aliviaderos spillways

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Hydraulics ofSpillways and

Energy Dissipators

Copyright 2005 by Marcel Dekker.


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Civil and Environmental Engineering

A Series of Reference Books and Textbooks

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Michael D. Meyer

Department of Civil and Environmental Engineering

Georgia Institute of Technology

Atlanta, Georgia

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Marcel Dekker New York

R. M. Khatsuria

Hydraulics ofSpillways and

Energy Dissipators



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the author(s) nor the publisher, nor anyone else associated with this publication, shall beliable for any loss, damage, or liability directly or indirectly caused or alleged to be caused

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To My Parents



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Preface

The need for a comprehensive book dealing in hydraulics of spillways and energy

dissipators has been realized since long. Various topics pertaining to the spillways

and energy dissipators are available in the sources devoted mainly to the design

of dams, text books on hydraulics and open channel flow and handbooks of

hydraulics. However, advances in research and design, generally published

through papers presented at the specialty conferences and journals, are seldom

disseminated wide enough for application on a general scale. Consequently, the

rift between the advancements in knowledge and its formal documentation in the

books and treatise grows wider. Of the many examples illustrating this lag, a

typical one is the aerator on spillways to mitigate cavitation damage. Although,

the beneficial effects of aeration were known in the early fifties, considerable

research had been pursued, to understand hydraulics of the phenomenon, from

the sixties and aeration devices were installed on the existing structures in the

late seventies, it was not until the eighties that aeration devices became an integral

part of spillway design. It is noteworthy that no book on spillways published

until the late eighties included the topic of aeration, and reference sources re-

mained scattered in journals and proceedings.This practice of lag continues, as several topics of vital significance have not

been embodied comprehensively and coherently into any of the book literature. A

few to mention include: spillway construction stages, spillways serving dual pur-

pose of flood as well as sediment disposal, overtopping protection of earth dams

used as spillways, prediction of and protection against detrimental forces such

as uplift, cavitation, scour etc. It is obvious that such a book would be the easiest

way for a reader to access the information on the latest developments in the field.

The present book is the outcome of such an attempt.The book has been organized into four sections dealing with spillways,

energy dissipators, cavitation and air entrainment, and hydraulic modeling. Em-

phasis has been on discussing first the hydraulics of different types of spillways

and energy dissipators and to illustrate its application to practical design problems.

To this end, illustrative examples have been included at appropriate places.

v



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Prefacevi

The first two chapters in section I introduce the topic and broad design

philosophy. The chapter on spillway design flood defines two distinct aspects:

the estimation, which is hydrologists regime and the selection, which is the

responsibility of the designer. Subsequent chapters have been devoted to discus-sion on hydraulics and general design features of different types of spillways

such as ogee, chute and side channel, stepped, siphon, shaft, tunnel, labyrinth

and duck bill, free jet and fuse plug etc. Special features such as spillways for

flood and sediment disposal, inflatable rubber weirs and overtopping protection

of dams used as spillways have also been included. Separate chapters on spillway

crest gates and spillway construction stages have been written.

Discussions on the three most common types of energy dissipators for

spillways, viz. hydraulic jump stilling basins, trajectory buckets and submergedroller buckets in section II, have been quite elaborate, obviously in view of the

large amount of information published during recent years. Energy dissipators for

shaft and tunnel spillways warrant a special chapter in view of peculiar hydraulic

conditions at the outfalls. Separate chapters have been devoted to the discussion

of impact type energy dissipators and some unconventional or special designs of

energy dissipators.

Section III includes chapters on the topics of cavitation and air entrainment

and aerators concerning the design of spillways and energy dissipators.

Hydraulic modeling of spillways and energy dissipators has been covered

in section IV. No attempt has been made to discuss the theory of similitude and

hydraulic models, found in many books. On the other hand, emphasis has been

placed on topics of scale effect; dynamic flow measurement and aspects of analy-

sis and interpretation of model results. It is hoped that this will be useful, to not

only research engineers, but also to the designers and practicing engineers direct-

ing the model studies.

