p e s
ratio
bedding
of
field
factor.
strength
Various
to
laboratory
types
of
bedding
b e d d i n g f a c t o r s a r e l i s t e d b e l o w (CPA,
TABLE 7.1
strength and
1967; ACPA,
is
defined
the corresponding
1970):-
Bedding factors
120" R.C. c o n c r e t e c r a d l e o r a r c h
3.4
Class A
120° p l a i n c o n c r e t e c r a d l e o r a r c h
2.6
Class B
Granu Ia r bedding
1.9
Class A
Class C
H a n d s h a p e d t r e n c h bottom
1.5
Class D
H a n d trimmed f l a t bottom t r e n c h
1.1
For
as
rigid
concrete
pipes
the
lateral
support
of
the
sidefill
in
the t r e n c h does n o t a d d n o t i c e a b l y to t h e s t r e n g t h .
A
factor
of
safety
forced concrete pipe.
K of
1.25
to
1.5
i s normally
When p i p e i s p r e s s u r i z e d ,
used w i t h u n r e i n -
i t s h o u l d be designed
so t h a t : -
external load f i e l d strength Unreinforced
+ or
internal pressure bursting pressure reinforced
(not
<
1
(7.1
K
prestressed)
concrete
pipes
are
129 normally
only
drains.
for
non-pressure
The
concrete
may
to
internal
pressures,
subjected certain
used
tensile
strength,
be
pipes
stressed
in
and
such
as
tension
even
if
though
c r a c k s may develop a n d
sewers the
and
pipe
concrete
leaks a r e
was
has
a
likely
if
the tensile stress i s maintained (Kennison, 1950). Concrete Special
pipes
normally
precautions
may
do
be
not
necessary
stance sewers a r e often made w i t h r a t e of corrosion of thus
require for
lining
certain
or
wrapping.
liquids,
for
in-
limestone aggregate to m a i n t a i n the
the aggregate a t
m a i n t a i n i n g an even surface.
the same r a t e as the
cement,
The f r i c t i o n coefficients of concrete
pipes, especially when c e n t r i f u g a l l y w i t h those of l i n e d steel pipes.
cast,
can
compare
favourably
PRESTRESSED CONCRETE PIPES
Prestressed pressure for
long
ses
than
that for
pipes
when
becoming
a popular
over
competes
medium for
800 mm
approximately
large-bore
economically
with
diameter.
It
steel
has
the
the prestressing steel can be stressed to h i g h e r stres-
plain-walled must
be
and d i s t o r t i o n even pressures.
is
Prestressed concrete
pipelines
advantage
steel
concrete
pipes.
pipes.
reasonably if
The
wall
thick
to
the
use
of
manufacturing plain-walled
p l a i n walled
buckling,
collapse
i s not r e q u i r e d to r e s i s t i n t e r n a l
the thickness
Consequently
thickness o f prevent
high-tensi le
steel
pipes,
steels
is
restricted
b u t t h i s i s not the case
w i t h prestressed concrete pipes which a r e more r i g i d than steel pipes. Prestressed wires core
onto
a
forming
concrete core.
pipes
The
helical
the b a r r e l of
each
i n a mould o r c e n t r i f u g a l l y then
steam
cured
to
the core may
mortar.
steel
cylinder
load
under
concentrated forcing.
Plain
stressed
longitudinally
winding
by
is
winding
subsequently
rapid
strength
improves
the
wire,
are
as well
pretensioned
increase
and
often
acts
as
lined with
longitudinal
The
is
winding.
distributes
reinforced with
as c i r c u m f e r e n t i a l l y .
vertically
The concrete before
a steel c y l i n d e r
watertightness,
The
coated.
p i p e may be concrete cast
be formed w i t h
concrete cores
reinforcing resists
formed
i n a h o r i z o n t a l position.
ensure
Alternatively The
are
bars or
the
reinpre-
longitudinal
l o n g i t u d i n a l bending i n the trench as well as local
130 bending
stress
longitudinal
i n the core w a l l s d u r i n g c i r c u m f e r e n t i a l
wires
are
pretensioned
and
released once
winding.
The
the
has
core
set.
Fig.
7.2
Prestressed concrete p i p e
The prestressing close
wire
to y i e l d p o i n t .
It
i s wound loses a
and s h r i n k a g e before the p i p e
h e l i c a l l y onto the core a t a stress
proportion i s put
of
i t s stress
due to creep
A concrete c o a t i n g
into service.
i s a p p l i e d as soon as possible a f t e r w i n d i n g to get as much stress as possible t r a n s f e r r e d to the c o a t i n g d u r i n g the s h r i n k a g e of the core. The
tensile
of
manufacture
inherent
do
on
some
seepage
cause
the
pipe of
Further
in
tees)
may
the
or
the
after
through
neglected
in
accounting
for
design of
soon
seal
h y d r o s t a t i c test
core
but
may
due is
to
before c o a t i n g
be
immediately
permitted
the
usually
at
and this
before dispatch of
and i n the field. joined with
The socket may
spalling
cracks A
winding
the
load tests may be done
insertions.
stressing
is
concrete.
immediately water
The pipes a r e u s u a l l y
needed
core
cracking,
t h e pipes from the works,
rubber
the
i f t r a n s i e n t stresses i n the f i e l d o r i n the process
h e a l i n g p r o p e r t i e s of
done
stage.
of
strength
f i e l d pressures b u t
of the
integral socket
be f a b r i c a t e d from steel
spigots a n d sockets sealed w i t h
be of
steel
o r concrete b u t care i s
concrete will
sockets
occur.
o r cast
iron,
to
Specials
ensure (bends
no and
and are f i t t ed with
matching
spigots
up
a
over
and
number
sockets.
Small
angle
joints
which
may
take
the prestressing
wires
of
bends
are
up
n o r m a l l y made
2"
to
deflection,
depending on the type of j o i n t .
C i rcurnferent i a l The
Prestressing
tensile
stress
wound
i s less than
wire
is
i s because the core deforms under the p r e s t r e s s i n g
instant
of
the
the core
immediately a f t e r
This
section
onto
in
prestressing
i s under
core
at
relaxation
of
any
section,
stress whereas
the
point
the
steel
of
the
the other
winding
stress a f t e r
the a p p l i e d tensile
is
pipe side
half
winding
to
its
final
wi II
stress.
force.
one
i s free.
side
the
At the of
the
The s t r a i n strain.
in The
therefore correspond
to h a l f the t o t a l s t r a i n of the concrete core and
Afs
i f
=
n co 1
i s the r a t i o of
where n,
the concrete a t
the
i s the steel stress, fso =
f
where f
.
so
i f
fco
elasticity
of
i s t h e core stress a f t e r
steel
to that of
w i n d i n g and f
hence
n co 1
i s the
51
winding. f
. -
SI
the modulus o f
time,
initial
steel
stress and f
so i s the steel stress a f t e r
Since f o r e q u i l i b r i u m of forces
s =
f
t co c
(7.2)
and
fSo
where S
=
(7.3)
fcotc'S
i s the steel cross sectional area per u n i t length o f p i p e , a n d
tc i s the core thickness.
Circumferential After static may
test
to
undergo
amount of
Prestress a f t e r
winding
the core,
detect has
cracks.
usually
concrete creep
Losses
the p i p e Any
taken
is usually
creep place
has occurred.
which by
this
subjected to a hydrothe
prestressing
time,
and
a
steel
certain
The concrete stress j u s t before
the test becomes f .
CI
=
fco
(7.4)
132 where
is
u
the
combined steel a n d concrete creep
winding and testing.
fsi The
stress
for
The corresponding steel stress i s :
(7.5) any
particular
test
loading
may
be
calculated
using
- 7.15 b u t r e p l a c i n g subscripts 2 b y 1 a n d s e t t i n g the core
7.9
thickness
tb equal
as q u i c k l y and
between
fCitC/S
=
Equs.
coefficient
The c o a t i n g should be a p p l i e d and cured
as possible a f t e r of
creep
to zero.
the
testing.
concrete core
This ensures t h a t the s h r i n k a g e
transfer
as
much compression
to
the
c o a t i n g as possible. The c o a t i n g adds to
the cross sectional
area
a n d reduces stresses
thereby a l s o l i m i t i n g the creep of the core. After up
to
the
pipe
has
been
three months a f t e r
cured and
i s r e a d y for
service
(usually
m a n u f a c t u r i n g ) the c i r c u m f e r e n t i a l tension
is
taken by the core and the coating: fS,SCf
(7.6)
t + f t c2 c b2 b
Equating
the
movement due to e l a s t i c compression,
creep
and s h r i n k -
age of the core a n d coatings to that of the steel: Deformation of the core:
w
-fc2-f + - c1 Ec2
c
Ec2
( E l a s t i c ) (Creep )
f .+f CI
c2
+ v c2
2
=
sl -fs2
(7.7)
ES
( E l ast ic-steel )
(Shrinkage)
Deformat ion of coating : Sl b2
b2
- f
b2
52
ES
( E l a s t i c ) (Creep) ( S h r i n k a g e ) ( E l a s t i c deformation of steel) Now
if
the properties of the concrete core and coating are s i m i l a r ,
the e l a s t i c modulus E
c2
-
Eb2
and the s h r i n k a g e coefficient Solving Equs. 7 . 5 - 7 . 8 f o r f
v
c2
= vb2 = v
sl - f52’
say.
133 2+ w v E c 2 ( t c + t 6 K b ) + tcfcl w c
fsl - fS2 =
(7.9)
S ( l + wc ) + (tc+tb2+wc)/n __ 2 2 2+Wb
Hence from 7.8
(7.10)
(7.11)
Circumferential There
are
Stress Under F i e l d Pressure
a
number
of
field
loading
conditions
which
should
be
examined i n c l u d i n g :-
In open
(1)
trench
internal
with
test
operating
or
pressure p l u s
self weight a n d weight of water.
(2)
I n b a c k f i l l e d trench
with
i n t e r n a l pressure p l u s l i v e load p l u s
self weight a n d weight of water.
(3)
I n backfilled
trench
with
live
load p l u s self
weight
and pipe
empty.
(4)
In
backfilled
trench
with
internal
pressure,
self
weight,
crown
(due to
weight o f water a n d t r a n s i e n t pressures. The
most
highly
prestressing sures), cal
at
plus
sections
bending
the haunches
load p l u s
sing
stressed
plus
plus
usually
external
at
loads
the plus
internal
pres-
( d u e to prestressing p l u s bending p l u s v e r t i -
i n t e r n a l pressure)
bending
are
under
vertical
a n d a t the support plus
horizontal
( d u e to prestres-
loads
plus
internal
pressure). Compressive area
per
unit
and
tensile forces a r e taken
length
of
wall
comprising
the
d i r e c t l y on
the effective
p i p e core
pl us coating
p l u s transformed steel section:
A = t
+ tb + ( n 2 - 1 ) S
Bending weight
of
moment
of
moments pipe
plus
inertia
I
due
(7.12)
weight per
soil
to
of
unit
loads,
water length
are of
external resisted wall.
The
live by
loads
the
effective
distance
c e n t r o i d of t h e effective section from the i n s i d e of the core i s :
and
of
the
134
(7.13) where d
i s the diameter of
the prestressing
wire.
The corresponding
distance to the outside of the c o a t i n g i s : e
= t c + t b - e
(7.14)
0
The moment of e3 I=____
+
e
i n e r t i a of the effective section i s :
+ ( t c + ds/2 - e I 2 ( n 2 - 1 ) S.
0
(7.15)
3
Long itud in a I Prestressing Some
prestressed
circumferential l y . tensile c r a c k s the
pipes
The
are
prestressed
longitudinal
prestressing
is
i n the concrete d u r i n g w i n d i n g of
longitudinal
bending moment i n service.
wires a r e p l a c e d i n the. mould f o r before
casting
causes
local
in
longitudinal
the
longitudinally
the
core.
When
the
assists
added
as
prevent
to
the core a n d due to l o n g i t u d i n a l b a r s or
The
the concrete core a n d pretensioned wire
bending stress and shear bars
we1 I
as
in
is
wound
onto
i n the core walls.
reducing
the
the
core,
it
The tension
resulting
principle
stresses b y i m p a r t i n g a compressive stress to the concrete core. As
for
the c i r c u m f e r e n t i a l
wires,
the
longitudinal
stress due to creep of the steel a n d concrete. ly
stressed
to
.
f
their
SlL’ core cross sectional area
uL,
total is A
bars
lose some
I f the b a r s a r e i n i t i a l -
cross sectional
i s AS,
area
the p i p e
and the creep r e l a x a t i o n coefficient
then immediately a f t e r release of the l o n g i t u d i n a l b a r s ,
is
the stress
i n the core becomes: u
L
f c o ~-
f . A SlL s + nlAS
(7.16)
a n d the l o n g i t u d i n a l steel stress becomes fsoL = fcoLAc’As The
core
release of
is
normal l y
the
of
prestressed circumferential l y
longitudinal bars.
end to the other. application
(7.17)
The h e l i c a l
wire
immediately
i s wound from one
The r a d i a l shear stress i n the core, the
winding,
is
derived
from
after
at the p o i n t of
elastic
pressurized c y l i n d e r s (Timoshenko and Woinowsky-Krieger,
theory
for
1959) and i s
135 approxima tel y q
0.54 S f S O / v
=
(7.18)
f
i s t h e circumferential steel so the e x t e r n a l diameter of the core. where
The
maximum
due to bending
local
longitudinal
stress a f t e r
tensile
and
winding,
and D
is
compressive stresses
i n the core w a l l d u r i n g w i n d i n g h a v e been determined
experimental l y to be approximately fcmL = 0.3fco
(7.19)
where fco i s the core c i r c u m f e r e n t i a l stress a f t e r winding. The effect of the l o n g i t u d i n a l steel on the cross sectional a r e a has been
neglected
neutral mum
in
Equs.
7.18
and
7.19
as
the
a x i s a n d the expressions a r e approximate
tensile
stress
in
the
core
wall
steel
is
near
the
anyway.
The rnaxi-
may be d e r i v e d w i t h
the assis-
tance of a Mohr d i a g r a m ( F i g . 7 . 3 ) : I f fcmL > fcoL, c t L =/qz
which i s u s u a l l y the case, - f
fcml
+
( 2
and
i f
""4
2-
then
-
+
COL
2
f c o L > fcmL
then f c t L =
h2
+ ( f C 0 L - FcmL 2
2
-
-
fcoL
cmL
2
I
SHEAR
STRESS
Fig.
7.3
( 7.20a )
Mohr c i r c l e f o r stress i n core d u r i n g w i n d i n g .
(7.20b)
136 It
will
be
longitudinal
seen
from
prestress,
Equs.
which
7.20
a
b
and
i s proportional
the p r i n c i p l e t e n s i l e stress in the core f
that
to
f
the
larger
the
the smaller
COL
is
ctL'
Longitudinal S t r e s s e s A f t e r L o s s e s
The
longitudinal
in the f i e l d .
pipe
points
the
in
creep
and
act
to
At
this
have occurred
stress
longitudinal neglected.
bedding.
will
compressive
bars
resist
longitudinal
bending
of
the
The p i p e a c t s a s a beam s p a n n i n g between uneven
will
stress
stage in
h a v e been
is
not
S h r i n k a g e of
high,
the
a
c e r t a i n amount of
concrete
and some
t r a n s f e r r e d to the
concrete
shrinkage
longitudinal
the c o a t i n g .
creep
can
As
the
usually
be
t h e c o r e does r e d u c e t h e t e n s i l e s t r e s s i n t h e
b a r s and t h e c o m p r e s s i v e s t r e s s i n t h e c o r e becomes:
u f A L siL s fc2L
=
Ac
Once added
(7.21 )
pipe
the
ESAS
n2AS
+
the
to
v
-
is
stress
in
service,
due
to
longitudinal
prestressing.
The
bending extreme
stresses fibre
are
bending
stresses a r e
-
MD 21
-
fc3L
-
where M
(7.22)
i s t h e b e n d i n g moment
t h e e f f e c t i v e moment o f
and
inertia of
the section i s
I
l
-64
=
(l D 4-
d
(d
4
+ (n2
-
+ 2t + d 5 ) *
1 ) AS
(7.23)
8
P r o p e r t i e s of Steel and C o n c r e t e The
steel
used
w i n d i n g prestressed concrete p i p e should h a v e
for
a s h i g h a y i e l d s t r e s s a s p o s s i b l e and a y i e l d s t r e s s o f 1650 N/rnmz (240 000 p s i ) shrinkage concrete it
is
i s n o t uncommon.
have
taken
is fairly
normal
to
place,
high.
This will
e n s u r e t h a t a f t e r c r e e p and
the r e m a i n i n g compressive stress
The steel stress w i l l d r o p a f t e r w i n d i n g ,
confine
working
stresses
to
less
than
50% o f
the
in
and
yield
stress. Steels work
with
w i t h and
high
yield
in f a c t
stresses
are often
b r i t t l e and
difficult
to
the u l t i m a t e s t r e n g t h may not be much h i g h e r
137 than
the
yield
stress.
The to
may creep s l i g h t l y
distinguish test,
stress
in
therefore
between concrete
so
the
necessary
in
of steel
selecting
the
i s approximately
(30 x 10
steel
works
is
T h e modulus of e l a s t i c i t y 6 psi).
prestressing w i r e . 200 000 N/mm2
Care
they
steel
are is
a f t e r prestressing a n d steel
usually
creep
considered
typically
around
but
it
is difficult
between w i n d i n g and
together.
5% a n d
This
occurs
loss
in
w i t h i n a few
hours a f t e r w i n d i n g . Concrete day
achieved.
are
the
under of
High e a r l y strength
cube
cracks
cast
strengths
vibration or
60 N/mm2
(e.9.
will
strength
at
the
most p r o b a b l y
time
centrifugally
and
28
( 8 700 p s i ) a r e f r e q u e n t l y
50 N/mm2 o r
w i n d i n g as e a r l y as possible.
able for of
cores
cube c r u s h i n g
7 200 p s i ) i s desir-
Compressive stresses u p to 50%
a r e permitted d u r i n g w i n d i n g
(any
h e a l ) . Working compressive stresses should
be confined to less than 1/3 of the 28 day cube strength. The less
bending
than
tensile
about
calculated
10%
bending
bending
in
the
strength
i n order
stress of
tensile
field
in
the
strength
stress
should
be
to a l l o w f o r
i t y of cracks developing.
the core d u r i n g w i n d i n g
cube
in
the
limited
at
that
core to
due
about
should be
age, to
and
the
longitudinal
5% of
the
cube
unknowns a n d to prevent any p o s s i b i l -
No c i r c u m f e r e n t i a l tensile stress i s permitted
i n the core i n the f i e l d f o r normal o p e r a t i n g conditions b u t tension i s sometimes the
p e r m i t t e d under
coating
(This
should
i s for
be
transient
less
b u r i e d pipe.
than
conditions. about
The
10% of
the
tensile stress cube
in
strength.
Exposed pipes may develop cracks
a n d the
tensile stress should be less t h a n t h i s . )
4625
BS
operating 0 . 7 4 7 m if 0.623
/
F
does
plus
not
permit
backfill
water
tensile
pressures,
stress but
in
permits
hammer pressure i s included,
during
works
hydrostatic
test.
the a
core
for
tensile
normal
stress
of
a n d a tensile stress of
(Where F
is
the
crushing
strength of 150 mm cubes a t 28 d a y s , a l I i n N/mm2 . ) The
modulus of
elasticity
of
and v a r i e s from 20 000 N/mm2 ( 6 000 000 p s i ) (BSCP 2007,
The creep coefficient, creep s t r a i n
=
AL/L
increases
( 3 000 000 p s i )
1970; Ferguson,
w,
= w
concrete
to
w i t h the s t r e n g t h
40 000 N/mm2
1958).
of concrete i s defined b y the equation
fc/Ec
138 where
fc
is
the
average
creep occurs a n d E
compressive
i s the f i n a l
stress
during
Creep i s high f o r
the r a t e of
time.
creep reduces w i t h
casting
(at
the
time
three
months a f t e r casting.
Hence f o r
test
be 30% h i g h e r f o r
I t may
' g r e e n ' concrete and
i s approximately 0.3
w
factory
that
testing
the
core)
the coating,
two days
and
is
1.3
the coefficient
1.3
b u t f o r the core, the creep coefficient f o r
i s used to c a l c u l a t e creep, the time between f a c t o r y
of
time
w varies with
modulus of e l a s t i c i t y .
time a n d the method of c u r i n g .
after
the
i s 1.3 - 0.3 = 1.0.
a n d f i e l d conditions
pipes not p r o p e r l y cured o r exposed to the
elements i n the f i e l d . Shrinkage ing,
typical
of
concrete also depends
l a r g e l y on the method of c u r -
values of s h r i n k a g e per u n i t length,
v,
v a r y i n g from
to Example
Calculate
circumferential
after
winding,
curing
concrete
and
and
under
field
steel
stresses
conditions
during for
the
prestressed concrete p i p e described below: Effective p i p e tc = 75 mrn,
15 mrn c/c. 8
length L = 4 m,
coating
=
S = 0.00131
diameter,
mm
tb
N/mmz.
Vertical
lateral
soil
loading
pressure 0.5 of
steel
m2/m of pipe.
A S = 0.00121
e f f e c t i v e l y over 30"
bore d i = 2 000 rnm,
25 mm,
due x
arc.
m2. to
winding
L o n g i t u d i n a l wires 24 N o .
Maximum
soil
vertical
=
core thickness
5 mm diameter at
internal
and
live
0.02
N/mmz.
pressure
load 0.04
x
0.8
N/mrn2,
Bottom support
Neglect selfweight a n d weight of water
inside. Steel: L o n g i t u d i n a l prestress = 400 N/mm2 .Winding prestress = 1000 N/mmz. ES = 200 000 N/mm2. Creep coefficient u = 0.95. Concrete:
E
= 30 000 N / m m 2 , CI from f a c t o r y test to f i e l d test. n
n
1
2
=
200 000/30 000
= 6.7
=
200 ooo/38 000
= 5.3
Ec2 = 38 000 N/mmz,
= 1.0
Wb
.
= 1.3,
Creep w 4 : v = 10 shrinkage
Stresses due to w i n d i n g -
fco
-
1 000 x 0.0131 0.075 i 0.00131 x 6 . 7 / 2
=
16.5
N/mm2
(7.2)
139
16.5
=
so
0.075 0.00131
= 880 N/mmz
(7.3)
Works t e s t o f c o r e : fcl fSl
=
0.95 x 16.5
=
15.7 N/mm2
=
0.95 x 880
=
840 N/mm2
(7.4)
a f t e r curing :
f
-f
=
s2
s2 fb2
2+1 .o 1 O-4x38x1 0 ' (0.075+0.025m)+O. 075x15.7xl.O 0.00131 (ld$)+(0.075+0.02*)/5.3 2+1 0
=
76 N/mmz
=
840-76 = 764 N/mmz 76 (200 000
= -
c2
38 Oo0 = 6.4 N/mmz 2+1 .3
764~0.00131-6.4x0.025 0.075
Under f i e l d
(7.9)
=
(7.10) (7.11)
11.2 N/mm2
loading:
Transformed section A =
0.075 + 0.025 + (5.3-1)0.00131 =
C e n t r o i d to inner surface e
0.105 m'/m
(7.12)
=
0.12/2+(5.3-1)(0.075+0.005/2)(0.00131) 0.1+0.00131(5.3-1)
=
0.0515
Cent r o id t o outer surface e
=
0.1
Moment o f
I = 0*05'53+0*04853 + (0.075+0.005/2-0.0515)2
inertia
-
(7.13) 0.0515
=
(7.14)
0.0485
3
x(5.3-1)(0.00131) Stresses a t b a s e B : ( t e n s i o n
-
=
85.9~10-~m~/m
(7.15)
v e f o r concrete stresses)
T e n s i o n d u e to n e t i n t e r n a l p r e s s u r e :
ft =
0.8 x 2 - 0.02 x 2.2
-
-7,4 N/mmz
2 x 0.105
B e n d i n g moment c o e f f i c i e n t s f r o m F i g . For vertical
load,
Nb =
8.2:
0.235, and f o r h o r i z o n t a l l o a d ,
NS
=
0.125 Net b e n d i n g moment = =
0.235 x 0.04 x 2.2/2 - 0.125 x 0.02 x 2.2/2 0.00755
140 Stress on o u t e r face f
Stress on i n n e r face f Steel s t r e s s :
e
=
b3
c3
0.075
- f
-
fb2
=
11.2-7.4-
t
+ -MeO I 0.00755 85.9
+ 0.005/2-0.0515
x 0.0515=
-IN/mm2
x
= 0.026
(on outer side of centroid)
= 764
+ 5.3
(7.4
0.00755
x 0.026)
=
791
N/mm2
85.9 x Although stresses
the stresses a t at
similarly,
other
points
t h e b a s e a r e u s u a l l y t h e most s e v e r e , on
the
circumference
should
the
be checked
and c h e c k s s h o u l d b e d o n e b o t h w i t h and w i t h o u t t r a n s -
ient winding,
t e s t i n g and i n t h e f i e l d .
REFERENCES
C o n c r e t e P i p e A s s n . , 1970. D e s i g n M a n u a l - C o n c r e t e P i p e , A r l i n g ton. BSCP 2007 P a r t 2, 1970. R e i n f o r c e d and P r e s t r e s s e d C o n c r e t e S t r u c t u r e s , BSI, L o n d o n . C o n c r e t e P i p e Assn., 1962. L o a d s o n B u r i e d C o n c r e t e P i p e s , Tech. B u l l e t i n No.2, T o n b r i d g e . C o n c r e t e P i p e Assn., 1967. B e d d i n g and J o i n t i n g o f F l e x i b l y J o i n t e d C o n c r e t e P i p e s , Tech. B u l l e t i n No. 1 , T o n b r i d g e . F e r g u s o n , P.M., 1958. R e i n f o r c e d C o n c r e t e f u n d a m e n t a l s , Wiley,N.Y. 1950. D e s i g n of p r e s t r e s s e d c o n c r e t e c y l i n d e r p i p e , J. K e n n i s o n , H.F., Am. W a t e r W o r k s Assn., 42. T i m o s h e n k o , S.P. and W o i n o w s k y - K r i e g e r , S., 1959. T h e o r y o f P l a t e s and S h e l l s , 2 n d Edn., McGraw H i l l , N.Y.
Am.
L I S T O F SYMBOLS
A
-
d
-
inside diameter
D
-
outside diameter
e
-
distance from centre of g r a v i t y
E
-
modulus of e l a s t i c i t y
cross sectional area
f
-
stress
F
-
c r u s h i n g s t r e n g t h o f 150 mrn c u b e s a t 28 d a y s
(compressive o r tensile)
141 I
-
moment of
inertia
K
-
factor o f safety
L
-
length
M
-
bending moment
n
-
e l a s t i c modular r a t i o E
q
-
shear stress
s
-
steel area per u n i t length of p i p e
t
-
thickness
u
-
creep coefficient f o r steel and concrete before f a c t o r y test
v
-
s h r i n k a g e coefficient
w
-
creep coefficient
Subscripts b
-
coating
c
-
core
s
-
steel
m
-
bending
9
-
shear
t
-
tensile
L
-
longitudinal
I
-
initial
0
-
after winding
1
-
at time of f a c t o r y test
2
-
a t time of
3
-
under f i e l d pressure
laying
/E c
s
142
CHAPTER 8
STEEL AND FLEXIBLE P I P E 1 NTERNAL PRESSURES
The
highest
pressure
to
internal
fluid
due pipe
there
and
weight
are
effects.
pressure.
general
has
The
bending
no
The
pipe
a
to
resist
pressure
stresses
are
is
uniform
except
equations
for
normally
for
the
those
around
the
and
self
water
stresses
resulting
in a hollow cylinder are:
Circumferential
wal I stress
p.d.' I
Fw
-
I
where p is
Fr
i s pressure,
internal
diameter
f o r p l a i n stress, For
i.e.
-
doL
podo'
i s diameter at
and
d
-
) (8.1 )
d.'
1
d i z do2 ( P,-P
+
do2 - d.'
=
d
d i 2 doZ( P-,P
do2 - diL
=
p.d.' I 1
Radial stress
podo'
(8.2)
doZ - d i z
w h i c h the stress i s sought,
i s external
diameter.
a cylinder free to expand
d.
The e q u a t i o n s a r e
longitudinally.
the p a r t i c u l a r case of n o e x t e r n a l p r e s s u r e the c i r c u m f e r e n t i a l
s t r e s s i s a m a x i m u m on t h e i n n e r s u r f a c e a n d i s di2 F max
=
W
In with
practice
the
resist
where
di
+ do2 P + do 2t the
diameter,
wall
thickness
a n d the w a l l
is
normally
small
in
comparison
thickness of a steel p i p e designed to
i n t e r n a l pressure i s obtained from the formula
t is t h e w a l l t h i c k n e s s p
i s the i n t e r n a l pressure
d i s the e x t e r n a l diameter f
i s t h e y i e l d s t r e s s o f t h e steel
G i s the design factor
J i s the j o i n t factor. E q u . 8.4
of t/d.
overpredicts
On t h e o t h e r h a n d ,
the
true
stress
by
some
just u s i n g d instead of
3 r e d i c t s t r e s s b y 1% f o r e v e r y
1% t / d .
1%
(d-t)
for
every
1%
would under-
143 The
design
factor
depend on
will
have
been
a
many
the
burst.
over-pressure, are
the accuracy
assessed,
quences of
allows
G
a
safety
with
which
working
margin.
What
factor
to use
loads a n d t r a n s i e n t pressure
pressure,
economics and
the conse-
I f the p i p e l i n e i s protected a g a i n s t water hammer
unknown
o r even 0.7
of 0.6
a factor
loads,
use of
i s reasonable,
a factor
of
the order
b u t i f there to 0.5
of 0.3
would be wiser. The j o i n t varies
J allows
factor
0.85
from
for
for
furnace
imperfections
butt-welded
i n welded seams,
joints
1.0
to
and
for
seamless
resist
internal
pipes. Smal I-bore, pressures
the
only,
the
wal Is,
high
fluid
internal
but
more
the
pressure
pipe
pipes
larger
important
the
in
pressure
the
designed
diameter
also
be
be
the
loads.
possible,
considered
to
and
become the e x t e r n a l
may
should
are
acting
thinner
the
Vaporization
in
which
case
in
conjunction
of
this with
e x t e r n a l loads. If
the p i p e
magnitude
i s restrained
is
VF
induced
TENS I ON R I NGS TO RESIST
which
strengthened to
form
some
v
is
a
longitudinal
Poisson's
and
tension of
F
is
the
have
I NTERNAL PRESSURES
to
resist
very
high
internal
b y b i n d i n g w i t h hoops a n d s p i r a l s .
pipes
ratio
wal I tension.
circumferential
Pipes
longitudinally,
where
in
the
thick
h i g h pressures.
It
may be
i s often d i f f i c u l t
p l a t e s which would be r e q u i r e d to r e s i s t
the
On
pressures
other
hand
it
may be possible to form
the p i p e of t h i n n e r p l a t e than would be r e q u i r e d f o r an unstrengthened pipe,
a n d w i n d i t w i t h s t r a p s o r rods.
