THE HYDRAULICS OF
STEPPED CHUTES
AND SPILLWAYS
HUBERT CHANSON
Reader in Environmental Fluid Mechanics and Water Engineering,
Department of Civil Engineering, The University of Queensland,
Brisbane, Australia.
A.A. BALKEMA PUBLISH ERS l LISSE l ABINGDON l EXTON (PA) l TOKYO
Contents
PREF ACE .". """""""" "" ". """". "" ". ". "" " " "" "" "" .".". """. """". "" ."."" V li
ACKNOWLEDGEMENTS .......................................................................... xi
LTST OF SYMBOL S ................................................ .................................... xv
GLOSSARY ......................................... ......................................................... XXlll
l. INTRODUCTION: BASIC CONCEPTS IN STEPPED CHUTE
HYDRAULICS l
1.1 Presentation ................ ...................................................................... l
1.2 Applications ...................................................................................... 12
1.3 Flow regimes ............ .. ............ .......................................................... 17
1.4 Air entrainment on stepped chutes.................................................. 24
1.5 Structure of the book ............. .......................................................... 30
2. HISTORICAL DEVELOPMENT OF STEPPED SPILLWAYS,
CHANNELS AND CASCADES: FROM ANTIQUITY TO THE
20TH CENTURY 35
2.1 Introduction ...................................................................................... 35
2.2 History of stepped spillways ........................................................... 36
2.3 Ancient waterway systems .............................................................. 37
2.4 Stepped cascades in Roman aqueducts ........................................... 53
2.5 H~storic_al development of water staircases and stepped fountains 58
2.6 DtSCUSS1011 ...... . ....... . ... . .... ... .. .. .. .. . ... . ... . ..... .. . ......................... ......... . ... 65
3 HYDRAULJCS OF NAPPE FLOW REGIME 87
3.1 Introduction .......................................................... .. .. ........................ 87
3.2 Basic flow characteristics ................................................................ 90
3.3 Hydraulic characteristics of nappe flows with hydraulic jumps ... 99
3.4 Hydraulic characteristics of nappe flows without hydraulic
jumps ................................................................................................. l 04
3.5 Design of chutes with nappe flow regime...... ................................ 114
4 THE TRANSITION FLOW REGIME 119
4. 1 Introduction ...................................................................................... 119
4.2 Flow patterns .................................................................................... 119
4.3 Air-water flow properties ................................................................ 122
4.4 Design flow properties ..................................................................... 128
4.5 Discussion: Instabilities in transition flows ................................... 128
5 HYDRAULICS OF SKIMMING FLOWS 137
5 .l Presentation .... .... .... ........ .... ... .. .............. ............. ... .... ..... .... ......... .... . 13 7
5.2 Developing flow region and inception of air entrainment ............ 146
5.3 Fully-developed flow characteristics .............................................. 154
5.4 Energy dissipation ............................................................................ 175
6 MASS TRANSFER ON STEPPED CASCADES AERATION, DE-
AERATION, OXYGENATION, STRIPPING, DEN ITRIFICATION 181
6.1 Introduction ... .... .... .... .... ... .. ... ... ..... .... ... .. .. .. .. .... .... .. ....... .... .. .. .... .... ... 18 1
\'l The hrclrau/ics o/si<'Jlj! l'd chwes ali(/ spi/111·".'"s
6.2 Basic mass transfer equations .... ..................................................... 183
6.3 Nappe tlow regime.. .................... ..................................................... 186
6.4 Skimming flow regime ............... ................... .................................. 193
6.5 Discussion ............. ....................... ..................................................... 197
7 DESIGN OF STEPPED CHANNELS, CHUTES AND SPTLLWAYS 199
7.1 Tntroduction ....................................................................................... 199
7.2 Design of stepped fountains and water staircases .......................... 205
7.3 Concrete stepped spillways and '"'eirs ............................................. 212
7.4 Overflow embankments: ( l) Concrete protcction ........................... 220
7.5 Overflow embankments: (2) Earth dam spillway with precast
concrete blocks ............................. ..................................................... 224
7.6 Gabion stepped weirs and chutes ..................................................... 230
7.7 Unlined rock cascades ...................................................................... 237
7.8 Timber and timber crib dams ........................................................... 238
7.9 Debris dams .... .... ................... ............... ........ ........... ........ .... .... .......... 241
8 ACCIDENTS ANO FAILURES : LEARNING FROM EXPERIENCE 253
8.1 Presentation ....................................................................................... 253
8.2 Failures and accidents....................................................................... 253
8.3 Design safety for stepped chutes and spillways ............................. 272
8.4 Discussion .......................................................................................... 284
9 WAVE PHENOMENA ANO INSTABILITTES TN ST EPPED
CHUTE FLOWS 289
9. 1 rntroduction .. .. .. .. .... .... ..... ... .... .. .. ... ... ....... ... .... .. .... .. .. .. ... ..... .... ..... .... .. 289
9.2 Shock waves and associated standing waves .................................. 289
9.3 Roll waves ......................................................................................... 293
9.4 Flood waves and dam break waves ................................................. 295
lO SUMMARY, CONCLUSIONS AND RECOMMENDA TTONS ........... 301
l O. l Practical considerations for stepped chute design ...................... 30 l
l 0.2 Summary .............................. .... ............... .... .... ....................... ....... 307
l 0. 3 Future research ............................................................................. 3 1O
APPENDICES 3 13
Appendix l Physical and chem ica1 properties of fluids ...................... 313
Appendix 2 Unit conversions ................................................................ 319
Appendix 3 Nappe flow trajectory at a drop structure ........................ 322
Appendix 4 Bubble rise velocity ..... ...................................................... 332
Appendix 5 Mode ll ing form drag and flow resistance in sk imming
flows .................................................................................. 334
Appendix 6 Void fraction distributions in chute flows ....................... 33 7
Appendix 7 Stepped spHiway chute flow calculations (skimming
flow ) ............................. ..................................... ........ ......... 340
Appendix 8 Modelli ng a ir-water gas transfer in skimm ing :flows ...... 345
Appendix 9 Conectio ns ....................................................... ....... ........... 350
ABOUT THE AUTHOR .............................................................................. 353
REFERENCE ................................................................................................ 355
INDEX...... ..................................................................................................... 375