In the field of technology, a continuous stream of development and improve-

ment adds to the knowledge. Therefore, nothing can be claimed as exhaustive orfinal. Similarly, it is equally difficult to decide what is old or obsolete. The

difficult task was therefore to evaluate every piece of information from the stand-

point of practical utility, be it for the researcher, designer, practicing engineer or

student. While this book is not intended to be a textbook to cater to any specific

curriculum, nor a handbook, it is expected to serve as a comprehensive reference

source for all concerned. It is hoped that the reader will be able to obtain an

extensive exposure of the topic, beyond which the references listed at the end of

the chapters will be useful for locating additional details.Experience gained during my association, of nearly four decades, with the

Central Water and Power Research Station, Punean institution of international

reputation and discussions with several experts in the field of their own specialist

knowledge, have greatly contributed to writing of the book. Thanks are also due

to friends and colleagues for their help and encouragement which lent a strong



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Preface vii

impetus toward the completion of this book. My wife Kala, daughters Pallavi,

Reshma, and son-in-law Praveen extended support throughout the writing of the

book.

I have pleasure in placing on record, my appreciation for the excellentcoordination by Mr. B.J. Clark, Executive Acquisitions Editor, Mr. E.F. Stannard,

Senior Production Editor and Ms. Kerry Doyle, Director, Book Editorial, Marcel

Dekker, Inc. at various stages of publication of the book.

Feedback from the readers in respect of any omission or error as also their

comments and suggestions to improve upon the contents of the book, shall be

gratefully appreciated.

R. M. Khatsuria5/4, Krutarth Society

Behind Sharda Bank

Off: Satara Road,

PUNE - 411 037, INDIA

Email - [email protected]

mailto:[email protected]:[email protected]:[email protected]


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Acknowledgments

The author acknowledges with thanks, the following institutions, organizations

and individuals who permitted to refer/reproduce their publications in this book.

The details of the materials have been listed in the appropriate reference sections

within the chapters.

American Society of Civil Engineers, New York, USA

Aqua-Media International Ltd, UK (Jnl of Hydropower and Dams)

Bacchiega, J.D, Fattor, C.A and Barrionuevo, H.C (INA, Argentina)

Back, Paul, Berks, UK

BHR Group Limited, Cranfield, UK

Canadian Society of Civil Engineers, Canada

Central Board of Irrigation and Power (CBIP), New Delhi, India

Chanson, H (The University of Queensland, Australia)

Damulevicius, V and Ruplys, B (LZUU, Lithuania)

Ervine, D.A. (The University of Glasgow, UK)

Gao, JiZhang, IWHR, Beijing, China

Hager, W.H., ETH, Switzerland Iguacel, C.M, CEDEX, Spain

Indian Institute of Science, Bangalore, India

Indian Society for Hydraulics, Pune, India

Institution of Civil Engineers, London, UK

Institution of Engineers Australia, Melbourne, (XXI IAHR 1985)

Institution of Engineers (India), Kolkata, India

International Association for Hydraulic Research, (IAHR), Madrid, Spain

(Jnl of Hyd Res, VIVII IAHR, 1955, 1957) International Congress on Large dams (ICOLD), Paris, France (ICOLD

Publications)

Japan Society of Civil Engineers, Tokyo, Japan

Jongeling, T (Delft Hydraulics), The Netherlands

National Hydroelectric Power Corporation Ltd, New Delhi, India

ix



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Acknowledgmentsx

National University of Singapore (IX APD-IAHR, 1994)

Rathgeb, A (Wasser-und Schiffahrtsamt, Stuttgart), Germany

SAF Laboratory, University of Minnesota, USA

Sardar Sarovar Narmada Nigam Ltd (SSNNL), Gandhinagar, India Schleiss, A, EPFL, Switzerland (XXII IAHR 1987)

Swets and Zeitlinger Publishers, (Balkema Publishers), The Netherlands

Technische Akademie Esslingen (TAE), Germany (IAHR Symp 1984)

Thomas Telford Publishing, London, UK (XXVI IAHR 1995)

Plate, E, University of Karlsruhe, Germany (XVII IAHR 1977)

United States Army Corps of Engineers (USACE), USA

UNESCO Publishing, Paris, France

United States Bureau of Reclamation (USBR), USA United States Society on Dams (USCOLD), USA

Virginia Polytechnic Institute, USA

Wang, Lianxiang IWHR, China (XXIX IAHR 2001)

Wilmington Publishing, Kent, UK (Jnl of Water Power and Dam Con-

struction)

Wilmington Publishing, Kent, UK (Dam Engineering)

Yugoslav Association for Hydraulic Research (YAHR), Belgrade, Serbia

Yasuda, Y (Nihon University), Japan



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Contents

Preface .......................................................................................................... v

Acknowledgments ......................................................................................... ix