The r i n g s r e q u i r e d to r e s i s t same
function
against in
tension
resist the
as
external
stiffening
loads.
and
external
the
does load,
not
I n fact
the
need
which
to
should
through
pressures do not perform the
rings
The w i n d i n g
l o n g i t u d i n a l section
possible.
internal
required
to r e s i s t be
as
to
resist
internal
prominent
as
col lapse
pressures acts the
increase the moment of
rings
to
i n e r t i a of
the p i p e a n d therefore be as h i g h as
tension r i n g s , as they w i l l be c a l l e d ,
should be
144 a n d b r o a d as possible to keep the distance between them to a
as f l a t
minimum.
There
will
be
high
circumferential
stresses
are f a r apart.
I n comparison,
are
usually
also
be
spaced
used
to
in
a
the
number
strengthen
longitudinal pipe
wall
bending
between
stresses
rings
if
and
the r i n g s
s t i f f e n i n g r i n g s to r e s i s t e x t e r n a l loads of
old
diameters a p a r t . pipes
which
are
Tension r i n g s may to
be
subjected
to
h i g h e r pressures than o r i g i n a l l y designed for. Using
the
stress-strain
r e l a t i o n s h i p and
the d i f f e r e n t i a l
equations
equil i b r i u m f o r c y l i n d e r she1 I s under the action of r a d i a l pressure,
of
Timoshenko
(1959) d e r i v e d a n equation f o r
a
subjected
cylinder
to
a radial
the
radial
displacement of
pressure a n d w i t h tension r i n g s at
equi-spaci n g
.
Put
b4
=
12(1-v2) dZt'
(8.5)
and
a
=
bs
(8.6)
where v t
i s the P o i s s o n ' s r a t i o (0.3
i s the w a l l
Let
x1
thickness a n d s the centre-to-centre
r i n g spacing.
-
cosh a sinh a
+
cos a sin a
(8.7)
-
sinh a sinh a
-
sin a sin a
(8.8)
-
cosh a sinh a
-
x2
x3
for s t e e l ) , d i s the p i p e diameter,
Then the r i n g stress,
+ +
+
Fr,
cos a sin a
i s g i v e n by
(8.11) where A = cross sectional area of The
circumferential
pipe
wall
the r i n g .
stress,
Fw,
mid-way
between
rings
is
given by = FW
a n d the
@[l+ 2 ( F 2t - 1 ) X 4 ] 2t r Pd
longitudinal
i s given by
bending
stress
(8.12) in
the p i p e under
the
rings,
Fb
P
2
I
I -0 .
I
I < 0
1
I
N
d
I
”
g! r
>
i
i
a,
3
C
D
m L a,
m
c
[r
C .a, C
U
m
m In L a,
m
I
a .-C LL
D
m
a .-C L
145
m
a L
.-C
C
m
.-0 a,
C
-
5
r.-
U
E
D .-
m
m m
.-Um m
a, m
QJ
m
c
5
-
3 -
LL
.-a
m
-
m
i a,
vi
- .-5
C
L a, a, c
5 .-i V
m
146 (8.13) The
stresses
shown A)
that
are
indicated
by
Fig.
a s s i s d e c r e a s e d t h e r i n g s t r e s s Fr
w h i c h c o u l d h a v e been anticipated.
to equal
for
8.1,
the circumferential
f o r s m a l l s,
wall
v
0.3.
=
tends to
It
f
pds/
a p l a i n pipe,
the circumferential p i p e wall stress F
pd/2t.
tends to
W
+ A ) , w h i c h w o u l d b e e x p e c t e d , and t h e l o n g i t u d i n a l
be
(ts +
Fr tends
N o t e t h a t f o r s m a l l A,
stress of
may
Also,
4 pds/(ts
beding stress
Fb
tends to zero. For l a r g e r i n g spacing ( > approx.
pd
1
F tends to
1
+ 0.9lA/t&
pd
+ 0.91
tJtd/A
(8.14)
2t
1.65
Fb tends to
2-1,
(8.15)
2t
t e n d s to @ i.e. t h a t f o r a p i p e w i t h o u t r i n g s . 2t I t may be observed b y comparing F F r and Fb f r o m F i g s .
and F
W
8.la,
W’
8.lb in
and 8 . l c
fact
Fw,
reduced
if
t h a t t h e m a x i m u m s t r e s s f o r most p r a c t i c a l r i n g s i z e s i s the
circumferential
r i n g spacing should be area
A
pipe
wall
stress.
s / J y z i s l e s s t h a n a p p r o x i m a t e l y 2.0.
should
longitudinal
be of
cross
l e s s than
the
same
sectional
2 J l d
order
area
of
Also,
is
only the
the r i n g cross sectional
and
magnitude
between
Fw
I n other words,
rings,
as the p i p e w a l l to
ts,
enable
the
r i n g s t o b e o f use.
DEFORMATION O F CIRCULAR P I P E S UNDER EXTERNAL L O A D
large
For
diameter
sures,
the external
under
external
bending,
Spangler
critical occur
at
pipes
load is frequently
load
by
buckling,
under
low
t h e c r i t i c a l one.
overstressing
due
internal
pres-
Pipes may f a i l to
arching
or
excessive deflect ion. elastic
For
only,
flexible
and
rings
under
plane
stress
subjected
to
vertical
loads
(1956) e v a l u a t e d t h e b e n d i n g moments and d e f l e c t i o n a t
points around the crown,
the
the
circumference.
The
i n v e r t or t h e s i d e s .
worst
b e n d i n g moments
T h e b e n d i n g moments p e r
147
Angle of bottom
suwor? p degrees
Angle of tmttom support
Fig.
8.3
p
D e f l e c t i o n c o e f f i c i e n t s for
degrees
loaded pipe.
148 u n i t length a r e g i v e n b y a n equation of the form
M
R
where and
(8.16)
NWR
=
is
N
is
the a
pipe
respectively).
The
W
radius,
coefficient.
(Nt,
vertical
i s the v e r t i c a l
Nb
and
and
NS f o r
horizontal
load per top,
changes
unit
length
bottom and in
sides
diameter
are
p r a c t i c a l l y equal a n d opposite a n d a r e of the form A
NnWR3/EI
=
where N
(8.17)
i s a coefficient.
A
The moment of i n e r t i a I per u n i t length of p l a i n p i p e w a l l I
t3/12
=
Figs.
(8.18)
8.2
and
at
vertical
deflections
unit
the
8.3
moments
line
load or
a
length),
Collapse of
to
been
and
of
the
and
pipe
for
Nt,
sides
Nb a n d Ns f o r the
respectively,
diameter.
The
coefficients
across the w i d t h of
different
angles
of
and
N
bending
A
are
the p i p e
bottom
for
support 6
the
for a
( W per
,
as
8.4.
a steel p i p e w i l l p r o b a b l y not occur u n t i l the diameter
distorted
normally
linings,
bottom
load d i s t r i b u t i o n
5 percent of
should
g i v e values of
top,
indicated i n Fig.
has
is
the be
some 10 o r 20 percent. diameter limited
are
to
I n p r a c t i c e deflections
sometimes
about
2
tolerated.
up
The deflection
percent to prevent damage to
a n d for pipes w i t h mechanical j o i n t s .
The h y d r a u l i c properties,
i.e.
the cross sectional area a n d wetted
perimeter a r e not affected noticeably f o r normal d i s t o r t i o n s . LOAD W /UNIT LENGTH OF PIPE
UPTHRUST
F i g . 8.4
Pipe l o a d i n g and deflections
149 Effect of L a t e r a l Support The of
lateral
flexible
lateral
support
pipes
support
of
sidefill
in a
considerably
and
trench
increases the s t r e n g t h
reduces
deformations.
to a p i p e the r i n g bending stresses a t
Without
the s o f f i t a n d
haunches o r deflections would l i m i t the v e r t i c a l e x t e r n a l load the p i p e could
carry.
But
l a t e r a l l y as the
it
sidefill
be
may
a
is
in
the
established
compacted
sides
with
the
of
the
will
fill
deflect
outwards
i n c r e a s i n g the pressure of
pipe.
vertical
a r c h action as well
load
An
equilibrium
being
condition
transferred
as b y r i n g action.
The
to
the
stress due
i s compressive so that the load which the p i p e can
to the a r c h action
i s considerably h i g h e r than i f the p i p e were a c t i n g in bending.
carry the
extreme case,
the
lateral
stress a n d the p i p e wal I w i l l equal
a
loaded v e r t i c a l l y thereby
against
haunches b y
In
pipe
stress
will
equal
the v e r t i c a l
be i n p u r e compression,
load
w i t h the stress
to wd/2t
where If could
w
W/d
=
the
p i p e underwent
support
whatever
(8.19)
arch
would
no noticeable
be
strength
the sides of the pipe,
determined
i s given i.e.
by
lateral
distortion bending
the
to the p i p e b y
the
load
strength
it
plus
the s o i l pressure on
the permissible v e r t i c a l
load per u n i t area
on the p i p e i s
w
w
=
+ w
b
(8.20)
a
i s the permissible b bending stress or more l i k e l y
where
equal
w
to
lateral
servatively, greater
load
(limited
this
pressure on
as
lateral
indicated
dead
by
ring
i s the a r c h i n g load, a the sides of the p i p e , which, con-
in
subsequent
pressure i s approximately
pressure due to soil
either
by deflection). w
may be taken as the a c t i v e soil pressure,
than
the a c t i v e
soil
bending
load o n l y
one
but i s usually
equations.
For
sand,
t h i r d of the v e r t i c a l
and for clay
i t i s approximately
h a l f the v e r t i c a l pressure. I f the v e r t i c a l active and away
lateral
increase the from
load i s g r e a t e r than the sum of the r i n g load p l u s
soil
the
pressure,
lateral pipe
the
pressure.
and
pipe wall
will
deflect out
laterally
The h o r i z o n t a l stress w i I I decrease
Barnard
(19571,
using
elastic
theory,
150 suggests assuming a pressure equal wall
triangular
to total
stress d i s t r i b u t i o n w i t h the horizontal
vertical
pressure minus r i n g load a t the p i p e
decreasing l i n e a r l y to zero at 2.5d away from the p i p e w a l l .
corresponding AX/2
1.25
=
where E 1.25
i s the effective modulus of
pressure
factor
becomes 1.4
time,
a
e l a s t i c i t y of the s o i l .
The factor
increased as the l a t e r a l deflection increases, since the
radial
for
(8.21 )
d/ES
(w-w,)
should be
1.7
The
l a t e r a l deflection of each side of the p i p e i s
increases for
deflection
as
the
r a d i u s of
2 percent of
a deflection of
of
5 percent.
and an a d d i t i o n a l
c u r v a t u r e decreases.
The deflection
The
the diameter
also
and
increases w i t h
25 to 50 percent of the i n i t i a l deflection can
be expected e v e n t u a l l y . If
the
creep
decrease. e.g.
On
deflection
the
plastics,
other
of
the
hand
soil
pipe
can compensate f o r
large,
is
materials
this,
lateral
which
support
exhibit
can
creep,
a n d could even shed v e r t i c a l
load. The
relationship
determined modulus
from
of
degree of of
between stress and s t r a i n f o r
laboratory
elasticity
of
triaxial
soil
varies
for
N/mmz
for
fill
widely
compaction o r n a t u r a l density,
l o a d i n g and moisture content.
modulus
consol i d a t i o n
loose c l a y
is
or
approximately
as
it
loosely
density
Values h i g h e r than
be
The effective on
soil
c o n f i n i n g pressure, may be as
as 20 N/mm2 f o r
3 N/mmzfor
compacted to 90% Proctor
Proctor density.
depending
F o r example
high
the s o i l should tests.
type,
duration as 2
low
dense sands.
compacted f i l l ,
The
5 N/mrn2
a n d 7 N/mmz f o r f i l l
to 95%
100 have been recorded for moist
compacted sands. The r i n g
load on
indicated
by
as
ponds
to
bottom
the p i p e
Equ.
8.17.
support
i s p r o p o r t i o n a l to t h e e l a s t i c deflection
T a k i n g N,
over
30'
and
equal the
t o 0.108,
load over
which corresthe entire
pipe
width and p u t t i n g AY A -
d
AX
--
0. 108wd3 8E I +0.043ESd3
=
For p l a i n
a
A , then s o l v i n g f o r A/d
=
function
of
pipe
and 8.21, (8.22)
I = t3/12,
diameter,
from 8.17
so one has an equation f o r deflection
loading,
soil
modulus
and
the
ratio
as
wall
th i ckness/di ameter. A -
d
--
0.108~ 0.67E(t/d)'
+ 0.043Es
(8.23)
151 The r e l a t i o n s h i p between deflection a n d wal I thickness f o r p l a i n p i p e i s p l o t t e d i n F i g . 8.5. I t w i l l be observed that a steel p i p e wall
thickness
restrain
5MPa a n d soil Pipes trench
are
to
diameter.
as
low
distortion
as
to
4%
of
the
2% p r o v i d e d
diameter
the
soil
will
be
sufficient
modulus
is
greater
to
than
load i s less than 50 kPa. sometimes
increase The
the
lateral
strutted
internally
vertical
diameter
support
increases
during and
when
backfilling
reduce
the
of
the
horizontal
the s t r u t s a r e removed
a n d the p i p e tends to r e t u r n to the r o u n d shape.
The v e r t i c a l deflec-
tion a n d tendency to b u c k l e a r e consequently reduced considerably.
STRESS DUE TO C I RCUMFERENT I A L BEND I NG
It
i s possible to compute w a l l stresses due to bending a n d a r c h i n g
(Stephenson, the f u l l
1979).
w i d t h of
If
i t can be assumed that the load i s spread over
the p i p e
( a =
180')
and the bottom support i s over
( 6 = 60") f o r f l e x i b l e p i p e , then from (8.17) a n d F i g . 8.3,
60'
AY
=
0.103wbd
4
/8E1
(8.17b)
Now from (8.21), A X = 2.5(w-wb)d/ES Equating
AY a n d A X ,
the total
load,
w The
=
b
w I /d3 I/d3
bending
+
(8.21b)
a n d s o l v i n g for w b
the r i n g load i n terms of w
(8.24)
0.006ES/E
moment
in
the
wall,
M,
is
due
to
ring
load a n d
is a
maximum a t the base a n d from (8.16)
M
=
where
r
the
W
is
the
distance from
extreme f i b r e
i s taken
a
-
(8.25)
0 . 1 9 ~ d 2 / 2 hence b e n d i n g stress f = Mr/l b b the centre of
(t/2 for p l a i n wall
g r a v i t y of
pipe).
the section
The balance of
the
to
load
in a r c h action of the p i p e according to (8.20) so
0. 006wES/E
I /d'
(8.26)
+ 0. 006ES/E
The bottom w a l l hoop stress i s fa
=
wad/2a
where
a
is
the
plain wall pipe).
(8.27) cross
sectional
area
of
wall
per
unit
length
( t
for
152 The =
total
+
fb
lateral
fa,
permissible stress f
+
(l/d3 w
=
permissible
ES to steel
+
i n terms of
(8.28)
load w
The r e l a t i o n s h i p
i s a f u n c t i o n of
moduli of soi
a n d the r a t i o o
i s plotted
i n Fig.
the permis
f o r p l a i n wal
8.5
w i t h E = 210 000 N/rnmz, a n d f = 210 N/mrn2.
pipe,
For t h i c k as
the base i s f
0.003 dE /Ea
the r e l a t i v e thickness t / d
E.
at
is
Thus the permissible v e r t i c a l s i b l e stress,
i n the w a l l
l o a d i n g p e r u n i t area
0.006ES/E)f
r/d
0.1
compressive stress
therefore
more
load
can
deflection
becomes
the
is
pipe
the permissible load increases w i t h wal I thickness
pipes,
be
taken
large
i n r i n g bending. that
so
the
i n p u r e compression,
hoop stress.
Actually
side w a l l
so (8.27) p l u s (8.25)
soil
and
For t h i n n e r
side-thrust
the
limit
pipes,
increases
i s due
the
to
the
until wall
hoop stress exceeds that a t the base,
i s not the l i m i t i n g stress f o r h i g h a r c h i n g .
On the same c h a r t i s p l o t t e d b u c k l i n g load
The
(8.29a)
/32ESEl/d3
=
W
b u c k l i n g equation,
support. gated
This
by
proposed b y
ClRlA
(1978)
allows
for
lateral
may be compared w i t h an a l t e r n a t i v e equation
the
Transport
and
Road
Research
Laboratory
investi-
(which
is
found to o v e r p r e d i c t w ) : W
The
=
( 1 6 E s 2 E l / d 3 )1 / 3 g i v i n g a deflection of
load w d
on the c h a r t for
any
is
selected
(8.29b)
from
2% i n the diameter
The c h a r t
(8.23).
p a r t i c u l a r w a l l thickness r a t i o . in
each
case
from
the
The lowest permissible load w
chart
by
comparing
overstressing and b u c k l i n g lines f o r the r e l e v a n t t / d Similar
charts
should
be
i s also p l o t t e d
thus y i e l d s the l i m i t i n g c r i t e r i o n
p l o t t e d where
and E
stiffening
deflection,
.
rings
a r e used
a n d where a l t e r n a t i v e m a t e r i a l moduli and permissible stresses a p p l y . By
careful
design
it
is
c r i t e r i a a t the same load.
possible
to
reach
the
limit
in
two
or
more
T h i s i s c a l l e d balanced design.
More General Deflection Equations Spangler the
backfill
(1956) in
a
allowed more
for
lateral
theoretical
he d e r i v e d f o r v e r t i c a l deflection i s :
way
support than
to
the
Barnard.
pipe The
due
to
equation
153 UZWd3 8 E l + 0.06Esd”
A =
(8.30)
T h i s corresponds to ( 8 . 2 2 )
i s substituted for N
i f UZ
A
and a v a l u e of
0.15 i s assumed f o r N A i n the denominator ( i n s t e a d of 0.108 i n 8.22) s o i l consolidation time l a g factor
Here U = Z =
bedding
constant
(varies
from
( v a r i e s from 1.0
0.11
for
point
to 1.5). support
to
0.083 f o r b e d d i n g the f u l l w i d t h of p i p e ) , n o r m a l l y taken as 0.1. 1
moment of i n e r t i a of p i p e w a l l per u n i t length.
=
passive resistance modulus of s i d e f i l l .
E = The Due
to
pressure
inside a
pipe
the
that
vertical
fact
the
may
also
contribute
diameter
to
its
stiffness.
i s compressed to s l i g h t l y
less t h a n the h o r i z o n t a l diameter,
the v e r t i c a l u p t h r u s t due t o i n t e r n -
al
the s i d e t h r u s t b y an amount of
pressure becomes g r e a t e r
which
tends
to
return
the
than
p i p e t o a c i r c u l a r shape.
2@
A more general
expression f o r v e r t i c a l deflection thus becomes A
=
UZWd3
8 E I + 0.05ESd’
(8.31)
+ 2 UZpd3
W
Q
0.002
0.005
0.01
0.02
Relative thickness t / d
F i g . 8.5
Permissible load on p l a i n p i p e
0.03
154 ST
FFENING RINGS TO Morley
pipes
BUCKLING W I T H NO SIDE
RESIST
(1919) developed a
under
uniform
stiffening
ring
tice.
theory
The
external
bined internal
for
of
stiffened
often
indicates
i s considered necessary
in p r a c -
pressure.
spacings wider also
theory
than
neglects
the
the
SUPPORT
The
buckling theory
possibility
of
failure
a n d e x t e r n a l pressures and bending.
under
com-
The equations do,
however, y i e l d an i n d i c a t i o n of s t i f f e n i n g r i n g spacing. Using which
an
indicates
axial
the
she1 I
cylindrical no
analogy
a
take
without
and
assumes
comparison w i t h the diameter. w
2E
=
1
-
developed
external
b u c k l ing. the
wall
an
equation
w,
which a
pressure,
The equation a l lows f o r thickness
is
small
in
v i s Poisson's r a t i o , (8.32)
d7 I = t3/12, so
For p l a i n p i p e ,
w
Morley
El
24 1 - v 2
=
strut,
maximum v e r t i c a l
can
expansion,
with
t
(3)
v2
(8.33)
Experiments i n d i c a t e d a p e r m i s s i b l e stress 25% less than the theoretic a l , so f o r steel,
1.65 E
t
w
=
For
thick-wal led
stresses the w a l l
(8.34) tubes,
the
material
to
intermediate wal I thickness, and
elastic
yield.
An
col lapse i t s elastic
pressure limit
wi II
be
( w = 2ft/d)
that
which
whereas f o r
f a i l u r e w i I I be a combination of b u c k l i n g
empirical
formula
indicating
the
maximum
permissible pressure on a p i p e of intermediate thickness i s (8.35) where f
i s the y i e l d stress.
The e x t e r n a l resist w, s,
buckling.
load may be increased i f s t i f f e n i n g r i n g s a r e used to It
was
found
i s i n v e r s e l y p r o p o r t i o n a l to if s
by
experiment t h a t
the collapse
load,
the distance between s t i f f e n i n g r i n g s ,
i s less than a c e r t a i n c r i t i c a l length,
L.
155 From experiment L = 1 . 7 3 E
(8.36)
so i f w
=
2E ( t / d ) 3 for s t i f f e n i n g pipe, then f o r s t i f f e n e d p i p e ,
w
=
L2E ( t / d j 3 = 3.46
The
actual
permissible
(8.37)
stress
is
less
than
the theoretical
due to
imperfections i n the m a t e r i a l a n d shape of p i p e , so the p r a c t i c a l r i n g spacing i s g i v e n by
(8.38) If
the
full
vertical
elastic
external
r e n g t h of pressures
i.e.
he p i p e i s to be developed w
=
'Jt,
then
the
ring
o resist spacing
shou I d be
(8.39) t be of use i f w >1.65E ( - ) 3 . I t should also be ascerd 2f t tained that w z - , which i s the e l a s t i c y i e l d p o i n t . d = Pft/d, then r i n g s w i l l o n l y be of use i f If w
Rings w i l l o n l y
t/d
=
1/30
f o r m i l d steel.
(8.40) F u r t h e r studies of b u c k l i n g of s t i f f e n e d p i p e a r e g i v e n
b y Stephenson (1973) a n d Jacobsen (1974).
W
Y
Fig.
8.6
Pipe w i t h s t i f f e n i n g r i n g s
156 Example 1 :
Tension Rings A The
500 mm bore p i p e i s to take an maximum
N/rnm*,
permissible
and
the
working
maximum
wall
stress
in
thickness
mm.
Assume a
10 rnm diameter w i r e
and
calculate
the
required
internal
the
which
wall can
is av ai l abl e for
spacing
of
the
5 N/mm2.
pressure of is
be
to
be
rolled
100
is
10
b i n d i n g the p i p e
binding.
An
unstiffened
p i p e c o u l d take an i n t e r n a l pressure of
pd
“ow
=
2t
500 100
2 x
=
Tension r i n g area parameter By
inspection of Figs.
s o we r e q u i r e F/@ 2t
125,
1 82A r‘td
t
8.la
=
1 00 125
=
0.8
1 . 8 2 ~ ~ ~= 1o 0 . 2~
10 ~ ‘ 1 0 x 5 0 0
and 8.1b,
the r i n g spacing r e q u i r e d to
reduce both the c i r c u m f e r e n t i a l p i p e w a l l stress a n d the r i n g stress to the desired v a l u e i s g i v e n b y s
/
m = 0.45,
:.
Notice t h a t
s = 0.45
the
amount
x 500
J10 of
steel
=
32 mm.
required
i s s l i g h t l y more than
the p i p e were merely thickened to take the e x t r a pressure. becomes more noticeable the wider the r i n g spacing. it
is
stress
usually in
the
the
circumferential
system,
r i n g s i f the p i p e w a l l
there
so
wall
stress
i s l i t t l e point
if
T h i s effect
For wider spacing
which
is
the
i n using high-
limiting tensile
i s of m i l d steel.
Example 2:
St i f f e ning R i n g s
Design a 3 m diameter a
uniformly
distributed
steel
load of
pipe with stiffening 60
kN/m2
with
a
r i n g s to support
soil
modulus of
3
N/mm2. Maximum steel stress = 103 N/mm2, delection 2%. Select t = 10 mm Then s / d
=
(210 000/503) ( . 0 0 3 3 ) 3 / 2
(8.39)
157 0.39
=
Use
:.
s = 1177 mm; Select
100 mm h i g h r i n g s w i t h h/b
1200 mm.
= 10 m a x f o r
no b u c k l i n g
i.e.
ring
t h i c k n e s s b = 10 mm Centroid from c e n t r e w a l l c
I
Moment o f i n e r t i a =
=
(h+t)bh 2( bh+ts)
h3b + S ( t c ) ' -
=
+
hb
12s
=
t3 12
+
4.25
mm
tC2
(8.41) (8.42)
3104 mm3/mm
Extreme f i b r e d i s t a n c e r
=
h
+ (8.43)
100.8 mm
=
Deflection:
A/d
=
0.1~0.060~3~
(8.22b)
8x210 0 0 x 3 1 0 4 ~ 10-9+0.05x3x33 0.017
=
1.7%
=
Maximum w a l l s t r e s s
(0.1x0.10/3.0+0.003x3x3/(210000x0.011
f =
) ) 0.06
3 1 0 4 ~ 1 0 - ~ /+0.006x3/210000 3~ 1.7 N/mm2.
=
The tions,
section an
could
optimum
or
thus
be modified.
balanced
design
By
v a r y i n g the r i n g p r o p o r -
may
be
possible
i.e.
both
deflection l i m i t a n d stress l i m i t a r e attaine d simultaneously.
REFERENCES
B a r n a r d , R.E., 1957. D e s i g n a n d d e f l e c t i o n c o n t r o l o f b u r i e d steel p i p e s u p p o r t i n g e a r t h l o a d s a n d l i v e l o a d s , Proc. A m . SOC. f o r T e s t i n g M a t e r i a l s , 57. C l R i A ( C o n s t r u c t i o n I n d u s t r y Research a n d I n f o r m a t i o n A s s o c i a t i o n ) , 1978. D e s i g n a n d C o n s t r u c t i o n o f B u r i e d T h i n - d a l l P i p e s , Report 78, L o n d o n , 93 p p . Jacobsen, S., 1974. B u c k l i n g o f c i r c u l a r r i n g s and c y l i n d r i c a l t u b e s u n d e r e x t e r n a l p r e s s u r e , Water Power, 26 ( 1 2 ) . Morley, A . , 1919. S t r e n g t h o f M a t e r i a l s , L o n g m a n s Green E. Co., pp 326-333. S p a n g l e r , M.G., 1956. Stresses i n p r e s s u r e p i p e l i n e s and p r o t e c t i v e c a s i n g p i p e s . Proc. Am. SOC. C i v i l E n g s . , 82(ST5) 1054. 1973. S t i f f e n i n g r i n g s f o r p i p e s , P i p e s and P i p e l i n e s Stephenson, D., I n t l . , 18 ( 4 ) . Stephenson, D. ,1979. F l e x i b l e p i p e t h e o r y a p p l i e d to t h i n - w a l I nPVC p i p i n g , P i p e s a n d P i p e l i n e I n t l . , 24 ( 6 ) , 9-17.
158 Timoshenko, S.P. and Woinowsky-Krieger, S., 1959. a n d Shells, 2nd Ed., McGraw H i l l , N.Y., Ch. 15.
Theory
of
Plates
LIST OF SYMBOLS
a
-
bs, o r area per u n i t length
A
-
cross sectional a r e a of r i n g
b
-
C
-
distance from centre of w a l l to c e n t r o i d of w a l l section
d
-
p i p e diameter
d.
-
i n t e r n a l p i p e diameter e x t e r n a l p i p e diameter modulus of e l a s t i c i t y passive resistance modulus of s i d e f i I I permissible w a l l stress
F
-
wal I stress bending stress circumferential
stress
bending stress under r i n g r i n g stress,
o r r a d i a l stress i n p i p e w a l l
circumferential
wal I stress
design factor r i n g height depth of b a c k f i l l above pipe I
-
moment of
J
-
j o i n t factor
K
-
inertia
r a t i o of a c t i v e l a t e r a l pressure of f i l l to v e r t i c a l pressure c r i t i c a l r i n g spacing bending moment moment or deflection coefficient i n t e r n a l pressure pipe radius distance from c e n t r o i d to extreme f i b r e of beam r i n g spacing wal I thickness
159 deflection time l a g factor
V
-
W
-
vertical
U
Poisson's r a t i o pressure,
subscript
a
refers
bending a n d d to deflection
W
-
vertical
Y
-
r i n g thickness
z
-
bedding constant
A
load p e r u n i t length ( W = wd)
def I ect ion
to
arching,
b
to
160
CHAPTER 9
SECONDARY STRESSES
STRESSES AT BRANCHES
If in
a
the
stress
hole i s cut wall
on
will
the
in
the w a l l
increase on
horizontal
of
a pipe,
each
axis
at
side
the
S
where the a
+ 2
S(l
=
is
horizontal
the pipe
the
may
also
axis a
force
the w a l l
able
to
minimize
entrance
the main
pipe
forcing
may
angles
to
to
is
the
piece
the
collar
diameter
walls
are
on
a
each
side
of
plate
is
given
it
will
common
In
the bore o f
a
length.
is For
branch
hole o r
in be
branch
stress
The
If
9.1.
Fig.
on a
necessary
to
the
rein-
Reinforcing i s also desirespecially
with
low
the b r a n c h connection to m i n i -
such
necessary.
cases
the
the
size of
hole cut
in
the b r a n c h p i p e and r e i n -
For small
a s u i t a b l e method of onto
axis
the
practice
than
collar
plate,
in the p l a i n pipe.
that
loss.
a
the
hole o r
circular
significant
A
to
vertical
b r a n c h p i p e occurs.
assuming otherwise
out
of
thickness, t
the
that
the
a
head
by
cut
and
assuming
hole
i s consequently three times
larger
would
is
tangential
elliptical
b r a n c h pipes at r i g h t
strengthening
main
pipe
the p i p e con-
around
the
branch
The w i d t h of c o l l a r may be c a l c u l a t e d f o r any p a r t i -
thickness which
in
the
use s k i r t s at
weld
9.2).
of
times
all
a
is
applied
i s to
barrel
of
is
is
stress
hole
b
case
three
be especially
a
(Fig.
force
the
distortion.
mize
cular
and
at
where
pipework
pipe
the stress S '
to
is
pressure
nection
and
beside a stress
stress
b In
increase
wall
the
vertical
circumferential
pipe
The
small
1951),
length =
stress.
distribution
hole.
a
stress
(9.1
uniform
hole
applied
the of
a/b)
the
circular
of
side
i n a p l a t e i s (Tirnoshenko a n d Goodier,
S'
the circumferential
the
same,
the w'
the
col t a r
have
been
main
pipe,
the
thickness
of
permissible and
that
w i t h the b r a n c h p i p e diameter.
width, the
the
i.e.
D
wall
stress
the
takes taken
in
collar
the of
circumferential
across 2t'w'
the
tD,
=
branch the
main
the c o l l a r width
is
diameter where
t'
p i p e outside pipe.
and main small
This pipe
compared
161
s t
Fig.
9.1
Fig.
9.2
t
f
t
t
t
t
t
t
Stress d i s t r i b u t i o n beside a hole i n a p l a t e under a uniform stress S.
Collar reinforcing at a branch pipe
7-
lp-Sornetimes
used
LI Fig.
9.3
L a t e r a l w i t h e x t e r n a l crotch plates
162 For
l a r g e r diameter b r a n c h pipes and branches at
to the m a i n pipe,
v a r i o u s angles
crotch p l a t e s a r e p r e f e r a b l e to c o l l a r s ( B l a i r , 1946).
