Table of Contents
Cover
Environmental Hydraulics of Open Channel Flows
Contents
Preface
Acknowledgements
About the author
Dedication
Glossary
A
B
C
D
E
F
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List of symbols
Reminder
Dimensionless numbers
Notes
Part 1 Introduction to Open Channel Flows
1. Introduction
Summary
1.1 Presentation
1.1.1 Discussion: hydraulic engineering through history
1.2 Fluid properties
1.3 Fluid statics
1.4 Open channel flows
1.5 Exercises
2. Fundamentals of open channel flows
Summary
2.1 Presentation
Basic definitions
2.2 Fundamental principles
Discussion: the Bernoulli equation
Applications to open channel flow situations
2.3 Open channel hydraulics of short, frictionless transitions
Application to horizontal channels
Application to non-horizontal channels
Froude number
Discussion
2.4 The hydraulic jump
2.5 Open channel flow in long channels
2.5.1 Presentation
2.5.2 Uniform equilibrium flows
2.5.3 GVF calculations
Integration of the GVF equation
2.6 Summary
2.7 Exercises
Part 2 Turbulent Mixing and Dispersion in Rivers and Estuaries: An Introduction
3. Introduction to mixing and dispersion in natural waterways
3.1 Introduction
Discussion
3.2 Laminar and turbulent flows
Shear stress
3.3 Basic definitions
3.4 Structure of the section
3.5 Appendix A – Application: buoyancy force exerted on a submerged air bubble
Spherical bubble
Bubble rise velocity in still water
Bubble rise velocity in a non-hydrostatic pressure gradient
3.6 Appendix B – Freshwater properties
3.7 Exercises
3.8 Exercise solutions
4. Turbulent shear flows
4.1 Presentation
Summary
DISCUSSION
The Couette flow
4.2 Jets and wakes
Discussion
4.3 Boundary layer flows
Velocity distribution
Applications
Turbulent boundary layer development along a smooth flat plate
4.4 Fully developed open channel flows
4.5 Mixing in turbulent shear flows
4.5.1 Presentation
4.5.2 Discussion: effects of contaminants on shear flows
4.6 Exercises
4.7 Exercise solutions
5. Diffusion: basic theory
5.1 Basic equations
Summary
5.2 Applications
5.2.1 Initial mass slug
DISCUSSION
5.2.2 Initial step function C[sub(m)](x, 0)
5.2.3 Sudden increase in mass concentration at the origin
DISCUSSION
5.2.4 Effects of solid boundaries
5.3 Appendix A – Mathematical aids
Differential operators
Error function
Notation
Constants
Mathematical bibliography
5.4 Exercises
5.5 Exercise solutions
6. Advective diffusion
Summary
6.1 Basic equations
6.2 Basic applications
6.2.1 Advective diffusion of a sharp front
6.2.2 Initial mass slug introduced at t = 0 and x = 0
6.2.3 Transverse mixing of two streams with different concentrations
6.2.4 Sudden mass contamination in a river
6.3 Two- and three-dimensional applications
6.4 Exercises
6.5 Exercise solutions
7. Turbulent dispersion and mixing: 1. Vertical and transverse mixing
Summary
7.1 Introduction
7.2 Flow resistance in open channel flows
7.3 Vertical and transverse (lateral) mixing in turbulent river flows
Discussion
7.4 Turbulent mixing applications
7.4.1 Transverse mixing downstream of a continuous point source
7.4.2 Transverse mixing downstream of a mass slug injection
7.4.3 Complete transverse mixing
7.5 Discussion
7.5.1 Initial mixing
7.5.2 Applications
7.6 Appendix A – Friction factor calculations
7.7 Appendix B – Random walk model
7.8 Appendix C – Turbulent mixing in hydraulic jumps and bores
7.9 Exercises
7.10 Exercise solutions
8. Turbulent dispersion and mixing: 2. Longitudinal dispersion
Summary
8.1 Introduction
8.2 One-dimensional turbulent dispersion
8.3 Longitudinal dispersion in natural streams
8.3.1 Basic equation
Discussion
8.3.2 Dispersion coefficient in natural rivers
Applications
8.4 Approximate models for longitudinal dispersion
8.4.1 The ‘frozen cloud’ approximation