Section I: Spillways

1. Spillways: Functions and Classification ............................................. 1

1.1. Introduction ............................................................................. 1

1.2. Necessity of a spillway ........................................................... 1

1.3. Functions of a spillway ........................................................... 2

1.4. Classification of spillways ...................................................... 5

2. Spillway Design: An Overview .......................................................... 7

2.1. Introduction ............................................................................. 7

2.2. Analysis of existing structures ................................................ 7

2.3. Various aspects involved in a spillway design ...................... 9

2.3.1. Hydrology .................................................................... 92.3.2. Topography and geology ............................................ 10

2.3.3. Utility and operational aspects ................................... 10

2.3.4. Constructional and structural aspects ......................... 12

2.4. Economic analysis ................................................................... 13

3. Spillway Design Flood: Estimation and Selection ............................. 15

3.1. Introduction ............................................................................. 15

3.2. Estimation of spillway design flood ....................................... 163.3. Methods based mainly on flow data ...................................... 16

3.3.1. Historical method ........................................................ 16

3.3.2. Empirical and regional formulas ................................ 17

3.3.3. Envelope curves .......................................................... 17

3.3.4. Flood frequency analysis ............................................ 18

xi



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Contentsxii

3.4. Methods based mainly on rainfall data .................................. 19

3.4.1. Development of the PMS and PMP ........................... 20

3.4.2. Unit hydrograph method ............................................. 22

3.4.3. Hydrologic modelling ................................................. 223.4.4. Gradex method ............................................................ 24

3.5. Flood estimation methods: Critical analysis .......................... 24

3.5.1. Estimation of design flood for the Sardar Sarovar

Dam on River Narmada, India ................................... 25

3.6. Selection of spillway design flood ......................................... 27

3.6.1. Economic risk analysis (ERA) ................................... 28

3.6.2. Comments on ERA ..................................................... 29

3.6.3. Design flood standards and regulations ..................... 303.6.4. Comments on design standards .................................. 34

3.6.5. Quantitative risk assessment ....................................... 34

3.6.6. Incremental hazard evaluation .................................... 35

4. Ogee or Overflow Spillways ............................................................... 41

4.1. Introduction ............................................................................. 41

4.2. The spillway crest profile ....................................................... 41

4.3. Discharge characteristics ......................................................... 48

4.4. Discharge coefficient versus crest pressures .......................... 554.5. Determination of design head ................................................. 57

4.6. Crest piers ................................................................................ 59

4.7. Downstream slope or rear slope ............................................. 59

4.8. Water surface profile ............................................................... 59

4.9. Spillway toe ............................................................................. 60

5. Chute and Side Channel Spillways ..................................................... 63

5.1. Introduction ............................................................................. 63

5.2. Principal elements ................................................................... 64

5.3. Approach channel .................................................................... 64

5.4. Spillway structure .................................................................... 67

5.5. Side channel spillway-trough and control section ................. 69

5.6. Chute ........................................................................................ 78

5.6.1. Contraction and Expansion ......................................... 79

5.6.2. Curvature in plan ........................................................ 86

5.6.3. Special layouts ............................................................ 89

5.6.4. Longitudinal profiles ................................................... 895.6.5. Tail channel ................................................................. 91

5.7. Numerical and physical modeling .......................................... 91

6. Stepped Spillways ............................................................................... 95

6.1. Introduction ............................................................................. 95



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Contents xiii

6.2. Historical background ............................................................. 95

6.3. Flow regimes on a stepped chute ........................................... 95

6.4. Characteristics of the nappe flow ........................................... 96

6.4.1. Nappe flow occurrence ............................................... 986.4.2. Energy dissipation and residual head for nappe flow 98

6.4.3. Pooled step cascades ................................................... 101

6.4.4. Transition flow regime ............................................... 105

6.5. Characteristics of the skimming flow ..................................... 106

6.5.1. Estimation of flow resistance ..................................... 107

6.5.2. Air entrainment ........................................................... 110

6.5.3. Energy dissipation ....................................................... 114

6.5.4. Pressure fluctuations and cavitation susceptibility .... 1216.6. Guidelines for design of stepped spillways ............................ 122

6.6.1. Crest profile and the transition ................................... 122

6.6.2. Step height ................................................................... 123

6.6.3. Freeboard for sidewalls ............................................... 124

6.6.4. Design of energy dissipator ........................................ 124

6.7. Hydraulic model studies ......................................................... 124

7. Siphon Spillways ................................................................................. 1297.1. Introduction ............................................................................. 129

