Hydraulic Canals Design_ Construction_ Regulation and Maintenance

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Hydraulic Canals

Hydraulic Canals

Design, construction, regulationand maintenance

Jose Liria Montanes

First published 2006by Taylor & Francis2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Simultaneously published in the USA and Canadaby Taylor & Francis270 Madison Ave, New York, NY 10016

Taylor & Francis is an imprint of the Taylor & Francis Group

2006 Jose Liria Montanes

All rights reserved. No part of this book may be reprinted orreproduced or utilised in any form or by any electronic, mechanical, orother means, now known or hereafter invented, including photocopyingand recording, or in any information storage or retrieval system,without permission in writing from the publishers.

The publisher makes no representation, express or implied, with regardto the accuracy of the information contained in this book and cannotaccept any legal responsibility or liability for any efforts oromissions that may be made.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication DataLiria Montanes, Jose.Hydraulic canals : design, construction, regulationand maintenance / Jose Liria Montanes.1st ed.p. cm.

ISBN 0415362113 (hardback)1. CanalsDesign and construction. 2. CanalsMaintenanceand repair. I. Title.

TC745.L573 2005627 .13dc22

2005013676

ISBN10: 0415362113ISBN13: 9780415362115

This edition published in the Taylor & Francis e-Library, 2005.

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(Print Edition)(Print Edition)

ISBN 0-203-01242-9 Master e-book ISBN

Contents

List of figures xiPreface to the Spanish edition xviiPreface xix

1 Hydraulic operation of a canal 11.1 Basic general principles for its calculation 11.2 Calculation of average traction 11.3 Application to the calculation of the rate of flow

circulating through a canal 41.4 Localized head losses 71.5 Variation in traction throughout the section 101.6 Stable canal forms 121.7 Subcritical and supercritical motion 131.8 Stable varied flow 151.9 Unsteady flow 17

2 Water loss in canals 192.1 Worldwide importance 192.2 Causes that affect water losses due to leakage 222.3 The way to stop leakage in a canal: Other reasons

for putting in linings 232.4 Canals that must not be lined: Drainage canals 252.5 Types of lining 262.6 Resistant side walls 282.7 Possibility of obtaining the desired waterproofness 32

3 Study and definition of the canal layout and earth movementworks to be carried out 383.1 Introduction 383.2 Basic studies 383.3 First solution fitting-in 39

vi Contents

3.4 Construction project 403.5 Planning of the construction process 41

4 Mass concrete lining 484.1 The suitability of concrete as a canal lining 484.2 Study of joints in concrete-lined canals 49

4.2.1 Construction joints 504.2.2 Longitudinal joints 514.2.3 Acceptable movement between transversal

contraction joints: Predicted movements 544.2.4 Transverse expansion joints: Their

location and expected movements 574.3 Forces that must be supported by the joints: Joint

models 634.3.1 Models for transverse contraction joints 644.3.2 Longitudinal joints 674.3.3 Transverse expansion joints 70

4.4 Quality of materials required for joints 744.4.1 Non-vulcanizable putty for joint

impermeabilization 744.4.2 Vulcanizable materials for filling joints in canals 774.4.3 Impermeabilization strips 814.4.4 Materials for filling dead spaces in joints 82

5 Construction of concrete linings 835.1 Manual lining compaction and surfacing

smoothing system 835.2 Quick assembly and disassembly formwork systems 865.3 Transverse sliding formwork systems 885.4 Longitudinal sliding formwork systems 915.5 Concreting systems for circular canals 995.6 Lining thickness 1035.7 Concrete quality 104

6 Prefabricated slab and brick linings: Rubble-work linings 1106.1 Prefabricated slabs 1106.2 Brick linings 1156.3 Rubble-work linings 116

7 Asphalt linings for canals 1197.1 General characteristics 1197.2 The fight against vegetation 120

Contents vii

7.3 Asphalt concrete linings 1217.4 The shape of the canals cross section 1247.5 Asphalt membrane linings 125

8 Plastic membrane linings 1278.1 PVC membrane linings with protective

gravel layers 1288.2 Unprotected membrane linings 131

9 Canal drainage 1389.1 The need for drainage 1389.2 Types of drainage 1399.3 Drainage for slope stability 1399.4 Studies of longitudinal drains under the bottom 1459.5 Drainage layer studies 1559.6 Analysis of those cases where the employment

of internal drainage is necessary in a lined canal 158

10 The cross section in a lined canal 16010.1 Criteria for obtaining the most economic

lined canal 16010.2 Transitions 16310.3 Freeboard 16410.4 Covered canal sections 170

11 Unlined canals 17211.1 General 17211.2 Tractive force theory 17311.3 Improving the tractive force formula 17511.4 Localized erosion: Choice of trapezoidal

transverse section 17711.5 Optimum section for an unlined canal 18011.6 Erosion at bends 18211.7 Solid flow 18411.8 Settling basins 18511.9 Concept of the Regime Theory 18911.10 Ground quality for the construction of unlined

canals 19211.11 Canals in which the ground is improved 19411.12 Ground correction: Cement-treated soil,

bentonite, chemical gel 196

viii Contents

12 Canals with peculiar problems 20012.1 Introduction 20012.2 Canal in expansive clay 20012.3 Canals constructed in gypsum ground 20412.4 Canals in loess 20612.5 Lining water-filled canals 209

13 Navigation canals 21113.1 Introduction 21113.2 Route 21213.3 Cross section 21313.4 Locks 21413.5 Flow rates, slopes and speeds 21613.6 Tow paths 21813.7 Multi-purpose canals 218

14 Watercourse crossing works 22014.1 Elevated flumes 220

14.1.1 Purpose 22014.1.2 Flow rate evaluation in watercourses 22114.1.3 Types of flume structures 22814.1.4 Hydraulic study of flumes 232

14.2 Inverted syphons 23414.3 Tunnels 240

14.3.1 Why they are needed? Shapes ofCross sections 240

14.3.2 Pressurized galleries 24714.3.3 Hydraulic operation of free level tunnels 24714.3.4 Impermeabilization problems in

hydraulic tunnels 25114.3.5 Cut and cover tunnels 252

14.4 Bridges over canals 253

15 Flow rate measurement works 25615.1 Flow rate measurement: Use of weirs 25615.2 Sharp cresterd weir measuring structures 25815.3 Triangular weirs 26315.4 Thick-walled weir measuring structures 26315.5 Propeller measuring structures 26815.6 Ultrasound measuring structures 26915.7 Flow divisors 269

Contents ix

16 Spillways 27116.1 Need for spillways: Types, locations

and capacities 27116.2 Operation of fixed-crest lateral spillways 27416.3 Functioning of the lateral syphon-type spillways 27816.4 Outlets and sluices 280

17 Height loss works 28117.1 Need for height loss works 28117.2 Functioning of the chutes 28117.3 Drops 287

18 Ditches and tertiary canals 29018.1 Special characteristics 29018.2 Tertiary canals constructed onsite 29118.3 Precast concrete tertiary irrigation canals 29318.4 Tertiary canal plan layout 29718.5 The prefabrication of inverted syphons

and turnouts 298

19 Canal regulation 30219.1 Introduction 30219.2 The traditional way of regulating irrigation canals 30319.3 Modern times problems 30519.4 Manually operated regulation gates 30619.5 Automatic regulation gates 31019.6 Hydraulically operated derivation

gates: Distributors 31119.7 Automatic hydrodynamically controlled

regulation gates 31519.7.1 Upstream constant level gates 31619.7.2 Downstream constant level gates 31919.7.3 Automatic mixed constant level gates,

upstream and downstream 32219.8 Other considerations with respect to automatic hydraulically

controlled gates 32419.9 Duckbill weirs 32519.10 Automatic electric gates in response to

annexe variations 32819.11 Data sensors 32919.12 Programmable Logic Controllers (PLCs) 33119.13 Possible automation methods 332

x Contents

19.14 Reservoirs 33419.15 Centralized control canal regulation 337

20 Mathematical models in canals 33920.1 Introduction 33920.2 The bases for mathematical canal models 34020.3 Calculation structures for mathematical

canal models 34120.4 Boundary conditions 34320.5 Model characteristics that define their quality 34420.6 Operational example of a mathematical model 34520.7 Computer applications for canal network design 348

21 Canal rehabilitation and modernization 34921.1 Introduction 34921.2 Repairing canals 35021.3 Modernizing irrigation canals 35221.4 Modernizing tertiary irrigation canals 354

22 Maintenance and conservation of canals 35622.1 Definition 35622.2 Characteristics of canals 35622.3 Types of maintenance 35722.4 Maintenance and conservation of civil works 358

22.4.1 Vegetation control 35922.4.2 Early detection of filtration 36122.4.3 Cleaning up sediments 362

22.5 Conservation of metal elements 362

23 Canal safety 366

Appendix 1 Discharge of standard contracted rectangularweirs 370

Appendix 2 Free flow discharge values for ParshalMeasuring Flume 373

Appendix 3 Standard dimensions of the Parshal flume 377Bibliography 379Index 385

Figures

1.1 Average traction 21.2 Mixed flow: spill and counter-pressure 91.3 Isotachs curves 111.4 Tractive force along the perimeter of the canal 111.5 Water surface types 162.1 Device for measuring specific leakages (according to