Crotch P l a t e s
Various
types of
ing laterals. of
crotch
s t i f f e n i n g p l a t e s have been proposed f o r r e i n f o r c -
The Swiss f i r m Sulzer Bros.
plates,
and
a design a i d
l a t e r p u b l i s h e d b y Swanson et a l plates
which
pipes.
The
cases.
Trial
and
would
be
welded
on use
sections were selected were
to 9.7
Swanson's in
plates
the j u n c t i o n of
nomograph was p r e p a r e d b y a n a l y s i n g a
deflections
9.3
a nomograph was
(1955). The design was f o r e x t e r n a l
i n t o the c r o t c h a t
compatible.
any
l a r g e number of
and r e v i s e d u n t i l forces balanced
Only
r e c t a n g u l a r sections f o r crotch
a r e design c h a r t s f o r e x t e r n a l crotch
results,
system
(normally
but
of
for
expressed
units. small
the
T sections may have g r e a t e r r i g i d i t y .
p l a t e s were considered although Figs.
(1941) pioneered the design
i n the form of
in
p l a t e s based
dimensionless
parameters f o r
The design c h a r t s a r e f o r s i n g l e c o l l a r diameter
laterals)
and
for
double crotch
p l a t e s ( f o r l a t e r a l diameter n e a r l y equal to the m a i n p i p e diameter). The method of design u s i n g the c h a r t s i s as follows: C a l c u l a t e Pd / f t knowing t h e maximum i n t e r n a l pressure P, the 1 main p i p e diameter dl, the permissible p l a t e stress f a n d an assumed p l a t e thickness t. Read
off
terms of plate
from
Fig.
9.5
the
crotch
the main p i p e diameter dl.
widths
for
a
90"
lateral
plate bl
with
width
and cl
expressed
in
a r e the crotch
the same diameter
as the
main pipe. If
the
are
branch
unequal,
is
at
an a n g l e to the b a r r e l ,
Kb
read
K
and
from
crotch p l a t e w i d t h b y m u l t i p l y i n g bl The
plate
Read
the
c/dl
and
widths
the
c a l c u l a t e a,
angle
whether
plate
thickness. the
now
depth of
or
9.6
the diameters
and
correct
b y K b a n d c1 b y Kc.
b=d (bl/d,) K a n d c=dl(c,/dl)K 1 b r a t i o a/dl corresponding to b/dl
the
the
lateral
from
Fig.
9.7
and
. or
hence
the top depth of each plate.
Check
increase
are
p l a t e top
Fig.
either plate width
plate
If
so,
the
thickness
i s g r e a t e r than 30 times the
plate and
is
try
liable again.
weight of p l a t e s could be optimized b y t r i a l .
to
buckle,
The
shape
so and
163
9.4
Fig.
The
E x t e r n a l crotch p l a t e s
shape
developing often
be
together
of
the
bent at
p l a t e should of
intersection
then of
be the
intersection
point,
and
if
b /d,
8
1.0
0.5
0.5
20
pd
-1
f t
Fig.
9.5
Single
plates
be f i l l e t
t h i n enough,
Crotch p l a t e side w i d t h
1.5
by may
welded
may a l s o be
the intersection of the b r a n c h a n d the b a r r e l .
c, dtJ,
0
drawn for fabrication pipes.
i n t o shape whereas double p l a t e s w i l l
the
bent to follow
the line
164
Fig.
9.6
Effect of
l a t e r a l diameter and angle on c r o t c h p l a t e s i z e .
165 For right
large
angles
installations the
to
design c h a r t s f o r
a
t h i r d p l a t e may
a x i s of
3-plate
the
main
pipe
(see F i g .
designs a r e not a v a i l a b l e ,
t h i r d p l a t e t o a 2-plate
merely a d d i n g a
be r e q u i r e d ,
design.
9.3).
placed at Although
Swanson suggests
Discretion should be
used i n r e d u c i n g the thicknesses o r widths of the two c r o t c h p l a t e s i n such
circumstances.
The
deflections
are
reduced
considerably
by
a d d i n g a t h i r d p l a t e though. Whether judgement.
crotch The
p l a t e s should
author
advises
be
using
design pressure P
i s g r e a t e r than
of
the
safety,
diameter
t,
of
is
Certain
the b r a n c h p i p e a n d
Wyss L t d . pipe
in
(Suss a n d Hassan,
'Y's.
material
(Stephenson,
disadvantages
External
inefficiently
at
all
crotch
i s also a matter of
plates
if
the
internal
y t a"/135Gd2 where G i s the factor 1 thickness of the main p i p e , d2 i s the
wall
the b r a n c h p i p e a n d b a r r e l . y
Internal Bracing
used
a i s the a n g l e between the a x i s of
i s y i e l d stress.
1971) external
crotch
plates
prompted
Escher
1957) to i n v e s t i g a t e i n t e r n a l b r a c i n g for
crotch
plates
and
require
act
in
more
p l a t e s which could be i n p u r e tension.
bending, steel
than
consequently internal
use
crotch
An
internal
web may also act
as a guide vane.
T h i s effect,
b i n e d w i t h a g r a d u a l taper of the pipes a t the j u n c t i o n , losses
for
through
some
two
flow
pipes
considerably
is
configurations.
For
to a confluence, less
than
the
the head
with
a
case of
water
loss w i t h
'T'
standard
com-
reduces head flowing
internal
webs
junction.
The
arrangement of the b r a n c h p i p e j o i n i n g the main p i p e a t a skew angle with
both
pipes
gradually
flared
at
the
confluence,
9.8)
i n t e r n a l b r a c i n g f o r the acute a n g l e (see F i g . pcmping into
station
two
delivery
branch
pipes.
pipes,
such
For
as
with
i s recommended f o r
water f l o w i n g from a main p i p e
pumping
penstocks f o r
hydro-electric
performed
determine the best angles of
to
together
stat ions,
station
suction
h y d r a u l i c model
pipes
and
tests should be
divergence a n d taper,
and
the arrangement of the i n t e r n a l b r a c i n g . The o v e r a l l external
weight
of
c r o t c h plates.
steel
The
for
internal bracing is
less than f o r
compact arrangement f a c i l i t a t e s
transport
a n d reduces excavation costs. Unless
the
confluence, ing
pipes
internal
increased
there w i l l
designed
bracing will
velocities
crotch p l a t e s o n l y .
diffusers
are
and
be a h i g h head rapidly
appears
to
be
flares
head
losses
than
h a n d i f the expansion
at
paths, with
the
caus-
external
i s too a b r u p t
loss.
The head loss coefficient f o r conical
with
the
between the w a i l a n d a x i s exceeds s u i t a b l e compromise f o r
cone-shaped
p r o t r u d e i n t o the flow
higher
On the other
increases
with
a n g l e of
flare
about 7; degrees
once
the
(Rouse,
angle
1961). A
the angles of f l a r e f o r a 45-degree confluence
74 degrees
to
the
axis
for
the
main
pipe
and
15
degrees to the a x i s f o r t h e b r a n c h p i p e . The
use
branch
and
of main
internal pipes
bracing to
a
confines
practical
the
range.
angle
For
between
the
confluence angles
approaching 90 degrees ( I T ' j u n c t i o n s ) the b r a c i n g web would obstruct the
flow
in
the
main
pipe.
hole cut
in
the
main
p i p e becomes l a r g e r a n d the b r a c i n g would be
impractically
heavy.
a
confluence,
45-degree
branch
pipe
would
before the f l a r e .
For
very
small
angles of confluence the
T h e design c h a r t s presented here a r e confined to and
have
Note that
to
for
any
other
be constructed the use of
angle with
a
of
approach
bend
the
immediately
i n t e r n a l b r a c i n g i s confined to
the
acute
obstruct
angle,
flow.
as
internal
The obtuse
bracing
a n g l e must
at be
the
obtuse
strengthened
angle with
would
external
crotch plates. To minimize head losses,
the diameters of the main incoming p i p e ,
the b r a n c h p i p e a n d the confluent
p i p e should be such t h a t the velo-
c i t i e s i n a l l pipes a r e approximately equal. If
all
branches
of
whose centre l i e s a t the surfaces w i l l flat. the
There may main
the
are
tangential
the intersection of t h e i r axes,
be i n planes.
flare
meets
resulting
continued
beyond
would
strong
be
confluence
to
a
sphere
the intersection of
T h i s means t h a t the b r a c i n g webs a r e
be a k i n k i n the obtuse a n g l e intersection l i n e where
pipe
eliminate
the
the
the
confluent
problems
point
of
where
should
it
enough to t r a n s f e r
pipe
(see
torsion,
Fig.
9.8).
To
'B'
may
be
plate
bend.
The
pipe
loads to t h i s p l a t e ,
the
walls
and the
r e s u l t i n g arrangement simp1 i f i e s f a b r i c a t i o n . To
determine
surfaces, and
the
the
p r o f i l e s of
the
lines of
intersection of
equations
were set
up r e l a t i n g the cone r a d i i a t any
horizontal
distance
along
the
that
the elevations of
intersection I ine, The
a n g l e of
the
the equation t a n confluence a x i s and The ceeding
point
i n t e r s e c t i n g p l a n e to the dis-
tance from the intersection of the axes along the main a x i s . fact
the cone
Using the
the surface of both cones a r e equal on the
the coordinates of the intersection I ine were derived. intersection
B
angle,
=
is
@
p l a n e to the main a x i s , 8 ,
e
) / s i n a cos
the
branch
(cos Q - cos a cos the
angle of
e ,
i s given by
where a i s the
cone surface to
its
e i s the a n g l e of the main cone surface to i t s a x i s .
intersection in
steps
profiles
along
the
w e r e obtained b y computer a n a l y s i s pro-
i n t e r s e c t i n g plane.
T h i s was done simul-
taneously w i t h the stress a n a l y s i s . Although simple must
pipe
it
i s possible to
'Y's
analytically,
be solved by computer,
intersection
line.
study
In
fact
the
stresses
the general
case
in
the
bracing for
i s v e r y complex a n d
proceeding i n small increments a l o n g the previous
studies
have
relied
on
model
studies to o b t a i n the stresses a t the intersecting plane. The
analysis
was
based on
can take no b e n d i n g stress. is
membrane
theory
i.e.
the
pipe walls
The c i r c u m f e r e n t i a l w a l l stress in a cone
PR/(cos 0 ) per u n i t w i d t h a n d the l o n g i t u d i n a l w a l l stress PR/(2
e
cos
)
per
unit
where P
width
l i q u i d pressure a n d R
i s the
i s the
r a d i u s of the cone p e r p e n d i c u l a r to the a x i s . The
forces
due
to
the
wall
stresses
results
indicated
force
intersection l i n e of
an
in
line,
action
the
that
the
plane,
was
of
element
of
the
p e r p e n d i c u l a r to
v e r t i c a l l y a n d h o r i z o n t a l l y in the plane. perpendicular
section p l a n e were i n a l l cases zero. resultant
on
I i n e were resolved i n t o three components,
intersection
the intersection plane, The
cone
to
the s i d e of
plotted g r a p h i c a l l y .
the r e s u l t a n t
forces on the
inter-
The p o s i t i o n and d i r e c t i o n of four
It
was
was constantly
points
the
along
the
observed that
the
i n s i d e the
intersection
p l a n e a n d a c t i n g i n tension on the i n t e r n a l b r a c i n g p l a t e . The
most
tension. centre
line
bracing
of
the
plates
crown,
is
Hence
economical
internal
the
plate.
indicated
twice
the
plate
Thus
of
the
stress,
be
force on found
that
impractically and
the
rower
plate
the
crown
to
plate
may
most
the
be
i n pure
from
+ F/tw,
where f
resultant
question
on
thickness.
A
to
in
terms
of
the
the r e s u l -
economical
the
a
bracing thicker
bending
I n some cases i t w i l l
from
and
plate
resultant for
thickness
p l a t e may
tension
force
at
extreme f i b r e
is
be selected,
the c h a r t s . and
p l a t e in p u r e tension.
the
equation
r e s u l t a n t force.
anywhere
l i n e of the cones.
i n combined
the
or
and position and magnitude of
interpolated
perpendicular
the
internal
centre,
calculated
shape
than
the
else
corresponding are
widest
at
derived
width
case
more steel
tude of
from
which
obtained /tw2
the
the
9.10
intersecting
thin,
of
to
in
plates
contain
the
width
9.8
and
knowing the p l a t e thickness
the
Figs.
in
distance
thickness
permissible
tant
b r a c i n g p l a t e would be one
T h i s s t a t e could be assured i f the r e s u l t a n t force f e l l on the
The n a r -
consequently
The w i d t h of
various
stress,
f
points 6F
=
i s permissible p l a t e tensile stress,
the was
(u-w/Z)
F i s magni-
force which acts a t a distance u from the p o i n t
the
intersection
similar
line,
analysis
was
w
is
plate
performed
width
for
and
t
is
the e x t e r n a l
in
plate crotch
p l a t e s b r a c i n g the obtuse angle. The design flare
charts, of
to
Figs.
crotch the
9.8
to
plates for
main
pipe
and
9.10, a
were compiled and f a c i l i t a t e the
45 degree ' Y ' branch
pipe.
and The
various
most
angles should be selected from h y d r a u l i c considerations. determine head losses could be conducted i f warranted.
angles
suitable
of
flare
Model tests to
169
I
-.---
6;
/
/
j
e
Lc=!23 tcn2 2 G.03303
..L
\
0 "
\
WITH R E C O M M E N D E D A N G L E S
b
TOP H A L F OF EXTERNALCROTCH PLATE B
c TOP HALF OF INTERNAL C R O T C H ~ P L ,TE
F i g . 9.8
Crotch p l a t e s f o r 7io/15O confluence.
4
170
b TOP H A L F OF EXTERNAL CROTCH PLATE 6
c TOP HALF OF INTERNAL CROTCH PLATE A Fig.
9.9
Crotch plates f o r p l a i n p i p e confluence
171
I
0.2
OL
b
0
02
0.L X / D
0.6
TOP HALF O F EXTERNAL CROTCH PLATE B
c TOP HALF OF INTERNAL CROTCH PLATE A Fig.
9.10
Crotch p l a t e s f o r confluence pipe.
plain
pipe
with
15"
taper
172 The design procedure f o r a
trial
plate
width,
p l a t e thickness, crotch
plate
t,
say
the crotch p l a t e s would then be to select
the
maximum
the
obtuse
angle
buck1 i n g under bending compression, than
w/30.
less
than
the
a g a i n s t wear.
and
from the corresponding formula.
for
less
indicated,
The
plate
is
the
To ensure that the
enough
withstand
to
the p l a t e thickness should not be
thicknesses the
rigid
compute
should also p r e f e r a b l y
main p i p e ,
not
be
to ensure d u r a b i l i t y
wall
thickness
of
After
selecting
the p l a t e thicknesses,
the corresponding
p l a t e shapes a r e interpolated from the a p p l i c a b l e c h a r t .
STRESSES AT BENDS
The than
wall
those
stresses
stresses
bending
induced
stresses wall,
are
and
as
the outside of
normally is
inside
the
caused
the
to
design the
of
bend by
or
cast
bend.
only
The the
for
The
iron
to
blocks
stresses
on
w a l l on the
worst
thickness
on
the
f
=
-PD
2t i.e. ratio
is
stress a n d stress
outside of
i s taken o n l y of
i.e.
on
the
it the
bend
circumferential
as on the i n s i d e of
assuming the p i p e w a l l
to
the t h r u s t
due to the
the i n s i d e segment of p i p e shown shaded i n F i g . (R-D/2)
i n s i d e i s less than
takes no bend-
the c i r c u m f e r e n t i a l force on a length of w a l l on the inside
the bend i s equated
ft
the
the bend
stresses a r e c a l c u l a t e d below.
Using membrane theory i n g stress,
local
against
inside of
circumferential
be reduced i f account
the b l o c k . Circumferential
out,
increase in c i r c u m f e r e n t i a l stress
i s safe to keep the same thickness
it
higher
Longitudinal
thrusting the
could a c t u a l l y but
are
straighten
stress,
of
bend
increase i n l o n g i t u d i n a l
the
wall
tends
anchor
l e n g t h of
the bend.
more severe than
safe
fabricated
circumferential
a r e m a g n i f i e d because on
a
i n a p l a i n p i p e w i t h the same w a l l thickness.
are
outside
in
0
=
P(R-D/4)
i n t e r n a l pressure on 9.11,
0D/2
(R-D/4)
(9.2)
(R-DJ2)
the normal (R-D/4)
/
w a l l thickness at the bend should be increased i n the (R-D/2)
the p i p e diameter.
where R
i s the r a d i u s of
the bend a n d D
is
173
9.11
Fig.
In
Stress concentration a t a bend
addition
etc.,
discussed
work
caused
variations designed pipeline
A
and
analysed bution,
so-called
piping in
pipe
using
systems.
if
in
the
form
and design
or
in pipe-
temperature
a n d should be or
at
large
thrust
anchors a r e
as a s t r u c t u r a l
system w i t h
movements.
The
techniques
such
standard
or
pipework
joints or
f i n i t e element
of
strains
plant
can be treated
structural
Crocker a n d K i n g ,
and
junctions
t e r t i a r y stresses
elastic
no movement
thrusts
bends,
These stresses a r e r e a l
chemical
system
slope-deflection
available
movements,
exposed
lateral
secondary stress at
there a r e sometimes
relative
interconnections
installed. axial
the
above,
by
in for
to
methods,
computer
system as
could
be
moment-distri-
many o f
programs.
which a r e (See
also
1967).
THE P I P E AS A BEAM
Longit udi na I Bend ing
Pipes should longitudinal settlement between
of
normally
direction the
supports,
be
even
if
designed they
bedding
could
Three
possible
are
cause
to to
r e s i s t some bending be
buried.
sections to c a n t i l e v e r
bending
patterns
i n the
Unevenness o r
together
o r span with
the
174 corresponding critical The
maximum
b e n d i n g moments a r e i n d i c a t e d i n F i g .
span
which
modate i s c a l c u l a t e d below.
Fb
simply
supported
pipe
.
9.12
could
accom-
The m a x i m u m f i b r e s t r e s s i s
M/Z
=
where
a
(9.3)
M is t h e b e n d i n g
p i p e whose w a l l
moment and Z
thickness,
t,
is t h e s e c t i o n m o d u l u s .
is small
For a
in comparison w i t h the i n t e r n a l
d i a m e t e r D,
Z
nD2 t / 4
=
So if M
Fb
and
WL2/8
=
(9.5)
W L Z / ( 2 n D 2t )
=
o r L2
(9.4)
2nD2 t Fb/W
=
if a
pipe of
specific weight
weight
yw
L
J8DtFb/(ywD
=
Thus f o r =
ys
(9.6)
D = 1 m,
+
4ySt)
t
=
80 000 N/m
is conveying
water
at a specific
(9.7)
0.012 m,
then
y
the
F b = 100 N/mm2,
maximum
yw
permissible
- 10 000 N/m simply
3 ,
supported
s p a n L = 26 m or 86 f t . For
low
internal
water
pressures,
b u c k l i n g of
the w a l l s
may
also
b e a p r o b l e m and t h e p o s s i b i l i t y s h o u l d b e i n v e s t i g a t e d ( e s p e c i a l l y a t t h e s u p p o r t s w h e r e t h e s h e a r s t r e s s is h i g h ) . See also P e a r s o n ,
1977.
P i p e S t r e s s at Saddles The m a x i m u m
local stress in a continuous o r s i m p l y supported p i p e
supported in a s a d d l e i s (Roark, F
(0.02 - 0.00012
=
where
Q
span,
Q
due
to
1954):
( B - 90°))(Q/t' )Loge (f)
i s the total saddle reaction.
(9.8)
Note t h a t f o r a s i m p l y s u p p o r t e d
i s the r e a c t i o n d u e to two ends r e s t i n g o n the support, the
weight
continuous pipe.
of
pipe
of
length
equal
to
the
span,
as
i.e.
for
If Q i s i n Newtons a n d t i n mm t h e n F i s i n N / m m 2 .
a
175
WlUNlT LENGTH
REACTION
WL12
WlUNlT LENGTH
Wll2
MAXIMUM BENDING MOMENT.
WLI2
WL
5 x 2 3 z
a.
El
Simply Supported
F i g . 9.12
Cantilevered
c.
Fixed Ends
b.
Beam moments and deflections
The a n g l e of or
width
0
WLl2
wL2/a
DEFLECTION
crete
WlUNlT LENGTH
strap
of
the
support
To t h i s
diameter.
,
bottom support, 6 saddles.
mum l o n g i t u d i n a l
i s n o r m a l l y 90"
The stress provided
it
local stress a t
is practically is
small
120'
or
for
con-
independent of
compared
with
the
the pipe
the saddle must be added the rnaxi-
bending stress a t the support f o r the p i p e a c t i n g as
a continuous beam,
unless a j o i n t occurs a t the support.
R i n g Girders Steel ground may
pipes etc.
may
be
B u c k l i n g of
laid
and
be
the
back
plain
the
vicinity
developed
under
the
a r e useful
rectangular
fixed
in
over
ground,
ravines,
of
all
in
cross
r o u n d the pipe.
there
i s no s i d e f i l l
the
Chapter
ring
8.
may The
be
Rigid r i n g
i n these circumstances. section, The
or
local
evaluated
longitudinal
marshy
i n these circumstances as
the p i p e saddles cause stress concentrations.
g i r d e r s at each support may
ground
t h e p i p e a n d stresses
be more severe than
support
above
The rings
T o r H shaped,
with
p i p e bending stress using
the
bending stress
ring
theory
i n the p i p e
w a l l under a r i n g is
1.65 0.91
Pd
+
h J%T/A
2h
in
(9.9)
176 A
where be
i s the cross sectional
added
any
longitudinal
area of
stress
in
the r i n g . the
pipe
To
t h i s stress must
due
to
beam
action
between supports. T h e r i n g stress i n the r i n g g i r d e r i s
1
1 0.91A/(hj hd)
+
In
addition
the
there
r i n g girder
Pd
(9.10)
2 7 will
be
local stresses
to the supports.
g i r d e r a n d rest on a s l i d i n g or of
the p i p e a n d contents
due to
t h e method of
Legs a r e securely
fixed
fixing
to the r i n g
r o l l e r b e a r i n g on a p i e r .
The weight
i s t r a n s f e r r e d to the bottom h a l f of the r i n g
g i r d e r a n d thence through the legs to the p i e r .
A
more comprehensive a n a l y s i s
presented
in
Crocker
and
King
of
the stresses
(1967).
See
i n r i n g girders
also
Cates
(1950)
is
and
( 1933).
Scharer
TEMPERATURE STRESSES
Pipes outside
with
will
high
differences
be subject
temperature
differences.
have
maximum
their
compressive the and
on
the
temperature on the
heat flow
the p i p e diameter,
in
to r a d i a l The
value
temperature
the
inner
the
inner
and
wall
is
above
I f the w a l l
l o n g i t u d i n a l stresses
a n d outer
i n n e r surface and tensile on
i s steady.
inside
a n d c i r c u m f e r e n t i a l stresses due to
circumferential and on
between
surfaces,
the outer
t h a t on
is thin
being
surface
the outer
if
wall,
i n comparison w i t h
the stresses may be approximated b y the f o l l o w i n g
equations: on the i n n e r surface F
a n d on the outer surface F where
a
i s the thermal
elasticity,
T
a ET
=
Fe c
=
F
(9.11)
-20
=
P
=
aET -2(1-u)
(9.12)
coefficient o f expansion,
i s the temperature difference,
E i s the modulus of
v i s Poisson’s r a t i o ,
c i r c u m f e r e n t i a l stress and Fe i s l o n g i t u d i n a l stress. i s compressive a n d
is
always
and l o n g i t u d i n a l stresses, For
normal
c I imatic
less
than
the
Fc i s
The r a d i a l stress
maximum c i r c u m f e r e n t i a l
b e i n g zero on both boundaries.
temperature differences
the stresses
are rela-
177 tively ‘C,
low. v =
A
Thus f o r
longitudinal
longitudinally
as
The m a g n i t u d e o f after
10°C, E = 200 000 N/mmz, a
T =
0.3 f o r s t e e l p i p e , t h e n F m a x
installation)
stress a
may
result
t h i s stress (see
Ch.
also
of
be
=
induced
temperature
i s aET
10 f o r
= 12 x
per
17 N/mmz. in
change
a
pipe
after
restrained
instal lation.
(tensile if the temperature drops an
analysis
including
effects
of
supports).
REFERENCES
B l a i r , J.S.,
1946. R e i n f o r e c e m e n t o f b r a n c h p i p e s . E n g i n e e r i n g , 162.
Cates, W.H., 1950. D e s i g n s t a n d a r d s f o r l a r g e d i a m e t e r s t e e l w a t e r p i p e , J. Am. W a t e r W o r k s Assn., 42. C r o c k e r , 5. and K i n g , R.C., 1967. P i p i n g H a n d b o o k , 5 t h E d . , M c G r a w H i l l , N.Y. P e a r s o n , F.H., 1977. Beam b e h a v i o u r o f b u r i e d r i g i d p i p e l i n e s . P r o c . Am. SOC. C i v i l E n g r s . , 108 ( E E 5 ) 767. 1954. F o r m u l a s f o r s t r e s s and s t r a i n , McGraw H i l l , N.Y. R o a r k , R.J., p . 418. Rouse, H., 1961. E n g i n e e r i n g H y d r a u l i c s , W i l e y , N.Y., S c h a r e r , H., 1933. D e s i g n of l a r g e p i p e l i n e s . T r a n s . Am. SOC. C i v i l Engs., 98 ( 1 0 ) . Stephenson, D., 1971. I n t e r n a l b r a c i n g f o r p i p e c o n f l u e n c e s . T r a n s . , S.A. I n s t n . C i v i l E n g r s . , 13 (11). Sulzer, 1941. P a t e n t e d s t i f f e n i n g c o l l a r s o n t h e b r a n c h e s o f highpressure p i p e l ines f o r hydroelectric power works. Sulzer Technical R e v i e w , 2 ,lo. Suss, A. and H a s s a n , D.R., 1957. R e d u c t i o n o f t h e w e i g h t and loss o f in d i s t r i b u t i o n p i p e s f o r h y d r a u l i c p o w e r l a n t s . Escher energy Wyss News, 30 (3) 25. Swanson, H . S . , C h a p t o n , H.J., W i l k i n s o n , W.J., King, C.L. and N e l 1955. D e s i g n o f w y e b r a n c h e s f o r s t e e l p i p e s . J. A m . son, E.D., W a t e r W o r k s A s s n . , 47 ( 6 ) 581. Timoshenko, S. and G o o d i e r , J.N., 1951. T h e o r y o f E l a s t i c i t y , McGraw H i l l , N.Y.
L I S T OF SYMBOLS
A
-
a r e a of r i n g g i r d e r
a,b
-
h o r i z o n t a l and v e r t i c a l
a,b,c
-
c r o t c h p l a t e t o p and s i d e w i d t h s
D or d-
a x e s o f an e l l i p s e
p i p e diameter
E
-
modulus of e l a s t i c i t y
f
-
permissible crotch p l a t e stress
F
-
r e s u l t a n t force on c r o t c h p l a t e a t a n y point,
G
-
wal I thickness
h
factor o f safety
o r stress
178 span o r length bending moment water pressure (same u n i t s as f ) saddle reaction radius stress a p p l i e d to a p l a t e crotch p l a t e thickness temperature difference distance from p i p e w a l l to F w i d t h of crotch p l a t e at any p o i n t load p e r u n i t l e n g t h horizontal
distance
from
crown
along
mid-plane
or
centre-I ine
of
crotch p l a t e
Y
-
vertical
distance
above
crown
of
crotch
plate section modulus a n g l e of confluence of b r a n c h p i p e w i t h main p i p e coefficient of temperature expansion a n g l e between crotch p l a t e and main p i p e a x i s , o r a n g l e of support
specific weight angle
of
flare,
or
taper,
of
main
pipe
a x i s to cone) a n g l e of f l a r e , Poisson's r a t i o
o r taper,
of b r a n c h p i p e
(measured from
CHAPTER 10
PIPES, FITTINGS AND APPURTENANCES
PIPE MATERIALS
Steel Pipe Steel
i s one of
i s d u c t i l e yet work,
the most
has a
high
versatile materials for tensile
It
strength.
pipe walls,
is
relatively
as
it
easy
to
i s the strongest
a n d the welded j o i n t f r e q u e n t l y used w i t h steel
type of j o i n t . Steel
grades
p i p e s i n the U.K.,
used f o r
and
their
corresponding
minimum y i e l d stresses a r e as follows:
BS 4360
Grade 40
230 N/mm2
:
Grade 50
355 N/mm2
Grade 55 US 572
450 N/mm2
:
290 N/mm2
Grade 4 2 Grade 50
345 N/mm2
Grade 60 Grade 65 The for
higher
grades
are
preferred
they
a r e easier
Small-bore seams,
but
welded
either
to
weld,
(less
a n d on
than
larye-bore
450
pipes
448 N/mm2 high-pressure
account
pipelines
but
horizontally or
asbestos cement
pressures,
and
it
of
steel
made
spirally. site.
pipes
from
are
steel
wall
thickness
rolled
plate,
Pipes a r e made Steel
and plastic
requires
the e x t r a
loads.
mm)
are
10 m and more a n d j o i n t e d on
than concrete, low
: for
low pressure p i p e l i n e s the lower grade steels a r e more economical,
they a r e more r e s i s t a n t to e x t e r n a l
to
414 N/mm2
:
pipe
pipe
coating
and
is
in
and
lengths
up
more expensive small
for
without
bent
sheathing
bores to
2nd
prevent
corrosion.
Cast Iron Pipe Cast
iron
is
more
expensive and more r i g i d . used f o r p l a i n p i p e , tapers
and
flanges.
corrosion-resistant I n fact
actual
steel,
sand c a s t i n g
a l t h o u g h i t i s used f o r Plain
than
'specials'
but
more
i s now r a r e l y such a s bends,
p i p e s a r e n o r m a l l y formed of
grey
iron
180 or
ductile
and
iron
by
dimensions
of
centrifugal ductile
spinning.
iron
pipes
Standard
are
pressure
specified
classes
BS 4772
in
and
i r o n p i p e s i n 854622.
of grey
Asbestos Cernent Pipe Asbestos cement is
able
to
cement
resist
is
p i p e i s made of relatively
relatively
high
cheap,
cement
tensile
strong
and asbestos f i b r e , stresses.
and
Although
which
asbestos
corrosion-resistant,
susceptible to shock damage and cannot be used f o r
it
is
'specials'.
Joints a r e made w i t h a sleeve f i t t e d w i t h r u b b e r sealing r i n g s .
Concrete Pipe Reinforced ical
for
loads
large
easier
and in
or
are
prestressed concrete pipes a r e s u i t a b l e and econom-
diameters. than
corrosion
jointing
and
They
steel
on
are
resistant.
making
able
account Their
later
to
resist
their
of
main
external
extra
wall
weaknesses
connections.
There
buckling thickness,
appear
i s as
to
be
yet not much
long-term experience w i t h prestressed concrete pipes.