7.2. Types of siphon ....................................................................... 129

7.3. Hydraulic action ...................................................................... 131

7.4. Hydraulic design considerations ............................................. 133

7.5. Discharging capacity ............................................................... 134

7.6. Priming depth .......................................................................... 140

7.7. Flow regulation ....................................................................... 141

7.8. Stability of functioning ........................................................... 1437.9. Effect of waves ....................................................................... 143

7.10. Cavitation ................................................................................ 143

7.11. Vibration .................................................................................. 147

8. Shaft Spillways .................................................................................... 151

8.1. Introduction ............................................................................. 151

8.2. Types of shaft spillways ......................................................... 151

8.3. Shaft spillways with axial flow .............................................. 1528.3.1. Hydraulic action .......................................................... 154

8.3.2. Analysis of alternatives ............................................... 154

8.4. Free shaft spillways ................................................................. 156

8.4.1. Crest profile ................................................................. 157

8.4.2. Transition from crest to shaft ..................................... 159



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Contentsxiv

8.4.3. Discharge characteristics ............................................. 160

8.4.4. Air entrainment in drop shafts .................................... 162

8.4.5. Air entrainment in tunnels flowing partly full ........... 171

8.5. Pressure shaft spillways .......................................................... 1728.5.1. Devices to ensure pressurized flow in the shaft ........ 173

8.5.2. Release of air in pressurized tunnels .......................... 174

8.6. The vortex drop ....................................................................... 179

8.6.1. Configuration of vortex-flow intakes ......................... 181

8.6.2. Standard scroll intake ................................................. 181

8.6.3. Tangential vortex intake ............................................. 186

8.6.4. Designs of drop shafts to increase discharge

capacity ........................................................................ 1888.6.5. Air entrainment and transport in vortex drops ........... 188

8.7. Shaft spillways with swirling flow in outlet tunnel ............... 190

8.8. Siphon-shaft spillway .............................................................. 192

9. Labyrinth and Duckbill Spillways ...................................................... 197

9.1. Introduction ............................................................................. 197

9.2. General characteristics of labyrinth weirs .............................. 197

9.3. Parameters affecting performance .......................................... 1999.4. Discharge characteristics ......................................................... 202

9.5. Design of labyrinth spillway ................................................... 207

9.6. Duckbill spillway .................................................................... 209

9.7. Designs relevant to existing and new structures .................... 213

10. Tunnel and Culvert Spillways ............................................................. 217

10.1. Introduction ............................................................................. 217

10.2. Tunnel spillways: Design considerations ............................... 21710.2.1. Control structure ......................................................... 217

10.2.2. Discharge tunnel ......................................................... 220

10.2.3. Other forms of discharge tunnels ............................... 222

10.3. Culvert spillway ...................................................................... 223

10.3.1. Full bore flow (Pipe culverts) .................................... 225

10.3.2. Box and MEL culverts ................................................ 226

10.4. Conduit pressures .................................................................... 227

11. Free Jet and Straight Drop Spillways ................................................. 231

11.1. Introduction ............................................................................. 231

11.2. Free jet spillways: Design considerations .............................. 231

11.2.1. Overflow crest ............................................................. 232

11.2.2. Stilling basin ............................................................... 232



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Contents xv

11.3. Characteristics of the free falling jets .................................... 232

11.4. Guidelines for the design of a stilling basin .......................... 241

11.5. Nappe splitters and dispersers ................................................ 244

11.6. Bottom outlets: Design considerations ................................... 24811.7. Straight drop spillway ............................................................. 254

12. Fuse Plugs and Fuse Gate Spillways .................................................. 261

12.1. Introduction ............................................................................. 261

12.2. Fuse plug ................................................................................. 261

12.2.1. Criteria for selection of fuse plug .............................. 262

12.2.2. Design considerations ................................................. 262

12.2.3. Providing a fuse plug in an existing dam .................. 26612.2.4. Hydraulics of flood discharge through fuse plug

opening ........................................................................ 266

12.3. Fuse gates ................................................................................ 269

12.3.1. Functioning of fuse gates ............................................ 269

12.3.2. Stability of fuse gates ................................................. 271

12.3.3. Design of fuse gates .................................................... 274

12.3.4. Recoverable fuse gates ............................................... 280

13. Spillways for Flood and Sediment Disposal ...................................... 283

13.1. Introduction ............................................................................. 283

13.2. Reservoir sedimentation and flushing .................................... 283

13.3. Alternatives available .............................................................. 284

13.4. Flushing discharge .................................................................. 284

13.5. Gated overflow spillway ......................................................... 285

13.6. Orifice spillways ..................................................................... 286

13.7. Bottom outlets ......................................................................... 286

13.8. Design considerations ............................................................. 28813.8.1. Discharge characteristics of spillway ......................... 288