Florentino Santos) 242.2 Drainage canal 262.3 Reinforced concrete lining 272.4 Cross section of a retaining wall 292.5 Canal on land with a strong cross slope (Canal of Las

Dehesas (Extremadura, Spain)) 302.6 Stepped resistant wall 312.7 Reinforced concrete retaining walls 322.8 Darcys experiment 332.9 Most unfavourable cross section for leakages in a canal 342.10 Application of Darcys formula for open drains 343.1 Access ramp in the Orellana Canal 433.2 Cross sections in excavation and in backfill 443.3 Prohibitive range of spoils 453.4 Outline of machinery employed for canal construction 464.1 Joints in the Provence Canal (France) 494.2 Joint between floor and slopes 504.3 Sketch of longitudinal joints 514.4 Ground swelling Orellana secondary canal 534.5 Calagua Canal in Bella Union (Uruguay) 544.6 Location of contraction joints 554.7 Tertiary canal ruptured by expansion 584.8 Lining movement at the expansion joint 604.9 Old construction joints 644.10 Construction of alternate slabs 654.11 Stepped construction joint 66

xii Figures

4.12 Contraction joint 664.13 Joint for lateral walls of canals 684.14 Joint for Burro Flume 694.15 Burro Flume (Orellana Canal, Spain) 694.16 Strip for longitudinal joints 704.17 Longitudinal joint with a plastic strip 704.18 Simplest expansion joint 714.19 Copper sheet-type joint 724.20 Joint with elastic strip 734.21 Problem of a strip horizontally positioned 734.22 Piece for creep test 764.23 Adherence test 775.1 Spreading the concrete with a plank 845.2 Alberche Canal (Spain) 855.3 Steel beams to support the formwork 875.4 Panel of formwork 875.5 Sliding formwork 895.6 Concreting intermediate slabs with a sliding formwork 905.7 Machine with sliding formwork 905.8 Longitudinal sliding machine for canal construction 925.9 Longitudinal joints constructed with a disc saw 935.10 Construction of the Navarra Canal (Spain) 935.11 Trimming machine sketch running on caterpillar 955.12 Trimming machine excavating the whole cross section of

the Tajo-Segura Canal (Contractor: Ferrovial S.A.) 965.13 Applying curing paint 985.14 Machine for circular canals 1005.15 Sliding formwork for circular canals 1015.16 Barragn rimming machine 1025.17 Zjar Canal (Spain) 1036.1 Prefabricated slab lining 1126.2 Unacceptable slab installation 1136.3 Unacceptable excavation for prefabricated slabs 1136.4 Canal V Orellana Perimeter 1146.5 Joints between slabs 1156.6 Lining with two layers of bricks 1156.7 A small brickwork canal in Argentina 1166.8 Possible cross section with high ground water layer 1176.9 A small canal in Argentina 1177.1 Permeability of asphalt concrete 1238.1 Cross section of a canal with buried membrane 1298.2 Sheet anchorage 1328.3 Sheet anchorage in Lodosa Canal 1338.4 Overlapping and flow direction 134

Figures xiii

8.5 The Chongn-Subeybaja Canal with polyethylene lining 1358.6 Leaks in the Orellana Canal 1368.7 Impermeabilization of the Orellana Canal with PVC sheets 1369.1 Canals located in different morphologies 1409.2 Protection ditches 1419.3 Inclined drills to drain heterogeneous soils 1429.4 Upper part of lining 1449.5 Backfill destroyed by drainage problems 1459.6 Canal with drainage pipe 1479.7 Drain gradient 1489.8 For drain length calculation 1499.9 For drain length calculation 1529.10 For drain length calculation 1539.11 For drain length calculation 1549.12 Using the canal as drain outlet 1559.13 Drainage layer 1569.14 Drain layer calculation 157

10.1 Circular cross section of the Zjar Canal (Spain) 16110.2 Optimal trapezoidal section 16210.3 Transition of trapezoidal sections 16310.4 Transition between a trapezoidal section and a smaller

rectangular one 16410.5 Transition between a rectangular section and a circular

one (Castrejn Canal, Spain) 16510.6 Grashoff Formula 16710.7 Freeboard curves 16910.8 Torina Canal (Spain) 17111.1 Forces acting on a solid particle 17811.2 Cross sections of equal resistance at all their points 18111.3 Stirred sugar in a glass of water 18211.4 Transversal circulation and erosion at bends 18311.5 Gate arrangement in front of a settling basin system 18611.6 Inlet to the Huaral Canal (Peru) 18711.7 Settling tank for the Huaral Canal (Peru) 18911.8 Kennedy formula, modified by the Bureau of Reclamation 19011.9 Thick compacted earth lining 19511.10 Calagua Canal (Uruguay). Lining of cement-treated soil 19812.1 Cross section of the Subeybaja-Javita Canal in Ecuador 20212.2 Calanda Canal (Spain) 20312.3 Canal above the ground, with foundations in gypsum

(Illustration of Canal Bajo for water supply to Madrid) 20512.4 Prefabricated pieces (Ebro Canals, Spain) 20812.5 Reinforced concrete prefabricated pieces (Ebro Canals,

Spain) 208

xiv Figures

12.6 Lining constructed under water in Imperial Canal ofAragon (Spain) 210

13.1 Imperial Canal of Aragon 21213.2 Lock implementation 21613.3 Cacique Guaymalln Canal (Mendoza, Argentina) 21914.1 Structure for passing water over the Carrizal Canal 22114.2 Graph for working with the Gumbel law 22714.3 Flume on top of vaults 22914.4 T type flume in the Tajo-Segura water transfer 22914.5 Thrusts in a beam flume 23014.6 Alcollarn Flume (Spain) 23014.7 Flume with side walls braced by reinforced

concrete beams 23114.8 Tardienta Flume (Spain) 23214.9 Alcandre Flume (Spain) constructed with pre-stressed

concrete 23314.10 Gargaligas Flume (Spain) 23314.11 Rectangular cross section for syphon pipelines 23614.12 Simplest and traditional shape of syphon inlet or outlet 23714.13 Syphon inlet or outlet with less head losses 23814.14 Trapezoidal cross section with two vaults for tunnels 24114.15 Cross section of the Atazar Canal for water supply 24214.16 View of the Atazar Canal for water supply to Madrid 24314.17 Egg-shaped cross section for hydraulic tunnels 24314.18 Protodiakonov theory of ground loads 24514.19 Reinforced concrete lining of the Transvase Tajo-Segura

Canal 24814.20 Flow rate law in circular tunnel sections 24914.21 Flow rate law in Atazar Tunnel section 24914.22 Flow rate law in egg-shaped tunnel section 25014.23 Bridge over a canal, using their standing side walls as

abutments 25314.24 Lateral roadway of the Trasvase Tajo-Segura Canal (Spain) 25414.25 National Water Carrier in Israel 25415.1 Sharp crested weir 25715.2 Thick crested weir 25715.3 Prefabricated sharp crested weirs 26215.4 Triangular weir 26315.5 Plan and elevation of a Parshall Flume 26515.6 Chart for computing the flow rate correction in a 30.5 cm

Parshall Flume with submergence 26615.7 Parshall Flume made in PVC Bella Union (Uruguay) 26815.8 Flow divisor in San Martn Canal (Mendoza, Argentina) 27016.1 Lateral fixed crest weir Sobradinho Canal (Brazil) 272

Figures xv

16.2 Syphon Spillway (Einar) 27216.3 Different locations for a spillway 27316.4 Water surface when overflowing lateral spillways 27516.5 Spillway syphon with fixed feeding level Big Thomson

Canal (Colorado, USA) 27917.1 Villagordo Chute (Picazo Canal, Spain) 28217.2 Waves in San Martin Canal (Argentina) 28317.3 Turn out in a chute San Martin Canal (Argentina) 28417.4 First part of a chute 28517.5 Sketch of a drop (Bureau of Reclamation) 28818.1 Formwork for small canals and ditches 29318.2 Cross sections of prefabricated tertiary canals 29418.3 Cracking of a tertiary canal 29518.4 Impermeabilization of joints for tertiary canals 29618.5 Prefabricated syphon inlet 30018.6 Syphon outlet reinforcement 30019.1 Manual gate 30719.2 Gate guides formed by two thin plates 30819.3 Manual gate for submerged orifices 30919.4 Gates with counterweight 31019.5 Orifice of a derivation gate 31219.6 Level/flow-rate curve of a distributor 31319.7 Distributors battery and a regulation gate (Orellana Canal) 31319.8 Two-baffle distributor 31419.9 Level/flow-rate curve of a two-baffle distributor 31519.10 Upstream constant level gate 31619.11 Canal regulated with constant upstream level gates 31819.12 Downstream constant level gate 31919.13 Canal regulated with downstream constant level gates 32119.14 Bottom turnout with a downstream constant level gate 32219.15 Sketch of a mixed gate (Einar) 32319.16 Mixed gate in the ToroZamora Canal (Einar) 32419.17 Duckbill in Orellana Canal 32619.18 Duckbill plan (Liria and Torres Padilla Collection) 32619.19 Safety device in Guarico Canal (Venezuela) 32819.20 Electric control gates in the Genil-Cabra Canal (Spain) 33419.21 Pressure chamber for a hydroelectric plant 33720.1 Water level oscillations turbining 12 hours a day 34620.2 Water level oscillations turbining 12 hours a day 34720.3 Water level oscillations turbining 12 hours a day 34721.1 Pisuerga Canal (Spain) 35021.2 Slope slippage of a canal in Santa Elena (Ecuador) 35122.1 Vegetation in Huaral Canal (Peru) 36022.2 Dehesilla Syphon in Orellana Canal 363