Plastic Pipe Technological this
has
advances
been o f
special
cized p o l y v i n y l c h l o r i d e gases,
drains,
Kingdom for
and
small
UPVC
for
in
interest
Europe.
large
pipes
Glass
it
is
It
fibre is
Polyethylene although
diameters.
suitable
Although is still
a r e causing The
resin
for
some
were
engineering.
sewer
also
is
used
usually
density
r a p i d and Unplasti-
f o r chemicals,
pipes
i n the United
to
limited
a
more
extent
expensive
polyethylene
has
than
recently
l a r g e diameter p i p e l i n e s .
also
used
expensive
specialised
to a
but
l i m i t e d extent
used
applications
with as
an it
for
pipe-
inert
filler
i s corrosion-
l i g h t and strong.
pla sti c pipe not
and
is
it
High
is
comparatively
resistant, r i g i d ,
and
and
1960's
the
pipeline
irrigation
been used w i t h some success f o r
lines.
in
in
pipes a r e now used extensively
waterpipes,
bore
plastics
has
not
yet stood the r i g o r o u s test of
acceptable under many by-laws,
time
i t s many advantages
i t to g a i n r a p i d acceptance amongst engineers.
working
stress
of
plastic
i s less
14 N/mrnz
so p l a s t i c cannot
be used f o r limited
l a r g e diameter
strength
buckting
and
pipes. be
The
used
subject
deterioration w i t h
collapse.
can be used
high-pressure
in difficult
friction
as
to encrustation
to
I t i s also subject to
its flexibility
many
can cause
corrosive f l u i d s a n d
locations such as undersea o u t f a l l s
loss
beneficially
time a n d
i s resistant
It
mains.
a n d gas
i s lower than f o r
most m a t e r i a l s a n d
a
types of
l i n i n g to other
than other types of p i p e ,
pipes.
i t can
It
is
less
accommodates g r e a t e r
ground movements a n d i s easier a n d l i g h t e r to l a y . On the other h a n d it
has
a
loosened and
high
coefficient
of
thermal
expansion,
i f the p i p e contracts on cooling.
may
distort
or
even
collapse
joints
so
may
be
I t i s susceptible to damage
under
load.
Ribbed
and
stiffened
pipes a r e b e i n g developed to overcome these l i m i tations. P l a s t i c p i p i n g i s n o r m a l l y made of thermoplastic which i s r e l a t i v e ly
easy
to
extrude
As
PVC i s f l e x i b l e a n d e x h i b i t s creep,
plastics. in
an
when
heated.
u n p l a s t i c i z e d form is
ethylene
easier
to
were
with
developments
Polyethylene
(UPVC) f o r
work
than
and it
PVC
are
pipes.
the manufacture of
UPVC
polyethylene.
and
With
for
thermo-
i s generally
this
reason
improvement
used Poly-
earlier
i n production
techniques UPVC i s now cheaper than polyethylene a n d i t holds c e r t a i n other
advantages.
thermal
expansion
high-density lene for
is
stronger
than
and
has
polyethylene,
polyethylene
(HDPE)
has
a
smaller
although improved
coefficient
of
recent ly-developed
properties.
Polyethy-
i s more d u c t i l e than UPVC a n d f o r t h i s reason i s often p r e f e r r e d gas p i p i n g .
developed
in
It
the
for
Rubber toughened p l a s t i c s such as ABS have a l s o been
flexible
appendix.
pipework.
Because
of
Properties
the
low
of
plastics are tabulated
elasticity
of
plastics,
water
hammer pressures a r e less severe than f o r other m a t e r i a l s . Plastic
pipes
may
be j o i n t e d
though
these
methods
are
factory
fitted
flanges
or
by
difficult spigots
solvents for
and
large
sockets
of
fusion
welding,
diameters. with
rubber
al-
Screwed o r rings
are
also used. The
manufacture of moulded bends,
tees a n d branches
i n UPVC a n d even more so i n HDPE so steel o r C.I.
is difficult
f i t t i n g s a r e fre-
quen t I y used. The p r i c e of the 1960's,
PVC pipes
i n the U.K.
dropped b y more than
30%
in
whereas other p i p e m a t e r i a l s a r e c o n t i n u a l l y i n c r e a s i n g i n
182 cost.
In
the
U.K.,
cast
iron
than
1 N/mmz.
pipes
PVC
for
pipes
are
cheaper
diameters
less
than
than
asbestos cement
450 mm and
I t i s r a p i d l y r e p l a c i n g salt-glazed
and
pressures
less
and asbestos-cement
pipes f o r sewers a n d low pressure systems. least 5700 m i l l i o n was
At out
the
pipes
world.
are
The
used
figure
in
ever
may yet r e v o l u t i o n i z e BVMA,
1964; P a u l ,
spent
is
i n 1972 on p l a s t i c p i p i n g through-
likely
to
increasing
pipeline
r i s e considerably
proportions
engineering
and
(see
as
new
also
plastic
discoveries
Boucher,
1948;
1954).
LINE VALVES
There a r e many which
types of v a l v e s f o r use i n p i p e l i n e s , the choice of
depends on the d u t y .
depend on economics. the
pipe
diameter,
waterworks the
same
trapped, be
lined
weighed certain
level
and
as
up.
v a l v e s a n d the size w i l l
Normally v a l v e s a r e sized s l i g h t l y
practice i t
whereas
The spacing of
installed
with
a
reducer
on
soffit
the
I n choosing the
circumstances
either
side.
In
i s p r e f e r a b l e to keep the s o f f i t of the v a l v e at of
the
pipe,
to
prevent
in sewerage a n d sol i d s t r a n s p o r t ,
against
smaller than
cost it
the of
may
size, the
the cost of
head
loss
desirable
be
being
the v a l v e should be
through
to
air
the i n v e r t s should
it,
maintain
although the
full
in
pipe
bore ( t o prevent erosion o r b l o c k a g e ) . Isolating km,
valves
the
spacing
problems.
Sections
leaks
and
waste
would
the
valves
are
are
frequently
being of
a
function
the p i p e l i n e may
volume of
be
a
installed at
water
f u n c t i o n of
i n s t a l l e d at
which
of
intervals
economics
and
of
1
to
5
operating
have to be isolated to r e p a i r would
the spacing of
h a v e to
be d r a i n e d
i s o l a t i n g valves.
the bottom of each major d i p
to
Scour
i n the p i p e l i n e
profile. It around
i s sometimes a d v i s a b l e to in-line
facilitate
i n s t a l I smal I-diameter
by-pass
valves
v a l v e s to equalize pressures across the gate a n d thus
opening
( w h i c h may
be manual o r
by
means of
an e l e c t r i c
o r mechanical a c t u a t o r ) .
Sluice Valves Sluice v a l v e s ,
o r g a t e valves,
a r e the normal type of v a l v e s used
183 for
isolating or
scouring.
They
seal
well
under
high
pressures a n d
when f u l l y open o f f e r l i t t l e resistance to f l u i d flow. There spindle
are
which
handwheel,
two
types
is
attached
and
attachment
of
spindles to
the
a non-raising
gate
raising
and
the
does
s p i n d l e which
10.1).
i n the gate ( F i g .
for
A
gate:
rising
not r o t a t e w i t h the
i s rotated i n a
screwed
The r i s i n g s p i n d l e type i s easy to
I u b r ica t e. The
gate
be
may
para1 lel-sided
or
wedge-shaped.
seals best b u t may be damaged b y g r i t . gunmetal
sealing
the wedge-gate
For low pressures r e s i l i e n t o r
faces may be used b u t f o r
high pressures s t a i n l e s s
steel seals a r e preferred. Despite sometimes
sluice
valves'
troublesome
to
simplicity operate.
and
They
need
them a g a i n s t a high unbalanced pressure, minutes to t u r n open o r closed.
positive a
action,
big
force
they to
are
unseat
a n d l a r g e v a l v e s t a k e many
Some of the problems can be overcome
b y i n s t a l l i n g a v a l v e w i t h a smaller bore t h a n the p i p e l i n e diameter.
Fig.
10.1
Sluice v a l v e
Butterfly Valves ( F i g . 10.2) Butterfly a n d occupy for
sluice
fairly
valves less
are
space.
valves,
cheaper The
especially
h i g h resistance to flow
the thickness of
than
sealing at
valves
for
larger
sizes
i s sometimes not as e f f e c t i v e as
high
even
the d i s c obstructs
sluice
pressures.
i n the f u l l y the flow
They
also
open state,
even when
offer
a
because
i t i s rotated
184 90 degrees
to
the
the
gates
high
fully
open
position.
Butterfly
valves,
as
well
as
a r e not s u i t e d f o r operation in p a r t l y open positions as
s l u i c e valves, and
torques
seatings to
open
would them
erode
against
As
rapidly. high
both
pressure,
types
they
require
often
have
geared handwheels o r power d r i v e n actuators.
Fig.
10.2
Butterfly valve
Globe Valves Globe v a l v e s have a c i r c u l a r seal spindle pipe
and
axis.
handwheel. The
flow
The
seating
changes d i r e c t i o n
r e s u l t i n g i n h i g h head losses. bore pipework
connected a x i a l l y is
a n d as taps,
a
ring
through
to a v e r t i c a l
perpendicular
to
the
90 degrees twice thus
The v a l v e s a r e n o r m a l l y used i n small-
a l t h o u g h a v a r i a t i o n i s used as a control
valve.
Needle and Control Valves ( F i g . 10.3) Needle v a l v e s a r e more expensive than s l u i c e a n d b u t t e r f l y v a l v e s but are w e l l ing
action
l i t t l e flow
suited for
as
they
t h r o t t l i n g flow.
close
whereas
They
sluice
resistance u n t i l p r a c t i c a l l y shut
damage.
Needle
valves
springs,
accumulators
may or
be
used
actuators
butterfly
counterbalance
maintain
constant
conditions e i t h e r upstream o r downstream of the v a l v e , a constant
flow.
even
at
axial
needle o r
throttl-
valves
offer
and may suffer c a v i t a t i o n
with to
have a g r a d u a l
and
weights, pressure
o r to m a i n t a i n
They a r e streamlined i n design a n d r e s i s t a n t to wear
high flow
velocities.
spear-shaped
The cone
method of i n t o a seat.
sealing
is
to
push
an
There i s often a p i l o t
needle which operates f i r s t to balance the heads before opening.
A v a l v e w i t h a s i m i l a r h y d r a u l i c c h a r a c t e r i s t i c to the needle v a l v e
185 is
the
sleeve
valve
atmosphere or orifices spray,
around
the
thereby
an
electric for
valve.
cone
The
cone
tube
used
and
is
as
a
discharging
into
the
which s l i d e s over
i n a n umbrella-shaped
Needle a n d sleeve
valves are
hammer release v a l v e s when coupled
actuator
away
use
for
b y a sleeve
spread the flow
water
maintenance valve
seal
the energy.
as
rotates
suitable
They
hydraulic
or
dismantling
sealing
is
dissipating
a l s o occasionally to
which
an open b a y .
the
(see Chapter working
variation from
the
of
the
pipe
4). They
parts
are
needle v a l v e
axis
require
inside
instead
but of
the the
being
withdrawn a x i a l l y .
Fig.
10.3
Needle v a l v e
Spherical Valves
( F i g - 10.4)
Spherical
have
valves
it.
When the v a l v e
the
bore
i s equal
the sphere,
a
rotary
p l u g with
is fully
opened
there
to
that
a n d normally
of
the pipe.
an
axial
hole t h r o u g h
i s no resistance to flow
The v a l v e s close b y
have a n offset
r o t a t i n g the sphere into the open position.
action
as
rotating
to unseat them before
186
10.4
Fig.
Spherical
Reflux Valves
used
normal
to
flow
the flow
(Fig.
or
Reflux, are
flow
the
or
check
the gate
the horizontally
gate
valves
in
automatically
conditions
stops,
keep
10.5)
non-return,
stop
the a i d o f s p r i ngs. to
valve
as
the
they
i s k e p t open
by
A counterbalance can be f i t t e d to the gate s p i n d l e fully
open a t
practically
all
flows,
the flow
a l s o sometimes
u s e d to a s s i s t c l o s i n g .
Larger reflux
obstruct
the
in
which
flow,
to
flutter
at
case
and
Mounted in h o r i z o n t a l tend
Under
and when
the flow,
in r a p i d c l o s i n g when
multi-gates,
direction.
h i n g e d g a t e closes b y g r a v i t y o r w i t h
to assist
used
a r e also known,
reverse
the
swabbing
pipes,
low
thickness of
the
t h e g a t e s of
flows,
and
for
does
or
stop.
it
Springs are
v a l v e s may h a v e
of e a c h g a t e w i l l pipeline
could be
may
be
partially difficult.
some t y p e s o f r e f l u x v a l v e s this
reason
an
offset
hinge
w h i c h c l i c k s t h e g a t e open is sometimes used.
AIR
VALVES
Two One
types
is a
(see a l s o 1943). of
air
small-orifice
large-orifice
Lescovich,
release
1972;
valves
automatic
air
are
Parmakian,
normally
1950;
used
Sweeton,
i n pipelines.
release v a l v e a n d the other i s a
a i r vent v a l v e .
A i r Vent V a l v e s When a p i p e l i n e i s f i l l e d , profile,
thereby
increasing
a i r could be trapped a t peaks along the head
losses a n d r e d u c i n g
the capacity
of
187 the
Air
pipeline.
permit also
air
let
in
air
the into
pipeline.
Without
collapse,
or
It
is also
cause
valves
pipe the
normally
to escape when
installed
displaced
by
p i p e l i n e d u r i n g scouring o r
at
peaks
the f l u i d .
to
They
when emptying
the
them vacuum may occur a t peaks a n d the p i p e could
u n d e s i r a b l e to hammer
have a i r
pressure
T h e s e a l i n g element
full,
are
i t may not be possible to d r a i n the p i p e l i n e completely.
water
pipeline. is
vent
i s seated
pockets in the p i p e as they
fluctuations
during
operation
i s a buoyant b a l l which,
a g a i n s t a n opening a t
the top of
may
of
the
when the p i p e
the v a l v e .
When
t h e pressure i n s i d e the p i p e f a l l s below the e x t e r n a l pressure the b a l l
drops thereby p e r m i t t i n g a i r to be drawn i n t o the pipe. is
being f i l l e d
pipe and
the
valve
will
remain
l i f t s the b a l I a g a i n s t
open u n t i l
the seating.
When the p i p e
the water f i l l s
The v a l v e w i l l
the
not open
a g a i n u n t i I the pressure fal I s below the e x t e r n a l pressure.
10.5
Fig.
The
Reflux v a l v e
valve
will
tend
should be r e a l i s e d t h a t psi)
will
cause
sonic
Pressure differences close
some
air
vent
blow
to
closed
a differential velocity
of
0.027
around valves.
The
at
high
air
velocities.
pressure of o n l y 0.1
air N/mrn2
through
the
valve
N/mmz
It
(13
(300m/s).
( 4 p s i ) h a v e been found to
slamming
closed
may
damage
the
hollow b a l l seal. In
practice
a
diameter
approximately
l/lOth
of
the p i p e diameter
188 is
used,
although
preferable.
t i o n diameter, The
larger
The v a l v e
size
diameters
duplicate
installations
the size of
the
are
i n l e t connec-
a n d the o r i f i c e diameter i s u s a l l y s l i g h t l y smaller. of
air
vent
scouring
through
an o r i f i c e i s approximately
pressure
rate
valve w i l l
desired
same
and
i s r e f e r r e d to b y
of
the
difference,
depend on
pipe.
The
r a t e of
flow
of
air
40 times the flow of water f o r the
ful I
but
filling or
the r a t e of
volume
vacuum
pressure
should
not
be
a1 lowed to develop.
A i r vent relative
v a l v e s should be i n s t a l l e d a t peaks i n the p i p e l i n e ,
to
Various
the
possible
during
a
rule
is
the
of
During vent
free
the
air
fitting
as a l l
air
flow is
release air
the
equal
the a i r
valves area
most the
the
gradient.
including
reverse
gradients
They
normally
fitted
r a t e of
should
initial
difficult r a t e of
discussed
derived
m2
at
are
as
are in
the
both
hydraulic
valve,
in m 3 / s
air
operations,
will
to
gradients
orifice
of
relative
b e considered.
sizing
thumb
valves
taken
an
for
r a t e of
of
should
with
sec t ion. Equations
and
hydraulic
scouring,
Combination
flow
horizontal
to
evacuation the
the
in
Chapter
be
Q/lOO
pressure.
factor
filling
in
air
line.
next
5.
As
where
Q
The r a t e of
determine of
in
though.
through
all
Care should be
i s evacuated as the flow of water w i l l suddenly
be stopped a n d water
hammer
i s possible.
A i r Release Valves Air
i s e n t r a i n e d in water
suction r e s e r v o i r o r pockets there
or
velocity
the
by
vortices in the pump
suction
reservoir.
The
air
may
be
at air
released when
i n pressure,
e i t h e r a l o n g a r i s i n g main o r where the
i s increased through
a r e s t r i c t i o n such as a p a r t i a l l y closed
An
valve. from
in
i s a drop
in many ways;
merely b y absorption a t exposed surfaces,
increase i n temperature w i l l
solution.
Small
orifice a i r
also cause a i r
release
valves
are
to be released
i n s t a l l e d on
the
p i p e l i n e to bleed o f f the a i r which comes out of solution. Smal I size,
orifice
usually
air
valves
are
designated
12 to 50 mm diameter.
by
a i r release o r i f i c e size which may be from 1 larger size.
the
pressure
in
the
pipeline,
which
is
on
the
average
i n l e t connection
to 10 mm diameter.
the smaller
The volume of a i r to be released w i l l
entrained
their
This has n o t h i n g to d o w i t h the
2% of
be a f u n c t i o n of the
The
need be t h e o r i f i c e
volume of
the a i r
water
(at
189 atmospheric p r e s s u r e ) , (see Chapter 5 ) . The small
o r i f i c e release v a l v e s a r e sealed b y a f l o a t i n g b a l l , o r
needle which i s attached to a f l o a t . accumulated or
the
i n the connection on
needle
release v a l v e s
valve
will
a r e often
When a c e r t a i n amount of a i r has the p i p e ,
top of
open
and
release
combined w i t h
double
air
valve,
(see
Fig.
air.
drop
orifice
vent
valves
The arrangement i s c a l l e d
An
10.6).
will
Small
large orifice a i r
on a common connection on top of the pipe. a
the b a l l
the
isolating
sluice
valve
is
normally f i t t e d between the p i p e a n d the a i r valves.
n
LAREE ORIFICE AIR VENT VALVE
SMALL ORIFICE FIlTINQ
10.6
Fig.
Double a i r v a l v e
Double a i r
valves
should
be
installed
at
peaks
in
the
pipeline,
b o t h w i t h respect to the h o r i z o n t a l a n d the maximum h y d r a u l i c g r a d ient.
They
should
also
be
points
along
a
l e n g t h of
grade
line.
It
should
installed
be
borne
a l o n g i n the d i r e c t i o n of flow in
sections
Double a i r
falling
at
p i p e l i n e which
slowly
in
in
the
ends
is parallel
mind
that
air
and
intermediate
to the h y d r a u l i c may
be
dragged
i n the p i p e l i n e so may even accumulate relation
v a l v e s should be f i t t e d every
to
4
the
hydraulic
gradient.
to 1 km along descending
sections, especially a t p o i n t s where the p i p e d i p s steeply.
A i r release v a l v e s should a l s o be i n s t a l l e d on a l l
long ascending
190 lengths of due
to
pipeline
the
where
lowering
of
in g r a d i e n t .
decrease discharge
side
of
air
the
is
likely
pressure,
to
be released from solution
again
especially
at
p o i n t s of
Other places a i r v a l v e s a r e r e q u i r e d a r e on the
pumps
and
at
high
points
on
large
valves
and
upstream of o r i f i c e p l a t e s a n d r e d u c i n g tapers.
THRUST BLOCKS
1969)
!See also Morrison,
Unbalanced
thrust
results
at
a
bend
in
a
pipeline
due
to
two
due to the change i n d i r e c t i o n of flow.
The
act ions:
(1)
The dynamic force
thrust
any
in
direction
proportional
is
to
the
change
in
momentum in that d i r e c t i o n a n d is: Fxl
F
where
is
direction
x.
compared
force,
the
and A Vx
flow
(10.1)
oqAVx
=
is
p
the
the reduction of T h i s force
with
the
is,
force
fluid
mass density,
q
i s the
the component of velocity
i n the
under normal conditions,
due
to
the
internal
negligible
pressure
in
the
pipe.
(2)
The t h r u s t
i n the d i r e c t i o n of each
leg of the bend due to the
pressure i n the p i p e i s : Fx2
where p of
(10.2)
PA
=
i s the i n t e r n a l pressure,
p i p e flow a n d
10.7).
The
A i s the cross sectional area
0 i s the a n g l e of d e v i a t i o n o f the p i p e ( F i g .
resultant
outward
thrust
is
the
forces i n both d i r e c t i o n s of the p i p e a x i s , Fr
=
vector
sum of
the
and is
2pA s i n 0 / 2
(10.3)
The unbalanced t h r u s t may be counteracted b y l o n g i t u d i n a l tension in
an
all-welded
pipeline,
or
against
the foundation m a t e r i a l .
size of
the
addition and
to
block
a
concrete
thrust
block
bearing
I n the case of a j o i n t e d p i p e l i n e the
may be c a l c u l a t e d u s i n g s o i l mechanics theory.
frictional
resistance on
the circumference of
against
by
the outer face of
the
the
pipeline,
bottom there
the p i p e a n d block.
of
is
a
the
thrust
lateral
In
block
resistance
The maximum r e s i s t i n g
191 pressure
a
mass w i l l o f f e r
soi
f
1 + sin@ + ~ s 1h - s i n @
=
P
i s termed the passive resistance and
1969)
i s (Capper and Cassie,
1
+
sin<
2cJ 1 - s i n @
i s the r e s i s t i n g pressure a t depth h, y s i s the s o i l d e n s i t y , P the effective i n t e r n a l a n g l e of f r i c t i o n of the soil a n d c i s i t s
where f
@
is
cohesion.
If
the
thrust
'
HZ =
1
Ys-2
This thrust
maximum
block
extends from the surface to a depth H
a n d i t s l e n g t h i s L, the total r e s i s t i n g t h r u s t i s
below the surface,
P
block
-
+
+
sin6
sin6
kHLJ
possible
1 + sin$ 1 - sin
resistance
will
i s a b l e to move i n t o the soil
ponding
maximum
minimum
pressure
pressure,
which
soil
pressure
which may
be
is
termed
(10.5) only
be
developed
mass s l i g h t l y . the
passive
may occur on the t h r u s t block developed
if
the
thrust
block
if
the
The corres-
pressure.
The
i s the a c t i v e were
free
to
y i e l d away from the s o i l mass. This i s
Ifa
=
which
ysh 1
sin4 -
+ s i n @ "1
i s considerably
$-si+ nm sin4
(10.6)
less than the passive pressure and w i l l o n l y be
developed i f the force on which i t i s a c t i n g i s free to move away from the soi I e x e r t i n g the pressure.
Fig.
10.7
T h r u s t a t a bend
192
10.6
Fig.
Thrust block
I n p r a c t i c e the pressure which may be r e l i e d upon i s s l i g h t l y than
the
p a s s i v e pressure,
not permissible. the
soft
block
the
to
activate
excavation.
rest"
full
of
The
horizontal
used
These
in a l l o w i n g
internal
stress
soil
to 0.7
for
friction
i n Table 10.1.
to
for very
pressure
(CP
1972),
are
seldom
vertical
less
usually
least 2 should be used w i t h
at
i n w a r d movement of
passive
movements
the p i p e i s
varies
soil
p l a sti c clays.
stress
the top of from
where H
T h e "at varies
H/20
a
for
i s the depth
permissible,
coefficients a r e p r o b a b l y more r e a l i s t i c .
loose sands
of
safety
movement of
c l a y s to H/200 f o r dense sand,
"at of
of
passive resistance formula.
thrust
of
A factor
as f u l l
and the
rest" r a t i o
from
0.4 for
An impact factor should be
water hammer pressures. T y p i c a l values of a n g l e $ a n d cohesion
c
for
v a r i o u s soils a r e
indicated
193 Strength of Soils - t y p i c a l
TABLE 10.1 Type of soil
values
Angle of f r i c t i o n
4
Cohesion N/rnmz
Gravel
35 O
0
Sand
30
0
Silt
28 O
0.007
Dense c l a y
5"
0.035
Soft s a t u r a t e d c l a y
0
0.15
Exarnp I e Calculate pressures a t
the
size of
N/rnrnz.
block
to r e s i s t
the u n b a l a n c e d
L e n g t h of 1 p i p e l e n g t h = 10 r n ,
C = 0.005
@ = 30°,
thrust
i n a 1 000 rnrn d i a m e t e r p i p e o p e r a t i n g a t
a 45O b e n d
a p r e s s u r e o f 2.0
1 m,
a
N/mmz.
depth =
L a t e r a l f o r c e F = 2 x 2.0
3 x -If
4
s i n 2 2 i 0 = 1.20 MN. T r y a t h r u s t b l o c k 3 x 3 ~ 3rn: Weight of t h r u s t b l o c k 3 x 3 ~ 3 ~200x9.8/10 2
3
Weight of 10 rn l e n g t h of p i p e Weight of w a t e r
i n p i p e 0.785x1zx10x9.8x1
OOO/lO'
=
600kN
=
40kN
=
80kN
Weight o f s o i l a b o v e p i p e l x l x 7 x l 8O0x9.8/1O3
=
130kN
Total weight
=
850kN
F r i c t iona I resistance 0 . 3 ~ 8 5 0
=
250kN
=
889kN
=
640kN
L a t e r a l r e s i s t a n c e o f soi I a g a i n s t b l o c k :
1 + sin$ ~1
-
-
sin$
1 + 0.5 1 - 0.5
=
32 ~+32/ ~1 5 ~' v3 3~ 3 F = 18 0 0 0 ~ ~ ~ 3O3 L a t e r a l resistance of soil a g a i n s t p r o j e c t i o n of p i p e : (18 000x1 . 5 x 3 / 1 0 3 x 2 x 5 j 3 ) Total
1x6.5
l a t e r a l resistance
= 1770kN
F a c t o r o f s a f e t y 1.77/1.20
=
1.48
A t h r u s t b l o c k s h o u l d b e d e s i g n e d so t h a t t h e l i n e o f a c t i o n o f the resultant the
pipe.
may
best
of
the
resisting
This w i l l
forces
prevent
be done g r a p h i c a l l y
of the p i p e .
coincides w i t h
overturning or or by
taking
the
l i n e of
t h r u s t of
u n b a l a n c e d stresses. moments a b o u t
This
the centre
194 Thrust
blocks
horizontal not
be
alignment able
coupl ings.
to
needed
of
the
not
only
pipeline,
changes
in
vertical
or
b u t also a t f i t t i n g s which may flexible
V i k i n g Johnson o r s i m i l a r coupl i n g s a r e frequently
i n s t a l led
removal
transmit
at
as
on one side of and
are
a valve
of
the
longitudinal
forces,
i n a v a l v e chamber,
valve.
The opposite
such
to f a c i l i t a t e i n s t a l l a t i o n
wall
of
the
valve
chamber
would thus h a v e to be designed as a t h r u s t block.
-li;
10.9
Fig
s t a n d a r d med i urn-rad i us 900 f a b r i ca t ed
Segment geometry bend.
FORCES INDUCED BY SUPPORTS
The There
i n t e r a c t i o n of are
involved. above a
many The
ground,
tendency
of
effects on the
circumferent i a l l y tial
a p i p e and
secondary
temperatures,
are
plinths pipe
under
and
i t s supports tertiary
general ly or
to
the
secondary
by
effects
greatest
other
expand of
strains
i s a complex subject.
forces
or
isolated contract
and in
displacements
pipes
supports.
There
longitudinally
temperature change, due
supported is
and
differen-
to the Poisson r a t i o effect,
195 and
partial
pipe
or
f i x i t y of
total
vertically,
supports which
longitudinally
and
impose
forces on the
laterally.
iio
completely r i g i d a n d the more f l e x i b l e the support
the
support
is
less force or
reaction i t imposes on the pipe. The stresses on the p i p e may be loosely c l a s s i f i e d as follows: Primary;
circumferential
longitudinal Secondary;
due
to
due to
internal
internal
pressure
bending a t elbows,
across
supports.
Temperature
strains
at
angle
right
to
pressure across diameter; across
branches, effects.
primary
the
cross
section.
changes i n section a n d Poisson
strain.
ratio
Due
to
counter-
reaction
of
supports. Tertiary;
l a t e r a l deflection due to l o n g i t u d i n a l expansion.
Al though
the
secondary
accounted f o r i n p i p e design,
and
tertiary
stresses
are
often
not
they can be very s i g n i f i c a n t .
Longitudinal Stress If
the end of
a p i p e i s b l a n k e d o f f a n d u n h e l d the l o n g i t u d i n a l
stress i n the p i p e w a l l
i .e.
4
The
Poisson
and
the circumferential
if
Wpd/2t
is
the and
modulus,
stress.
ratio
effects
ends
are
tries
held
corresponding
t
the
wall
r a t i o (about 0.3
reduce
to
the
wall
force
is
thickness,
e
the
tensile
length
Vp-irdz/2 where the
strain
by
stress E
and
vLpd/2tE
becomes is
w
the is
Ee
=
elastic
Poisson's
for s t e e l ) .
Temperature stresses A pipe w i l l
expand or
contract
by aAT where a i s the coefficient
of expansion a n d LT the temperature change i n time.
A where
pipe the
restrained coefficient
"C a n d for p l a s t i c , If
there
Circumferential
is
a
longitudinally of
expansion
will for
undergo
steel,
a
a
, is
stress 12 x
aEAT
-6
10
per
50 x temperature
gradient
across
the
stress i s created equal to +_ aEAT/2(1-v).
pipe
wall
a
196 Forces at Bends The force due to water is
PA.
The
where
is
8
with
net
a
pressure along each a x i s at
resultant
force
the bend angle.
thrust
block
it
acting
outwards
i s 2pA
I f the r e s u l t a n t force
creates
a
longitudinal
a p i p e bend sin
(8/2)
i s not countered
force
in
the
pipes
equal to 2pA s i n 2 ( 8 / 2 ) .
Lateral Movement A
straight
outwards
a
a t u r e etc.,
pipe
of
relatively
length big
x
fixed
amount
at
under
both
ends
expansion
will
due
to
buckle temper-
b y an amount (10.8)
dy since dy2
+ (x/2)*
(x/2 + d ~ / 2 ) ~
=
dy = x =
loom,
dy =
400 x
e.9.
I f the
pipe
-6 d x = xaAT = 100 x 12 x 10 0.02/2
supports
or
to
required
to
that
t i o n of
= lm.
restrained
is
between
x 20 = 0.02m
twist
laterally
supports
prevent
a simple supported
the
or
it
could
exert
buckling.
a
try
lateral
For example,
( l a t e r a l l y ) p i p e beam,
dy,
to
buckle
force
equal
the deflec-
under a force
F is
-
dy =
1
=
:.