DISCUSSION
Application
8.4.2 Discussion: the Hayami solution
DISCUSSION
8.5 Design applications
8.5.1 Application No. 1
8.5.2 Application No. 2
DISCUSSION
8.6 Exercises
8.7 Exercise solutions
9. Turbulent dispersion in natural systems
Summary
9.1 Introduction
Definitions
9.2 Longitudinal dispersion in natural rivers with dead zones
9.2.1 Introduction
9.2.2 Basic equation
9.2.3 Analytical solutions (instantaneous mass slug injection)
9.3 Dispersion and transport of reactive contaminants
9.3.1 Basic equation
9.3.2 Applications
Sudden mass slug contamination in a river
Sudden increase in mass concentration at the origin
9.3.3 Discussion
9.4 Transport with reaction
9.4.1 Basic equation
9.4.2 Application to dissolved oxygen content (DOC) in natural streams
Re-oxygenation rate constant and decay rate
9.4.3 DO sag analysis
9.5 Appendix A – Air–water mass transfer in air–water flows
9.6 Appendix B – Solubility of nitrogen, oxygen and argon in water
Solubility of oxygen
Volumetric solubility of nitrogen, oxygen and argon
9.7 Appendix C – Molecular diffusion coefficients in water (after Chanson 1997a)
9.8 Exercises
9.9 Exercise solutions
10. Mixing in estuaries
Summary
10.1 Presentation
Seawater properties
10.2 Basic mechanisms
10.2.1 Mixing caused by winds
10.2.2 Mixing caused by tides
Shear effect in estuaries
Tidal pumping
Tidal trapping
10.2.3 Mixing caused by the river
10.2.4 Discussion: mixing induced by tidal bores
10.3 Applications
10.3.1 Salt wedges
10.3.2 Steady vertical circulation
10.4 Turbulent mixing and dispersion coefficients in estuaries
10.5 Applications
10.5.1 Application no. 1: Ino-hana Lake, Hama-matsu (Japan)
Discussion
10.5.2 Application no. 2: Eprapah Creek, Queensland (Australia)
Discussion
10.5.3 Application no. 3: Strait of Gibraltar
Discussion
10.6 Appendix A – Observations of mixing and dispersion coefficients in estuarine zones
10.6.1 Field observations of mixing in tidal bores
10.7 Exercises
10.8 Exercise solutions
Part 2 Revision exercises
Assignment solutions
DISCUSSION
Part 3 Introduction to Unsteady Open Channel Flows
11. Unsteady open channel flows: 1. Basic equations
Summary
11.1 Introduction
11.2 Basic equations
11.2.1 Presentation
11.2.2 Integral form of the Saint-Venant equations
11.2.3 Differential form of the Saint-Venant equations
Discussion
11.2.4 Flow resistance estimate
Discussion
Flood plain calculations
11.3 Method of characteristics
11.3.1 Introduction
Discussion: graphical solution of the characteristic system of equations
11.3.2 Boundary conditions
Initial and boundary conditions
Types of boundary conditions
DISCUSSION
11.3.3 Application: numerical integration of the method of characteristics
11.4 Discussion
11.4.1 The dynamic equation
Simplification of the dynamic wave equation for unsteady flows
11.4.2 Limitations of the Saint-Venant equations
Flood plains
Non-hydrostatic pressure distributions
Sharp discontinuities
DISCUSSION
11.4.3 Summary
11.5 Exercises
11.6 Exercise solutions
12. Unsteady open channel flows: 2. Applications
Summary
12.1 Introduction
12.2 Propagation of waves
12.2.1 Propagation of a small wave
12.2.2 Propagation of a known discharge (monoclinal wave)
12.3 The simple wave problem
12.3.1 Basic equations
12.3.2 Application
Discussion
12.4 Positive and negative surges
12.4.1 Presentation
12.4.2 Positive surge
Simple wave calculations of a positive surge
Positive surge propagating in uniform equilibrium flow
Discussion
12.4.3 Negative surge
Sudden complete opening
Sudden partial opening
Negative surge in a forebay
12.5 The kinematic wave problem
12.5.1 Presentation
12.5.2 Discussion
12.6 The diffusion wave problem
12.6.1 Presentation
12.6.2 Discussion
12.6.3 The Cunge–Muskingum method
Empiricism: the Muskingum method!?