xvi Figures

23.1 Fenced-off area at the entrance to Tunnel 2 on the OrellanaCanal 367

23.2 Step ladder at the exit of the Talave Canal tunnel 36823.3 Ropes stretched over the canal from side to side with

hanging leather straps 368

Preface to the Spanish edition

Although the section on canals is a very important topic within the subjectof Hydraulic Engineering, the technical literature that has been written isaimed more directly at other work, such as dams, hydroelectric plants,piping, drinking water supply to towns, etc.There are many excellent books on canals from the theoretical hydraulic

performance point of view, but publications from the engineering design,construction and handling points of view are few and far between.Many engineers, when starting out on their professional careers within

this specialty, needed and could not find a text that resolved theirdoubts about details, that gave hints as to how to obtain complementarydocumentation and, above all, that gave an overall view of the subject.By dint of asking first some and then other people, by searching ceaselessly

for the most diverse bibliography and having made countless mistakes, itseemed to us that the writing of this book could be very useful.It is aimed at hydraulic engineers and therefore it involves a large amount

of theoretical knowledge on this science, without which a large part of itsusefulness would be lost. Notwithstanding this, when it seemed to us tobe useful to the reader for references to the theoretical basis on which apoint is founded to be made, we have not hesitated in quoting them, evendeveloping some mathematical demonstrations which, as they are not veryusual, could run the risk of becoming forgotten. Likewise, the first chapterincluded serves as a reminder of the most important points of Hydraulicsto lay out the background for all the problems studied in the book.We have tried to fill the book with the experience acquired in 45 years

of professional work, carried out in many different countries, sometimesthrough participative experience and at other times through observation.Also, everything that has been learnt from study, from conversations withother technicians and a very important point from the questions that ourcountless students have asked us is included. To all those who have helpedus to learn something (engineers, students, builders, water users, etc.) wewould like to express our deepest gratitude. We believe that, as in certainbranches of Civil Engineering (for example in the calculation of Structures)

xviii Preface to the Spanish edition

there are physicsmathematical theories that lead to calculations that arevirtually exact, on the subject of Canals there is still a gap in the scientificstudy that should be filled in to be used as a basis to the calculation anddesign of certain building elements. We must fight to replace a recipe ofmethodologies, which is passed on from one to another, with a theoreticalbasis that is scientifically proven. On this aspect, we have spared no effortin analysing and justifying certain design criteria, and therefore we believethat this book has some original points, which we have had the opportunityto check out in practical experience.

Preface

The reasons for writing this book, which were given in the preface to theSpanish edition, continue to be perfectly valid. In fact, we believe that ithas been of great use to many Spanish and Latin American engineers and,because of similarity in languages, also to quite a number of Portuguese-speaking engineers. However, there are many hydraulic engineers through-out the world who do not understand Spanish and for this reason we feltit necessary to produce this English edition.The time that has elapsed between the two editions (some three years)

has allowed the opinions of many experts to be received and this enabled usto continue analysing what we could call Canal Engineering. We feel thatthere is a significant demand in the engineering field for information on red-hot issues, such as canal operations, their rehabilitation and maintenance.For this reason we have enlarged the chapters referring to these subjects.However, we have not been able to escape from the very evident fact thatcanal design and construction is a much more developed technical themethat has led to a large part of the book being dedicated to it.We want to point out that the sole purpose of this book is to be of help

to engineers working on Canals. But the possible problems are so manyand so diverse, and may be so complicated that the book cannot act as asubstitute for the knowledge and good judgement of the engineer who hasto take decisions under his own responsibility, without placing it upon theauthor of this book.Looking back on our long professional life, we can see such a large

number of people who, consciously or not, have helped us in acquiring theknowledge included in this book that we find it impossible to name themall, without running the risk of forgetting some. We would, therefore, liketo take this opportunity of offering all of them our most sincere gratitude.

xx Preface

Professor Jos Liria Montas has a Ph.D. Degree in Civil Engineering andis also a retired university professor.His professional career has almost always been involved in hydraulic

works and very especially dedicated to canals employed for irrigationspurposes, as well as hydroelectric installations and drinking water supplies.He has worked on the design, construction and operation of canals for theHydrographic Confederation of the Guadiana River for many years and asProject and Works Manager for the Isabel II Canal, Madrid.He has also been deeply involved as a consulting engineer, not only in

Spain, but also in many other countries, such as Venezuela, Brazil, Ecuador,Uruguay, Argentina and Peru, etc. This experience has provided him witha wider, more generalized view of the problems that can arise in canals.He has written several books on the piping of water and others related

to canals, at the moment only in Spanish, such as Town Water SupplyNetworks and Modelling Special Works in Small Canals.His double activities both as a professional and in teaching have meant

that he has had to analyse canals, not only from his own personal experi-ence, but also from the point of view of the reasoned justification for thesolutions to be adopted.He is currently the Secretary for Spanish Committee on Irrigation and

Drainage.

Chapter 1

Hydraulic operation of a canal

1.1 Basic general principles for its calculation

A canal is nothing but an open artificial channel used to carry water bymeans of a man-made river.The water circulating inside a canal runs at a certain speed, producing

mechanical forces between the water and the walls and the bottom of thecanal due to its rubbing against them.The influence is mutual; on the one hand, the wet inner surface of the

canal rubbing on the water tends to slow down its movement. On the otherhand, the water tends to erode the walls and bottom of the canal, and theenergy of the moving water is capable of carrying solid particles that havebeen either broken off from the canal itself or entered the canal otherwise.The force of the water on the walls and bottom of the canal is a shear force

and is usually called an erosive force (because of its ability to erode the canalby pulling off particles) or tractive (because of its ability to carry the saidparticles). By the principle of action equal to reaction, the force of the wetperimeter of the canal rubbing on the water is equal to the former and istherefore called by the same names.

1.2 Calculation of average traction

From the theoretical viewpoint and especially the engineering point of view,it is very important to be able to have an idea, albeit only approximate,of what the traction is in a given section of a canal. Suffice it to thinkthat if the resistance to erosion (which can be measured experimentally forthe various types of soil) is greater than the erosive force, there will be noerosion. The opposite is also true.As we will see, traction is not constant throughout the entire inner perime-

ter of a cross section of a canal; there are points in a single section inwhich it is much less than in others. Nevertheless, in the first attempt, letus calculate average traction along the inner perimeter of a single section,i.e. that uniform rate of traction that produces an effect on the water closeenough to that which would be produced by the real rate of traction.

2 Hydraulic operation of a canal

Erosive force

A = Cross-sectional area

P = Wetted perimeter

s = Gradient

= Specific weight of the liquidt = Tractive or shear force

F = Force moving water

R = Hydraulic radius = A/P

Figure 1.1 Average traction.

Figure 1.1 is a schematic representation of a section of a canal with asloping floor in relation to the horizontal plane, measured by angle a, thetrigonometric tangent of which we shall call s.For our estimate we shall consider a stretch of moving water, of length

L, which is actually prismatic in shape.Active thereon are forces that tend to compel it to slide in a downhill

direction (the component of its weight parallel to the canal floor) and otherforces that tend to brake its movement (the force of the terrain rubbing onthe water, which is equal to the traction).If we call A the area of the cross section, P the wet perimeter of this cross

section, and define the hydraulic radius R as the quotient A/P , the volumeof the prism formed by the section of the canal is A L.We note that the hydraulic radius has the dimensions of a length.Calling the specific weight of the liquid circulating through the canal

(for us this will always be water, i.e. = 1000kg/m3, although in a generalcalculation it may be that corresponding to any liquid), the weight of theprism will be A L .That weight acts as a vertical force, which is divided into two, one

perpendicular to the bottom or floor of the canal (and which is resistedthereby), and the other parallel to the floor, whose value is A L sin a.This is precisely the force that tends to move the section of water in adirection parallel to the slope of the floor, i.e. downhill.