F
FL3/EI
48
=
f o r above example. 1 x 210 x
= 40
lo9
1 13x.01/(1003x-~
2
48
8
kN
The l a t e r a l deflection
is
referred
pipes to fa1 I o f f the side of supports,
A
pipe
fixed
at
both
ends
with
to
as
snaking
and
can
cause
or bend the supports. an
elbow
will
bend outwards
under expansion by an amount: dy = d x / ( y / a where
dx
is
+ y/b)
the
net
expansion
in
length
( a + b ) = c due to temperature, pressure etc.
of
pipe
with
length
197 Forces on Supports The equal
forces and
on
the
opposite
support
to
the
blocks or
forces
p i l l a r s or
exerted
by
hangers w i l l
the
supports
on
be the
pipe. Free
to
Slide:
The
h e l d p i p e equals IJ
is
the
the
Fixed force pipe
on
force
of
the f r i c t i o n force on
f r i c t i o n coefficient
pipe
snaking
longitudinal
the
block.
W
and
There
is
a freely
the block.
sliding or i s pW,
This
i s the normal force also
a
lateral
the
smaller
highly where
( w e i g h t ) of
force
to
resist
.
to
Block:
which and
The
resulting
force
is
can
be
imposed on block
block,
or
(ii)
ance of
support a t
tudinal
force
in
sliding
the other end, pipe
due
to
or
f r i c ion between
b y p i p e e.g.
resistance of
i ) maximum
of
block,
( i v ) maximum net
temperature
( i i i ) resist-
or
change,
total
longi-
Poisson
ratio
effect a n d bends. There i s thus a d i s t i n c t i o n between the f r e e to s l i d e case a n d the fixed
case
a n d case
in
that
( i ) or
(ii) will
apply
to a
"free
to s l i d e "
pipe
( i i i ) a n d ( i v ) w i l l g e n e r a l l y a p p l y to a p i p e r i g i d l y f i x e d
to the support. Thus
be
the force
i s computed as above,
as
above etc.
no
force
at
that end,
F o r the f i r s t
a n d then case ( i i i ) or For case
10.9) then there w i l l
a p i p e i s free (see F i g .
i f one end of
obviously
few
a n d beyond the f i r s t
a n d beyond the second support also lengths case
( i v ) w i l l take over
( i v ) the "force a t
support
( i ) or
as one
the other end"
may
( i i ) may
of
these
i n fact
is
apply less.
be that due
to other support blocks.
Unba Ianced Forces Generally balance out.
it
can
That
be
a n d opposite to those at however bends
there
may
expected
i s forces
be
i n one
that
the other end.
bending
there a r e net forces of
to t r y to s t r a i g h t e n the bend.
forces
direction
moments.
in
welded
pipework
a t one end a r e equal
Along the length of the p i p e
For
instance a t
l i q u i d on the p i p e w a l l
elbows
or
inside a c t i n g
198 During
transient
unbalanced instance
forces
pressure
direction. length
unbalanced
could
closure at
Although
and
conditions
which
following
hammer
flow
one the
eventually forces
which
of
end
there
pull
a of
pressure
line
wave
re-balance can
however
pipe
off
pocket
in
the
vapour a
may
may
force
may
travel there
cause s i g n i f i c a n t
large
supports. a
pipe
the
forces,
be
pipe
along are
For water
in
the
one pipe
momentary
movement s t a r t i n g at
bends.
4
Support resistance length x + dx
l a t e r a l movement dy Fig.
10.10
L a t e r a l movement due to temperature expansion
total force F1 + F2 + F3
Temperature Movement
5" E L T
loose c o u p l i n g
I
f r i c t i o n on supports
Fig.
10.11
L o n g i t u d i n a l forces i n p i p e w a l l created b y f r i c t i o n on supports
FLOW MEASUREMENT
Venturi Meters The with
Venturi
minimum
pipelines.
(Fig.
10.12)
meter
offers
an
accurate
head
loss.
It
is
The v e n t u r i
throat
used
method of mainly
has a converging
flow
for
measurement
large-diameter
section and g r a d u a l l y
d i v e r g i n g section to minimize head losses. Flow
measurement
r e a r r a n g e d as
is
based
on
the
Bernoulli
equation
which
is
199 v22
29
--29V 1 2
-
h , - h 2
h
=
(10.9)
Solving f o r discharge
,/=
Q = CdA2
(10.10)
(10.11 )
where d
i s the diameter and C
for
separation
flow
and
downstream
calibrated pipe
in
at
conditions
place
diameters f o r
i s a velocity
V
the throat in
the
double
bends,
smal I t h r o a t / p i p e
is
required
100 p i p e
lengths
10.12
meter
should
l e n g t h of a t
diameter r a t i o s ,
l a r g e r throats,
downstream
impart
be
least 5
increasing
o r from branches
s w i r l i n g motion may
before a
v e n t u r i meter i s o n l y approximately O.1V
Fig.
venturi
(BS 1042). F u l l bore branches, p a r t l y
closed valves a n d f i t t i n g s which to
A
pipe.
a n d should have a s t r a i g h t very
to 10 o r even 20 p i p e diameters f o r or
coefficient which allows
a n d includes a f a c t o r f o r upstream
meter.
The
head
need up loss
in a
‘/2g. 2
Venturi meter
Nozz 1 es A contracted form of v e n t u r i a short
meter
i s the nozzle meter,
which has
bellmouth rounded i n l e t a n d a b r u p t expansion beyond i t . The
discharge
equation
is similar
to
that
for
the
venturi
meter
but
the
v e l o c i t y head recovery beyond i s very small.
O r if ices An
o r i f i c e consisting
of
a
thin
plate with
a central ori f i c e i s a
200 popular
method
appreciable 0.61.
of
measuring
orifice
contraction
flow
in
large
coefficient
which
The discharge formula i s s i m i l a r to Equ.
The
velocity
straight
pipe.
head it
recovery
i s short
The
is
low
may
There be
as
is
an
low
as
10.10 where
-
a d v a n t a g e that
pipes.
but
the
orifice
has
the
a n d can be i n s t a l l e d i n a short l e n g t h of
lengths of
straight
the o r i f i c e a r e s i m i l a r to those f o r
p i p e r e q u i r e d on each side of
v e n t u r i meters.
The o r i f i c e should
be c a l i b r a t e d i n place f o r accurate results.
Fig.
10.13
O r i f i c e meter
Bend Meters
A g r e a t e r pressure i s exerted on the outside of a bend i n a p i p e than can
on be
the used
inside,
due to c e n t r i f u g a l
to measure the flow.
force.
The meter should be c a l i b r a t e d
place, b u t the discharge coefficient f o r E q u .
Cd
=
The pressure difference in
10.10 i s approximately (10.13)
r/2d
where r i s the r a d i u s of c u r v a t u r e of the centreline. Mechanical Meters Flow
to
meters which
water
consumers
is
invariably
i n t e g r a t e the flow over
has a r o t a t i n g t i l t e d disc w i t h types have r o t a t i n g wheels,
a
measured
a p e r i o d of time.
by
mechanical
A common type
s p i n d l e which rotates a d i a l .
lobes o r propellers.
Other
201 There
also
is
deflected vane
a
type
immersed
of
meter
which
i n the flow.
reacts
to
the
drag
on
a
The meter records f o r p a r t l y f u l l
conduits as well. The
rotometer consists of
has a taper
in
the
that
increasing
upward
flow
the d r a g on
a
diameter
in
through
it
calibrated
the
vertical
A
upwards.
tube.
The
tube
which
is suspended
float
float
( w h i c h depends on the flow
glass
positions
itself
so
p a s t i t a n d the tube
diameter) e q u a l s the submerged weight. The object may be e l t h e r a sphere o r to make i t r o t a t e a n d centre i t s e l f
Electromagnetic
By
motive
and
force
advantage including nique
there
an
and no
is
can
be
does
around
can
not
l o s s of
obstruct
shock
pipe
measured.
of
head
The
and
a
non-conducting
this
means.
the
flow
and
and
i s also
A
has
the
liquids
of
similar
tech-
i s based on sonic
being
downstream
an electro-
method
variety
by
wave,
upstream
a
i n s e r t i n g electrodes,
be
measured
impressed
between
field
I i q u i d by
the
induced
also
of
difference
magnetic
ionizing
sewage
which
velocity
a
is
that
i n the tube.
Induction
creating
material
a tapered shape w i t h vanes
developed.
sonic
velocity
The is
measured.
Mass and Vol ume Measurement The or
most
accurate
volumetrically.
over
a
volume
certain flow
To
time
may
be
methods
of
measure
the
the
flow
measurement mass
or
i s diverted
measured
from
the
of
flow
weight
of
are
i n t o a weighing volume
filled
by
fluid
in
tank. a
mass
flowing The
certain
t ime.
TELEMETRY
Automatic systems. ling
which
methods. Data
data
Telemetry is
transmission
a n d control
systems a r e tending
more
expensive
and
i s often used on p i p e l i n e
to replace manual less
reliable
d a t a hand-
than
automatic
Cables may be l a i d simultaneously w i t h the p i p e l i n e . which
pressures,
may
flows,
be
required
opening
of
include
valves,
water
levels
temperature,
in
reservoirs,
qua1 i t y
or
pro-
202 perties
of
the
fluid,
mation
is
read
by
pump a
speed
standard
or
power
consumption.
instrument
linked
by
The
a
infor-
mechanical
device to a local d i a l or c h a r t , or to a coder a n d transmitter. S i g n a l s may uous are
analogue usually
expensive uously
than
by
the
systems
relays,
numbers. as
private
sent
a
The
transmitter
are
are
signals
or
multiplex
cables.
common
to
termed
binary
contacts.
in
of
electric
possible
series
and
via
of
level
binary
in
groups
telephone
conductors
number
less
scanning.
code
Every
transmitted
pair
A
also
a d e f i n i t e combination of
be
One
feed.
messages
but
repeat messages contin-
intervals,
transmitted may
Analogue
accuracy)
converted
cores
i n the form of contin-
digits.
may
regular
i s represented by
a
of
2 percent
to
at
data
Signals
plus
series
(up
The
bits.
bit,
in
magnetic
measurand
known
each
from a t r a n s m i t t e r
interrogated
coded
or
or
digital.
be
digital
pulses
waves
out
less accurate
or
With
of
be sent
is
u n i t s of
lines
needed for
data
may
be
in r o t a t i o n v i a the same conductors.
Alternatively over
short
hydraulic
distances
by
or
pneumatic
pipe.
Radio
signals
may
transmission
be
conveyed
becomes
economic
f o r systems w i th long transmi ssion distances. The linked from
transmission to
a
information the
extreme a or
decoder
analogue
play
to
to
a
data
of
diagram
dials
at
the
will
digital
or
digital
readings
values
mimic
system
and
bank
or
stored may
the
measurand.
(a
for be
on
p a p e r or directly
decision-making programmed
pumps which to
information
be fed
which would
close
may
or
would
valves
r e l i e f mechanisms.
or
means or
The
of
be
fed
of
discs
later
stage
manipulat i n g
result
the
system, in
or
the
The
hydraulic
data or to
sound
decoded
feeds
the
alarms
at
displayed
on
system
with
tights
These diagrams
storage
cards. a
data.
for
minimum
power demand. operate
a
to
tapes,
a
a
be
rooms.
also
at
receiver
decoder
frequently
is
picture)
a
a servo motor can dis-
lights
Data
to
S i g n a l s can
the u n i t being observed.
magnetic or
messages
versa.
charts
diagramatic
to optimize
match
by
dials,
p o s i t i o n of
the
comparater. vice
on
a r e mounted i n c e n t r a l control The
send
system
The
computer
information to
be
L a r g e computers
instance b y selecting pumping
cost,
computer could machinery
or
and
or
send water
used can those
turbines signals hammer
203 Mini of
digital
computers
but
They
be
can
automatically which or
computers
telemetered
they
systems.
are
considerably programmed but
are
cannot
not
now
They
the
are
most
popular
sI ight ly
cheaper
cheaper to
be
perform used
programmed.
than
larger
certain
easily
They
can
for
other
of control
than
digital
tasks
be
form
or
analogue computers.
computat ions
computations
increased
for
in c a p a c i t y
l i n k e d to l a r g e r computers as t h e need a r i s e s .
REFERENCES Boucher, P . L . , 1948. Choosing v a l v e s , K i Imarnock. B r i t i s h V a l v e M a n u f a c t u r e r s Assn. 1964. V a l v e s f o r the C o n t r o l of Fluids. BS 1042, Flow measurement, BSI, London. C a p p e r , P.L. a n d Cassie, W.F., 1969. The M e c h a n i c s o f E n g i n e e r i n g Soils, 5 t h E d . , Spon, London. CP 1972. L a t e r a l S u p p o r t i n S u r f a c e E x c a v a t i o n s , S.A. Instn. C i v i l Engs. L e s c o v i c h , J.E., 1972. L o c a t i n g a n d s i z i n g a i r r e l e a s e v a l v e s . J. Am. Water Works Assn., 64 ( 7 ) . M o r r i s o n , E.B., 1969. Nomograph f o r the d e s i g n of t h r u s t b l o c k s , C i v i l Engg., Am. SOC. C i v i l Eng. P a u l , L . , 1954. Selection of v a l v e s f o r w a t e r s e r v i c e s . J. Am. Water Works Assn., 46 ( 1 1 ) 1057. P a r m a k i a n , J., 1950. A i r i n l e t v a l v e s f o r steel p i p e l i n e s . T r a n s . Am. SOC. C i v i l Engs., 115 ( 4 3 8 ) . Sweeten, A.E., 1943. A i r i n l e t v a l v e d e s i g n f o r p i p e l i n e s . E n g g . News Record, 122 ( 3 7 ) .
L I S T OF SYMBOLS A
-
C
-
soi I cohesion
-
con t r a c t i o n c o e f f i c i e n t
-
d i sc h a r g e coef f i c i en t
-
velocity
d
-
i n t e r n a l diameter
e
-
strain
E
-
e l a s t i c modulus
f
-
stress
F
-
force
9
-
gravitational
h o r H
-
d e p t h below s u r f a c e
cC
‘d
cross sectional a r e a
coefficient
cV
acceleration
f l u i d pressure flow r a t e r a d i u s of c u r v a t u r e wal I
thickness
temperature velocity normal force length direct ions
I a t e r a I d i s p I acement temperat u r e c o e f f i c i e n t soil density f r i c t i o n coefficient Poisson's r a t i o s o i l mass d e n s i t y a n g l e of
i n t e r n a l f r i c t i o n of s o i l
205 CHAPTER 1 1
LAYING AND PROTECTION
SELECTING A ROUTE
The
selection of
bearing is
on
the
selected
on-site
a suitable route for
capital
from
inspections
obstacles
and
have
the
profile
conditions
should
hydraulic
gradient
above
the
obviously
pumps
may
result
i n water
of
level grade
the
be
to
is
data
In
selecting
considered. the
i s flattest line
and
Care
a
pipeline
on
route,
the
the
grade as
low
flows).
the
input
If
be
p o i n t s of
(Low-flow
r o u t e should
possible
to
On
as
the
were
a peak heads,
t h i s peak.
separation
the other
be kept
as
discharge
p o s s i b l e water column
hammer overpressures.
and
to ensure
rates,
there
and
terrain,
line.
peak
route plans,
costs
should be taken
well
important
cadastral
available
as
for
between
A
costs.
hydraulic
considered
pipeline as
other
below
be
operating
topographical
would have to be designed to pump over
also
lines
any
services.
grade
Peaks
and
photos,
and
local
prcticability ground
cost
aerial
a p i p e l i n e has an
which
h a n d the general
near
to the h y d r a u l i c
minimize pressures a n d consequently
pipe
costs. Once
a
surveyor. regular tions. in
Pegs
Offset
for
is
2
in
along
changes
laying.
and
depth
in
the
it
is
pegged
centre-line
out
10
at
i n g r a d e a n d at
The
l e v e l s of
pegs
the
drawing
office,
at
peg.
indicated
identify
may
selected,
to
horizontal
by
a
100 m deflec-
5 m from the centre l i n e pegs a r e also put
to
plotted
tests
is
at
then
the r o u t e to
Strength
route
put
pegs,
use d u r i n g
levels
along
are
intervals and
profile bed
preliminary
each
a r e observed a n d the with Holes
ground may
levels,
be augered
m a t e r i a l s which w i l l have to be excavated.
be done on s o i l
samples to decide whether
trench
s h o r i n g w i l l be necessary. Underground at and
this
stage
and or
underground
at
overhead least
cables
services
before
may
excavation
have
a heading c o u l d be hand-excavated
should
to
be
to
be
accurately
avoid
supported
under them).
them. on
located (Drains
bridges,
or
206 L A Y I NG AND TRENCH I NG
type of
The
of
p i p e to be used for
economics,
although
materials
and
delivered
pipes
rigidity,
size of
pipes
are
be
supplied
and
to
in
i n t o the
For
small
may
be
lines
for
at
trench.
varies
small
pipe
Concrete
pipes may
p l a s t i c p i p e s may
handled
carefully
They
w a l l e d welded pipes,
side of
the trench,
The
working
width
the
method
laying
is
pipes. and
widths
of the
to
should
avoid
be
Pipes may
stored be
low-
b e l t s l i n g s from mechanical booms or t r i p o d s .
thick
laying
w h i l e steel
walled
pipe
weight,
jointing.
sandbags.
or
the
lengths
the
method of
be
of
The
pipe,
distortion.
the
diameter
working
or
of
thin
should
padded c r a d l e s
with
and
excavation, ally,
on
diameter
excavation
Pipes
or
life
decision.
m lengths,
and
l a r g e l y be a matter
laying,
type and
to 4
long,
will
job
for the
the
vehicles
m
trench by
done
i n t o the
of
rolls.
coatings
transported
ered
20
even
on
in 2
often s u p p l i e d
over
affect
depend
transport
any
facilities
factors
will
10 or
be
damage
other
the
done On
to
up
wrapping 'snaked'
required for
of
excavation
by
hand,
the
possibly
20 to 30 m a r e common,
j o i n t i n g and
a n d the p i p e then
construction of pipeand
hand for
other
m may
be
be
If
wide
large
even s i t e coating
50
laying.
3 m may
the
enough
mains where
i s done mechanic-
required.
Reserve
widths
f o r one or two a d d i t i o n a l pipe-
a n d allow
l i n e s at a l a t e r stage. Once the
the
trench
trench with
i s excavated,
the
centre
sight
of
line
w i t h the assistance of these (BSCP, Pipes to
m
is
may case
are
avoid
necessary
in
be reduced a
concrete
0.5
normally widening
300
normally damage
mm
and
m
the
with
U.K.
cover to
0.8
which
a
to
minimum
may m
be
more
for are
loads.
prevent
steep
i n rocky o r
pipe
be
set
marked
up across
thereon.
The
1970).
superimposed
deepening
diameter
jointing).
laid
by
the
may
above the bed a n d the pipe l e v e l l e d
frames a r e set a d e f i n i t e height
m
rails
frost
cover
A
0.9
of
minimum
m
penetration.
than
joints. difficult
the
(0.8 to
The pipe
m
is
width
of
diameter, used
straddle
for
while
of
1
The depth
ground to minimize costs
necessary.
1.2
to
cover
i n which trench
is
with
local
pipes
over
laying
and
207 The
sides of
hesive
or
shoring
wet
open
the
soils
and
for
the sides of
angle.
should
deep
trenches,
Spoil At
least
be
one
the trench may
kept
trench
r e q u i r e d i n the bottom of dry
h a v e to be supported
will
for
safety
should be designed to r e s i s t the a c t i v e
Alternatively
slips.
trench
while working,
to
enable
be
open
the
to
away
trench
is
advisable.
i n wet
to
and
ground
lead
away
to a safe
in
water.
a
In
to a v o i d
D r a i n s may be
to keep the trench
of embankment s l i p s a n d
be compacted p r o p e r l y . bedded
The
l a t e r a l s o i l pressure.
away from the excavation
depth a
reasons.
be b a t t e r e d back
to reduce the p o s s i b i l i t y
backfill
jointed
cross-drains
well
i n unco-
stone
very
D r a i n p i p e s should
filter
wet
with
ground
frequent
cutoff
drains
beside the trench may be necessary. Pipes
may
bedding reduce
is
be
damage
shaped
to
sandy
fit
to
or
may
haunches of settlement
the
and
flat
minimize pipes.
profile
crushed
the
on
to
rigid
the
material
gravel
bedded
preferable
of
The the
pipe,
up
b e d of
pipe.
20
to
a r e often
a r e easy
should
bottom, of
the
In
but
trench
rocky
to
used,
compact.
be continuous
in
mm
as
be a
to
the
do not e x h i b i t much
they
beds
and
haunches o r
low-pressure r i g i d p i p e s a n d sewers.
under
joints
but
haunches should stop
11.1
typical
bedding
bedding.
pre-
bed of
up
Fig.
of
to
Beds of sand,
brought
short of j o i n t s to f a c i l i t a t e r e p l a c i n g damaged pipes. types
proper
may
ground
size,
Concrete
a
f l e x i b l e pipes o r
be b u i l t up a n d trimmed to shape. stone
surrounds a r e sometimes used f o r Bedding
trench
deflections
(Refer
to
Chapter
associated w i t h d i f f e r e n t types of b e d d i n g )
7
to
(CPA, 1967; ACPA,
shows factors
1970).
The best method of b a c k f i l l i n g a n d compaction depends on the type of
soil.
(PI), with
Soil properties
liquid low
may
For
stampers o r
vibrators.
the
compact
Proctor
high
should
LL
often soils,
be
dynamic
Density.
the bed w i t h a w i d t h of at
be up
100
compacted
index
( P I = LL-PL).
satisfactorily
compacted
compaction
B a c k f i l l densities may be
Standard
the p i p e to 95 to
density
be described in terms of the p l a s t i c l i m i t
(LL) and plasticity
limit
PI'S fill
inundation.
of
may
% in
For
pipes
required
by i.e.
specified i n terms it
is
practice
to
least h a l f the p i p e diameter under
Proctor density. 100 to
large
is
For soils merely
150 mm
The soil f i l l around the p i p e l a y e r s to 90 or
95% Proctor
to haunch level or to 3 / 4 of the depth of the pipe.
I t may
208 be necessary to s t r u t f l e x i b l e p i p e i n s i d e to prevent d i s t o r t i o n d u r i n g t h i s operation.
fill
The
around
the
top
half
of
the pipe,
to 300
up
mm above the crown should be compacted to 85 to 90% Proctor density. For b a c k f i I1 under roads, ed
90-95%
to
Proctor
85%
quired.
is
the top
density,
normally
l a y e r s may have to be compact-
while
for
sufficient
in
as low as 80% a r e obtained i f control
open
h a v e stones
width of
to
in
it.
compensate
topsoi I
and
Surplus for
spoil
and
fill
around
re-
densities
the p i p e should
may be spread over
settlement
vegetation,
country
be
i s b a d ( R e i t r , 1950).
To a v o i d damage to p i p e o r coatings, not
110% may
runways
carted
or
p r o v i s i o n of
land
away.
the
trench
Reinstatement
drainage,
and
fencing
1956).
o f f of w o r k i n g areas should be considered (see also Sowers,
THRUST BORES
To
avoid
traffic soil
on
for
be
a
thrust
r o a d over
short
block
jack or
Small
timber
pipes
shoe
the
d i r e c t i o n of
the
pipe.
the
may
pipe
is
inserted The
in
stick.
by
the
then
With
auger
the
force
to 1 200 tons,
pipes
if
an
in
auger
end of
the
i t s back
may
the
pipes
and
length to
have
of
a
the
the
soil
bore a
the
sharp
deviate
lubricated stop
for
or
the
pipe The
r e t r a c t e d a n d another
pipe
and
a
ahead of
with
long
pipe.
pipe
i s used,
a
load a n d main-
is
never
removed
the j a c k
push
pipe
should
the
against
up on r a i l s i n front
diameter)
of
Pushing
to
disrupting
the s l i g h t e s t obstacle w i l l
outside
hand
each
to ease the j a c k i n g
larger
or
required
but
at
avoid
be j a c k e d through
hole w i t h
rnrn
as
pushed i n f u r t h e r ,
behind
one
600
than
reduce f r i c t i o n .
jacking
i s dug
up
to
or
the p i p e may
hole
the p i p e ,
Occasionally to
out
pipe,
f i t t e d to the f r o n t
bentonite pipe
excavations,
a n d the p i p e set
(less
tain
dug
a
i s set
head or
is
deep
A
lengths.
A
jacked.
jack.
excessively
through
the
with
the
process a
shoe
100 ton j a c k
repeated.
may
be up
may suffice.
PIPE BRIDGES
Pipes f r e q u e n t l y rigid
jointed
pipes
h a v e to span r i v e r s o r may
have
sufficient
gorges.
strength
For short spans, to
support
them-
209
Class A bedding Reinforced A,: RamforcedA,
Dt 200 v m mln
M= 4
8
0 4%M. 3
4
I 0% :
M.28
PI","
0 IZ5H 150 mm l l i "
0 25 d I O O m m mm Plain or Reinforced
bncr.1e 1 5 0 m k mi Compocted Gronulor t4 Y
CONCRETE ARCH
Class B bedding M=
19
Dens@ Compacted Bochf~l1
Class C bedding M : I ~
01251'
Lightly tO"'p0ct. Bocuftll
GRANULAR IFOUNDATION CiKANULAK WUNUAII~
Class D bedding
NOTE For rock or other incompresrible malert316,the trench should be ovaexcovoled 0 minimum of 150mm and
refi1l.d
wrlb gronulor mat.rm
M-bedding
Fig.
11.1
support from
Types of beddings
plus
selves
an
factor
the
the pipe
existing
fluid.
For
larger
spans,
it
may
on trusses or concrete bridges, traffic
bridge.
If
a
truss
be or
bridge
necessary
to
h a n g the
pipe
is
con-
to
be
210 structed for
the
the bottom, of
or
bridge
is
Two
cables
the
hangers
pipe.
as
one
with
attached
an
ing,
wind
the
at
but
on
stays
an
preferably
could
The
be
along
the
tension member at
A n a t t r a c t i v e form
from may
suspension
could
also
support to
act
erected.
would
together
In
the
all
pipe
the
wind forces
be
designed
to
be
necessary
-
w i t h cross brac-
cases
should
p i p e to prevent
and
p l a n e through
the p i p e against
pipe
cables.
be spaced a p a r t
the v e r t i c a l
lateral
bridge,
the
T h i s means there w i l l
steel.
joint
they
to
designed
independent
welded
expansion
as
to support
again be
as
the top.
supported
angle
helps
p i p e s could
cable
or
pipe
an
act
member a t
vibrations.
arch,
two
ported
p i p e could
a r e p r e f e r a b l e to one,
reduces
either
of
the
T h i s arrangement
and act
pipe,
the compression
except
be
if
sup-
r i g i d jointed;
h a v e to be some form thermal
stresses
devel-
oping.
UNDERWATER P I PEL I NES
The
often
is
it
laying or
is
and
through depend
In
common.
is
very
addition Gas
and
which
on
pipes.
conditions
The
such
under-water
Floating
to
river lines
as
currents,
crossings, from
undersea
undersea
a r e also many
or
sludge
into
underwater
wave
In
calm
water
out
and
sunk.
thus.
Care
is
needed
on
nevertheless
height,
beds
industthe
sea
laying
will
type
of
bed
pipe:
floated
laid
winches
There
effluent
method used for
a n d Sinking:
shore,
been
discharge
expensive,
oil
t a n k e r b e r t h s a r e frequent.
towns
undersea
on
underwater
inescapable.
a n d length of (1)
pipes
becoming
off-shore
ries
of
laying
barges
should
be
the p i p e may
Lengths in
up
sinking
positioned
be j o i n t e d
500
to
the
along
have
rn
pipe
the
and
line
to
assist.
(2)
Bottom be
Towing:
assembled
towed
along
Lengths
on
land
the
bed
are
jointed
bouyed to
each
Strings
sea.
is
pipe,
i n strings,
to
sea
at
the
up
the
The to
pipe
of
anchored pipe
of
up
by
air
reduce f r i c t i o n
in on
by
the the
a
few
up a
kilometres
may
long,
and
km
1
to
winch
together pipe sea
or
a
barge
on
the
shore.
by
buoys
of
bed.
If
the
tied pipe
211 i s f i l l e d with
air
crete
to
coating
would
be
line.
get
susceptible
The stresses
caused The
i t may
by
the to
correct side
buoyancy.
currents
i n the p i p e due
underwater
lateral
h a v e to be weighted down
drag
per
currents unit
to
the
or
length
and
light
may
to
a cona
bend
tension
waves
due
Too
by
pipe
out
of
and bending
may
waves
be
critical.
and
currents
is ( u + v ) ~D/2g
Cow
where C weight
pipe),
(about 0 . 9 ) ,
i s the d r a g coefficient
D of
current
(11.1)
the
water,
velocity
D
is
u
(or
the
is
the
their
wave
components
outside diameter of
i s the s p e c i f i c
w
velocity
and
v
perpendicular
the p i p e a n d g
is
the
to
the
is gravi-
t a t i o n a l acceleration.
(3)
Lay
Barge:
jointed an
on
arm
Pipes a
may
special
(or
be
taken
lay-barge
stringer)
into
to
sea
in
a
pipe
barge,
a n d lowered continuously
place.
The
barges
down
proceed f o r w a r d
as l a y i n g proceeds.
(4)
Underwater pipe
has
Jointing:
to
be
Underwater
accurately
jointing
aligned.
which l i m i t s the method to shallow
It
i s usually
currents. the
to b u r y
is
trench
before
fluidizer
the
pipe
is
depths (Reynolds,
passes of
the f l u i d i z e r
long length.
a
The
trench
High-pressure
a r e r e q u i r e d so that
Too
deep
.
1970)
to
or be washed into
normally
jets
of
has
water
to
be
a
fluidize
A number of
the bed under the pipes a n d the p i p e s i n k s into the bed.
over
each
l a y i n g the p i p e i n soft beds i s w i t h a
1971).
(Schwartz,
as
be r e q u i r e d ,
the p i p e to a v o i d damage due
laid.
A novel way of
difficult
diver w i l l
Dredging i s d i f f i c u l t as sediment may f a l l
over-excavated. bed
necessary
A
the p i p e s i n k s g r a d u a l l y
trench may cause bending stresses i n
the p i p e at the head of the trench. Most joints
underwater
should
be
pipes
well
d e s i r a b l e under the sea.
are
cwted
steel and
with
lined
welded and
joints.
cathodic
Pipes
protection
and is
212 JOINTS AND FLANGES
The of
type
pipe,
joint,
of
the
joint
to
use on
facilities
strength
and
flexibility
of j o i n t s a r e used ( E E U A ,
(I)
Butt-welded:
1968)
The
approximately
joint
is
clamped
right
around
walls
may
of
good
depand
cost,
on
the
type
watertightness
The
steel
back,
following
in
more
runs.
a
weld
the
pipe
leaving
tacked
or
require
make
the
30'
one
will
site,
requirements.
and/or
with
also
to
pipeline on
of
types
:-
ends
bevelled
difficult
a
available
places
and
root.
then
pipes
inside,
lining
trued
mm
and
Large
pass
internal
are
2
a
The
welded
with
thick
although
it
in
pipes
less
may
be
flared
is
than
600 mm bore. (2)
Sleeve to
welded:
form
a
barrel
of
welded
inside
and
One
socket the
the
end
and
other too.
of
a
the pipe.
If
lining,
if
pipe edge
possible
11.2).
