Tables for the Hydraulic Design of Pipes, Sewers and Channels Pt. 1, v. 1

308 Pages·1998·74.93 MB·English

by  D. I. H. Barr

Tables for the hydraulic
design of pipes, sewers
and channels
Seventh edition - Volume 1
Z H R W allingford and D. 1. H. Barr
17
Thomas Telford, London
Published by Thomas Telford Services Ltd, Thomas Telford House,
1 Heron Quay, London El4 4JD, UK
Distributors for Thomas Telford books are
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First published 1963
Seventh edition 1998
Reprinted in 2001,2004
A catalogue record for this book is available from the British Library
ISBN : 0 7277 2637 4
0 HR Wallingford and D. I. H. Barr, 1998
All rights, including translation, reserved. Except for fair copying, 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 or otherwise, without the prior written
permission of the Book Publisher, Publications Division, Thomas
Telford Services Ltd, Thomas Telford House, 1 Heron Quay, London
El4 4JD, UK
While all reasonable efforts have been made to ensure the accuracy
of the information given in these Tables, no warranty, express or
implied, is given by the publishers or by the authors
Set in Helvetica by D. I. H. Barr
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He/veticaTMi s a trademark of Linotype AG and its subsidiaries in the UK and other countries
iv
Preface
This Seventh edition of the Wallingford Tables continues the two
volume arrangement of the Sixth edition. The two volumes are
designed both to be mutually supportive and to be individually
free-standing in use.
The arrangement of the Sixth edition provided a significant increase
in the number of diameters treated by the established form of solution
table for the Colebrook-White equation. This allowed coverage of
sizes already associated with newer materials and planned for most
pipes in the future. For this edition the coverage of diameters is the
same but the tables have been redone so as to eliminate the possible
need for interpolation between pages.
Since the publication of the Sixth edition, HR Wallingford has
undertaken new work on the assessment of roughness size in
commercial pipes manufactured from materials currently utilised to
give a comparatively smooth finish and also on the assessment of
additional losses at bends in such pipes. These results are
incorporated in this edition.
Volume II uses a newer, alternative, route to support the application
of the unit size method. For this route, Manning equation tables also
act as a carrier for obtaining solution of the Colebrook-Whitee quation.
For Volume II of this edition, the Manning equation tables have been
redone reducing the increment in gradient between entries to ease
interpolation. As before, the coverage of discharges continues well
into the order of scale of continental rivers.
In Volume II, a wide range of conduit and channel shapes is covered
by tables of properties based on unit size, with key examples of these
tables also included in Volume I. This gives illustration of solutions
supported by the established form of Colebrook-White tables, as is
possible for most conduits and smaller channels, when the two
volumes are used in conjunction.
In both volumes, the tables of unit properties tables provide aid for
both gradually varied and rapidly varied flow problems. Also, there
is more detailed coverage of the possible effects of variation in water
temperature within the normal water resources and drainage range of
temperatures.
The authors acknowledge the contribution of Ronald Baron,
Computer Officer, Department of Civil Engineering, University of
Strathclyde, to the production of the various forms of table.
Users of these Tables are invited to provide comments or corrections,
particularly on conduit or channel shapes which are in common use
but which are not covered. The authors are grateful for various
comments which have been received already, many of which have
influenced the content of this Seventh edition.
vi
Foreword to First Edition
Hydraulics Research Papers Nos 1 and 2 were published in 1958
under the titles Resistance of fluids flowing in channels andpipes and
Charts for the hydraulic design of channels and pipes. These dealt
with the application of the Colebrook-White equation for turbulent-
transitional flow in determining the discharge capacity of channels and
pipes. The Wallingford Charts have achieved wide circulation, but
there have been requests for the design data to be made available in
tabular form.
With the collaboration of the Road Research Laboratory of the
Department of Scientific and Industrial research, the present
publication has been prepared, as part of the programme of the
Hydraulics Research Board, to meet this demand. It is hoped that it
will be of particular value to civil engineers engaged on the design of
urban drainage systems.
F H ALLEN
Director of Hydraulics Research
Hydraulics Research Station
Wallingford, Berks
March 1963
Foreword to Seventh Edition
The Tables for the hydraulic design of pipes, sewers and channels
continue to provide a valuable reference for civil engineers working
in the field of hydraulics.