Hydraulic operation of a canal 3

If we call t the average rate of shear force by surface unit, which wesuppose is constant throughout the entire perimeter of the canal section,for purposes of simplification, the force that opposes the movement of thewater, as a result of the terrains rubbing against the water, will be t P L.The section of water considered may be moving at an increasingly faster

rate of speed, an increasingly slower rate of speed, or at a uniform rate. Itall depends on the relation between the forces that tend to move it or slowit down.The case most frequently studied in canals, at least in an initial approach,

is that of uniform movement. This we define as that in which the waterthroughout the canal neither speeds up nor slows down; therefore, themolecules in the stretch travel at the same rate of speed and the water prismretains the same form throughout. The surface level of the water must beparallel to the floor, in order for the section being considered to adopt thesame condition and form as that of the following section, which space willbe ocuppied by the next section.In order for this constant rate of speed to occur, the difference between

the forces that cause the water to move and those that slow it down must bezero, so that there will be no increase in the rate of speed (recall that force isequal to mass by acceleration), or, stated otherwise, A L sin a= t P L.The grade in canals is usually very slight (for example, 1020 cm of drop

in level per kilometre in very large canals, or from 80100 cm/km in themost frequent size canals). For such small values the angle in radians isknown to be the same as its trigonometric tangent or its sines; therefore,we may say sina= s.By substituting this value, and by simplifying and recalling our definition

of hydraulic radius, the former equality may be expressed as R y s = t,which gives us an initial value for average traction.As stated earlier, we generally only manage water. Therefore, upon sub-

stituting the value for , we will have t = 1000 R s, a very useful formulaand one of great importance, as we will see further on.This means that if, for example, we have a canal with a 20 cm/km slope,

i.e. a gradient of 2/10 000 and a hydraulic radius of 3m (a large canal isinvolved), the tractive force will be

1000kg/m33m00002= 06kg/m2

If the canal had a gradient of 90 cm/km and a hydraulic radius of 1.10m,the traction would be:

1000kg/m3110m00009= 099kg/m2

If the terrain has a resistance of over 06kg/m2 in the first instance or099kg/m2 in the second, there will be no erosion; otherwise, there will be.


1.3 Application to the calculation of the rate offlow circulating through a canal

The interrelationship between the erosive force of the water on the onehand and the force of the land rubbing on the water on the other is the basisfor our ability to calculate traction. Yet equally it enables us to calculatethe velocity of the water that produces such force.The study of hydraulic theory teaches that head losses (or losses in height

of the hydraulic grade line) of the water are different depending on whetherthe water movement is laminar or turbulent. In the first instance, the headloss of the water is proportional to the speed. In the second, it is proportionalto the square of the velocity.A typical example of laminar movement is that of underground water

approaching a well, or that of slow moving water in very small diameterdrip irrigation tubes, whereas water that runs in canals and ditches is almostalways turbulent.Therefore, the equation that will give us the tractive force in a canal in

function of speed v will be:

T = k v2

Substituting therein the value obtained for tractive force, we will have:

T = c R s = k v2

One deduces thereby that

V = c R s1/2

which enables us to calculate the speed in a canal in terms of its hydraulicradius and gradient, and is the well-known Chezy formula, in which c

is a coefficient that varies essentially depending on how rough the canalperimeter is, which we shall simply call c from now on.But the value c used in estimating the head loss caused by rubbing in the

canal also depends, as can be easily understood, on the shape of the crosssection of the canal; therefore, giving it a fixed value, dependent only onthe roughness of the walls, is merely a first approach.In order to better attune the formula of speed and bearing this concept

in mind, attempts have been made through laboratory studies and studiesof actual canal cases to obtain values of the c value in the Chezy formulathat somehow includes the shape of the canal, in addition to the roughnessof the walls.It is easily apprehended that a simple parameter that varies with the shape

of the section, and to a certain extent that helps classify the properties of itsdifferent basic forms, is the hydraulic radius. For very wide canals with littledepth, the hydraulic radius is quite similar to the depth y. If it is a matter of


a rectangular section the width of which is double the depth, the hydraulicradius is 05y, a value that drops to y/3 for the square cross section. As aresult, the hydraulic radius is a coefficient multiplied by the depth. When thecanal becomes very deep and narrow, such coefficient tends to drop to zero.All canal calculation formulas are basically the same, for they are all

derived from the Chezy formula, substituting a value based on the hydraulicradius for the coefficient of roughness c.Manning proposed substituting the following formula for the value c in

the Chezy formula:

c = 1/n R016

which gave way to the formula bearing his name, which is:

V = 1/n R2/3 s1/2

in which n is a coefficient of roughness.Bazin proposed the following:

c = 871+/R

This resulted in the formula given below that bears his name, in which isthe coefficient of roughness:

= 87 R s

1+/RIn the same way, many other researchers and engineers (e.g. Kutter,Pavloski, etc.) proposed diverse formulas, based on approximate values forc in the Chezy formula according to diverse expressions based on R.The classic values of the coefficients of roughness in the prior formulas

are the following (46):

Bazins Formula

Coefficient ofroughness ( )

Plaster or layer of very good cement. Brushed plank. Sheet plateswithout rivets, etc. All with straight lines and clean water

0.06

The same case as above with rough water and medium-radius curves 0.10Cement layer less refined than in the prior case Brushed plank but

joined. Riveted steel plate. Lining made with cutstone. Not widecurves. Clean water

0.16


(Continued)

Coefficient ofroughness ( )

Cement plaster careless made. Plank not brushed, with joints.Unlined canals with excellent construction and maintenance, withbottom and slopes without vegetation. Wide Curves. Bottomwith scarce sediment

0.36

Gun cement, etc. 0.40Concrete walls with no outer layer, with protruding joints. Slime or

moss on the walls and bottom. Tortuous design. Covering withregular stone work

0.46

Uniform sections on land or covered with gravel, no vegetation, andwide curves. Irregular stone work; smooth floor with mud deposit

0.85

Well preserved unlined canals; smooth walls or flat floor with lowvegetation on the walls. Old stone work lining and muddy bottom

1.00

Unlined canals, with low weeds on the bottom and walls. Rivers andstreams with irregular course but without vegetation

1.30

Unlined canals, abundant vegetation, erosion and irregular depositsof gravel. Neglected maintenance

1.75

Poorly maintained canals, with unconnected banks; canals withvegetation making up large part of the section

2.30

As a reference, we note that the Standards for the Design and Construc-tion of small Irrigation Canals, published by the then Spanish Ministry ofPublic Works, stipulated that the design of concrete irrigation canals built insitu and manually should be done with Bazins formula and 0.30 coefficientof roughness.For Mannings formula, and according to the same source (45), the fol-

lowing values may be used:

Mannings Formula

Coefficient ofroughness (n)

Very smooth layers of plaster 0010Ordinary layers of plaster, coarse wood 0011Packed-down concrete, good stone work 0012Regular concrete, masonry 0013Used metallic ducts, regular stone work 0017Fine gravel, stone work in poor condition 0020Stone-free natural canals and rivers 0025Natural canals and rivers with stone and grass 0030

It should be pointed out that some books and authors, in using Manningsformula, place the roughness coefficient n not in the denominator but in the


numerator. Actually we are then in Stricklers formula and the coefficientsto be used are logically the inverse values of those given for Manning.Once the coefficient of either Bazin or Manning has been chosen, if one

wants to determine the equivalent coefficient in Chezys formula, one needonly introduce the coefficient selected in the matching formula among thosementioned and that links Chezys coefficient with that of Bazin or Manning.The value that multiplies to

R s1/2

is that of the coefficient of Chezy.

1.4 Localized head losses

Localized head losses at given points are caused by water turbulence atmore or less manifest obstacles scattered throughout the canal.As explained earlier, the normal motion in canals is turbulent and head

losses are proportional to the square of velocity and therefore respond tothe general formula P = k v2. What is needed is to know what value shouldbe adopted for k in each case.The most frequent points where load losses occur are curves.Boussinesqs formula is:

J = 2

R c2 1+34

br

and is applicable for calculation, where

J is the total hydraulic slope by unit length in curvev is the speed of water, in m/secR is the hydraulic radius of the canal section, in mc is the Chezy coefficientb is the maximum width of the canal sectionr is the radius of the curve.

It should be pointed out that the term v2/R c2 is the gradient (according toChezys formula), which therefore is known in the canal we are designing.The sum in the second parenthesis indicates the hydraulic gradient excesscaused by unit of length in the curve and which must be added to the normalslope.This means that the loss of total load is figured by multiplying the value

given by the formula by the length of the curve.The loss due to the curve effect increases with the square root of the quo-

tient b/r. This makes it advisable to adopt large radii not less than five times


the width. The square root will then be less than 0.44 and the 3/4 factorreduces the loss from the loss of curve load to 0.33 of the normal slope.As the length of each curve, measured in kilometres, is very small (we

mentioned earlier that the normal slope losses per kilometre in canals arevery slight), the losses in absolute value are usually very small on eachcurve, except in cases of high-velocity sections, which exist in canals forhydroelectric use, but are infrequent in irrigation canals.Therefore, it is usually acceptable in many instances not to take into

account the localized losses on curves and include them in an average valuethroughout the entire canal, based on reasonably increasing the roughnesscoefficient of the canal. Nevertheless, there will be instances when theindividual calculation will be advisable, because of either high speeds orvery small radii.Another source of localized losses are the syphons. Since these will be the

subject of a special study to be made further on, we will not discuss theircalculation until that time.Section changes are frequent in canals and often go hand in hand with

changes in speed. The load losses in these transitions are expressed by thegeneral formula:

P = k v21v22where v1 and v2 are the two rates of speed. The value of k depends on thetype of transition and its length.As a general rule, it can be said that the length of the transition should

be about five times the difference in maximum widths of the canal, whichis the same as saying that the total angle of transition is some 22 or 25degrees. Under these conditions the losses are slight.When the canal narrows and the length of transition meets the prior

condition, the head loss is almost none.To the contrary, a less favourable case is the widening of the canal. Even

in cases of smooth widening, values of the order of 0.350.50 must beassigned to the coefficient k.Lastly, the gates are a source of other localized losses in canals. Naturally,

one of the purposes of the gates is to more or less intercept the passageof water when they are closed or semi-closed, which is equivalent to theinsertion of a strong head loss. But at this moment we are referring insteadto the losses caused even when the gates are totally open, due to the sectionchanges made in the canal for its implementation. In each instance, thecalculation should be made bearing in mind the section variations and howbrusque the transition is, in accordance with what was said earlier andknowledge drawn from books on hydraulic theory, which will have to beconsulted in some specific instances.In the case of partially closed gates, the water upstream stops flowing

and the water level differs depending on the conditions downstream.


