Tables for the Hydraulic Design of Pipes, Sewers and Channels Pt.1, v.2

317 Pages·1998·47.93 MB·English

by  Barr, D. I. H

Tables for the hydraulic
design of pipes, sewers
and channels
Seventh edition - Volume 2
7
&
HR Wallingford and D. 1. H. Barr
1 1 T homas Telford, London
Published by Thomas Telford Services Ltd, Thomas Telford House,
1 Heron Quay, London El4 4JD, UK
Distributors for Thomas Telford books are
USA: American Society of Civil Engineers, Book Orders,
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Australia : DA Information Services, 648 Whitehorse Road, Mitcham,
Victoria 313 2
First published 1963
Seventh edition 1998
Amended Reprint 2004
A catalogue record for this book is available from the British Library
ISBN : 0 7277 2638 2
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
Printed and bound in Great Britain by Pear Tree Press Ltd
Stevenage, Herts SGl 2BH
He/veticaTMis 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-White equation.
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 ~~
Page
INTRODUCTION
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 II ..................... 2
REVIEW OF HYDRAULIC RESISTANCE
The Colebrook-White equation ............................ 4
The linear measure of surface roughness .................... 5
Simplified forms of the Colebrook-White equation .............. 5
The Manning equation arranged for parallel usage ............. 5
Formation of Tables D and Tables E ....................... 9
Proportioning exponents arising from the structure
of the Manning equation ................................ 9
ARRANGEMENT AND USE OF TABLES D AND TABLES E .....1 0
General ............................................ 10
DESIGN OF CIRCULAR SECTION PIPELINES AND SEWERS
Use of the Tables D and E to find velocity. V. and discharge. Q ...1 2
Solutions for gradient and for pipe diameter ..................1 2
Adjustments for effect of variation of temperature from standard ...1 3
Interpolation between entries in Tables D for intermediate
values of diameter and gradient ........................... 14
Solution involving an intermediate roughness size ..............1 4
Multiplying factors on tabulated values of mQ for standard
but non-tabulated diameters ............................. 15
Perimeters involving dissimilar roughness .................... 15
NON-CIRCULAR CROSS-SECTIONS OF FLOW
Calculation of discharge and velocity in part-full circular pipes .....1 7
Calculation of depth in part-full circular pipes .................1 7
Use of factors for temperature variation as given in Annexure 1 ....1 8
Hydraulic equivalence .................................. 18
‘Unit size’ measures for shapes of conduits and channels ........1 9
...............
Tables of properties of unit sections (Tables C) 19
Finding discharge in a rectangular open channel ............. 21
SOLUTIONS FOR EGG-SHAPE SEWER
Finding (i) discharge. or (ii) gradient. or (iii) size
where proportional depth is stipulated ..................... 22
Finding depth of flow in a conduit of specified boundary shape
and size. with discharge. gradient and roughness size fixed ..... 25
Use of factors for temperature variation as given in Annexure 1 ... 25
SOLUTIONS FOR TRAPEZOIDAL OPEN CHANNEL .......... 26
MANNING-WILLIAMSON SOLUTIONS FOR
PRECEDING EXAMPLES .............................. 27
OTHER SOURCES OF RESISTANCE ..................... 27
..............
Calculating with additional head losses present 28
vii
Contents (continued)
CHECKS ON MEAN VELOCITY. REYNOLDS NUMBER
AND FROUDE NUMBER .............................. 30
VISCOSITIES OTHER THAN THAT OF WATER AT 15OC ...... 30
CRITICAL DEPTH AND CRITICAL DISCHARGE ............. 30
USE OF TABLES WITH DATA FROM NATURAL CHANNELS ... 30
GRADUALLY VARIED FLOW IN PRISMATIC CHANNELS ...... 31
Solution for gradually varied flow in a trapezoidal channel ....... 32
RAPIDLY VARIED FLOW .............................. 33
REVIEW .......................................... 35
References ........................................ 36
Nomenclature ...................................... 37
.
........
Tables within text
... ....
Table : Overall .so.lu.t.io.n ... uniform flow problems . . . . . . .
Table 2: Values o.f. m.u.l.tip.ly.i.ng. f.a.ct.o.r
Colebrook-White equations .................
Table Value.s. .........M.a.n ning-William.so.n equation ........
Table 4: Values turbulent flow ...............
Table 5: Predictions of proportional depth in Form 1 egg-shape
with combinations conditions .......
Table 6: Computation of M1 flow profile in trapezoidal channel . . 34
Figures within text
Fig. 1: Colebrook-White equation and direct solution
approximations ............................... 6
.
Fig 2: Solution of Colebrook-White equation in simplified
usage mode (SU) ............................. 7
.