13.8.2. Waterway of the structures ......................................... 289

13.8.3. Size and dimensions of structures .............................. 289

13.8.4. Energy dissipator ......................................................... 293

13.8.5. Power intakes .............................................................. 295

13.8.6. Gates ............................................................................ 295

13.8.7. Protection of flow surfaces ......................................... 296

13.9. Mathematical and physical model studies .............................. 297

14. Unlined Spillways ............................................................................... 299

14.1. Introduction ............................................................................. 299

14.2. Unlined rock spillways ........................................................... 299

14.3. Unlined cascade spillways ...................................................... 300



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Contentsxvi

14.4. General considerations ............................................................ 300

14.5. Conceptual framework ............................................................ 301

14.6. Rock-fill spillways .................................................................. 307

15. Inflatable Rubber Weirs ...................................................................... 313

15.1. Introduction ............................................................................. 313

15.2. Principal elements of a rubber weir ....................................... 313

15.3. Design considerations ............................................................. 315

15.3.1. Hydraulic design ......................................................... 315

15.3.2. Structural design ......................................................... 320

15.4. Problems associated with rubber weir installation ................. 321

16. Overtopping Protection of Dams Used as Spillways ......................... 323

16.1. Introduction ............................................................................. 323

16.2. Concrete dam overtopping protection .................................... 323

16.3. Embankment dam overtopping protection ............................. 325

16.4. Design considerations ............................................................. 325

16.5. Slope protection lining ............................................................ 327

16.5.1. Cast-in-place concrete ................................................. 327

16.5.2. Roller compacted concrete (RCC) .............................. 32716.5.3. Precast concrete block system .................................... 328

17. Spillway Crest Gates ........................................................................... 333

17.1. Introduction ............................................................................. 333

17.2. Factors influencing the decision ............................................. 333

17.2.1. Safety of the dam ........................................................ 334

17.2.2. Cost economics ........................................................... 334

17.2.3. Operational problems .................................................. 33517.2.4. Downstream conditions ............................................... 335

17.2.5. Special considerations ................................................. 335

17.3. Types of gates ......................................................................... 336

17.4. Mechanical gates ..................................................................... 337

17.4.1. Radial gates ................................................................. 337

17.4.2. Vertical lift gates ......................................................... 343

17.4.3. Flap gates .................................................................... 345

17.5. Semi-mechanical gates ............................................................ 34617.6. Automatic type: fusible ........................................................... 346

17.7. Automatic type: restoring ....................................................... 346

17.8. Vibration of gates .................................................................... 350

17.9. Stop log gates .......................................................................... 350

17.10. Some considerations on operating pattern of gates ............... 355



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Contents xvii

18. Spillway Construction Stages ............................................................. 359

18.1. Introduction ............................................................................. 359

18.2. Spillway construction program ............................................... 359

18.3. Construction flood ................................................................... 36018.4. Reservoir levels during construction stages ........................... 360

18.5. Spillway construction stages ................................................... 361

18.5.1. Discharge characteristics of partly constructed

spillways ...................................................................... 364

18.6. Flow downstream of partly constructed spillways ................. 366

Section II: Energy Dissipators

19. Energy Dissipators for Spillways ....................................................... 371

19.1. Introduction ............................................................................. 371

19.2. Classification of energy dissipators ........................................ 371

19.3. Principal types of energy dissipators ...................................... 372

19.4. Selection of the type of energy dissipator .............................. 373

19.5. Analysis of Parameters ........................................................... 375

20. Hydraulic Jump Stilling Basins .......................................................... 387

20.1. Introduction ............................................................................. 387

20.2. Hydraulic jump characteristics ............................................... 387

20.2.1. Classification of hydraulic jump ................................ 388

20.2.2. Length of the jump ..................................................... 390

20.2.3. Conjugate depth and energy loss ................................ 390

20.2.4. Turbulence characteristics of hydraulic jump ............ 39220.2.5. Air entrainment by hydraulic jump ............................ 399

20.3. Hydraulic jump stilling basins ................................................ 401

20.3.1. Basins with horizontal aprons .................................... 401

20.3.2. Basins with sloping aprons ......................................... 409

20.4. Optimization of designs .......................................................... 411

20.5. Structural design problems ..................................................... 411

20.5.1. Uplift ........................................................................... 411

20.5.2. Hydrodynamic forces .................................................. 42320.5.3. Cavitation .................................................................... 428