The formula that gives us the flow circulating through a submergedhole is:

Q= c A 2 g h1

in which

Q is flow in m3/secA is area of the hole in m2

g is acceleration due to gravity = 98m/sec2h1 is the depth of the axis of the hole under the water-free level above,if the exit is free or else the difference between upstream and down-stream water level if the exit of the jet is submerged.

c is a contraction coefficient which, in the absence of other criteria,may be about 0.6 or 0.7 (89).

Gates may either be submerged (like outlets) or not.When the opening they cause is a submerged hole, the prior formula is

applicable. Calling y and yy2 the upstream and downstream water depths,respectively, measured with the same datum, the applicable formula is:

Q= c A 2 g y2An important case is that in which a structure inserted in the canal causes

a difference in level between upstream and downstream waters, leading toa flow of water through the obstacle that may be broken down into twoparts: one that must overcome the pressure of the downstream level andanother that overflows freely. (For example, the pillars of a bridge placed inthe water, or a submerged dam above which the water passes.) (Figure 1.2).In this case, a close enough estimate may be made of the flow running

at counterpressure by means of the formula just cited of submerged orifice

Upstream level

Downstreamlevel

y y2

y2

y

Q2

Q1c

Figure 1.2 Mixed flow: spill and counter-pressure.


and the free-falling flow of the upper part, by means of the Weiz formula,which is:

Q= cL y23/2

in which c is a coefficient of about 2.00.

L is the useful width of the canal at that pointy and y y2 are the depths upstream and downstream of the obstaclerespectively.

At times grids must be placed at the entrance of the canal, in front oflarge syphons, etc. They are usually inclined to facilitate cleaning.The formula for the head loss is:

h= b sin(d

a

)4/3(2

2g

)

in which

h is head loss is the angle of the grid with the horizontald is the diameter of the bar, in cma is the free light between bars in cmv is the velocity in the vertical section prior to the grateg is the acceleration due to gravityb is the coefficient depending on the shape of the braces, as follows:

b = 179 if round in shapeb = 242 if rectangular in shapeb = 167 if rectangular with rounded endsb = 076 for airplane-wing shape.

1.5 Variation in traction throughout the section

The speed of water is not uniform in the entire cross section of the canal.Rubbing against the walls makes the water closest to the latter move moreslowly. The braking effect is gradually transmitted to the water farthestaway until the highest-speed area is reached.The speed deduced from the aforementioned formulas of Chezy, Man-

ning, Bazin, etc. is the average speed.If the points of the same speed in the cross section of the canal are joined

into a line t, the resulting curves are called ISOTACHS (in Greek this meansthey have the same speed) and may be as shown in Figure 1.3.


1.000.900.800.70

Figure 1.3 Isotachs curves.

If we imagine we are tracing the family of curves orthogonal to the iso-tachs, we will have the canal divided into a series of primary canals borderedby two contiguous orthogonal lines, the bottom and the surface of the canal.Each of these primary canals is characterized by the fact that the water

it carries rubs only against the floor of the canal, since laterally it borderson another canal and at each point of contact, the water particles of eachone travel at the same rate of speed (because they are in the same isotach),without either one slowing down the other.For each one of them the traction formula t = 1000 R s is still valid. But if

the canal is regular in shape, the sections of each primary canal have a widththat varies little and is relatively similar from one to another; therefore, thesize of their surface is approximately proportional to the depth of each canal.Thewet perimeter, which, as indicated earlier, is limited to the part in contactwith the floor, varies little from one primary canal to another. As a result, thehydraulic radius of each one is almost proportional to the respective depths.The tractive force for each one is equal to t = 1000 y s/ cos, where y

is the depth of each one and the angle of the slope.The result is, speaking in fairly approximate terms and as proven exper-

imentally, that the traction in a trapezoidal canal increases on the slopes ina lineal manner from zero in the upper part to a maximum value at a pointclose to the bottom, where it is almost constant (Figure 1.4, according tostudies conducted by the Bureau of Reclamation).

11.5

11.5

b

y

0.750 ys

0.970 ys0.750 ys

Figure 1.4 Tractive force along the perimeter of the canal.


In the areas next to points where the bottom joins the slopes, there isa notable decrease in tractive force. The reason is that at those points thewater particles are exposed to a great deal of rubbing (at the slope and thebottom), and therefore they move at very little speed (which is reflected inthe shape of the isotach curves). The decrease in speed, as we already know,causes a decrease in tractive force (shear stress).

1.6 Stable canal forms

Tractive force (shear stress) is different at each point of the cross section ofthe canal and is known, as we have just seen. But the stability of the particleson the canals perimeter depends both on erosion caused by tractive forcesand on the stability caused by the incline of the area where the particles arelocated. Obviously, the particles on the inclines, which may roll downhill,are in a worse situation than those on the bottom, which are on a morestable, horizontal surface.From the start one guesses that the shape of the cross section of an unlined

canal, in which all points have the same stability (stable canal form), is acurved surface that near the bottom (where the depth and tractive forceare greater) has a very mild transversal slope, next to the horizontal line inorder to give it greater stability. To the contrary, in the lateral areas nextto the bank of the canal, the water depth and the tractive force are verysmall, and therefore the slopes are more inclined.There have been many authors who have studied the stable canal form.

For example, Henderson (49) or Leliavsky (60) who concludes that itsequation is as follows

y = k cosx/cwhere x and y are the coordinates of any point in its perimeter with respectto rectangular axes originating at the centre of the free surface of the canal.The values k and c are constants that depend on the maximum flow andthe angle of rubbing against the terrain. We will go into this more deeplyin Sections 11.4 and 11.5.The shape of the stable cross section is therefore that of the function

cosines. The parabolic forms and, even more so, those of incomplete circulararc are quite similar, and, therefore, it can be said, in approximate terms,that the latter are very stable, making this one of their advantages.In strictly theoretical terms, the ideal would be to have unlined canals

(which are those most affected by tractive forces) with stable forms. Thiswould be like having houses with pillars and beams designed with the samesafety coefficient instead of, for example, having beams with too muchresistance and others with a strict degree of resistance. Still, there are otherreasons for not always adopting stable forms, which we will study in duecourse.


1.7 Subcritical and supercritical motion

A disturbance in the water of a pool (the waves caused by throwing a stoneinto the water, for example) is transmitted by the so-called celerity (wavevelocity), which in theoretical hydraulics is equal to

g y, where g is the

acceleration due to gravity and y is the water depth.If, instead of a pool, the question is a channel of moving water, any

disturbance in the water at any point in the channel is transmitted down-stream at a speed equal to the sum of that of the canal plus the wave speed,and upstream at a speed equal to the difference between the wave speedand that of the canal itself. But if the speed of the canal is greater thanthe wave speed the disturbance cannot be transmitted upstream, since thegreater speed of the canal drags the disturbance downstream.This property is well known but is essential in order to be able to analyse

the variation in the surface of a canal. If the rate of speed is slow (i.e. lessthan the wave speed), the temporary disturbances caused by gates, derivativeintakes, change in the operation of turbines, etc. influence in a downstreamto upstream direction, and, therefore, the study of the variation in thesurface of the canal should be made beginning downstream.If it is a matter of a section of canal in supercritical motion (speed higher

than celerity), the upstream part suffers no influence at all from temporaryvariations in the downstream area; quite the contrary, it is the upstream partthat governs downstream movement and, therefore, the study of surfacevariation should be made in the direction of the water movement.In a canal with exactly the critical rate of speed (equal to celerity), the

waves of the possible disturbances would travel in the direction of the water,but the wave part that tends to move upstream would have a stationaryfront and would remain immobile, since its rate of speed would be equal toand contrary to that of the canal.The critical rate of speed is

g y, in which y is the critical depth. The

critical rate of speed, if the cross section of the canal is not rectangular, isthe same as the former but for a fictitious average depth which is A/T , inwhich A is the area of the section and T the greatest width. In other words,it is

g A

T.