Fig 3: Solution routes for uniform flow in non-circular
cross-sections ............................... 23
Appendix 1 : Recommended roughness values ........... 38
Appendix 2: Values of coefficient mM.f or use
with Tables D ........................... 40
Appendix 3: Allowances for additional head losses
in turbulent flow ......................... 42
Appendix 4: Multiplying factors for discharges
in pipes and lined tunnels ................. 43
viii
Contents (continued)
Tables C
Tables of properties of unit sections (with separate proportional flow
tables for circular pipes only)
Table C1: Circular pipe .......................... 44
Table C1( a): Proportional discharges
in part-full circular pipes ...................... 46
Table C1( b): Corrections to assessed proportional
depths for circular pipes. as based on shift of 8 ratio . 47
Table C2: Form 1 egg-shape (3:2 old type) ............ 48
Table C3: Form 1 egg-shape with 5% lining ........... 50
Table C4: Form 1 egg-shape with 10% lining .......... 51
Table C5: Form 2 egg-shape (3:2 new type) ........... 52
Table C6: Form 2 egg-shape with 3% lining ........... 54
Table C7: Form 2 egg-shape with 6% lining ........... 55
Table C8: 4:3 egg-shape (WRc) .................... 56
Table C9: 4:3 egg-shape with 3% lining .............. 58
Table C10: 4:3 egg-shape with 6% lining ............. 59
Table C11 : U-shaped (free surface) ................. 60
Table C12: U-shaped capped
(running full .m odified table) .................. 62
Table C13: Oval (running full .m odified table) .......... 63
Table C14: Rectangular (free surface) ................ 64
Table C15: Rectangular capped
(running full .m odified table) .................. 66
Table C16: Standard arch culvert .r adius 0.5 breadth .... 68
Table C17: Wide arch culvert .r adius 0.5 breadth ....... 69
Table C18: Arch culvert .r adius 0.5 breadth
(running full .m odified table) .................. 70
Table C19: Arch culvert .r adius 0.75 breadth
(running full .m odified table) .................. 71
Table C20: Box culvert (9Y0 splays) (free surface) ....... 72
Table C21: Box culvert (9Yo splays)
(running full .m odified table) .................. 73
Table C22: Box culvert (16% splays) (free surface) ...... 74
Table C23: Box culvert (16% splays)
..................
(running full .m odified table) 75
Table C24: Box culvert upright (23% splays) (free surface) . 76
Table C25: Box culvert upright (30% splays) (free surface) . 77
Table C26: Standard Horseshoe .................... 78
Table C27: Metcalf and Eddy (M and E) Horseshoe ...... 80
Table C28: Babbitt and Bauman (B and B) Horseshoe .... 81
Table C29: M and E Semi-elliptical .................. 82
Table C30: B and B Catenary ...................... 83
Table C31: M and E Basket-handle .................. 84
Table C32: B and B Basket-handle .................. 85
Table C33: B and B Barrel ........................ 86
Table C34: Medial Semi-circular .................... 87
Table C35: 7% deposit, or filling, in circular pipe ........ 88
Table C36: 10% deposit. or filling. in circular pipe ....... 89
Table C37: 14% deposit. or filling. in circular pipe ....... 90
Table C38: 18% deposit. or filling. in circular pipe ....... 91
Table C39: 21 % deposit. or filling. in circular pipe ....... 92
(continued)
ix
Contents (continued)
Tables C (continued)
Tables of properties of unit sections
Table C40: 24% deposit. or filling. in circular pipe ....... 93
Table C41: 28% deposit. or filling. in circular pipe ....... 94
Table C42: 33% deposit. or filling. in circular pipe ....... 95
Table C43: 1.30 Pipe arch (corrugated sheet metal) ...... 96
Table C44: 1.35 Pipe arch (corrugated sheet metal) ...... 97
Table C45: 1.40 Pipe arch (corrugated sheet metal) ...... 98
Table C46: 1.45 Pipe arch (corrugated sheet metal) ...... 99
Table C47: 1.50 Pipe arch (corrugated sheet metal) ......1 00
Table C48: 1.55 Pipe arch (corrugated sheet metal) ......1 01
Table C49: 1.60 Pipe arch (corrugated sheet metal) ......1 02
Table C50: 1.65 Pipe arch (corrugated sheet metal) ......1 03
Table C51: 1.70 Pipe arch (corrugated sheet metal) ......1 04
Table C52: 1.75 Pipe arch (corrugated sheet metal) ......1 05
Table C53: 1.584 ASTM arch pipe (pre-cast concrete) ....1 06
Table C54: 1.643 ASTM arch pipe (pre-cast concrete) ....1 07
Table C55: 1.35 Horizontal ellipse (cor . sheet metal) .....1 08
Table C56: 1.45 Horizontal ellipse (cor . sheet metal) .....1 09
Table C57: 1.55 Horizontal ellipse (cor. sheet metal) .....1 10