Since the sixth edition was produced, HR Wallingford with support
from the Department of the Environment, Transport and the Regions,
has carried out more research on the hydraulic roughness of different
materials and in particular on pipes with smooth internal coatings. As
was promised in the foreword to the sixth edition, the results of this
work have been included in the present edition. Extra material has
also been included to aid the calculation of temperature effects. We
have also taken the opportunity provided by preparing a new edition
to make interpolation between entries easier, and to reduce the
increments between certain entries in the Tables.
It is hoped that by incorporating these changes into this new edition,
the usefulness of these Tables to the industry will be enhanced.
Dr S W Huntington
Managing Director
HR Wallingford
Wallingford, Oxfordshire
October 1997
V
Foreword to First Edition
Hydraulics Research Papers Nos 1 and 2 were published in 1958
under the titles Resistance of fluids flowing in channels andpipes and
Charts for the hydraulic design of channels and pipes. These dealt
with the application of the Colebrook-White equation for turbulent-
transitional flow in determining the discharge capacity of channels and
pipes. The Wallingford Charts have achieved wide circulation, but
there have been requests for the design data to be made available in
tabular form.
With the collaboration of the Road Research Laboratory of the
Department of Scientific and Industrial research, the present
publication has been prepared, as part of the programme of the
Hydraulics Research Board, to meet this demand. It is hoped that it
will be of particular value to civil engineers engaged on the design of
urban drainage systems.
F H ALLEN
Director of Hydraulics Research
Hydraulics Research Station
Wallingford, Berks
March 1963
Foreword to Seventh Edition
The Tables for the hydraulic design of pipes, sewers and channels
continue to provide a valuable reference for civil engineers working
in the field of hydraulics.
Since the sixth edition was produced, HR Wallingford with support
from the Department of the Environment, Transport and the Regions,
has carried out more research on the hydraulic roughness of different
materials and in particular on pipes with smooth internal coatings. As
was promised in the foreword to the sixth edition, the results of this
work have been included in the present edition. Extra material has
also been included to aid the calculation of temperature effects. We
have also taken the opportunity provided by preparing a new edition
to make interpolation between entries easier, and to reduce the
increments between certain entries in the Tables.
It is hoped that by incorporating these changes into this new edition,
the usefulness of these Tables to the industry will be enhanced.
Dr S W Huntington
Managing Director
HR Wallingford
Wallingford, Oxfordshire
October 1997
V
Contents
INTRODUCTION Page
The Wallingford Charts and the Wallingford Tables . . . . . . . . . . . . . 1
The Additional Tables .................................. 1
The 6th Edition of the Wallingford Tables (1994) in two volumes ... 1
This 7th Edition of the Wallingford Tables ................... 2
Arrangement and functions of Volume I ..................... 2
REVIEW OF HYDRAULIC RESISTANCE
The Colebrook-White equation ............................ 4
The linear measure of surface roughness .................... 4
Simplified forms of the Colebrook-White equation .............. 8
Tables of Colebrook-White solutions (Tables A1 -A58) ........... 8
DESIGN OF CIRCULAR SECTION PIPELINES AND SEWERS
UseoftheTablesA ................................... 8
Adjustment for effect of variation of temperature from standard .... 9
Interpolation between entries ............................. 9
Tables of proportioning exponents (Tables B) .................9
Solution using proportioning exponents ..................... 10
Multiplying factors on tabulated discharges for standard
but non-tabulated diameters ............................. 10
Perimeters involving dissimilar roughness .................... 11
NON-CIRCULAR CROSS-SECTIONS OF FLOW
Calculation of discharge and velocity in part-full circular pipes . . . . 12
Calculation of depth in part-full circular pipes ................ 13
Use of factors for temperature variation as given in Annexure .... 13
Hydraulic equivalence ................................. 14
‘Unit size’ measures for shapes of conduits and channels ....... 14
Tables of properties of unit sections (Tables C) .............. 15
Finding discharge in a rectangular open channel ............. 15
SOLUTIONS FOR EGG-SHAPE SEWER
Finding (i) discharge. or (ii) gradient. or (iii) size