An interesting concept is that of the critical depth: that for which theresulting speed in the canal, for a predetermined rate of flow, is the criticalspeed. Assuming a predetermined water depth, the critical slope is thatwhich originates the critical speed.If, in the design of the canal, the slope goes from values that cause a

low rate of speed (subcritical) to others that cause a high rate of speed(supercritical), the change always occurs at a point where the existing rateof speed is the critical one. If possible, the canal should be designed in sucha way that the critical speed occurs at an appropriate point, which is calledcontrol section. See Section 15.4.


If, to the contrary, the water goes from a supercritical to a subcriticalrate of speed, this almost always occurs by means of the formation of ahydraulic jump (see Section 15.4), and its study is found in virtually all theliterature on hydraulics (15), (16), (49), (98).The functioning of hydraulic jump is based on two fundamental equa-

tions: the preservation of the water mass (what comes in goes out) and thepreservation of the amount of movement, since there are no exterior forcesto the jump, just the interior forces that act between the two parts with adistinct depth.If we call y1 and y2 the water depths in metres before and after the

hydraulic jump, q the rate of flow per metre of width in m3/sec. (we areassuming a rectangular canal), the formula that relates the two depths is

y2 =y12

[1+

1+ 8q

2

g/y31

]

The water depth y2 is called a conjugate of y1 and is necessary in order for thehydraulic jump to occur. If it is smaller, the hydraulic jump does not occurand if it is greater, the hydraulic jump is drown and it is called submergedjump. For canals with trapezoidal cross section, the formulas are morecomplicated and not customarily used in practice since an approximatecalculation with equivalent rectangular sections is sufficient. At any rate,they can be seen in the literature on theoretical hydraulics (35), (98).The hydraulic jump may be successfully formed at a predetermined point

in the canal (if there is supercritical speed and the water depth downstreamis less than the estimated conjugate) by lowering the canal floor to makethe water depth somewhat greater than the required conjugate depth (it isalways a good idea to adopt a safety factor).The length of the hydraulic jump depends on the Froude number, and

is always from 3.2 to 5.5 times the conjugate water depth downstream.An interesting study on details of the hydraulic jump can be seen in anexcellent work by the deceased engineer Luis Torrent (93). On the otherhand, in canals, which are linear works, there are almost always enoughlength available. At any rate, if one wants to know more precisely the lengthof the hydraulic jump, there are publications that give suitable charts (29).The hydraulic jump is generally the best method for lessening the kinetic

energy of a current of water and is, therefore, the appropriate systemfor connecting the end of a reach of steep slope with a mild-slope reach,thus avoiding possible erosion. Nevertheless, the percent decrease in energydepends on the nature of the hydraulic jump. In the case of canals, whoserapid sections usually have Froude numbers of from 1 to 3, the energy loss isno more than 30%, less than those obtainable in dam spillways, where theFroude numbers are quite a bit higher. Let us recall that the Froude numberis F = V1/g y105, in which V1 is the velocity and y1 the depth of water.


It may be said a priori that if the hydraullic jump is covered with water,the rate of energy loss will be less. In the publicationsmentioned earlier, thereare methods for figuring the possible reduction in kinetic energy exactly.

1.8 Stable varied flow

Using the formulas cited in Section 1.3, regarding levels and flows andlocalized losses of charge, a canal can be designed with a predetermined,uniform flow (with the surface parallel to the bottom) and constant overtime. But for other rates of flow, even though constant over time, the surfacein that canal would not be parallel to the bottom, since the head losses inthe syphons, bridges and other singular points will be different and willno longer be in accord with the levels given by the Manning or similarformulas. Therefore, backwaters will be formed. For these cases, variedregime formulas must be utilized. Such formulas consider a regime that isconstant over time but varies along the length of the canal, with the surfacenot parallel to the floor.These formulas are based on the fact that the head loss due to varied

movement of the water is equal to the algebraic sum of that caused byhydraulic friction plus that required by the variation in kinetic energy.Calling x a short distance along the bottom, y the corresponding

variation in level, s the slope, c the Chezy coefficient (deducible from thetable shown in 1.3 for the Manning and Bazin coefficients), Q the flow ateach point, P and A the perimeter and area of the cross section, as averagevalues of the section included in the x interval; A1 and A2 the value of thearea at the ends of the canal section and a coefficient of losses of kineticenergy, the formula for gradually varied movement is:

x =y Q

2

2g(

1A1

2 1

A22

)

s(Q

c

)2 PA3

bearing in mind that in each calculation of a new section, one must figurePAcA1, and A2 of the new end of the canal stretch being considered.Using this formula, the levels of this curve, called backwater, can

be calculated. Starting from a point where the water depth is known(e.g. upstream of a half-closed gate which causes a backwater), other succes-sive slightly lower water depths are considered and each one of the valuesthat is part of the formula is calculated. The formula gives us the distancex to the point which has the considered water depth.Full information on this topic can be seen in numerous books on hydraulic

theory (49), (80), (98).


At present it is easy to make or find computer programs to perform thiscalculation. Programs that can do the general study of a complete canal,including all kinds of inserted singular works by the Bureau of Reclamation,should be mentioned (21).The water surface types that may occur in a canal in the gradually varied

movement are the subject of detailed study in many books (15), (16), (49),(89), (98). Curves corresponding to gentle slopes (subcritical) are usuallycalled M-type curves and S-type curves are those corresponding tosupercritical (steep) slopes, see Figure 1.5.The M1 curve occurs when, in a slow-moving section, the water rises

over a gate or for any other reason there is a narrowing or localized headloss downstream.The M2 curve occurs when water flowing at a slow rate speeds up because

it is approaching a section with a greater slope or drop or a syphon calcu-lated for a greater flow than that existing at that moment.

Type M (y0 > ycr)

Type S (y0 < ycr)

Type C (y0 = ycr)

y0 = ycr

S0 < Scr

M1

S1

S2

S3

S0 < Scr

S0 < Scr

M2

M3

LCN

Horizontal

Horizontal

LCC

LCN

LCC

c

c

c

o

oo

y0

y0

ycr

ycr

Figure 1.5 Water surface types.


The M3 curve occurs when water flows out from under a gate, with amild slope, at a high rate of speed and gradually slows down until it formsa hydraulic jump.Canals with a supercritical slope are less frequent and therefore the

S curves as well. The S1 curve occurs as a high rate of speed slows downbecause of a gate inserted in the canal.The S2 curve occurs when slow-moving water enters an area with a

supercritical slope and speeds up until it reaches critical speed.The S3 curve occurs when water moving at a fast rate of speed enters,

e.g. a section of canal with a lesser slope (though also supercritical).It should be pointed out that these types of surface generally occur only

in a stretch of those indicated in the figure, without its being necessary toinclude their beginning or end.

1.9 Unsteady flow

In a canal the rates of flow and levels forcibly vary over time, as requiredby the supply conditions. The flows feeding into the canal vary, as do theexit flows, the superelevation of the gates, etc.In such a situation the calculation of a canal and the variations in the

surface over time cannot be done as indicated thus far. One must take intoaccount the variations that occur over time, at times quite rapidly (closingor opening of gates).The equations that govern the water movement are the well-known Saint-

Venant equations. There are two of them: one requires that the rate of flowbe preserved (the water is neither created nor destroyed), and the otherthe preservation of the amount of movement, taking into account that thisvalue is affected not only by the change in speed but also by the change inthe water mass found in the section being studied.The cited equations, in partial derivatives of space and time, are as

follows:

y

t+ v y

x= 0

v

t+v v

x+g y

x= g s sf

in which

y is the depth of watert is the timev is the speedx is the distances is the slope of the canal floorsf is the dynamic slope


i.e. that which complies with the Manning formula if the real speed andhydraulic data are introduced therein.The system of both equations should be complied with at all points and

at all times, which means that the non-uniform movement in a canal overtime can only be calculated with a computer program. More informationon this point can be found in Chapter 20.

Chapter 2

Water loss in canals

2.1 Worldwide importance

According to an interesting study carried out by the International Commis-sion for Irrigation and Drainage (56), around a third of the water that usesirrigation canals all over the world is lost during transportation. Anotherthird of the water is lost on the plot of land or the farm when it is used forirrigation. Therefore, only one-third may be usefully applied.These horrifying figures refer to worldwide average values, since there

are cases, such as those quoted by Kennedy in 1981, where canals lose 45%of the water they are transporting.There are the individual cases in the USA where losses during water

transporting in canals reach 60% and on average they reach 23%.In many countries throughout the world water is scarce, therefore it must

be rationally used. The cases of North Eastern Brazil, South Eastern Spain,areas in the Middle East, etc. where the lack of water restricts productionare only examples known by the public in general, but they form part of amuch more widespread problem.Canals used for town water supply or for hydroelectrical use also lose a

significant amount, although we do not have any statistics for them.When water is lost in canals we must ask ourselves what benefits would

have been obtained with the construction from the beginning of canals thatwere less permeable or the improvement of the watertightness of existingones and therefore the profitability of this investment.In the case of irrigation, for example, it is clear that saving of these

water losses would mean irrigation in new areas, with significant increase inproduction. But similar considerations may be made for energy productioncanals, for town water supply canals, etc.In the cases of using purified waste water, desalinization of sea water,

expensive water transfer work from other basins, the interest in decreasingthe losses to the maximum economically possible is obvious, since a signifi-cant amount of water could be saved and could be transferred to other uses.Moreover, even in those countries where there is no lack of water, its