(see F i g .
internal
steel
leading
fillet the
welded
joint
The e x t e r n a l
possible,
should
Two
methods
welding
and
essential
to
A
thorough
metallic
testing
and
to
including
the
air
should
weld
are
pockets
ultra-sonic
tion
and
and
useful
pipes,
the
or
a
film
a
single
is
but
For
from
may
is
X-ray,
are
Gamma-ray
around smaller
may the
where
of
double,
to
the
pipe
but
Strips
a n d bent over and
Normally
etched field
for
tests
hi gh defini-
With in
to
magnetic
i s more
corners.
is
welding.
necessary.
p i p e to receive
pipes,
the
Gamma-ray,
inserted
gas
cavities.
possible
preferred
be
good
welding
lengths be
equipment
inaccessible
made
avoid
ground
inclusions.
X-rays
and
the p i p e w a l l
weld
be
Oxy-acetylene
accompany
short
e i t h e r by
equipment
wrapped wall.
on tests
The
otherwise
X-ray
should
should
off.
Top-class
strength
confined
slag
methods.
contrast for
be
cut
w i I I be non-destructive: or
welding.
welds
radius.
available:
weld
destructive
predetermined
reveal
arc
high
sample
field
are
programme
testing
occasional
a
welding
achieve
Destructive factory
of
the
p i p e coating
be
at the weld a f t e r a l l s l a g has been wire-brushed
out
to
large-bore
the the
portable
p i p e and
image from
overlapping
expo-
213
o m i t t e d for small
bore pipes
Fig.
11.2
Sleeve-welded
Fig.
11.3
Push-in
sures
are
made
joint
type j o i n t
from
outside,
thereby
exaggerating
defects
i n the near w a i l . Welding that
for
of
high
low-tensile
and post-heating
(3)
Screwed:
tensile steels.
steels
require
Pre-heating
better of
the
craftmanship pipe
ends,
f o r stress r e l i e f a r e n o r m a l l y desirable.
Threaded
and
used on small steel pipes.
screwed
ends
and
sockets
are
only
(4)
Spigot
and
quently
socket:
Concrete,
have one
male end socket
has
is
end
a
rubber
forced
cast
socketed sealing
over
the
is
to
caulk
to
and
p l a s t i c pipes fre-
the other
gasket
ring.
shaped r u b b e r r i n g s a r e used.
resin.
iron
and
end
plain.
f i t t e d over
(see
i t a n d the
11.3).
Fig.
The
Various
Another way of sealing the j o i n t
i t w i t h bitumen compound,
cement
mortar,
lead or
Joints f i t t e d w i t h r u b b e r r i n g s a r e often c a u l k e d as well
hold
getting rings
the
ring
into
the
can
in
place,
joint.
improve s e a l i n g
Spigot
normally
and
socket
accommodate
one
and
prevent
joints
or
with
two
dirt
rubber
degrees
of
available
for
def I ect ion.
(5)
Clamp-on
joints:
jointing a
plain
rubber
to
as
a
illustrates
fixed
to
tension. in
the
If
the
the
tension
the
of
The
and
as
brackets
type
and
diameter
parallel
ing
stresses all
resist
four of
the
to
the
are
for
this
the
for
transferring coupling
the
(also
referred
These
designed
joints
to
take
longitudinal
or
tension,
tiebolts
brackets
even
bolts
barrel
shaped
pipe
axis.
to
may take
In
in
fact
like
tie-bolt
used f o r
the
plan
to
take
bolts
are
it
be the
to
of
the
shear
are the as The legs
legs of
a n d bend-
i s impossible to e l i m barrel
flanges,
iron
the
with
length
pipe
load
cast
bolts
minimize e c c e n t r i c i t y .
The
the
tie
selected
that
longitudinal
on
rings,
two
is
so
to
"U"
stresses
reason
sleeve.
bending a n d tension stresses
designed
acceptable.
bending
be
clamping
cover
joint
pipes
by
or
should be such that
and
Victaulic
to
normal l y
a
a n d may cause damage unless care-
brackets
possible
bracket
pipe
of
may
pipe
involve
and
coupling).
between
to
are
normally
Dresser
each
Normally
the
are
the
inate
is
of
joints
barrel
The b r a c k e t s cause local
sufficient.
welded
such or
easily,
joint
designed.
close
pipe
deflection
barrel
walls
fully
one
movement of
They
each
Johnson
degrees
movement.
proprietry
pipes.
between
Viking
accommodate several
ended
seal
11.4
Fig.
Various
may
the
pipes,
with be
pipe
brackets
preferable wai I.
The
uses l i p s on the
ends of the pipes to t r a n s f e r tension to the coupling.
215
Fig.
(6)
11.4
Slip-on
Flanged: ends,
Steel
drilled
to
cast
if
Faces
rubber
rnrn
and
especially
frequently.
type coupling.
or
iron
p i p e s or are
pipes
machined
other
insertion
standard
are
often
fittings are
patterns
and
bolted
gasket
flanged
likely
together
between.
according
to
at
the
to be removed
the
with
3
Flanges
are
diameter
and
working pressure. Ful I used
face
for
flanges. than
to
over
pipe
the
pipe
but
end
around
the
front
around
the
pipe
inside
edges
of
method
The
to
of
tend
method
use
to
leave
of
flanges
dish
metal less
attaching
the
pipe
and
at
the
Alternatively
flange high
10
may
be
pressure
back
both
is
flanges
extending
then of
bevelled work
carried
the one
for to
bolts
the f l a n g e
mm
or
a
rings.
the
the
is
thick
have
joint
when
weld
are
slightly
with
approximately fillet
barrel.
bore, soft
simplest method i s to s l i p
A
for
or
iron
Some
for
pipe.
the
a n d the
diameter
pipes.
circle
the
of
preferred
cast
outside
rings
The
bolts
the b o l t holes a r e used f o r
bolt
though.
the
an of
joint
varies.
beyond
A
the
with
tightened the
with
for
and
low-pressure
inside
used
holes
joints
diameter
and
face
Flanges are
rings
inside
flanges
raised
with
high-pressure Joint
the
steel
gaskets,
flange of
the
welding.
have
a
lip
216 on
the
flange
projecting
Jointing
and
standard
thrust
codes of
the
end
of
the
pipe
that
so
w i l l be f l u s h a f t e r welding.
the bore at the j o i n t
the
over
flanges
are
fairly
practice,
and
must
thick,
as
indicated
be securely
welded
by
to the
p i p e or cast i n t e g r a l l y . Two other types of f l a n g e s a r e common:Puddle
(1)
flanges
of
water
is
to
as
are
retaining
prevent
thick
tudinal
used
of
flanges
pipe
pipes
structures.
leakage
as
on
water
which
stress,
are
The
object
and
they
are
although
which
of
flange
in
these
are
designed
the
cast
not
to
walls
flanges
necessarily
transfer
should
be
longi-
securely
attached to the p i p e w a l l .
(2)
Blank
flanges
ends.
Their
moments
at
clamped occurs where and
t
at
the
is
the
name
should
edges
implies,
be
the
the the
the
perimeter
the
is
clamped
as
fluid
bolts,
flange
thickness.
maximum
stress
to
resist
For a c i r c u l a r
maximum
radial
and
pressure,
i n s t a l l e d at
calculated
the edges and centre.
at
p
are,
thickness
d
is
blank
bending
disc
rigidity
bending
equal
to
3
stress
pdZ/16t2
i s the p i t c h c i r c l e diameter
If
the
would
edges were not
occur
at
the
rigidly
centre
and
would be 50% i n excess of t h i s amount.
COAT I NGS
Buried
steel
the p i p e during
pipes
i s coated.
transport
are
laying
attack,
should
h a r d enough
to
stones
to
the
in
pipe
the wall
to
Coatings should
and
biological be
subject
electric to
prevent yet
pipe, and
to
damage
moisture,
temperature
damage
sufficiently
flexible
and
unless
i d e a l l y be r e s i s t a n t to s c r a t c h i n g
the
currents
trench, and
of
corrosion
enough
to
during
chemical
variations.
and They
h a n d l i n g a n d due
adhesive
to
withstand
adhere
the
well
flexing
of
the p i p e w a l l ( P P l , 1975; Cates, 1953). The
most
followed outer
by
common a
coating
wrapping.
brushing, applied
The
sandblasting by
spray,
coating
for
reinforced pipe or
brush
pipes with
surface
is
acid pickling, or
dipping
is
fibres
a
thin
and
initially
adhesive
then
possibly
cleaned
a n d the prime coat
the
pipe
in
a
bath.
by is
coat an wire then
Bitumen
217 or
coal
coat
t a r enamel
the
woven
pipe
glass
pipe
bare
to
matting.
The coating or
jointing
in
may
to 6 mm t h i c k ,
cement be
primed
and
in
in
in the
followed tar.
by
felt
or
paper
or
The p i p e i s then
in
the f i e l d a f t e r
welding
which case the ends a r e field.
The
total
thickness
left of
tar
an asbestos f i b r e bitumen mastic 3
include
pitch,
epoxy
paints,
PVC or polythene tapes
bedded on an adhesive),
zinc
applied
painted
with
by
resins or
galvanizing.
bitumen
mortar
coatings
offer
the case
of
l a r g e bore t h i n
usually
12
to
Finished means of metal
the p r i m a r y
based
plastics,
Exposed p i p e s may
or
aluminium
enamel
1962).
Cement
are
After
impregnated
least 5 mm.
coal
and
be a p p l i e d
coated
adhesive o r
mortar
(AWWA,
with
i s sometimes
factory,
Other types of coatings
self
This
the
and
coating should be at
(either
wrapped
in detecting damage a n d to s h i e l d the c o a t i n g
assist
joints,
for
spirally
impregnated w i t h bitumen or coal
from the sun. the
be
fibre
asbestos f e l t whitewashed
i s the p r e f e r r e d prime coating.
may
Holiday
brushes
or
($
mm
coatings
a
electrical
20
may
rolling
potential
is
3/4
An
springs
applied
for
is run
across
(AWWA,
flaws,
electrical
pin
conductor
along
the
to
buck1 i n g
Cement mortar coatings
inch) thick
checked
detector.
resistance
walled pipes.
to
be
additional
1954,
1962).
holes etc. in
the p i p e coating.
coating and
by
the form of
a
current
An is
observed when f l a w s in the c o a t i n g a r e de ected.
LININGS
Steel
pipes a r e
friction
losses.
substances
in
particular, corrosion.
l i n e d to r e s i s t
Unlined the
the
steel
fluid.
oxide
Corrosion
In is
of
interna
pipe
the
rapidly
by
be
case of
scraped
adding
oxidized
by
solids-conveying
water-conveying
m a i n t a i n i n g a h i g h pH e.g.
corrosion and minimize the
may
off
pipes
leading
may
be
corrosive systems to
in
further
inhibited
by
lime.
Lime on the other h a n d
bitumen
(3
to 5 mm t h i c k ) o r coal
Bitumen,
which
could cause carbonate s c a l i n g . The tar
most
enamel
petroleum, Before
popular (2
to
3
linings mm
are
thick).
is
a
by-product
of
i s t h e cheaper of the two. applying
the
lining
the
pipe
wall
is
cleaned
by
sand-
218 b l a s t i n g or spray,
other
dipping
in particular resistant
to
moisture
the
to
tar
bitumen,
damage
enamels
i s then a p p l i e d by
lining
a smooth surface.
smooth f i n i s h .
than
subject coal
and
s p i n n i n g to o b t a i n
provides a
consequently Plasticised
methods
or
Coal
tar
although
by
impact
have,
enamel is
it
and
however,
i s also more
more b r i t t l e
flexing
now
brush,
Spun enamel
of
been
the
and pipe.
developed
to
overcome the problems of b r i t t l e n e s s . Epoxy
paints
are
careful
appl ication
to
other.
each
the in
type o f
2
portable
The
but
layers.
water
used
it
Coal
tar
as
they
pipes
Cement mortar
6
also to
used
12 mm
gally
by
large
( 1 / 4 to
successfully cleaned b y
lining,
for
3
to pipes
machine
thickness
for
of
the
lining
adhere
varies
with
the
should
water.
be
Lead
avoided
for
based p r i m e r s
a r e toxic.
pipes. thick.
the f i e l d . or
although
coats
the o r d e r of 0 . 3 mm a p p l i e d
linings
taint
I inings,
successive
applied centrifugally
inch)
in
ensure
epoxy
bore
wire-brushing
a
to
i s n o r m a l l y of
should also be avoided as they
is
successful l y
necessary
recommended
paint,
4
to
also
is
The
spinning
Mortar
lining
the p i p e , is
usually
l i n i n g s have been a p p l i e d
The o l d surface i s f i r s t thoroughly
sand b l a s t i n g , propelled
drawn or
by
applied
and then coated c e n t r i f u -
slowly
along
the
line
(Cole,
1956). On made
pipes good
over at
about
field
600
joints
mm
bore,
manually
most
or
by
factory
linings
mechanical
may
be
applicators.
CATHOD I C PROTECT I ON
Despite of
steel
fittings.
the
pipes
use
Corrosion
protective
of
often
occurs
coatings,
through
i s due p r i m a r i ly
flaws,
corrosion pin-holes
to two causes;
and stray current electrolysis (Uhlig,
of
the at
or
walls
exposed
g a l v a n i c corrosion
1948).
Ga I vanic Corrosion When lyte,
two
current
electric
dissimi l a r may
current
electrolyte.
flow
flows
Particles
materials
are
connected
from one m a t e r i a l from or
the
ions,
T h e cathode i s not attacked.
anode leave
to to
the
through
the other. the
cathode
anode
an
electro-
The r e s u l t i n g through
causing
the
corrosion.
219 Such
action
may
take
place
when
two
dissimilar
contact
in
material
to the p i p e ) . Another more frequent
osion
conductive
occurs
marked
c e n t r a t ions sulphur.
w i t h pipes
soi I w i t h
in
or
type of
has
been to
i n corrosive
water
is a
lime
instance
high
w i th
form
the
successfully
trench
in an e l e c t r o l y t e may also
a
are
in
different
of
gal v ani c corr-
The effect
is particularly
differential
chemical
oxygen con-
,
content
biochemical
action
especial l y in
the s o i l
a c t i o n r e s u l t i n g from b a c t e r i a . A method
galvanic
used
metals
of
fittings
soils.
i s alSo caused by
which add
(for
v a r y i n g characteristics,
in
Corrosion
which
to
soil
to
backfill.
counteract
soil
corrosion
Stress concentration
lead to corrosion.
was
in the steel
The amount of corrosion
due to the l a s t named two influences i s u s u a l l y small. Potential
corrosive areas may
pipe - soil potential If
the s o i l
ivity
resistivity
using
associated
a
bridge
circuit
drop.
Standard
volt
measurements,
or
survey
but
any
major
or
by
highly
conductive
soil
may
The
potential in
difference
measured
by
connecting
electrode
in
contact
frequently tial If the
of the
used
soil,
is
are
should
at
currents are
current
done
by
taken
and
the
for
these
an
exper-
have a
resistivity
500 ohm cm,
of
more than 10 000 ohm cm. a
corrosive
buried
voltmeter
between
A
soil.
pipe
conditions.
the
to 0.7
a
a
available be
and
The
the
copper
the electrode under normal
as
a p i p e i s 0.5 pipe
a
with
Readings a r e n o r m a l l y
1952).
between
evaluating
Soi I r e s i s t -
conducted.
measuring
surveys
a n d a poorly conductive s o i l ,
important
be
probes
ienced corrosion engineer (Schneider,
A
in the pipe.
as a s t a n d a r d p r a c t i c e f o r major should
i n ohm - centimetres.
i s measured
in-situ
be detected by s o i l resistance tests,
measurement of the c u r r e n t
i s a t a l l suspect,
soi I
pipelines, a
tests or
pipe
the
soil
potential and
sulphate
is
a special
half
conditions.
is
cell
is
The poten-
v o l t s below that of the s u r r o u n d i n g s o i l .
higher
voltage
likely
to flow
than
0.85
volts
below
from p i p e to s o i l ,
that
thereby
of
cor-
r o d i n g the pipe. To by
a
(Fig.
prevent
t h i s corrosion,
conductor 11.5).
preferably
to
the
a
pipe
sacrificial
in
the
anode
vicinity
of
may
be connected
possible
corrosion
The s a c r i f i c i a l anode i s b u r i e d i n a conductive s u r r o u n d , below
the
water
table
and
currents
will
tend
to
leave
220 from to
the
the
pipe be
anode
anode.
to
instead If
cause
applied.
fact,
magnesium,
zinc
nesium
the
electro-chemical
may
the
Magnesium
anodes
Common
ions
are
normally
per
the
further
give
of
1
to
designed
potential
need
installed
in
anodes metals.
iron,
has
k i logram
are Mag-
a
high
of
material) hydrogen
thereby
This
is
actively
termed
polar-
200 ampere hours per for
the
( A l a y e r of
anodes,
attack.
200
steel
these
from
polarization.
leaving
against anodes
alloys
hours
be
corrosion the
sacrificial
difference
(ampere
the from
electrical
sometimes
or
anodic
limiting
dissimilar
external may
potential
to
the
metal
Magnesium
no
aluminium,
resistant
thereby
sufficiently
current.
greatest
replace
insulating ization).
the
and
pipe,
is
resistor
equivalent
is fairly
ions
the
action
a
I imi t
to
has
of
anode
galvanic
In
connection
and
the
about
10
a
year
kg. life
b u t zinc anodes often l a s t 20 or 30 years.
Junction
BOI
Wilh
R o a l ~ t o ri f Required
Fig.
11.5
S a c r i f i c i a l anode i n s t a l l a t i o n f o r cathodic protection
T h e spacing requirements volts The
below
the
spacing
of
ductive
soil
soil
provided
imating pipe
by
the
a n d size of
to
bring soil
poorly
the p i p e required of
anodes pipe
potential
sacrificial
and
means
the
a
will
to
a
along
the
anodes w i l l coated
i s well
pipe
is
ground
bed
to
potential
entire
vary to
coated.
current
be determined by the c u r r e n t safe
from 3 m
30
in
least
of
the
d.c.
r e s u l t i n g p i p e to s o i l p o t e n t i a l a l o n g the pipe.
drain source
current and
0.85
pipe).
poorly
in
highly
con-
conductive
The most r e l i a b l e way
actually
and
m
(at
length
of
est-
from
the
measure
the
221 As
a
rule
i
where
is
and
a
pipe
may
the
factor
the
i s i = 10/r
current of
be
thumb,
of
a g a i n s t corrosion
as
low
amps,
in
safety
3
of
0.5
as
current
required
to
protect
a
pipe
per square metre of b a r e d p i p e surface,
i s the s o i l
r
is
resistance
incorporated.
per
cent
for
a
The
good
i n ohm cm
area
of
exposed
coating,
r i s i n g to
20 p e r cent f o r a poor coating. Once the
the
total
anode
(less
than
soils
with
a
required size
500
ohm
lower
of
number
draw-off may
be
cm)
current
calculated.
large
anodes
In
(greater
should
km
than
be
of
pipe
highly
(20 k g )
anodes
conductivities
smaller
per
used
known,
conductive
may
be
about
1
to
is
used
soils
but
in
000 ohm cm)
ensure
an
adequate
c u r r e n t output.
If use a
an
an
electricity
impressed
sacrificial
current
A
anode.
v i d e the necessary With
supply
impressed
type
of
it
i s usually
protection
transformer-rectifier
current
Scrap
iron,
frequently
used.
Steel
soils
available,
(Fig.
may
11.6)
be
cheaper
to
instead
of
i n s t a l led to pro-
dc c u r r e n t .
corrosive.
ductive
is
and
i n s t a l l a t ions,
or
graphite
anodes
for
this
will
reason
the anode need not
rods
buried
quickly
in
corrode
high s i l i c o n
cast
coke in
be selffill,
are
highly
con-
i r o n anodes a r e
preferred. The
type
of
omics.
Impressed
in
long
the
lations
are
impressed applied,
run,
anode the
have
general
to in
potential
be
installations
3
to
immediate volts
be
at
1
qua1 i t y
of
the p i p e coating.
ferable
to
sacrificial
anodes
about 3 000 to 5 000 ohm cm.
are
protect
a
vicinity
long
potential
100
high
point
km
spacing
the
soil
case
of
may
be
pipe
a The
than
a
off
rapidly
high
voltage
pipe-to-soil
should
b e i n g below
coatings.
instal-
the
fa1 I s
length.
Impressed c u r r e n t if
of
econ-
cheapest
fewer
voltage
length
the
the
In
consequently
of
damage
and
potential
though,
to
low
anodes.
longer
pipe-soil
long-term
frequently
relatively a
(the pipe may
costs
a
The
applied
are
sacrificial
voltage
voltages may
for
protects
could.
applied
the
exceed Larger
maintainance than
turn
depend on the
i n s t a l Iations
installations
in
away
soi I ) .
as
current which
sacrificial
may
current
required
from
to use w i l l
protection
not,
that
of
in
the
Impressed
current
depending
on
the
installations are pre-
resistivity
is
higher
than
222 Considerable only
"hot
economic
spots",
occasional
savings
points
or
shutdowns
can
are
subject
be
often to
tolerated
achieved
aggressive this
by
protecting
attack,
should
be
and
if
considered.
Stray Current E l e c t r o l y s i s The
most
currents
severe
leaving
form
a
pipe.
r e t u r n c u r r e n t s through as a steer
p i p e nearby,
the conductor steel
will
ampere
of
instead of
be
corroded
current.
measurements recordings
The
should
be
corrosion
Railways
rails,
but
is
often
and
if
caused
other
there
users
by
of
stray
dc
dc
current
i s another conductor such
a p r o p o r t i o n of the c u r r e n t may flow through the r a i l . at
a
Where the c u r r e n t
rate
current
taken
of
may
pipe/soi 1
from
or
of
9
a
Ibs)
be detected
potent iat
over
(20
kg
day,
leaves the p i p e , per
by
actual
measurements. the
as
year
per
current
Continuous
currents
may
fluc-
t u a t e w i t h time. B o r e d or S u b m r r g e d Hod8 Cothodic Rolotlv8 t o E l w . t r o l y t 8
Structure
Iron or grophite 1
Fig.
11.6
The
Impressed c u r r e n t corrosion protection.
corrosion
by
connecting
to
the
may would
associated
the
destination
leave have
sufficiently
the to low
pipe of
pipe be to
at the
along
with the
point
current, some
impressed prevent
stray
on
currents
where with
length, the
current
pipe
the
a
may
current
conductor.
in to
escaping.
be
which
A
leaves
The
case
maintain
it,
current
a
current
the
voltage
ground
transformer r e c t i f i e r may be r e q u i r e d f o r t h i s protection.
prevented
bed
and
223 When the
a
pipe
mechanical
across
them
i s cathodically joints
if
are
protected,
electrically
necessary.
Branch
from the main p i p e to control
c a r e should be taken
bonded,
pipes
may
by
welding
have
to
a
be
that cable
insulated
the currents.
THERMAL I NSULAT I ON
Fluid
the
in
surroundings.
pipeline
are
sometimes
the
interior
of
layer face
through
fluid
of
the
be
heated
or
cooled
by
the
serious
climates
conduction
often
i n a r c t i c climates a n d h e a t i n g i n t r o p i c a l
or
from
may
Ice formation
the
inside
pipe
a
of
an
pipe
the
and
by
problem.
exposed
pipe
wall
pipe and
wall,
a
is
transferred
number of
wrapping
by
convection
Heat
in
and
ways:
a
to by
boundary
r a d i a t i o n from the e x t e r n a l
and
wind
currents
in
the
air
s u r r o u n d i n g the pipe.
TABLE 1 1 . 1
Thermal c o n d u c t i v i t i e s
Therma I c o n d u c t i v i t y
k cal
Mater ia I
m sec
Water
0.000
C"
sq f t hr F o
4
14
Air
0.000 005
0.15
Steel
0.014
420
B i tum i n ized Wrapping
0.000
Concrete
0.0002
Slag wool
0.000 01
EEUA, The is
B t u in
0.3
01
6
0. 3
1968. heat
loss
proportional
to
by the
conduction temperature
through
an
gradient
homogeneous
across
the
pipe
wall
wall
a n d the
heat t r a n s f e r r e d per u n i t area of p i p e w a l l per u n i t time i s -Q - -
AT
k
T
A0
(11.2)
224 Q
where is
the
temperature k
is
the
is
area
the
of
amount pipe
difference
thermal
of
heat
across
conducted
T
surface,
is
wal I ,
the
conductivity,
the
kilocalories or
in
duration
time, wal I
t
is
the
tabulated
in
Table
et
at
Btu,
A0
is
thickness
11.1
for
A the
and
various
materials. An heat
equation transfer
equation
has
was
developed by
through
the
been modified
wall to
Riddick of
agree
a
pipe
with
(1950) for
conveying
relationships
the total
water.
The
i n d i c a t e d by
EEUA (1964) a n d i s converted to metric u n i t s here: Rate of heat loss of water kcal/kg/sec
(0. I - ' o ) / 250D _- _ _ _ t, + t o + 1 +
1 (11.3)
and since
the
temperature k c a I/kg/sec
in
,
specific
heat
degrees
of
water
Centigrade
is
per
unity, sec
the
equals
r a t e of the
drop
in
loss
in
heat
where
temperature of water C " ambient temperature outside C " diameter m thickness of p i p e m c o n d u c t i v i t y of p i p e w a l l
kcal/m sec C o
thickness of coating m c o n d u c t i v i t y of c o a t i n g kcal/m sec C o heat loss through boundary 0.34(1
+
0.020i)v0'8/D0'2
water velocity
layer =
kcal/m2 sec C"
m/s
heat loss by r a d i a t i o n = 0.054 E('O
+
100
273 1 3
kcal/m2 sec C o e m i s s i v i t y factor
=
0.9 f o r b l a c k a s p h a l t a n d concrete 0.7 for cast i r o n a n d steel 0.4
for aluminium p a i n t
heat loss by convection = 0.000 kcal/m2 sec C"
v
=
w i n d velocity
km/hr
34f1
+ 0.78V
(-
'i
-90 0.25
D
1
225 The h e a t
generation
although i t theoretically
by
fluid
friction
is
usually
negligible
i n c r e a s e s the t e m p e r a t u r e of t h e f l u i d .
Example
An
uncoated
thick
steel
water
at
300
walls,
an
mm
diameter
exposed
initial
to
a
1
pipeline 10
t e m p e r a t u r e of
km/hr 10°C.
000 m
wind,
long
5 mm
with
conveys
100 C / s
of
The a i r t e m p e r a t u r e i s 30°C.
Determine t h e e n d t e m p e r a t u r e of t h e w a t e r .
E
=
0.7
V
=
0.1/0.785
=
0.34
=
0.054
=
0.005 ~-
Kf Kr
tl -
x 0.32
= 1.42
x 1.42°'8/0.30.2 x 0.7
( 30
+
m/s
= 0.67
10-3 = 0.001
27313
- o.35
0.014
kl
(30 - 1 0 ) / ( 2 5 0 x 0 . 3 ) 0.35 + 1/0.67 + (0.001
=
+
= 0.00103°C/sec
0.0029)
T e m p e r a t u r e r i s e o v e r 1 000 m = 1 000 x 0.00103 1.42 The
insulation
erature fluids
of
industrial
i s a subject
on
pipework i t s own.
= 0.7"C
h i g h or
carrying The cost of
low
temp-
t h e heat t r a n s f e r
s h o u l d be b a l a n c e d a g a i n s t t h e cost of t h e l a g g i n g . Heat erature heat heat the used,
transfer of
the
transfer. transfer
to
from
surroundings, The
may
temperature
or
of
buried which
temperature vary the
with
turn
in
gradient
time
and
surroundings
o m i t t i n g the term l / ( K
pipelines
is
and
are is
depends
the
influenced
consequently
difficult
known,
on
to
Equ.
temp-
by rate
evaluate. 11.3
may
the of If be
+ Kc).
REFERENCES
American Concrete P i p e Assn., 1970. Concrete P i p e Design M a n u a l , Arlington. AWWA S t a n d a r d C602, 1954. Cement M o r t a r L i n i n g of Water P i p e l i n e s in P l a c e , N.Y.
226 AWWA S t a n d a r d C203, 1962. C o a l T a r Enamel P r o t e c t i v e C o a t i n g s f o r Steel W a t e r P i p e 30 Ins. and O v e r , N.Y. AWWA S t a n d a r d C205, 1962. Cement M o r t a r P r o t e c t i o n L i n i n g and C o a t i n g f o r Steel W a t e r P i p e 30 I n s . and O v e r , N.Y. BSCP 2010, 1970. P a r t 2, D e s i g n and C o n s t r u c t i o n of Steel P i p e l i n e s in Land, B S I , L o n d o n . Cates, W.H., 1953. C o a t i n g f o r s t e e l w a t e r p i p e , J. Am. W a t e r W o r k s Assn. 4 5 ( 2 ) . 1956. D e s i g n o f s t e e l p i p e w i t h cement c o a t i n g and l i n Cole, E.S., ing, J . Am. W a t e r W o r k s Assn., 4 8 ( 2 ) . C o n c r e t e P i p e Assn., 1967. B e d d i n g and J o i n t i n g of F l e x i b l y J o i n t e d C o n c r e t e P i p e s , Techn. B u l . No. 10, T o n b r i d g e . Engineering E q u i p m e n t U s e r ' s Assn., 1964. Thermal I n s u l a t i o n of P i p e s and Vessels, H a n d b o o k No. 12, C o n s t a b l e , L o n d o n . Engineering E q u i p m e n t U s e r s Assn., 1968. P i p e J o i n t i n g Methods, H a n d b o o k No. 23, C o n s t a b l e , L o n d o n . 1975. P i p e l i n e p r o t e c t i o n r e v i e w , P i p e s and P i p e l i n e s I n t e r n a t i o n a l , 20(4). Reitz, H.M. 1950. S o i l m e c h a n i c s and b a c k f i l l i n g p r a c t i c e , J . Am. W a t e r W o r k s Assn., 4 2 ( 1 2 ) . R e y n o l d s , J.M., 1970. S u b m a r i n e p i p e l i n e s , P i p e s and M a n u a l . 3rd Ed. S c i e n t i f i c S u r v e y s , L o n d o n . and T o m a s s i , A., 1950. F r e e z i n g of Riddick, T.M., L i n d s a y , N.L. w a t e r in e x p o s e d p i p e l i n e s , J. Am. W a t e r W o r k s Assn., 42(11). S c h n e i d e r , W.R., 1952. C o r r o s i o n and c a t h o d i c p r o t e c t i o n o f p i p e l i n e s , J. Am. W a t e r Works Assn., 44(5). Schwartz, H. I., 1971. H y d r a u l i c t r e n c h i n g of s u b m a r i n e p i p e l i n e s , P r o c . Am.Soc. C i v i l E n g r s . 9 7 ( T E 4 ) Sowers, G.F., 1956. T r e n c h e x c a v a t i o n and b a c k f i l l i n g , J. Am. W a t e r W o r k s Assn., 4 8 ( 7 ) . 1948. The C o r r o s i o n H a n d b o o k , W i l e y , N.Y. U h l i g , H.H.,
L I S T OF SYMBOLS
A AS
B
-
area
-
a r e a of steel
-
drag c o e f f i c i e n t
w i d t h of t r e n c h
d
-
inside diameter
D
-
outside diameter
E
-
thermal emissivi ty factor
f
-
stress
9
-
gravitational acceleration
H
-
backfi I I a b o v e t o p o f p i p e
I
-
c u r r e n t in amps
227 K C
Kf Kr
kl k2
heat loss by convection heat loss through water f i l m heat loss b y r a d i a t i o n c o n d u c t i v i t y of p i p e wal I c o n d u c t i v i t y of coating
M
bedding factor
P
pressure
Q
amount of heat
r
resistance i n ohms
T
time
tl t2
thickness of p i p e w a l l t h i ckness of c o a t i n g
u
component of wave v e l o c i t y p e r p e n d i c u l a r to p i p e
V
mean
water
velocity,
or
component
p e r p e n d i c u l a r to p i p e
v
w i n d velocity
W
s p e c i f i c weight of water
Y
depth of bedding m a t e r i a l below p i p e
0.
temperature i n s i d e p i p e
0
temperature outside p i p e
0
of
current
velocity
228
CHAPTER 12
PUMP I NG I NSTALLAT IONS
INFLUENCE OF The
pipeline
engineer
pumping
lines.
pump
opposed
as
inter-related Pumes
must
head,
hence
of
the
pipe
That
with
i s frequently
is,
to
a
fluid
the
gravity
the
overcome
fed
pumping line
is
concerned forced
line.