where proportional depth is stipulated ..................... 17
Finding depth of flow in a conduit of specified boundary shape
and size. with discharge. gradient and roughness size fixed ..... 18
Use of factors for temperature variation as given in Annexure . . . . 19
OTHER SOURCES OF RESISTANCE ..................... 20
Calculating with additional head losses present .............. 20
CHECKS ON MEAN VELOCITY. REYNOLDS NUMBER
AND FROUDE NUMBER .............................. 22
VISCOSITIES OTHER THAN THAT OF WATER AT 15OC ...... 22
CRITICAL DEPTH AND CRITICAL DISCHARGE ............. 22
GRADUALLY VARIED FLOW IN PRISMATIC CHANNELS . . . . . . 23
Solution for gradually varied flow in a circular pipe ............ 23
(continued)
vi i
~ Contents (continued)
RAPIDLY VARIED FLOW .............................. 24
REVIEW ......................................... 26
References ........................................ 27
Nomenclature ...................................... 29
Tables within text
Table 1: Overall solution paths for uniform flow problems ....... 3
Table 2: Values of multiplying factor
for SU Colebrook-White equations ................. 7
Table 3: Predictions of proportional depth in Form 1 egg-shape
with range of extreme combinations of conditions ..... 19
Table 4: Computation of S2 flow profile in circular pipe ........ 25
Figures within text
Fig. 1 : Colebrook-White equation and direct solution
approximations ............................... 5
Fig. 2: Solution of Colebrook-White equation in simplified
usage mode (SU) ............................. 6
Fig. 3: Solution routes for uniform flow in non-circular
cross-sections ............................... 16
Appendix 1: Recommended roughness values ........... 32
Appendix 2: Allowances for additional head losses
in turbulent flow ......................... 34
Appendix 3: Multiplying factors for discharges
in pipes and lined tunnels ................. 35
Tables A
Tables of Colebrook-W hite solutions
Diameters 20 mm to 150 mm
Table A1 : k, = 0.003mm .......................... 36
Table A2: k, = 0.006 mm .......................... 40
Table A3 : k, = 0.01 5 mm .......................... 44
Table A4 : k, = 0.030 mm .......................... 48
Table A5 : ks = 0.060 mm .......................... 52
Table A6 : k, = 0.1 50 mm .......................... 56
Table A7 : k, = 0.30 mm ........................... 60
Table A8 : k, = 0.60 mm ........................... 64
Table A9: k, = 1.50 mm ........................... 68
Table A10: k, = 3.0mm ............................ 72
Table All : k, = 6-0mm ............................ 76
viii
Contents (continued)
Tables A (continued)
Tables of Colebrook-W hite solutions
Diameters 750mm to 630mm
Table A1 2 : k, = 0.006 mm ........................ 80
Table A1 3 : k, = 0.01 5 mm ........................ 84
Table A14 : k, = 0.030 mm ........................ 88
Table A15: k, = 0.060mm ........................ 92
Table A1 6 : k, = 0.1 50 mm ........................ 96
Table A1 7: k, = 0.30 mm ........................ 100
Table A18: k, = 0.60mm ........................ 104
Table A19: k, = 1.50mm ........................ 108
Table A20: k, = 3.0mm ......................... 112
Table A21 : k, = 6.0mm ......................... 116
Table A22 : k, = 15.0 mm ........................ 120
Diameters 630mm to 1250mm
Table A23: k, = 0.006mm ....................... 126
Table A24 : k, = 0.01 5 mm ....................... 130
Table A25 : k, = 0.030 mm ....................... 134
Table A26: k, = 0.060mm ....................... 138
Table A27 : k, = 0.1 50 mm ....................... 142
Table A28: k, = 0.30mm ........................ 146
Table A29 : k, = 0.60 mm ........................ 150
Table A30: k, = 1.50mm ........................ 154
Table A31 : k, = 3.0 mm ......................... 158
Table A32: k, = 6.0mm ......................... 162
Table A33 : k, = 15.0 mm ........................ 166
Table A34 : k, = 30.0 mm ........................ 170
Diameters 1250mm to 2400mm
Table A35 : k, = 0.006 mm ....................... 174
Table A36 : ks = 0.015 mm ....................... 178
Table A37 : k, = 0.030 mm ....................... 182
Table A38: k, = 0.060mm ....................... 186
Table A39 : k, = 0.1 50 mm ....................... 190
Table A40 : k, = 0.30m m ........................ 194
Table A41 : k, = 0.60mm ........................ 198
Table A42: k, = 1.50mm ....................... 202
Table A43: k, = 3.0mm . ....................... 206
Table A44: k, = 6.0mm . ....................... 210
Table A45: k, = 15.0mm ....................... 214
Table A46 : k, = 30.0 mm ....................... 218
(continued)
ix
Contents (continued)
Tables A (continued)
Tables of Colebrook-W hite solutions
Diameters 2400mm to 4500mm