catchment, regulation and even more its elevation are expensive operations,

20 Water loss in canals

therefore preventing useless losses during the transport is an economicallyinteresting operation.You only have to imagine a canal that has to transport a certain amount of

water to a certain place. If, during this operation, it suffers from significantlosses, the water flow that we have to introduce through its main intakemust be greater, and equal to the sum of the required flow and the predictedleakage amount. This without doubt makes not only the energy to raisewater from a well (if this is the supply system) but also the construction ofa possible regulating reservoir (if surface water is taken) and even the workon the canal itself more expensive, which must have a greater transportcapacity, since as well as the final water requirements, it must transport theleakage itself that will be lost en route.Any of these considerations have justified the decision to line canals to

decrease their losses. In Spanish legislation there have been many economicaid rules for irrigators, wanting to line their tertiary irrigation canals. TheDecree of the 15 December 1939 is a simple example. The water savingthat it represented and the profitability its use on other applications meantit easily compensated the State for the economic expenditure carried out.Another important example is that of the Water Supply Consortium ofTarragona, which used a flow of almost 5m3/s saved thanks to the liningof the canals of the Bajo Ebro.When reaching this point an important question arises: given that the

civil work that we can build, repair and handle cannot be perfect and willalways have some losses, what maximum value can we aspire to and whattechnical possibilities have we to obtain this?Frequently it is considered that a canal that has losses due to leakage

between 25 and 50 l/m2 in 24 hours adequately fulfils its undertaking. Thisvalue is not clearly defined, but it represents an order of magnitude that isgenerally internationally accepted (56).It is obvious that many canals, because they are located in highly imper-

meable land or because they are covered with linings that are very wellconceived and very well made, can have lower leakage rates (at times almostnone), but it is no less true that in many cases, if greater precautions are nottaken, the losses are much greater, due to the high permeability of the land,due to performance faults or simply due to cracking of the linings. Thisdemands a very delicate care by the project engineer to study the solutionto be adopted and to carefully specify the conditions that must be compliedwith during the work. Only in this way may the leaks be kept within theabovementioned minimums.If, to bring our ideas together, we consider a real canal that transports

60m3/s, with a speed of 1.5m/s, a wet perimeter of 20m2 per lineal metreand total length of 100 km, the leakage surface area (wet perimeter) in thecase of the dimensions of the cross section being kept throughout the layoutwould be around two million square metres. If the canal were telescopic,

Water loss in canals 21

the wet surface area would be half of this, i.e. one million square metres.With the abovementioned leakage values, the losses would be from 25000to 50000m3 per day.The volume of water transported by this canal per day will be

60m3/s86400s/day, i.e. 5140000m3; therefore the relative loss is around0.51%.If the water speed were higher (as normally happens with canals in hydro-

electric plants), the loss percentage would be even lower.This percentage might seem small, but other causes that increase it con-

siderably must be taken into account.A canal such as this one that supplies an irrigation area supplies a network

of irrigation canals and derived canals the length of which is around tentimes greater (in the specific case that we are talking about, the length ofthe canal represents 2m/ha and the secondary channels around 20m/ha).Though the latter are much smaller (a tenth in size of the canal), their lossesdue to leakage are approximately equivalent to the losses of the main canaland the total losses are doubled.There is another important cause for water loss in canals, unfortunately

about which we can do nothing. Here we are referring to losses due toevaporation.In the real canal we are considering, the surface width is approximately

15m; therefore the evaporation surface area over the 100 km of the canalwill be 1500000m2 or 150 ha, which would be reduced by half if the canalwere to be telescopic. With a fictitious evaporation of 1 l/s per ha (whichcan be real on many occasions, but which in general errs on the side ofsafety), the loss would be 150 l/s, equivalent to 12960m3/day, or half ofthis if the canal were telescopic, i.e. a value around a quarter or eighth partof the values to which the losses would be reduced if we were to limit theleakages to 2550 l/m2 in 24 hours.We have no weapons to fight against evaporation. But we have to be

aware that the maximum desired leakage of 2550 l/m2 in 24 hours isequivalent to a loss percentage of around 12%, to which another 0.5%must be added due to evaporation.There is a third cause that produces water losses in canals that is worth

mentioning. We are referring to involuntary spills due to problems ofbad regulation in the handling of the canal. It is a subject we will talkabout in this book and that requires suitable facilities to be foreseen inthe canal and careful planning in its handling. With the correct precau-tions the losses due to this reason, together with the leakage, make a totalof 5% of the water flow, which is an admissible value, particularly if wecompare it to the 33% that we have given as the current average in theworld.In this book we will try to fight against losses due to leakage and due to

unsuitable spills.


However, since we are aware that we will not be able to design andconstruct canals in general that have no losses, we must oversize theircapacity to carry not only desired flow, but also the losses. Traditionally,with a safety margin and whenever great care in the design and the build-ing of the canal were taken, this concept means the calculated flow isincreased by 10%.

2.2 Causes that affect water losses due to leakage

The maximum losses due to leakage in 24 hours to which we aspire areequivalent to a water height of 2.55 cm over the entire wet inner surfacearea of the canal, a value that for many will not seem negligible.The fact that different causes can affect the leakage value in a canal must

be taken into account.The most important one is the permeability of the land (more, or less,

clayey) and together with this, the quality of the lining (if there is any) andits conditions.The cross-sectional shape of the canal is also important. A big depth

makes the hydrostatic pressure on the bottom increase the losses, assumingnaturally a water table that is below the bottom of the canal. As we want tolimit the losses due to leakage to 2550 l/m2 in 24 hours, it is obvious thatthe total loss will be greater in larger canals than in those with a limitedsize, not only due to their greater leakage surface area, but also due to thegreater leakage pressure that a big depth implies.The amount of sediment in suspension or carried in the water is highly

significant. If there is any loam, as the water leaks through the land itdrags fine particles that little by little sediment between the holes in theland, silting it up and decreasing its permeability. On the other hand, veryclear water, when it leaks, drags finer particles from the soil, making thepermeability increase. From this point of view, surface water from a not-so-high-mountain river is much better regarding leakage than water from awell, where the water is pumped after a significant leakage into the land.The frequency of the canals periods of use also affects the leakages.

It must not be forgotten that the soil swells when it gets damp and on theother hand, when it dries off, it retracts. In the retraction periods, cracksappear, which although frequently seem tiny aid leakage. From this pointof view it is advisable to keep the canal full whenever possible, to avoidchanges in the dampness of the surrounding land. We have known engineerswho build canals from their main inlet to the downstream area, supplyingwater from upstream to the new stretches and keeping them with still water,in an attempt to keep the same humidity from the very birth of the canal.The age of the canal is a highly important piece of information. As with

all beings and things, a canal will deteriorate as time goes by.


Weather conditions also affect canals, not only because the weathermight be better or worse and therefore, more difficult to bear withoutdeterioration, but because during dry periods the land evaporates watermore easily and leakage increases to replace this loss of humidity.The roots of vegetation around the canal dislocate the soil structure,

creating leakage routes. For aesthetic reasons, tree plantations are madealongside canals and particularly along service roads, since they are easy tomaintain, with irrigation from the canal itself. These should not be rejected,but they should be located at a reasonable distance from the canal.

2.3 The way to stop leakage in a canal: Otherreasons for putting in linings

The maximum values for losses due to leakage must be common to allcanals. If the soil itself already ensures lower losses, a canal may be builtwithout lining, if the conditions discussed in Chapter 11 for unlined canalsare also fulfilled. But if it is foreseen that the leakages are going to be greaterthan those admitted, the most common solution is to line the canal.The lining is nothing more than a layer of long-lasting material that is

placed over the excavated and profiled surface area of the canal. Takinginto account that its purpose is to decrease the canals leakages, it is obviousthat its basic characteristic must be its waterproofness. This solution meansthat the canals excavation slopes are perfectly stable, but the thin liningmust not be expected to support them.The decision as to whether a canal should be lined or not, to improve

its waterproofness, must be taken before its construction, after a studyof the characteristics of the land. If a well or hole is built, with specificmeasurements, next to the layout of the future canal and with the samedepth, the future leakage may be predicted. It only has to be filled withwater, and after 24 hours cube the primitive volume and the reduction inits level to calculate the leaked volume. Dividing this by the wet surfacearea of the well, we will have a value that, according to whether it is lesseror greater than 25 or 50 l/m2 in 24 hours, will indicate whether the soil issufficiently waterproof or not.If, on the other hand, the canal has already been built, there are other sys-

tems to evaluate the importance of the losses, although they are not alwaysas accurate as could be wished for. One of them consists of transforming thecanal into a series of successive reservoirs formed by some small provisionaldams that are built within the canal and that are filled with water. After acertain time (for example, 24 hours) the drops in the levels are measuredand the leakage per square metre may be calculated. There is the possibledisadvantage that the dams (or some of them) may not be waterproof andlet water through, meaning that the results may be hidden, at least in thelocalized results. Another disadvantage that cannot be forgotten is that to


carry out this study, the canal must be taken out of working order. Obvi-ously, the canals leakage surface area must also be calculated, since as thelevels of the reservoirs are horizontal, it is a different surface area to theone normally wet when the canal is in use.Another system, more frequently used, consists of measuring the water

speeds in the canal during normal service, using a current meter. As thespeeds at different points of the cross section of the canal are not equal,several measurements must be made at each section and the results must beintegrated. This system is not valid when there are intercalated derivations,unless these are endowed with reliable measurement data. The differencesin the water flow between different stretches give us the existing leakages.Specific leakages may be measured in a full canal using a piece of appa-

ratus similar to that shown in Figure 2.1 (83).This ingenious device measures the leakage through a canal surface lined

by a plate. The water leaked to the soil does not come from the canal; it

Handle

Plastic bag Water surface

Water

Plastic pipe

Infiltration bell

Same hydraulic pressureinside and outside

Bottom

30 cm

20 c

m

Figure 2.1 Device for measuring specific leakages (according to Florentino Santos).