The
equipment
friction
losses
The
engineer
The
pipe
Therefore
therefore
The system
engineers
selected
should
wall
their
(1969)
and The
have
considered
to
pump,
be i.e.
is
the
as
(1968).
aware
of
one
for
and
suction
the
in
thout
casing
electrical
a r e so s p e c i a l i z e d
that the following
It
various costs.
example, head
or
impeller
power that is
they
versa. static
function based
on
(which
considering
the
Pipeline
types of
pumps,
Stepanoff
(1957),
give
more
complete also
The d e s i g n o f
shape
material,
and
i s covered
the is
In fact
it
(1960),
K o v a t s (1964) and KSB
supply,
from
is
requirements w i l l
pumpstation design.
the manufacturer.
engineers.
the
pipe
hickness of the pipe. v,
and
(19551,
t h o s e b y K a r a s s i k and C a r t e r
electrical
view
be
size
optimum
Similarly
equipment by
design
a
net
turn
in
by
vice to
head a n d f l u i d velocity
characteristics
Addison pump
more the concern of such
the
and
addition
in
thickness
friction
cannot
therefore
information.
IWt
of
pipe
must be designed in a n integrated manner.
I i m i t a t ions,
their
the
design
a f f e c t s w a t e r hammer h e a d ) a l s o a f f e c t t h e w a l l
other.
the design of
with
through
t h e p u m p i n g h e a d a n d p o w e r r e q u l .ement a r e a diameter.
pressures.
interna I
DESIGN
PUMPS I N P I P E L I N E
motor design
in books
a n d control
should be selected o r designed
the
pipeline
engineer’s
point
of
still
used
in
i n f o r m a t i o n i s presented.
TYPES O F PUMPS
P o s i t i v e D i s p l a c e m e n t Types Least some
used
industrial
in
pipeline
practice
a p p l i c a t ions,
are
nowadays, positive
but
displacement
pumps.
229 The
reciprocating
to
move
to
to
enter
and
on
pump fro
a
A p i s t o n or
i s one such type.
i n a cylinder.
reverse
stroke
One-way
and
exit
ram
i s forced
v a l v e s p e r m i t the
into
the
receiving
liquid conduit
on a f o r w a r d stroke of the piston. The also
p i s t o n can
rotary
be
positive
replaced
by
displacement
a
flexible
pumps.
diaphragm.
These
There
include s pi ral
are
types
a n d intermeshing gears. Centrifugal Pumps Rotodynamic pumps move pressure like by
to
it.
through rotating
low
heads.
The
For an
latter
various
in
waterworks
may
high
may
the
form
is is
by
an
impeller
by
assembling
guide
centrifugal
the
most
engineering.
This
parallel is
are
limited
a number of
to
a
of
an
a
tabular
vanes
of
The
in
axial
the
casing
i s preferred.
the
pump
i s capable
head
pump
standard of
hand-
a n d to p e r m i t f l e x i b i l i t y , which
can
be
100 metres of
generated water,
but
i n series a wide r a n g e of heads
lcllcr
,nes
12.1
to
Here
centrifugal
practical ly
i s possible.
Fig.
flow
casing
l a r g e flows a n d
as
l i t t l e over
impellers
pump
and
accepted
For h i g h flows
common.
form
( r a d i a l ) c e n t r i f u g a l flow.
common,
type
and hence
along
i s most common f o r
universal ly
up to 20 cumecs.
in
the
forced
impeller creates an o u t w a r d
forms
pumps
in
is be
pump
heads
i m p a r t i n g a velocity
be
Liquid
There
T h i s type of
in
l i n g flows
action
propeller.
blades.
reduce s w i r l .
r o t a t i o n of
This
a
l i q u i d by
Sectional e l e v a t i o n of v o l u t e t y p e c e n t r i f u g a l pump (Webber, F l u i d Mechanics f o r C i v i l Engineers, 1971)
230 The
inlet
entrainment to
the
c o n d i t i o n must and
delivery
the
permissible
pressure of
instead of connecting of
be controlled
first
pumping
stage.
particularly
if
In
some
cases
i n series on a common shaft a number
independent pump u n i t s a r e i n s t a l l e d i n series.
flexibility
air
maximum suction pressure i s r e i a t e d
the
impellers
to a v o i d c a v i t a t i o n or
one
of
the
units
T h i s permits more be
to
is
driven
by
a
v a r i a b l e speed motor.
The
driving
device i n a c e n t r i f u g a l
pump
i s termed
the
impeller.
I t may be a series of
vanes shaped to f l i n g the water from a c e n t r a l
eye
the
outer
the
discharge
a
or
inlet
volute
type
of
motor
in
pump
units
large
pumping
towards
casing
into
may
be
together
sizes. solids
as
Pumping in
much
rarely
periphery.
90
as
installations can
for
have
it
The
percent
h a v e efficiences
suspension
Here
nozzle.
is
directed
efficiency
although
by
of
this
pump
and
above 80 percent except unusual
efficiencies
duties as
such
low
as
as 30
percent. Usually
the
inlet
to
the
impeller
eye
is
d r i v i n g shaft
to the motor on the other side of
s i t u a t i o n s an
i n l e t may
to
as
a
double e n t r y
be on each side pump.
This
on
one
side,
and
the impeller.
the
i n some
i n which case i t i s r e f e r r e d
involves
a
more expensive
casing
b u t i t r e s u l t s i n a balanced t h r u s t i n the d i r e c t i o n of the shaft.
Fig.
12.2 Section through a s i n g l e e n t r y horizontal pump
spindle centrifugal
231 Pump u n i t s may be mounted w i t h The
horizontal
the
maintenance
suction
well
preferable.
shaft
is
with
point
a
of
view.
required,
The motor
is
split
a
the s h a f t
casing
Where
is
vertical the
space
vertical
spindle
most
is
or
horizontal.
practical
limited,
or
arrangement
a
from deep
may
be
then mounted on a p l a t f o r m above the pump.
A N D DEF I N I T I ONS
TERMS
Head The water.
head It
in
i t s general
sense
comprises elevation
sure head p / w
p l u s velocity
is
above
the
a
energy
per
certain
datum,
excess
of
u n i t weight of z,
p l u s pres-
head v2/2g.
Total Head Total inlet
head
head
and
usually it
is
refers the
to
head
the
generated
by
12.3).
Fig.
12.3
discharge
the
D e f i n i t i o n of net p o s i t i v e suction head.
pumps
head
to
(see F i g .
232 Net Positive Suction Head In
order
to
avoid
in pumping efficiency The
net
cated The It
positive
by
a
cavitation,
suction
pump
requirement i s generally
head
referred
expressed
as
as
to
a
drop-off
the
can
function
the
net
absolute
u s u a l l y be
of
r a t e of
positive
head
head.
above
indi-
pumping.
suction
head.
vapour
pres-
I t is c a l c u l a t e d as follows:
( 2.1
= H r + H a - H s - H = head
P
and
- Pv/W
= Hp
where H
a
as
s u r e r e q u i r e d a t the pump inlet. NPSH
entrainment
(NPSH) r e q u i r e d
manufacturer is
air
a pump needs a c e r t a i n minimum suction
at
inlet,
f
- H
-
e
relative
( 2. 2)
PV/W to
centre
line
of
inlet,
equal to absolute pressure head p l u s velocity
head.
and
= vapour pressure
PV
= u n i t weight of water
W
= suction r e s e r v o i r head above datum
Hr
= atmospheric
Ha
pressure
head
10
(about
of
m
water
at sea l e v e l ) H S
Hf He
=
elevation
=
f r i c t i o n head loss between r e s e r v o i r a n d pump
=
turbulence head loss between r e s e r v o i r a n d pump
NPSH requirement drop-off
in
increases side of
figure
NPSH can tests
(Grist,
firstly at
at
al I
maximum impeller in
NPSH.
lishing at
discharge.
least
It
the head of should
be
1974).
flowrates
flowrates. erosion
the 3
At
an
due
NPSH.
NPSH
the f i r s t
the
NPSH
NPSH
to
stage of
at
above
i s not
this
datum
a sharp
value.
It
just
i s of
the
order
the pump b u t a more manufacturer's
the
tests.
c a v i t a t i o n o r from performance
i s reduced
less
than
the
cavitation
commences,
flowrate but eventually that
head
associated
generated
with
by
the
The head r a p i d l y decreases w i t h decrease in
NPSH r e q u i r e d 3%
there
level
requirement
from
cavitation
3% decrease
The the
suction
as
noise
away from best efficiency
l i m i t of
times
The
obtained
s t a r t s t o decrease.
A
figure
in
by observing
As
pump
i s p r e f e r a b l e to be on the conservative
NPSH.
be assessed
of
subjective increase
or
considering
10 percent of
re1 i a b l e
centreline
is a
efficiency
with
when
of
head
drop
head to
i s recommended for avoid
NPSH,
cavitation
though.
some degree of c a v i t a t i o n i s normally acceptable.
For
estab-
should this
be
reason
233 Specific Speed The
specific
pump's
Ns
speed
capabilities.
of
There
a
pump i s a useful i n d i c a t i o n of the
are
two
slightly
different
definitions
of
s p e c i f i c speed a n d the more general one i s g i v e n f i r s t : Specific
speed
to
relative
a
i s a c h a r a c t e r i s t i c velocity
characteristic
velocity
of
of
the
the r o t a t i n g element
water,
i.e.
it
is
the
v e l o c i t y of the impeller r e l a t i v e t o that of water. The
ND
speed
N
where will
(units velocity
Ns
is
the
be
periphery
impeller
introduced
i s proportional
is
vDb
the
of
b
is
the
the
rotational
later).
impeller speed
is
proportional
D
and
From B e r n o u l l i ' s
is
to
i t s diameter
theorum
the
water
to JgH where H i s the total head. Therefore
t o ND/ JgH.
proportional
where
of
width
But
of
the
p r o p o r t i o n b i s p r o p o r t i o n a l t o D,
Q
discharge
impeller.
is
proportional
For a n y
to
g i v e n geometric
so
Qa,&8D2
(12.3)
E l i m i n a t i n g D one a r r i v e s a t
/
NQf
O-
NS
This
(12.4)
is
a
dimensionless form of
are
consistent.
the
g
term
Unfortunately
and
express
r a d i a n s p e r second.
specific
most
N
in
speed p r o v i d e d the u n i t s
catalogues
revolutions
and per
text
books
minute
(12.5) units Q
imperial
is
u n i t s Q i s i n cumecs
S.1.
The
alternative
metrically similar (or
definition
gal.
per
min)
one
arrives
expression for N
of
Ns
the is
of
a
that
water
of
low
minute and H
per
NS i s the
of
such size that
against
the
1
metre
directly
former
impeller
associated
whereas
gallons
i n feet.
In
at
1
(or
the
speed
in
rpm
of
a
geo-
i t would d e l i v e r one cumec foot)
latter
head.
Then
dimensionally
by
sub-
dependent
.
reviewing size
in
( c u b i c metres p e r second) a n d H in metres.
pump of
stitution
By
not
One encounters the expression
NS = NQi/H3/4 In
omit
(rpm)
NS
with
t a n g e n t i a l component).
to
relative a
implies
(water
definition
thus
low a
pumping
head
high
has
a
NS,
of
and
head high
one head.
fast
and
radial
low
obtains In
fact
rotational
an
idea
a
high
speeds,
speed
relative
to
component
relative
to
234 Fig.
12.4
indicates
the
r e l a t i o n s h i p between
head per
stage
and
s p e c i f i c speed f o r a number of pumps selected from r e a l applications. i n r p m a n d w i n radians/sec
N is
(w
= 271
N/60).
Lo
7
0
Lo
\
W2 v u l t i - s t a g e 74-
t@
50
\-- n \ 7
Ln
0,
L
-
$20 E I
5
1
T e d flow
I
\ '
<
I
20
12.4
Fig.
\
50
Relationship
I
Ns
I
100
between
200 head
and
500
1000'
specific
speed
for
pumps
IMPELLER DYNAMICS
The shape of the
radiai
flow
A
acteristics. pump
the
impeller blades
pattern basic
which
in
understanding
i s therefore useful
i n a c e n t r i f u g a l pump influences
t u r n gives of
the pump c e r t a i n char-
relative
in selecting a type of
velocities
inside
the
pump f o r a p a r t i c u l a r
duty. Referring is
u,
the
to
Fig.
velocity
of
12.5 the
the absolute water velocity
the
circumferential
water
relative
i s v.
Torque T o n the water i s force x r a d i u s But force = change in momentum
to
speed the
of
the
impeller
is
impeller w
and
235 T h e r e f o r e i m p a r t e d T = c h a n g e i n moment of momentum = A(mvr) =
1 r2v2
Fig.
12.5
where
is
an
element
mass
of
discharge
per
unit
time,
where
P = A (mvr) w
(12.9)
.'.
P =
.*.
the
(12.8)
i s t h e r o t a t i o n a l speed
Now r w = u1 a n d r w = 1 2 P = 1 u 2 v 2 c o s a dm 2 A l s o P = pgHQ where Q
.'.
and
i s o v e r a l l the vanes.
Power P = T w
.'.
(12.7)
V e l o c i t y v e c t o r s a t i m p e l l e r of c e n t r i f u g a l pump.
dm
integral
(12.6) cos a dm 1
cos a dm - l r l v l 2
12.10)
u 2 /ulvl
cosa drn
12.1 1 )
i s the d i s c h a r g e r a t e
12.12)
gHJdm s i n c e p Q
1
12.13)
Jdm
=
12.14)
Head H = ( u v c o s a - UIVl cosal)/g 2 2 coscll i s n o r m a l l y r e l a t i v e l y s m a l l .
The term u,vl
cosa2 = u 2
Now v
-
t 2 cot
B2
(12.15)
where t 2 i s t h e r a d i a l component of v
.*. H
(u,
2 (12.16)
- t 2 cot B 2 ) / g
(12.17)
a n d Q = nDbt
...
2 A - BQ cot
H
where
A
density.
and The
0
B2 are
(12.18) constants,
blade angle
H-Q c h a r a c t e r i s t i c c u r v e ,
B2
g
is
gravity
therefore affects
as i l l u s t r a t e d
in Fig.
and
p is
water
t h e shape of 12.6.
mass
the pump
236
1
Q
Fig.
12.6
Effect of b l a d e a n g l e on pump c h a r a c t e r i s t i c s
PUMP CHARACTER I ST I C CURVES
The
head-discharge
usually
produced
pumping
system.
and
selection
of
by This
of
characteristic the
manufacturer
relationship
combinations
of
is
i s one
pumps and
used
useful
pumps
for
in
discussed l a t e r .
-BH
Fig.
12.7
Pump c h a r a c t e r i s t i c curves.
to
of
the
design
pipe
parallel
size as
curves
a
viable
selection will
be
237 Break and
horse
pump
Fig.
also
be
or
duty
H-Q
changed
shaft
power
any
head
is
proportional
to
the
i n d i c a t e d on the same d i a g r a m
c u r v e may a l t e r
on
required by
pump
with
by
pump (see
the d r i v e speed a n d
fitting
different
The BHP a n d E curves would also change then.
diameters. tant
The
(BHP)
E a r e often
efficiency
12.7).
could
power
impeller
The r e s u l -
NZ a n d D2, whereas the discharge
is
p r o p o r t i o n a l to N a n d D. The ally.
required
The
graph.
level and
A
for
and a
line
effect
pipeline
Thus
required
duty
a
Fig.
a
pump
12.8
illustrates
a's,
smooth
of
pipe,
between could
para1 lel i n g
the
assuming
more pessimistic f r i c t i o n somewhere
i s most e a s i l y
determined g r a p h i c -
c h a r a c t e r i s i t c s a r e p l o t t e d on a head - discharge
different new,
of
t w o or
(a)
and
(b)
factor be
head a
(static
friction)
h i g h suction sump a
low
suction
applicable
selected
more pumps
plus
can
for
to the
also
an
sump
level
older
pipe.
duty
line.
The
be observed
from
such a g r a p h .
I
2 in parallel
llow sump and old pipe
0flurves/
/
pipeline
a
\\
high sump level and new pipe
0
Fig.
12.8
P i p e l i n e a n d pump c h a r a c t e r i s t i c s .
water
238 Pumps a
pipeline line pump
more
pump
operate
within
are
the
a
or
lower
added one
discharge
difficult
station
increase c a p a c i t y
curves
parallel,
are
booster
to
to
series
in
however,
at
to
any
control. is
the
head
pressure. other, is
Frequently,
required
enable the f i r s t
design
above
to
12.9)
(Fig.
section of
In
for
i.e.
a
pipe-
such cases
whereas
added,
along
pumps
the in
the
abscissa
break
pressure
i s m u l t i p l i e d by the number of pumps i n operation. Booster
pumps
r e s e r v o i r or case one
a
certain
station.
reservoir
may
sump
The
level.
on
operate
in-line,
the
suction
side
balancing
volume
is
hydraulic In
the
grade
former
or of
required
l i n e must
case
with
the
water
I n the
in
of
also
12.9
Location of booster pump station.
case be
hammer
f a i l u r e i s more d i f f i c u l t to p r e d i c t a n d allow f o r .
Fig.
a
booster.
a
drawn due
to
latter
trip
at
down
to
a
power
239 MOTORS
The
driving
wheel
or
most
speed
of
the
current.
The
number of per or
be
a
an
electric
by
the
pump
speed
is
Slip
the e l e c t r i c a l
can
of
motor.
The r o t a t i o n a l of
N = 60Hz
alternating
divided by
the
frequency
in cycles
motors
per
second
to be made f o r s l i p between the r o t o r
be up t o 2 o r 5 percent
AC
water
where N i s the pump speed in r e v o l u t i o n s
i s a correction
types
turbine,
frequency
i s approximately
poles,
Hz
steam
a r e commonly
( f o r smaller motors).
used
for
driving
pumps:
s q u i r r e l cage induction motors (asynchronous) i n d u c t i o n motors (asynchronous)
synchronous i n d u c t i o n motors. Squirrel
require the
other
motor
cage motors
minimum
starting
two
with
types.
Their
However
starters.
it
i s usual
robust,
is
that
they
can be tolerated, offers
If
the
require
than large
a s q u i r r e l cage
most
direct-on-I ine
either star-delta
economic a n d
more e f f i c i e n t
economical
or
and
is
starting
not
auto-transformer
A l t e r n a t i v e s t a r t e r s compare as follows:-
S t a r t i n g Current ( p r o p o r t i o n of f u l l load)
and
full
induction h a v e the speed
0.5
to 2.5
1.2 t o 2.0
0.3
to 0.8
as r e q u i r e d
as r e q u i r e d
motors
are
started
a d v a n t a g e that
with
S t a r t i n g Torque ( f u l l load = 1 )
to 7.0
4.5
transformer
Slip-ring
to
this
to employ
Star - Delta
starters
design,
a r e general l y
disadvantage
starter
Direct - on
-
in
They
possible.
Type of Starter
Auto
simple
if
d i rect-on-1 ine
combination
permitted,
are
maintenance.
currents.
reliable
up
could
nowadays,
b ) wound r o t o r ( s l i p - r i n g ) c)
pump
controlled
is
p a i r s of
starter.
a
commonly
There
Three
of
pump
minute and Hertz.
and
a)
power
relatively
they
low
by
means
of
resistance
c a n be smoothly
starting
current.
brought
They
are
normal l y used when s q u i r r e l cage motors a r e impermissible. Synchronous the
motors
a d v a n t a g e of
a
are
high
used
load
on
factor.
large They
installations. may
They
be e i t h e r
have
induction
240 motors
or
speed.
Starting
ance o r
salient
pole
can
reactor
motors.
be
by
starters
They
run
at
direct-on-I ine,
depending
constant
synchronous
auto-transformer,
mainly
on
the
resist-
permitted s t a r t i n g
current. Variable
speed
motors
constant
speed
although
commutator
are
used
being can
as
well.
used
also
motors.
with
be
are Belt
motors,
for
on
motor
or
Thyristor savings
used
more expensive a n d drives
cost
in
and
for
two
less e f f i c i e n t units
are
v a r i a b l e speeds
small
motors.
speeds for
than
possible
resistances on s l i p - r i n g
starters
selecting
smaller
motors
are
now
Pole c h a n g i n g
squirrel
cage motors.
PUMPSTAT IONS
of
cost
the
machinery.
the as
of
The
pipeline will
he
the
structures While
engineer h a v e to
the
will
pump
with
control
will
effect
the
operation
hammer
protection
discussion The ant can
effect
its
of
reduce of
the
the
cost
details
cannot
be covered
here
concern
himself
with
The
the
is
and pump of
capacity
requirements
may
of of
may
A
be
more
layout to
sumps water
complete
al
(1974).
has an
import-
Twort
pipework
the
pipework
suction
there
by
inlet
of
the
stat ion.
given
Air
of
and
the
exceed
delivery
capacity
a pipeline.
efficiency. the
and
system, in
layouts
sump
operational
could
awareness
to
incorporated
the
house pumps
suction
valves.
pumpstation of
the
b e a r i n g on the capacity
turbulence The
of
design
need
install
each
to
design
et
Head losses i n t o the pump drawn the
the
in
by
pipeline entire
vortices
or
considerably.
pumping
system
therefore should be the d u t y of the p i p e l i n e engineer.
REFERENCES
H., 1955. C e n t r i f u g a l a n d Other Rotodynamic Pumps, 2nd Addison, Ed., Chapman a n d H a l l , London, pp 530. Grist, E . , 1974. Nett p o s i t i v e suction head requirements f o r avoidance of unacceptable c a v i t a t i o n erosion i n c e n t r i f u g a l pumps, Proc. C a v i t a t i o n conference, Instn. Mech. Engrs. London, p 153-162. I n s t i t u t i o n of Water Engineers, 1969. Manual of B r i t i s h Water Engineering Practice. V o l . I I , Engineering Practice, 4th ed. London, K a r a s s i k , I . J . a n d Carter, R., 1960. C e n t r i f u g a l Pumps, F.W. Dodge, N.Y. pp 488.
241 Kovats, A., 1964. Design a n d Performance of C e n t r i f u g a l a n d A x i a l Flow Pumps a n d Compressors, Pergamon Press, Oxford, p p 468. KSB, Pump Handbook, 1968. K l e i n , Schanzlin 0 Becker, F r a n k e n t h a l , p p 183. Stepanoff, A.J., 1957. C e n t r i f u g a l a n d A x i a l Flow Pumps, Theory, Design a n d Application, 2nd Ed., Wiley, N.Y., p p 462. Twort, A.C., Hoather, R.C. a n d Law, F.M., 1974. Water Supply, Edward Arnold, London, p p 478. 1971. F l u i d Mechanics f o r C i v i l Engineers, Chapman Webber, N.B., a n d H a l l , London, p p 340.
L I S T OF SYMBOLS
A,B
-
constants
BHP
-
break horsepower
b
-
width
D
-
di arneter
E
-
efficiency
9
-
g r a v i t a t ional acceleration
H
-
head ( s u b s c r i p t a - atmospheric, e - turbulence, f
-
friction,
p - inlet and s - elevation).
mass per u n i t time pump r o t a t i o n a l speed net p o s i t i v e suction head specific speed pressure power discharge r a t e radius torque r a d i a l component of velocity p e r i p h e r a l velocity velocity unit
weight
of
water
u n i t mass of water a n g I es
p 9.
(9800 Newtons per c u b i c metre)
242
GENERAL REFERENCES AND STANDARDS
BR I T I SH STANDARDS
Steel Pipes BS
534
Steel Pipes, F i t t i n g s and Specials
778
Steel Pipes a n d Joints
1387
Steel tubes and t u b u l a r s f o r screwing
1965Ptl
But-welding
2633
Class 1 a r c welding of f e r r i t i c steel pipes
pipe fittings.
291 0
Radiographic
ex.
Carbon steel
welded
circ.
butt
joints
in
steel
pipe
3601
Steel pipes a n d tubes - carbon steel
3602
Steel pipes and tubes for pressure purposes
3603
Steel pipes a n d tubes f o r pressure purposes
Carbon steel
- ordinary duties
: h i g h duties
Carbon a n d a l l o y steel pipes
3604
Low and medium a l l o y steel p i p e s
3605
Steel pipes a n d tubes for pressure purposes Austeni t i c stainless steel
Cast
I r o n Pipe
78-1
C
I spigot a n d socket pipes - p i p e s
78-2
C
I spigot a n d socket pipes - f i t t i n g s
143
Malleable C
41 6
C
I spigot a n d socket s o i l ,
437
C
I spigot a n d socket d r a i n p i p e s a n d f i t t i n g s
1 130
C I d r a i n f i t t i n g s - spigot a n d socket
121 1
Cast ( s p u n ) i r o n pressure p i p e s
I screwed pipes
I screwed pipes
1256
Malleable C
2035
C
4622
Grey i r o n p i p e s and f i t t i n g s
Wrought
788
waste a n d vent pipes
I f l a n g e d pipes a n d f i t t i n g s
I r o n Pipe Wrought
i r o n tubes a n d t u b u l a r s
243 1740
Wrought steel p i p e f i t t i n g s
D u c t i l e I r o n Pipe
L772
Ductile iron pipes a n d f i t t i n g s
Asbestos Cement Pipe
BS
L86
A C pressure p i p e s
582
A
201 OP t4
Design a n d construction of A
3656
A C sewer p i p e s a n d f i t t i n g s
C
soil,
waste
and
ventilating
pipes
and
fittings
C pressure pipes in l a n d
Concrete
556
Concrete pipes a n d f i t t i n g s
4101
Concrete unreinforced tubes a n d f i t t i n g s
4625
Prestressed concrete pipes ( i n c .
fittings)
Clay Pipe
65
Clay d r a i n a n d sewer pipes
539
Clay d r a i n a n d sewer pipes - f i t t i n g s
540
Clay d r a i n a n d sewer pipes
1143
Salt
glazed
ware
pipes
with
chemical l y
resistant
properties
1196
Clayware f i e l d d r a i n pipes
P l a s t i c a n d Other Pipe
1972
Polythene p i p e ( t y p e 3 2 ) for c o l d water services
1973
Spec.
3284
Polythene p i p e ( t y p e 50) f o r c o l d water services
polythene
pipe
(type
425)
for
general
3505
UPVC pipes ( t y p e 1420) f o r cold water supply
3506
UPVC p i p e f o r
3796
Polythene p i p e ( t y p e 5 0 )
3867
D i m s . of p i p e s O.D.
4346
Joints a n d f i t t i n g s for UPVC pressure p i p e
4514
UPVC s o i l a n d v e n t i l a t i n g p i p e
4660
UPVC underground a n d d r a i n p i p e
i n d u s t r i a l purposes
purposes
244 4728
Resistance t o c o n s t a n t
i n t e r n a l p r e s s u r e of
thermopl a s t i c p i p e 2760 CP312
Pitch f i b r e pipes and couplings P l a s t i c pipework
l n s u l at i o n 1334
Thermal
insulation
4508
Thermal l y i n s u l a t e d u n d e r g r o u n d p i p i n g systems
CP3009
Thermal l y i n s u l a t e d u n d e r g r o u n d p i p i n g systems
Valves
8s
1010
Taps a n d v a l v e s f o r water
1212Pt2
8 a l l valves - diaphragm type
1218 & 5163(m)
S I ui ce v a I ves
1415
V a l v e s f o r domestic p u r p o s e s
1952 & 51 54( m)
Copper a l l o y g a t e v a l v e s
1953
Copper a l loy check v a l v e s
2060
Copper a l l o y stop v a l v e s
2591
G l o s s a r y of v a l v e s
3464 & 5150(rn)
C
I wedge a n d d o u b l e d i s c v a l v e s
3948 & 5151 ( m )
C I parallel slide valves
3952 & 5155(m)
C
I butterfly valves
3961 & 5152(rn)
C I stop and check v a l v e s
4090 & 51 53( rn)
C
I check v a l v e s
4133 & 5157(rn)
F l a n g e d steel p a r a 1 l e l s l i d e v a l v e s
431 2
Stop a n d check v a l v e s
5156(m)
Screwdown d i a p h r a g m v a l v e s
5158(rn)
Plug valves
51 59(m)
Bal I valves
245 Jointing
10
Flanges a n d b o l t i n g f o r pipes etc.
21
Threads
1737
Jointing m a t e r i a l s a n d compounds
1821
Oxy-acetylene
welding of steel p i p e l i n e s
1965
B u t t we I d i ng
2494
Rubber j o i n t
3063
Dimensions of gaskets
4504
Flanges a n d b o l t i n g f o r pipes etc.
rings
Miscellaneous
1042
Flow measurement
1306
Non-ferrous pipes f o r steam
1553
Graphical symbols
1710
I d e n t i f i c a t i o n of p i p e l i n e s
205 1
Tube a n d p i p e f i t t i n g s
29’17
Graphical symbol s
3889
Non destructive testing of pipes a n d tubes
39 74
Pipe supports
4740
Control v a l v e c a p a c i t y
SOUTH AFRICAN BUREAU OF STANDARDS
Steel Pipe SABS 62
Cast
Steel pipes a n d f i t t i n g s up to 150 mm
71 9
E l e c t r i c a l welded low carbon steel p i p e s
720
Coated a n d l i n e d m i l d steel p i p e s
I r o n Pipe
50 9
Malleable C
746
C
81 5
Shouldered end pipes,
I soil,
I pipe f i t t i n g s
waste,
water a n d vent pipes f i t t i n g s and j o i n t s
Asbestos Cement Pipe
546
C
72 1
A C soil,
I
f i t t i n g s f o r A C pressure p i p e s waste and vent p i p e s a n d f i t t i n g s
246 946
A
C
pressure
pipe
286
A
C
pressure
pipes
819
A C sewer p i p e s
- constant - constant
internal
diameter
type
outside
diameter
type
Concrete Pipe 676
R C pressure p i p e s
677
Concrete non-pressure pipes
975
Prestressed concrete pipes
902
Structural
design
and
i n s t a l l a t ion of
precast
concrete
pipelines
Glazed Earthenware Pipe 559
Glazed earthenware d r a i n a n d sewer pipes a n d f i t t i n g s
P l a s t i c Pipe SABS 791
UPVC sewer a n d d r a i n p i p e f i t t i n g s
92 1
P i t c h impregnated f i b r e pipes
966
UPVC pressure p i p e
967
UPVC s o i l ,
997
UPVC pressure p i p e s f o r i r r i g a t i o n
waste and vent pipes
01 12
I n s t a l l a t i o n of PE a n d UPVC p i p e s
533
Black polyethylene p i p e s
Va I ves 144
C I s i n g l e door r e f l u x v a l v e s
191
Cast steel g a t e v a l v e s
664
C I gate v a l v e s
AMER I CAN WATER WORKS ASSOC I AT I ON
A W W AC20 1
F a b r i c a t i n g e l e c t r i c a l l y welded steel water p i p e
c202
M i l l type steel water p i p e
C203
Coal-tar
enamel
protective
coatings
for
steel
water
for
steel
water
pipe C205
Cement
mortar
p i p e of sizes 30"
protective a n d over
coatings
247 C206
F i e l d w e l d i n g o f steel water p i p e j o i n t s
C207
Steel p i p e f l a n g e s
C208
Dimensions f o r steel w a t e r p i p e f i t t i n g s
C300
R e i n f o r c e d c o n c r e t e w a t e r p i p e - Steel c y l i n d e r
C301
R e i n f o r c e d c o n c r e t e w a t e r p i p e - Steel c y l i n d e r
C302
R e i n f o r c e d c o n c r e t e w a t e r p i p e - Non-cyl i n d e r
type
-
not prestressed
t y p e - prestressed
type - not prestressed C600
-
54 T C602
I n s t a l l a t i o n of C I watermains Cement m o r t a r l i n i n g o f w a t e r p i p e l i n e s i n p l a c e
( 1 6"
and o v e r )
AMER ICAN PETROLEUM
API
INSTITUTE
T u b i n g and D r i l l P i p e
Std.5A
Spec.
f o r Casing,
Std.5AC
Spec.
f o r G r a d e C - 75 and C95 C a s i n g and T u b i n g
Std.5AX
Spec.
f o r H i g h S t r e n g t h C a s i n g and T u b i n g
Std.5L
Spec.
for Line Pipe
Std.5LA
Spec.
f o r S c h e d u l e 5 Alum.