20.5.4. Vibrations .................................................................... 431

20.5.5. Abrasion ...................................................................... 432

20.6. Environmental considerations ................................................. 433

20.7. Implications of various factors ............................................... 434



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Contentsxviii

21. Trajectory Buckets .............................................................................. 441

21.1. Introduction ............................................................................. 441

21.2. Types and classification .......................................................... 441

21.3. Design of bucket components ................................................. 44321.3.1. Shape of the bucket .................................................... 444

21.3.2. Invert elevation ........................................................... 445

21.3.3. Bucket radius ............................................................... 445

21.3.4. Lip angle ..................................................................... 446

21.4. Hydraulic characteristics of trajectory buckets ...................... 448

21.4.1. Pressures on buckets and sidewall ............................. 449

21.4.2. Free trajectory and throw ............................................ 453

21.4.3. Effect of submergence by tail water .......................... 45521.5. Scour downstream of trajectory buckets ................................ 465

21.5.1. Computation and prediction ....................................... 465

21.5.2. Analysis ....................................................................... 469

21.5.3. Scour control and remedial measures ........................ 470

21.5.4. Protection against scour .............................................. 471

21.6. Special forms of buckets ......................................................... 472

22. Solid and Slotted Roller Buckets ........................................................ 483

22.1. Introduction ............................................................................. 483

22.2. Solid roller bucket ................................................................... 483

22.3. Slotted roller bucket ................................................................ 491

22.4. Comparative performance based on prototype experience .... 495

22.5. Alternative designs for improvements .................................... 499

23. Energy Dissipators for Shaft and Tunnel Spillways .......................... 503

23.1. Introduction ............................................................................. 503

23.2. Full-bore pressurized flow ...................................................... 50323.2.1. Dissipation by friction ................................................ 505

23.2.2. Dissipation by head loss ............................................. 505

23.2.3. Swirling devices .......................................................... 505

23.3. Free surface flow ..................................................................... 507

23.3.1. Flip buckets ................................................................. 507

23.3.2. Hydraulic jump stilling basin ..................................... 509

24. Impact-Type Energy Dissipators ......................................................... 51924.1. Introduction ............................................................................. 519

24.2. Classification of impact-type energy dissipators .................... 519

24.3. Baffled chutes .......................................................................... 520

24.3.1. Energy dissipation by induced tumbling flow ........... 520

24.3.2. Baffled apron drops .................................................... 522



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Contents xix

24.4. Energy dissipators for spillways and outlets .......................... 524

24.4.1. USER Basin VI ........................................................... 524

24.4.2. Bhavani-type stilling basin ......................................... 526

25. Unconventional Designs ...................................................................... 531

25.1. Introduction ............................................................................. 531

25.2. Dissipating part of the energy on a spillway slope ................ 531

25.3. Interaction within the region of flow ..................................... 532

25.4. Bifurcation/bypass of flow ...................................................... 535

25.5. Hydraulic model studies ......................................................... 538

Section III: Cavitation and Air Entrainment

26. Cavitation in Spillways and Energy Dissipators ................................ 541

26.1. Introduction ............................................................................. 541

26.2. Cavitation ................................................................................ 541

26.3. Cavitation index ...................................................................... 542

26.4. Cavitation damage ................................................................... 544

26.5. Cavitation on spillway surfaces .............................................. 545

26.5.1. Inadequate design ........................................................ 546

26.5.2. Misalignment ............................................................... 547

26.5.3. Surface roughness ....................................................... 548

26.6. Cavitation in energy dissipators ............................................. 550

26.6.1. Fluctuating pressure depressions ................................ 552

26.6.2. Flow separation and reattachment .............................. 553

26.7. Cavitation due to sheared flow and vortices .......................... 556

26.8. Prediction of cavitation damage ............................................. 560

26.9. Prevention of cavitation in spillways and energy dissipators 56226.9.1. Design .......................................................................... 562

26.9.2. Construction ................................................................ 563

26.9.3. Operation of structures ............................................... 564

26.l0. Remedial measures and repairs .............................................. 564

27. Air Entrainment and Forced Aeration ................................................ 569

27.1. Introduction ............................................................................. 569

27.2. Air entrainment on spillways .................................................. 56927.3. Location of point of inception ................................................ 572

27.4. Properties of aerated flow ....................................................... 579

27.5. The region of varied flow ....................................................... 584

27.6. Effect of entrained air on stilling basin performance ............ 586

27.7. Forced aeration ........................................................................ 586



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aliviaderos spillways

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