Table C58: 1.65 Horizontal ellipse (cor . sheet metal) .....1 11
Table C59: ASTM Horizontal ellipse (pre-cast concrete) ...1 12
Table C60: ASTM Vertical ellipse (pre-cast concrete) .....1 13
Table C61: Narrow trapez’al channel - 0.2 to 1 side-slope . 11 4
Table C62: Narrow trapez’al channel - 0.3 to 1 side-slope . 115
Table C63: Trapezoidal channel .0 .125 to 1 side-slope ...1 16
Table C64: Trapezoidal channel .0 .25 to 1 side-slope . ...1 18
Table C65: Trapezoidal channel .0 .375 to 1 side-slope ...1 20
Table C66: Trapezoidal channel .0 .50 to 1 side-slope . ...1 22
Table C67: Trapezoidal channel .0 .625 to 1 side-slope ...1 24
Table C68: Trapezoidal channel .0 .75 to 1 side-slope . ...1 26
Table C69: Trapezoidal channel .0 .875 to 1 side-slope ...1 28
Table C70: Trapezoidal channel .1 .0 to 1 side-slope . ...1 30
Table C71: Trapezoidal channel .1 .25 to 1 side-slope ...1 32
Table C72: Trapezoidal channel .1 .5 to 1 side-slope . ...1 34
Table C72: Trapezoidal channel .1 .75 to 1 side-slope ...1 36
Table C74: Trapezoidal channel .2 .0 to 1 side-slope . ...1 38
Table C75: Trapezoidal channel .2 .5 to 1 side-slope . ...1 40
Table C76: Trapezoidal channel .3 .0 to 1 side-slope . ...1 42
Table C77: Regime trapezoidal 1.5 to 1 side-slope . . ...1 44
Table C78: Regime trapezoidal 2.0 to 1 side-slope . . ...1 45
Table C79: Regime trapezoidal 2.5 to 1 side-slope . . ...1 46
Table C80: Regime trapezoidal 3 to 1 side-slope .... ...1 47
Table C81: Regime trapezoidal 4 to 1 side-slope .... ...1 48
Table C82: Regime trapezoidal 5 to 1 side-slope .... ...1 49
Table C83: Narrow rectangular channel (free surface) ...1 50
Table C84: Wide rectangular channel (free surface) . . ...1 51
Table C85: Wide open channel (bottom friction) ..... ...1 52
Table C86: Arc invert (free surface) ............. ...1 53
Table C87: 10% concave bed river .............. ...1 54
Table C88: 5% concave bed river ............... ...1 55
Table C89: 3% concave bed river ............... . . .1 56
X
Contents (continued)
Tables C (continued)
Tables of properties of unit sections
Table C90: 2% concave bed river ...................1 57
Table C91: 1.5% concave bed river .................1 58
Table C92: 1.25% concave bed river ................1 59
Table C93: 1.0% concave bed river .................1 60
Table C94: 0.75% concave bed river ................1 61
Table C95: 0.625% concave bed river ................1 62
Table C96: 0.50% concave bed river ................1 63
Table C97: 0.40% concave bed river ................1 64
Table C98: 0.30% concave bed river ................1 65
Table C99: 0.20% concave bed river ................1 66
Table C100: 1.0 to 1 tangent river ...................1 67
Table C101: 1-5 to 1 tangent river ...................1 68
Table C102: 2.0 to 1 tangent river ...................1 69
Table C103: 2.5 to 1 tangent river ...................1 70
Table C104: 3.0 to 1 tangent river ...................1 71
Table C105: 4.0 to 1 tangent river ...................1 72
Table C106: 5 to 1 tangent river .................... 173
Table C107: 7 to 1 tangent river .................... 174
Table C108: 10 to 1 tangent river ...................1 75
Table C109: 15 to 1 tangent river ...................1 76
Table C110: Triangular open channel (modified table) ....1 77
Tables D
Values of m V and mQ deriving from the Manning equation
Table D1: Diameters 20 mm to 11 0 mm ..............1 78
Table D2: Diameters 11 0 mm to 350 mm .............1 84
Table D3: Diameters 350 mm to 700 mm .............1 90
Table D4: Diameters 700 mm to 11 25 mm ............1 98
Table D5: Diameters 1125mm to 1575mm .......... 204
Table D6: Diameters 1575mm to 2050mm .......... 210
Table D7: Diameters 2050 mm to 2650 mm .......... 216
Table D8: Diameters 2650 mm to 4000 mm .......... 222
Table D9: Diameters 4.000 m to 7.500 m ............ 228
Table D10: Diameters 7.500m to 13.50m ............ 234
Table D1 1: Diameters 13.50 m to 28.00 m ............ 240
Table D12: Diameters 28.00 m to 60.00 m ............ 247
Tables E
Values of mc deriving from the Colebrook-W hite equation in conjunction
with the Manning equation. and of Ackers’ parameter 8 for part-full flows
in circular pipes
Table El: k, = 0-003mm ....................... 254
Table E2: k, = 0.006mm ....................... 255
Table E3: k, = 0.015mm ....................... 256
Table E4: k, = 0-030mm ....................... 258
Table E5: k, = 0-060mm ....................... 260
Table E6: k, = 0-150mm ....................... 262
(continued)
xi