Std.5LP
Spec.
for Thermoplastic L i n e Pipe
Std. 5LR
Spec.
for
Glass
Fibre
Alloy Line Pipe
Reinforced
Thermosetting
Resin
Line Pipe Std.5LS
Spec.
Std.5LX
Spec f o r H i g h Test L i n e P i p e
f o r S p i r a l Weld L i n e P i p e
RP5C I
C a r e and Use o f C a s i n g ,
RP5L I
R a i l r o a d t r a n s p o r t of L i n e Pipe
T u b i n g and D r i l l P i p e
RP5L2
I n t e r n a l C o a t i n g of L i n e P i p e f o r Gas T r a n s m i s s i o n
RP5L3
Conducting Drop Weight Tear Tests o n L i n e P i p e
Bul.5C2
Performance
Properties
of
Casing,
Pipe Bul.5T1
Non-destructive
Testing Terminology
Tubing
and
DrilI
248 AMER I CAN SOC I ETY FOR TEST I NG MATER I ALS
Concrete P i p e s ASTMC14 C76
Concrete Sewer, Storm D r a i n a n d C u l v e r t P i p e Reinforced
Concrete
Culvert,
Storm
Drain
and
Sewer
Pipe I r r i g a t i o n or Drainage
C118
Concrete P i p e f o r
C361
R e i n f o r c e d Concrete Low-Head
C412
Concrete Cjrain T i l e
c443
Joints
c444
P e r f o r a t e d Concrete P i p e
c497
Determining
for
Circular
Pressure Pipe
Concrete
Sewer
and
Culvert
Pipe
w i t h Rubber gaskets
Physical
Properties
of
Concrete
Pipe
or
T i le C505
Non-reinforced
Concrete
Irrigation
Pipe
and
Rubber
Gasket J o i n t s C506
Reinforced
Concrete
Arch
Culvert,
Concrete
El I i p t i c a l
Storm
Drain
and
Sewer P i p e C507
Reinforced
C655
Reinforced
Culvert,
Storm
Drain
a n d Sewer P i p e Concrete
D-load
Culvert,
Storm
Drain
and
Sewer P i p e
Steel P i p e s ASA
Cast
836.10
Steel p i p e s
i r o n Pipes A1 42
C
I Pipes
A377
C
I pipes
A121.1
C
I pipes
Asbestos Cement P i p e s C296
A C Pressure Pipes
C500
A C Pressure Pipes
C428
A
C
Pipes
and
Fittings
for
Sewerage
and
Drainage
249 Plastic Pipes
D2241
U n p l a s t i c i s e d PVC p i p e s
USDI BUREAU OF RECLAMATION S t a n d a r d Spec.
f o r Reinforced Concrete P r e s s u r e P i p e
250 BOOKS FOR FURTHER READING
Addison,
H.,
1964.
A
treatise on
Applied
Hydraulics,
Chapman H a l l ,
London Albertson,
M.L.,
Barton,
J.R.
a n i c s f o r E n g i n e e r s , P r e n t i c e - H a l I, American Pipe,
Concrete
Pipe
Simons,
and
D.B.,
F l u i d Mech-
1960.
Association,
1970.
Design
Manual-Concrete
Arlington.
Am.Soc.Civi I
Engs.
and W a t e r
Pol In.
Control
Federation,
and C o n s t r u c t i o n o f S a n i t a r y and Storm Sewers,
Am.Water
Works
M a n u a l M11, Bell,
1960.
Assn.,
1964.
Steel
Pipe
-
1970.
M a n u a l 37,
and
Design
Design
N.Y. Installation,
N.Y.
H.S.,
1963.
(Ed.),
Petroleum
Transportation
Handbook,
McGraw
H i l l , N.Y. Benedict,
R.P.,
1977.
F u n d a m e n t a l s of
Pipe Flow,
Wiley
Interscience,
531 pp. Bureau
of
Criteria
Public
for
Roads,
Structural
Was hi n g t o n ,
Of f i ce, Clarke,
N.W.B.,
1963.
Reinforced
and
Design
Concrete
Instal lation,
Proc.
State
Inst.,
-
Printing
Buried
Pipelines
-
Univ.,
1971.
Control
of
A
Manual
of
Structural
Closed
Conduits,
London. Flow
in
Fort Collins.
S.
Crocker,
Culverts
Govt.
DC. 1968.
D e s i g n a n d I n s t a l l a t i o n , M a c L a r e n and Sons, Colorado
Pipe
U.S.
and K i n g ,
R.C.,
1967.
Sorensen,
K.E.,
P i p i n g Handbook, 5 t h Ed.,
McGraw
Hill. Davis,
C.V.
raulics,
and
3 r d Ed.,
E.,
Holmes,
1973.
McGraw H i l l , Instn.
Nolte, cations, Rouse,
of
Applied
Hyd-
Handbook
of
Industrial
Pipework
Engineering,
Engs.,
1969.
Manual
of
British
Water
Engg.
Practice,
London.
Littleton, Martin,
Handbook
N.Y.
Water
4 t h Ed.,
1969.
McGraw H i l l , N.Y.
C.T.,
W.L., C.B.,
1962.
Industrial Piping,
1961.
H a n d b o o k of
1978.
Optimum
McGraw H i l l ,
349 pp
I n d u s t r i a l Pipework,
Pitman,
Pipe
Size
Selection,
Trans
297 p p . H.,
1961.
Engineering Hydraulics, Wiley,
N.Y.
London.
Tech
Publi-
251 Stephenson, Streeter, Hill,
D.,
1984.
V.L.,
Pipeflow Analysis,
1961.
(Ed),
Handbook
R.C.
and
E l s e v i e r , 204 pp. of
Fluid
Dynamics,
McGraw
N.Y.
Twort,
A.C.,
Hoather,
A. A r n o l d ,
2 n d Ed., Walski,
T.M.,
Walton,
J.H.,
Analysis
N.Y.
1970.
G.Z.,
pipelines. Young,
1984.
2 n d Ed.
D.C.
and
A p p l i e d Science,
Water
Supply,
of
Water
Distribution
Systems.
Van
275 pp.
Structural
P i p e Development Association, Watters,
1974.
London.
1984.
Nostrand Reinhold,
F.M.,
Law,
Design
of
Vitrified
Clay
Pipes,
Clay
London.
Analysis
and
control
of
unsteady
1984.
Buried
Rigid
flow
in
Butterworths. Trott,
London,
J.J., 230 pp.
Pipes.
Elsevier
252 APPEND I X
SYMBOLS FOR P I P E F I T T I N G S
1
GENERAL
Jo.
ELBOW SLEEVED
TEE
BEND JPtKETED FRONT VIEW OF TEE
1
BACK VIEW OF TEE
FILLET WELDEOTEE CROSS OVER
I
HANGER
I
BELLMOUTH
D
-
A-
YMPLE SUPWRT CHANGE IN D I A
TAPER JOINTS
E L E CT RICALLY BONDED
FLANGED
BMT W E L D
ELECTRIULLY INSULATED FLEXIBLE
SCREWED
SWIVEL
SOCKET
E X PANS ION
SPIGOT 0 SOCKET
--+_3_
-4_f_
D
END CAP
S L E E V E COUPLING
VALVES __
EUl TERFLY ISOLATING WEDGE
NEEDLE
GATE
GLOBE
REFLUX
DIAPHRAGM
ROTARY PLUG
RELIEF AIR
w
MISCELLANEOUS STRAINER
HYDRANT
SPRAY
FLOW INDICATOR
VENT
SURFACE BOX DRAIN
M 0 TOR
t
0
P L A T E BLIND HANDWHE E L
--+
J--
+ T
253
PROPERTIES OF P I P E SHAPES
Ring AREA
-
F(D2-d2kTDt
fa -11
I
MOMENT OF INERTIA ABOUT DIAMETER =
fi (0'-
d')
=TD"
MOMENT O F INERTIA ABOUT CENTRE g ( D b - d L ) Z s D a t
PROPERT I ES OF WATER
Temperature
Specific Mass
F"
kg/rn3
Ib/cu f t
0
32
1 000
62.4
10
50
1 000
62.4
20
68
999
30
86
997
C O
Kinematic Viscosity
B u l k Modulus
s q ft/sec
N/rnm2
psi
1.79~10-~
1 .93x 1 0-5
2 000
290 000
1 .31XI 0-6 6 1.01x10-
1.41~10-~
2 070
62.3
1.09~10-~
2 200
62.2
0.81 x10-6
0.87~1 0-5
2 240
325 000
rn2/ s
Vapour Pressure N/rnmz
psi
0.6~10-~
0.09
300 000
l.2~lO-~
0.18
318 000
2 . 3 ~ 1 0 ~ ~ 0.34 3 0.62 4.3~10-
PROPERTIES OF P I P E MATERIALS
Coef.
of
exp.per
5x10
Clay Concrete Asbestos cernen t Cast
Iron
M i l d Steet
O C
Density kg/m'
Modulus of elasticity N/mrn2
psi
Y i e l d Stress N/rnrn2
psi
Tensile Strength N/mm2
Poisson's
psi
ratio
-300
0.2
6
1ox10-6
2 600
14 000-40 000
8.5~ 1 0-6
2 500
24 000
8 . 5 ~ 0-6 1
2x106-6x106
6
-70
-10
000
-2.1
2 500
7 800
100 000
3.5~10 6 15x10
1 1 .9x10-6
7 850
210 000
3 1 ~ 1 0 ~
1 1 .9x10-6
7 850
210 000
31x10
900
138
20 000
3
955
240
35 000
22
3 200
32
4 600
8
1 100
17
2 500
0.5~10
40
+ 6 000
52
7 500
22 000
25
3 600
30
4 500
17 150
22 000
225
23 000
0.25
210
30 000
330
48 000
0.3
1 650
240 000
1730
250 000
400
14
2 000
High Tensile Steel Pitch Fibre Polyethylene
6
40x 1 0-6 1 60x 1 0-6
Po I y e t h y l e n e (high density)
2oox 1 o-6
PVC
50~10-~
1 300
UPVC
50~10-~
1 400
3 500
91 2
150
Po I y p r o p y I ene
1 8ox10-6
6
0.38
256 CONVERSION FACTORS
Length
1 i n c h = 25.4 mm
1
ft
=
0.3048 m
1 m i l e = 1.61 k m Area
1
644 mrn'
sq i n c h =
1 a c r e = 2.47 ha
Vol ume
0.0929 mz
1 sq ft
=
1 ha
lo4
=
mz
35.31 c u f t
1 m3
=
1 gal.(imperial)
4.54 I i t r e s
=
1 US g a l .
=
3.79 I i t r e s
1
=
42 US gal.
=
barrel
=
35 i m p . g a l .
159 I i t r e s 0.3048 m/s
Speed
1 ft/sec
Acceleration
32.2 f t / s e c 2
Discharge
1 mgd (imperial)
=
1 m p h = 1.61 k m / h r .
35.3 c u s e c
=
0.981 m/s' =
= g
1.86 cusec
im3/s
=
13.2 g p m ( i m p e r i a l ) = 1 P / s Mass
1 I b = 0.454 k g 32.2 I b = 1 s l u g (US)
Force
1 Ib. f o r c e = 4.45 N ( 1 Newton
1 k g x 9.81 m / s ' )
=
Pressure
145 p s i = 1 MPa
Energy
14.5 p s i = 1 b a r 778 f t 16. = 1 B t u 1 Btu
=
=
1 MN/m2
252 c a l o r i e s
1 c a l o r i e = 4.18 J o u l e s Power
550 f t
Ib/sec
=
1 HP
1 HP = 0.746 kW Kinematic Viscosity
1 sq ft/sec =
=
929 s t o k e s
0.0929 m z / s
Absolute o r dynamic viscosity
1 c e n t i p o i s e = 0.001 k g / m s
Temperature
F o = 32
+
1.8C"
=
1 N/mmz
257 A b s o l Ute temperature R " (Ranki ne)
= FO(Fahrenheit1
+ 460
= Co(Centigrade)
+ 273
A b s o l Ute temperature KO (Kelvin) 71
= 3.14159
e
=
2.71828
258
AUTHOR INDEX
Abrarnov, N. 15 A d d i s o n , H. 228, 241, 250 A l b e r t s o n , M . L . 17, 35, 250 A n d e r s o n , O.A. 125 A v e r y , S.J. 105, 110 B a l l , J.W. 28, 35 B a r n a r d , R.E. 149, 157 B a r t o n , J.R. 17, 35 B e l l , H.S. 250 B e n e d i c t , R.P. 250 B e r n o u l I i , 16 B e r t h o u e x , P.M. 10, 15 B l i s s , R.H. 101, 111 B o u c h e r , P . L . 182 203 B u r a s , N. 49, 57 C a p p e r , P . L . 123, 125, 191, 203 C a s s i e , W.E. 123, 125, 191, 203 C a t e s , W.H. 176, 77, 216, 226 C h a p t o n , H.J. 177 C h e z y , 18 C l a r k e , N.W.B. 113, 125, 250 Cole, E.S. 218, 226 Col e b r o o k , 23 C r o c k e r , S. 173, 177, 250 Cross, H. 38,57 D a n t z i g , G.B. 51, 57 D a r c y , 21 D a v i s , C.V. 250 D e n n y , 9 . F . 101, 110 D i s k i n , M.H. 24, 35 D v i r , Y . 30, 35 Ervine,
D.A.
105,
110
F o x , J.A.
109, 110 F e r g u s o n , P.M. 137,
J a c o b s o n , S. 155, Johnson, S.P. 95 60 Joukowsky
157
,
K a l i n s k e , A . A . 102, 104, K a l l y , E. 48, 57 K a r r a s s i k , I.J. 228, 240 K e n n e d y , H. 121, 125 K e n n e d y , J.F. 74, 95 K e n n i s o n , H.F. 129, 140 K i n g , C.L. 177 K i n g , R.C. 173, 177 K i n n o , H. 74,95 K n a p p , R. 28, 35 K o v a t s , A . 228, 241 L a i , C . 66, 95 L a m , C.F. 56, 57 L a w , F.M. 240, 250 L e s c o v i c h , J.E. 186, 203 L i t t l e t o n , C.J. 250 L u d w i g , H. 68, 95 L u p t o n , H.R. 64, 95
M a n n i n g , 18 M a r k s , L.S. 107, 1 1 1 Marston, A. 114, 125 M a r t i n , W . L . 250 M i l l s , K.G. 32, 43, 57 Moody, 21 M o r l e y , A . 154, 157 M o r r i s o n , E.B. 190, 203 N e l s o n , E.D. 177 N e w m a r k , 122 Newton, 16, 58 N i k u r a d s e , 21 N o l t e , C.B. 250
140 Osborne,
110 Glass, W.L. G o o d i e r , J.N. 177 G r i s t , E . 232, 240
J.M.
7,
15
H a s s a n , D . R . 165, 177 Hazen-VJ i I I i ams , 18 H o a t h e r , R.C. 240, 250 Holmes, E. 250
P a r m a k i a n , J. 73, 95, 186, 203 P e a r s o n , F.H. 177 P a u l , L. 182, 203 P o i s s o n , 176, 195 P r o c t o r , 150 P r o s s o r , 1vl.J. 101, 111
Isaacs,
R e i t z , H.M.
L.T.
43,
57
111
208,
226
108,
111,
259 R e y n o l d s , 20 R e y n o l d s , G.M. 211, 226 R i c h , G.R. 78, 95 R i d d i c k , T.M. 224, 226 R o a r k , R.J. 174, 177 R o b e r t s o n , J.M. 104, 111 Rouse, H. 166, 177, 250 S c h a r e r , H. 176, 177 S c h l i c h t i n g , H. 20, 35 S c h n e i d e r , W.R. 219, 226 S c h w a r t z , H . I . 211, 226 S c h w e i g , 2. 48, 57 Sirnons, D.B. 17, 250 Sorenson, K.E. 250 Sowers, G.F. 208, 226 S p a n g l e r , M.G. 113, 125, 146, 152, 157 S t e p a n o f f , A.J. 228, 241 Stephenson, D. 56, 57, 69, 80, 9 5 , 110, 1 1 1 , 151 157, 165, 177, 25 1 S t r e e t e r , V.L. 66, 95, 251 Suss, A. 165, 177 Swanson, H.S. 162, 177 Sweeton, A.E. 186, 203
TSSYJ,
Tirnoshenko, S . P . 134, 140, 158, T r o t t , J.J. 113, 125, 251 T u l l i s , J.P. 35 T w o r t , A.C. 240 Uhlig,
H.H.
218,
Van d e r Veen,
B.
226 51,
57
W a l s k i , T.M. 251 Walton, J.H. 250 Watson, M.D. 24, 35 W a t t e r s , G.Z. 251 Webber, N.B. 229, 241 Weisbach, 21, 109 W h i t e , 23 W h i t e , J.E. 9, 15 W i l k i n s o n , W.J. 177 W i n n , W.P. 33, 35 W i s n e r , P. 102, 111 W o i n o w s k i - K r i e g e r , S. 134, Wood, D.J. 43, 57 W y l i e , E.B. 66, 95 Young, Young,
160,
D.C. 113, 125, 251 G.A.J. 101, 110
140,
157
177
260
SUBJECT INDEX
A b s o r p t i o n 99 A c t i v e s o i l p r e s s u r e 114, 149, 191 A c t u a t o r 92, 185 A d i a b a t i c 86, 107 Aesthetics 2 A i r pocket 89, 100 v a l v e s 106, 189 vessel 87 American Concrete P i p e Assn. 122, 125, 140 Anode, s a c r i f i c i a l 219 A p p u r t e n a n c e s 182 Asbestos cement 180 A x i a l e x p a n s i o n 176, 195 B a c k f i l l 113, 192 B a r g e , 211 Beam 213 B e a r i n g t e s t 128 B e d d i n g 115. 127 B e d d i n g f a c t o r 128, 207 Bend loss 27 meter 200 s t r e s s 173 B e n d i n g 144, 196, 213 B i n a r y n u m b e r 202 B i t u m e n 217 B o n i n g 206 B o u n d a r y l a y e r 22 B r a c i n g 161 B r a n c h 62, 68, 161 B r i d g e 208 B u b b l e 99 Buck1 i n g 152, 168 B u t t e r f l y v a l v e 27, 32, 184 B y p a s s 76, 79, 182 Cant i l e v e r 174 Capacity factor 4 Cash f l o w 1 1 C a s i n g 217 Cast i r o n 180 C a t h o d i c p r o t e c t i o n 218 C a v i t a t i o n 30, 97 C e l e r i t y 60 C e n t r i f u g a l f l o w 200 f o r c e 190 pump 229 C h a r a c t e r i s t i c method 66 pump 70, 73, 229
Chemicals 1 C l R l A 152 Clamp 212 C l a y 255 C o a t i n g , bi tumen 21 6 c o a l t a r 217 epoxy 217 g l a s s f i b r e 217 m o r t a r 23, 217 t a p e 217 Cohesion 191 Col l a p s e 148 C o l l a r 143, 161 Concrete p i p e s 127, 180 p r e s t r e s s e d - 129 180 p r o p e r t i e s 137, 255 Compound p i p e s 37 Compressibi I i t y 16, 60 Computers, a n a l o g u e 202 d i g i t a l 41, 202 Concrete P i p e Ass. 122, 125 C o n d u c t i v i t y 219, 223 Conductor 219 Cone v a l v e 30, 184 Consol i d a t i o n 149 C o n s t r a i n t 52 Container 2 C o n t r a c t i o n c o e f f i c i e n t 200 Convect i o n 224 Conversion f a c t o r s 256 Core 129 C o r r o s i o n , g a l v a n i c 218 Cost, p i p e 3 power 4, 12 p u m p i n g 4, 8 C o u n t e r b a l a n c e 186 C o u p l i n g 230 C r a c k 127 Creep 130 Cross section 253 C r o t c h p l a t e 161 C r u s h i n g 137 Current, electric219 impressed21 9 stray220 C y l i n d e r 129 D e f l e c t i o n 146, 150 Design f a c t o r 142 O i ameter 4
261 D i s c h a r g e c o e f f i c i e n t 200 t a n k 79 Discount r a t e 9 D i s s o l v e 99 D r a i n 207 D y n a m i c p r o g r a m m i n g 45 Economics 2 E l a s t i c i t y 64, 255 E l e c t r o d e 220 E I ec tro-chemi c a l e q u i v a l e n t 220 E l e c t r o l y t e 218 E l e c t r o m a g n e t i c i n d u c t i o n 201 El l i p s e 253 Embankment 1 1 6 Ernrnissivity 224 E m p i r i c a l 18 E n e r g y 16 E n t r a n c e l o s s 27 Epoxy 217 E q u i v a l e n t d i a m e t e r 37 Escher Wyss 177 E x c a v a t i o n 206 E x t e r n a l l o a d 115, 146 F a b r i c a t e d b e n d 194 F a c t o r o f s a f e t y 143 F i e l d p r e s s u r e 133 F l a n g e 212 b l a n k 216 p u d d l e 216 F l e x i b l e p i p e 142 F l o a t i n g 210 F i t t i n g s 182 Flow measurement 198 b e n d meter 200 e l e c t r o m a g n e t i c 201 mass 201 m e c h a n i c a l 200 n o z z l e 199 o r i f i c e 199 v e n t u r i 198 volume 202 Flow r e v e r s a l 75, 91 F l y w h e e l 76 F r i c t i o n 18, 68, 74 F r o u d e n u m b e r 104 G a l v a n i c a c t i o n 218 Gasket 215 Gate v a l v e 182 Globe v a l v e 184 G r a p h i c a l a n a l y s i s 14, 65
H a u n c h 128, 148 Head, loss 16, 37, 199, 232 v e l o c i t y - 16, 232 w a t e r hammer- 62 H e a d i n g 208 Heat loss 224 History 1 Hole 161 Hol i d a y d e t e c t o r 21 7 H y d r a u l i c g r a d i e n t 18, 68, 238 H y d r a u l i c j u m p 104 I m p a c t f a c t o r 121 I m p e l l e r 229 I n e r t i a 73, 94 I n f l u e n c e c o e f f i c i e n t 122 I n s u l a t ion, t herrna I 224 I n t e r e s t 10 I sotherrnal 86 J o i n t , b u t t - w e l d e d 212 clamp-on 214 f a c t o r 142 f l a n g e d 215 screwed 213 sleeve w e l d e d 212 s p i g o t a n d socket 130, 214 K i n e t i c e n e r g y 72 L a g g i n g 224 L a m i n a r f l o w 20 L a t e r a l s u p p o r t 149 L a y i n g 205 L i n e l o a d 122 L i n e a r p r o g r a m m i n g 52 L i n i n g , b i t u m e n 217 c o a l t a r 217 epoxy 218 m o r t a r 21 8 L i v e l o a d 120 L o a d c o e f f i c i e n t 114 soi I 113 superimposed 120 Longitudinal stress 21 3 Loop 38 Loss c o e f f i c i e n t 27 Losses 26 Mass, c o n s e r v a t i o n of 16 M a t e r i a l s 255 M e c h a n i c a l meter 200
134,
198,
262 Membrane t h e o r y 167 Meter b e n d 200 rnkchan i c a l 200 n o z z l e 199 o r i f i c e 199 r o t 0 200 v a n e 200 v e n t u r i 198 Model 165 M o d u l u s of e l a s t i c i t y 137, 255 M o d u l u s of s u b q r a d e r e a c t i o n 124 Mohr d i a g r a m 136 Momentum 16, 90 Motor 239 Needle v a l v e 91, 184 Network 38 Net p o s i t i v e s u c t i o n h e a d 232 Node 39 Non-l i n e a r p r o g r a m m i n g 56 Normal t h r u s t 190 Nozzle 199 O b j e c t i v e f u n c t i o n 56 Ohm 219 Oil 1 Operating factor 4 O p t i m i z a t i o n 8, 45 O r i f i c e 86, 199 P a r t l y f u l l p i p e 100 P a s s i v e s o i l p r e s s u r e 191 Pavement 123 P e r i m e t e r , w e t t e d 102 P i p e , asbestos cement 180, 255 c a s t i r o n 179, 255 c o n c r e t e 180, 255 p l a s t i c 180, 255 p o l y e t h y l e n e 180, 255 PVC 180, 255 p r o p e r t i e s , 255 s a l t g a l v a n i z e d c l a y w a r e 255 steel 179, 255 UPVC 180, 255 Planning 1 P l a s t i c 180 P o i n t l o a d 121 P o i s s o n ' s r a t i o 144, 195, 255 P o l a r i z a t i o n 218 P o l y e t h y l e n e 180, 255 P o t e n t i a l e n e r g y 90 Power 236 Present v a l u e 10
P r e s s u r e , e x t e r n a l 110, 146 i n t e r n a l 142 w a t e r hammer 58 P r e s t r e s s e d c o n c r e t e p i p e 129 P r o c t o r d e n s i t y 150, 207 Profile, pipeline 72, 106, 238 P r o t e c t i o n , c a t h o d i c 218 w a t e r hammer 69 P u d d l e f l a n g e 216 Pump, b o o s t e r 2, 9 c e n t r i f u g a l 75, 229 i n e r t i a 73 power 5 t y p e s 228 P u m p i n g c o s t s 3, 12 R a d i a l s t r e s s 142 R a d i a t i o n 224 R a d i o 202 R a d i u s o f s t i f f n e s s 124 Rail 1 Reducer 169 R e f l u x v a l v e 71, 81, 186 R e i n f o r c e d c o n c r e t e 1 , 127 R e i n f o r c i n g 127, 143, 162 R e l a x a t i o n o f s t r e s s 131 Release v a l v e 91, 184 R e s e r v o i r 14 R e s i s t i v i t y 219 R e t i c u l a t i o n n e t w o r k 37 R e y n o l d ' s n u m b e r 20 R i b b e d p i p e 154 R i g i d pavement 123 p i p e 113 R i n g g i r d e r 175 l o a d 149 s t i f f e n i n g 154 s t r e s s 142 t e n s i o n 142 Road 1 Roughness 21 Route 205 S a c r i f i c i a l anode 219 S a d d l e 174 S a l t g l a z e d 255 S a n d 192 Scale 6 S c o u r i n g 210 Screwed j o i n t 213 Sea 210
205,
263 Secondary s t r e s s 160 S e c t i o n m o d u l u s 174 S e r v i c e s 205 Settlement 118 Shape 253 S h r i n k a g e 135 S i n k i n g fund 9 S l u i c e v a l v e s 182 Snake 206 Socket j o i n t 130, 214 S o i l l o a d 115, 146 m e c h a n i c s 193, 208 p r o p e r t i e s 113, 192 Span 213 S p e c i f i c mass 254 S p e c i f i c speed 223 S p h e r i c a l v a l v e 185 S p i n d l e 182 S t a n d a r d s 242 S t a r t e r s 239 Steady f l o w 16 Steel, high t e n s i l e 136, 255 p i p e 180 p r e s t r e s s i n g 136 p r o p e r t i e s 255 S t i f f e n i n g r i n g s 154 S t r a y c u r r e n t e l e c t r o l y s i s 219 S t r e n g t h , l a b o r a t o r y 137 Stress, b e n d i n g 196, 213 S t r e s s , c i r c u m f e r e n t i a l 133, 142 Stress, l o n g i t u d i n a l - 134, 198, 213 t e m p e r a t u r e - 21 5 S t r u t t i n g 149, 154 S u l z e r 177 Superimposed l o a d 120 S u p p o r t 128, 148, 194 S u r f a c e l o a d 120 S u r g e 58 - t a n k 77 Symbols 252 Systems a n a l y s i s 44 Te I erne t r y 202 T e m p e r a t u r e 195, 215 T e n s i o n r i n g s 143 T e s t i n g 206 T h e r m a l i n s u l a t i o n 224 T h e r m o p l a s t i c 180 T h i c k n e s s 142, 162, 224 T h r o t t l i n g 28, 184 T h r u s t b l o c k 192 b o r e 208 T i e b o l t 214 T o r q u e 235
T o w i n g 210 T r a f f i c l o a d 121 T r a n s i e n t p r e s s u r e s 60 Transport and Roads Laboratory 152 Transportation, a i r 1 p r o g r a m m i n g 45 rail 1 road 1 waterway 1 T r e n c h 113, 206 T u r b i n e 77
Research
Uncertainty 1 1 U n d e r w a t e r l a y i n g 210 U n i f o r m l o a d 122 Unp I a s t i c i z e d p o l y v i n y Ic h l o r i d e 180, 255 Vacuum 97, 153 V a l v e , a i r r e l e a s e 106, 188 a i r v e n t 186 b u t t e r f l y 183 cone 184 c o n t r o l 29, 184 g l o b e 184 n e e d l e 184 r e f l u x 71, 81, 186 r e l e a s e 91, 184 s p h e r i c a l 185 s l e e v e 185 s l u i c e 182 Vane, g u i d e 165 V a p o r i z a t i o n 90, 97, 153 V e l o c i t y 16, 58, 199 V e n t u r i m e t e r 198 V i c t a u l ic coup1 i n g 194 V i k i n g l o h n s o n c o u p l i n g 194 V i s c o s i t y 23, 255 V o l u t e 229 V o r t e x 89 W a l l t h i c k n e s s 142, 162, 224 Water hammer 60 p r o p e r t i e s 254 s u p p l y 14 Wave 60 Web 162 W e l d i n g 212 'Wetted p e r i m e t e r 148 W r a p p i n g 216 X-ray
217
Y i e l d s t r e s s 152, 255
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