comes from a rubber bag the contents of which have been previously mea-sured. This device measures the leakage at a specific point. It is a drawbackbecause frequently the leakages in lined canals are highly irregular, beingvery high in the cracks and breakages and non-existent in the places wherethe lining is in good condition. It could be useful in unlined canals (withhomogeneous characteristics), etc.The lining may be made, as we will see under Section 2.5, from very

different materials. Some of the characteristics may be very interesting toresolve certain problems in canals, therefore at times canals are lined forreasons other than waterproofing.The most important cause (after waterproofing) for lining a canal is to

achieve a greater resistance to water erosion, an important problem in manycanals in soil, as we will see in Chapter 11.Another possible justification is the fact that a lined canal has a better

roughness coefficient and, therefore, a greater transport capacity. We mustremember the so-called hydraulic paradox according to which on liningcanal, occupying part of its useful section with the lining, its flow, however,is increased because the percentage increase in velocity is greater than thepercentage decrease in the cross section.Vegetation growing in a canal usually presents important problems,

which enforce frequent, problematic cleaning operations or trims.A lining makes it difficult for vegetation to grow and encourages cleanliness.

2.4 Canals that must not be lined: Drainage canals

Section 2.3 shows the cases when it is advisable to line canals and otherswhen it is not necessary or it is not justified. However, there is one typeof canal where lining is particularly advised against. We are referring todrainage canals, the purpose of which is not to move water from a supplypoint to a consumption centre (irrigation plot, water supply for a town,hydroelectric station that takes advantage of available waterfall, etc.), butrather for the canals to collect and take the water drained from irrigated orsoaked land to an evacuation place.If these canals were to be lined, they would have great exposures to under-

pressure problems, due to the water table that soaks the land, the possibleflows being so large that the drainage techniques for the lining that we willshow in Chapter 9 would not be applicable.These canals must be unlined, Figure 2.2, to be able to freely admit the

water that leaks from the land along its slopes, which may lead to otherdrainage canals that are tributaries of them. In this way, its drainage actionis complemented.The old Irrigation Canal Standards from the 1940s, drafted by the then

Ministry of Public Works of Spain, recommended trapezoidal cross sectionsfor canals, whose horizontal bottom was lined with concrete on site. This


Figure 2.2 Drainage canal.

cross section had the advantage of aiding the cleaning of sediments on thebottom and not preventing the leakage of water through the slopes.It is highly probable that when projecting drainage canals we find

problems of excessive speeds. As we cannot fight these with linings, a seriesof drops (described under Section 17.3) must be introduced into the canal,which allow the initial gradient to be replaced by a series of stretches ofcanal with smoother gradients and with less danger of erosion.As they are canals made in soil, with erosion danger, they are often

endowed with concrete transverse sills, embedded into the ground (as maybe seen in the Figure 2.2), a technique that is also frequently used to stabilizeriver beds, since they establish points on the bottom that have a contourheight fixed by the transverse beam (Figure 2.2).Drainage canals may have greater erosion where tributaries join them.

A short stretch of the largest canal should be lined to prevent erosion dueto the drop off.

2.5 Types of lining

The most commonly used lining in the world is bulk concrete made on site.The currently used thickness is between 8 and 15 cm. Its waterproofnessis magnificent, whenever it does not crack due to thermal forces or earth


movements. Lesser thicknesses than those indicated (with cement mortar)are not recommended since they crack and deteriorate easily (Chapter 4).Sometimes linings of concrete reinforced with iron bars are used to

combat cracking (33) (Figure 2.3). The main objection is its greater cost inrelation to bulk concrete, not only due to the price of the iron, but also dueto the fact that it is more expensive to lay. It is usually only used in specialcases, which we will indicate in this book when necessary.It should be mentioned that, as the lining is thin, it is difficult to guar-

antee the distances required from the iron bars to the concrete surface withsufficient accuracy. If building errors occur on this point, the lining couldresist the possible bending moments less than could be expected.The report by Chester W. Jones from the Bureau of Reclamation (35)

is very interesting, where he explains that this organism decided not toreinforce the concrete coverings with iron bars in 1948, except in specialcase, obtaining a saving of 1015%. The same is stated in (25) and (32).Reinforced concrete is more suitable for thick linings (which should really

be called retaining walls), which must also resist thrust from the outerland or the inner water. In these cases it can be a useful material.Concrete may also be used to make prefabricated slabs to line the canal.

It is a lining with special characteristics that we will analyse in depth inChapter 6.Rubblework linings (thick stones jointed with cement mortar) are infre-

quently used; however, they do have a field of application, as we will seein Chapter 6.3.Brick linings are indicated in countries with abundant clay soil and cheap

labour that allow low-cost manufacturing.Linings are made with bituminous agglomerate (also called asphalt

mix). They are similar to road pavement and they have the advantageover bulk concrete linings in the fact that they are more flexible (relatively),which allows them to bear the dilations and retractions due to changes intemperature and the flexions due to land settling better.

Symmetrical

Welded wire fabric

Note: Place reinforcementin center of slab

Joint with curing compound 23

Figure 2.3 Reinforced concrete lining.


Even more flexible are the membranes, made of different materials. Theyare studied in Chapter 8.Improved soil linings are highly interesting, formed by mixing natural soil

with other soil with better characteristics that is transported from anotherplace and then mixing it for waterproofing determinants and erosion resis-tance. It is really a canal in soil, but with higher quality than natural soil(Chapter 11).Other waterproofing systems or land protections may be obtained

using different procedures (soil-cement, bentonite, chemical products, etc.;Section 11.12).The choice of lining depends on many reasons, amongst which the most

important are the availability of materials, the cost of labour and of theauxiliary machinery, the level of waterproofing required with the lining, themaintenance expenses and the efforts to which it is going to be subjected,such as the water velocity or soil thrusts, changes in temperature, growthof vegetation, etc.In the following chapters we will study the most important characteristics

of the aforementioned linings, in order for engineers, in each case, withfull knowledge of the facts, to choose the most suitable one, repeatingthat, in any case, the efforts that are going to act on it are always veryhard.There are more canals in the world that are excavated in soil without

linings. Lower cost has a great influence on this fact. They can give goodresults if they are well designed and built, a fact that does not often happen.Most lined canals are those lined in bulk concrete.Although the statistics in the USA are not representative of the world

reality, due to their different technology and particularly the different econ-omy, the percentage of the canal length for each type that was built in thiscountry by the Bureau of Reclamation between 1963 and 1986 (30) couldbe interesting:

Reinforced and non-reinforced concrete 58%Compact soil 27%Membranes and mastic linings 7%

It is worth mentioning that the canals that appear as compact soil are nottruly canals only excavated in soil, rather they refer to canals with improvedsoil linings.

2.6 Resistant side walls

Sometimes canals are made with a bottom and sides that, as well as pre-venting water losses, are resistant elements. Often they are called retainingwalls. The basic difference with the linings is the fact that in these the


resistant element to the hydraulic pressure is the soil, the lining being merelya protective or waterproofing factor. The retaining walls, on the other hand,are used to resist the interior hydraulic thrust on the canal and often also thethrusts of the soil itself. They are therefore structural elements the resistanceof which must be calculated as opposed to all the possible combinations ofexterior efforts.They may be made in bulk (concrete or rubble work, infrequently in

brick) or reinforced concrete.If they are made of rubble work, brick or bulk concrete, their stability

relies on the weight itself, as if they were small gravity dams and the samethat they must also resist the possible uplift pressure due, in this case, tothe canal water that may be leaked under its support base (Figure 2.4).There are several situations when retaining walls are used, which are

listed below:

a When the water level must be above the land level. In this situation twodifferent solutions may be adopted: With resistant walls (Figure 2.4) orwith a canal on an embankment (Figure 3.2 (third diagram)). In thissituation a comparative study must be carried out, to choose amongthe technical solutions with a view for the economic studies.

b When the land has a highly unreliable resistance, and slopes that aretoo inclined would have to be adopted.

Figure 2.4 Cross section of a retaining wall.


c When the natural lands cross-sectional slope is too great or unstable,so that it would not stand the positioning of a canal with a smootherslope as m

Hydraulic Canals Design_ Construction_ Regulation and Maintenance

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