Cunge–Muskingum method
12.7 Appendix A – Gaussian error functions
12.7.1 Gaussian error function
12.7.2 Complementary error function
12.8 Exercises
12.9 Exercise solutions
13. Unsteady open channel flows: 3. Application to dam break wave
Summary
13.1 Introduction
Discussion: man-made dam failures
13.2 Dam break wave in a horizontal channel
13.2.1 Dam break in a dry channel
13.2.2 Dam break in a horizontal channel initially filled with water Presentation
Extension to non-zero initial flow velocity
Discussion
13.3 Effects of flow resistance
13.3.1 Flow resistance effect on dam break wave on horizontal channel
Dam break wave calculations with flow resistance
13.3.2 Dam break wave down a sloping channel
Basic theory
Dam break wave down a sloping stepped chute
13.3.3 Further dam break wave conditions
DISCUSSION
13.4 Embankment dam failures
13.4.1 Introduction
13.4.2 Embankment breach
Breach development
13.5 Related flow situations
13.6 Exercises
13.7 Exercise solutions
14. Numerical modelling of unsteady open channel flows
Summary
14.1 Introduction
Finite differences methods
14.2 Explicit finite difference methods
14.2.1 Lax diffusive method
Boundary conditions
14.2.2 Leap-frog scheme
14.2.3 Discussion
14.3 Implicit finite difference methods
Discussion
14.4 Exercises
Part 3 Revision exercises
Revision exercise no. 1
Revision exercise no. 2
Revision exercise no. 3
Revision exercise no. 4
Discussion
Part 4 Interactions between Flowing Water and its Surroundings
15. Interactions between flowing water and its surroundings: introduction
15.1 Presentation
15.2 Terminology
15.3 Structure of this section
16. Interaction between flowing water and solid boundaries: sediment processes
Summary
16.1 Introduction
Forces acting on a sediment particle
16.2 Physical properties of sediments
16.2.1 Introduction
16.2.2 Particle fall velocity
Discussion
16.3 Threshold of sediment bed motion
16.3.1 Introduction
16.3.2 Threshold of bed-load motion
16.3.3 Initiation of sediment suspension
16.4 Sediment transport
16.4.1 Bed-load transport rate
Discussion
16.4.2 Suspension transport rate
DISCUSSION
16.5 Total sediment transport rate
16.5.1 Presentation
DISCUSSION: BED FORMS IN RIVERS AND STREAMS
16.5.2 Flow resistance in natural systems
16.5.3 Design calculations
16.6 Exercises
17. Interaction between flowing water and free surfaces: self-aeration and air entrainment
Summary
17.1 Introduction
17.2 Free-surface aeration in turbulent flows: basic mechanisms
17.2.1 Presentation
17.2.2 Local/singular aeration mechanism: air entrapment at plunging jets
17.2.3 Interfacial aeration process: self-aeration down a steep chute
DISCUSSION
17.2.4 Interfacial aeration process: self-aeration at water jet interfaces
Discussion
17.3 Dimensional analysis and similitude
17.3.1 Introduction
17.3.2 Applications
Air entrainment at vertical plunging jets
Air entrainment in steep chute flows
DISCUSSION
17.3.3 Dynamic similarity and scale effects
17.4 Basic metrology in air–water flow studies
17.4.1 Introduction
17.4.2 Signal processing and data analysis
17.4.3 Unsteady flow measurements
17.5 Applications
17.5.1 Application to plunging jet flows
General considerations
Discussion
17.5.2 Application to steep chute flows
Drag reduction in self-aerated chute flows
17.6 Appendix A – Air bubble diffusion in plunging jet flows (after Chanson 1997a)
Two-dimensional plunging jets
Circular plunging jets
17.7 Appendix B – Air bubble diffusion in self-aerated supercritical flows
Discussion
17.8 Appendix C – Air bubble diffusion in high-velocity water jets
Two-dimensional free-shear layers
Circular jets
Discussion
17.9 Exercises
Appendix A: Constants and fluid properties
A.1 Acceleration of gravity
A.2 Properties of water
A.3 Gas properties
Basic equations
Physical properties
Atmospheric parameters
Viscosity of air
Appendix B: Unit conversions
B.1 Introduction
B.2 Units and conversion factors
References
Abbreviations of journals and institutions
Common bibliographical abbreviations
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
Y