Table A47 : k, = 0.01 5 mm ....................... 222
Table A48: k, = 0.030mm ....................... 226
Table A49 : k, = 0.060 mm ....................... 230
Table A50: k, = 0.1 50 mm ....................... 234
Table A51 : k, = 0.30mm ........................ 238
Table A52 : k, = 0.60 mm ........................ 242
Table A53: k, = 1.50mm ........................ 246
Table A54: k, = 3.0mm ......................... 250
Table A55: k, = 6.0mm ......................... 254
Table A56: k, = 15.0mm ........................ 258
Table A57 : k, = 30.0 mm ........................ 262
Table A58: k, = 60.0mm ........................ 266
Annexure to Tables A
Multiplying factors on velocity and discharge for variations
of temperature from 15'C in turbulent flow ................ 270
Tables B
Values of proportioning exponents in equations (8). (9) and (10)
Table 61 : Values of exponent x ................... 276
Table B2 : Values of exponent y ................... 277
Table B3 : Values of exponent z ................... 278
Table 64 : Values of exponent u ................... 279
Table 85 : Values of exponent v ................... 280
Table B6 : Values of exponent z ................... 281
Tables C
Tables of properties of unit sections (and proportional flow-d etails for
circular pipes only)
Table C1: Circular pipe ......................... 282
Table C1 (a) : Proportional discharges
in part-full circular pipes ..................... 284
Table C1 (b) : Corrections to assessed proportional
depths for circular pipes. as based on shift of 8 ratio . 285
Table C2 : Form 1 egg-shape (3:2 old type) .......... 286
Table C5 : Form 2 egg-shape (3:2 new type) . . . . . . . . . . 288
Table C14: Rectangular (free surface) ............... 290
X
introduction
The Wallingford Charts and the Wallingford Tables
The first editions of the Wallingford Charts’ and the Wallingford
Tables2 were published in 1958 and in 1963 respectively.
The continuing availability of these Charts and Tables in succeeding
editions has greatly facilitated the general adoption of the
’I2
Colebrook-White resistance equation3 in the United Kingdom and
elsewhere. This equation relates specifically to steady turbulent flow
in circular pipes flowing full. Before the publication of the 6th edition
in 1994, the Tables had concentrated on circular pipe flow, but with
coverage also of part-full flow in such pipes and of flow in two forms
of egg-shape. With the Colebrook-White equation increasingly
adopted for resistance calculations generally, whatever the
cross-section of flow, the 6th edition was expanded accordingly.
The 3rd edition of the Tables, as published in 1977, had introduced
a selection of 36 metric pipe diameters from 50 to 2100 mm for which
Colebrook-White equation assessed flow data was given directly in
Tables 1-33. This pattern was continued in the 4th and 5th editions.
The choice of individual nominal diameters was influenced greatly by
the standard metric sizes then adopted for concrete drainage pipes
in the United Kingdom. The arrangement of standard sizes was
based on existing manufacturing practices and has been termed ‘soft
metrication’
The Additional Tables
Published in 1993, the Additional Tables4 were designed as a
companion to Tables 1-33 of the 3rd, 4th or 5th editions of the
Wallingford Tables. The Additional Tables introduced a new
approach to calculation of flows in non-circular conduits and channels.
This approach uses tables (Tables C) which give geometrical and
hydraulic properties for a wide range of conduit and channel shapes.
Each table is based on a conduit or channel of unit size, and the data
is presented for appropriate increments of depth. A linear multiplying
factor, M, can then be used to give values of the properties for any
size of conduit or channel of the given geometry.
The 6th Edition of the Wallingford Tables (1994) in two volumes
For the mid-nineties and beyond, it seemed desirable to enlarge the
range of diameters covered with the established form of tables of
Colebrook-White solutions (Tables A). A selection of 65 diameters
from 20 to 4000 mm was made which included both the 1977
selection of standard diameters and most of the differing diameters
which were standard for newer pipe materials. This new selection
included also all the diameters specified in both appropriate existing
and draft European Standards. To the original ‘soft metrication’ sizes
were added the ‘hard metrication’ sizes of the currently manufactured
pipes in newer materials and of the intended future sizes for all cases.
There are, of course, a fair number of common sizes as between ‘soft
metrication’ and ‘hard metrication’. The resulting tables formed the
main element of Volume I of the 6th edition, which thus succeeded
the 5th edition.
1