Open Channel Flow Numerical Methods and Computer Applications

Dimensions, Terminology, and Review of Basic Fluid Mechanics
Introduction
One-, Two-, and Three-Dimensional Flows
Steady versus Unsteady Flow
Uniform versus Nonuniform Flow
Prismatic versus Non-Prismatic Channels
Subcritical, Critical, and Supercritical Flows
Turbulent versus Laminar Flow
Review of Basic Fluid Mechanics Principles
Physical Properties of Fluids and Their Effects on Open-Channel Flows
Conservation of Mass, or Continuity Equations
Energy Principle
Problems

Energy and Its Dissipation in Open Channels
Introduction
Approaches to Frictional Resistance
Combining the Chezy and the Chezy C Equations
Empirical Formula: Use of Manning’s Equation
Channels with Varying Wall Roughness, but Q = Constant
Specific Energy, Subcritical and Supercritical Flows
Flumes
Delivery Diagrams
Graphical Aids to Solving Critical Flow Problems
Upstream Depth When Critical Conditions Occur at Reduced Downstream Section
Dimensionless Treatment of Upstream Trapezoidal Channel to Downstream Rectangular Channel
Hydraulically Most Efficient Section
Problems
References

The Momentum Principle Applied to Open Channel Flows
The Momentum Function
Characteristics of the Momentum Function
Rectangular Channels and Momentum Function per Unit Width
Polynomial Form for Momentum Function
Dimensionless Momentum Functions
Celerity of Small Amplitude Gravity Waves
Constant Height Waves
Open Channel to Pipe Flow
Multiple Roughness Coefficient for Channel Section— Compound Sections Problems
Problems to Solve Using Program CHANNEL

Nonuniform Flows
Types of Nonuniform Flows
Ordinary Differential Equation for Gradually Varied Flow
Gradually Varied Flow in Prismatic Channels without Lateral Inflow or Outflow
Numerical Methods for Solving ODEs
Canal Systems
Simultaneous Solution of Algebraic and Ordinary Differential Equations
Flow into a Mild Channel with a Downstream Control
Different Modes of Gate Operation
Hydraulic Jump Downstream from a Gate in a Finite Length Channel
Nonprismatic Channels
Culverts
GVF Profiles in Nonprismatic Channels
GVF Profiles in Branched Channel Systems
GVF Profiles in Parallel Channels
Solutions to Spatially Varied Flows
Spatially Varied Inflows
Spatially Varied Flow in Nonprismatic Channels
Tile Drainage
Downstream Controls in Nonprismatic Channels
Gutter Flow and Outflow through Grates
Multiple Branched Channel Systems
Other Dependent Variables in GVF Computations
Varied Flow Function
Moving Waves
Moving Hydraulic Jump
Problems
References

Common Techniques Used in Practice and Controls
Introduction
Resistance to Flow in Natural Streams and Rivers
Techniques Used for Solving Steady Flows in Irregular Channels
Water Measurement in Channels
Design of Transitions
Gates
Submerged Flow Downstream from Vertical Gates
Series of Submerged Gates
Design of Side Weirs
Optimal Design of Trapezoidal Channels Considering Total Costs
Problems
References

Unsteady Flows
When Should Flow Be Handled as Unsteady?
Basic One-Dimensional Equations for Unsteady Channel Flows (The St. Venant Equations)Determination of Mathematical Type of St. Venant Equations
Taking Advantage of the Equation Characteristics
Solution to Unsteady Flows That Deviate Only Slightly from Uniform Conditions
Boundary Conditions
Maximum Possible Flow Rates
Extending the Methods to Non-Rectangular Channels
Maximum Flow Rates in Non-Rectangular Channels
Positive Waves
Control Structures
Partial Instant Opening of Gates in Rectangular Channels
Partial Instant Closing of Gates in Trapezoidal Channels
Partial Instant Closure Followed by Slow Movement Thereafter
Dam Break Problem
Problems

Numerical Solution of the St. Venant Equations
Background
Method of Characteristics
Boundary Conditions
Using Characteristics with Specified Time Increments
Iterative Solution Technique
Explicit Evaluation of Variables at Points L and R
Accuracy of Numerical Solutions
Implicit Methods
Gauss–Seidel or Successive-Over-Relaxation (SOR) Iterative Solution Techniques
Crank–Nicolson Newton Iterative Implicit Method
Weighting Current and Advanced Time Steps Differently
The Preissmann Implicit Method
Solving Preissmann Difference Equations Using the Newton Method
Two-Dimensional Free Surface Flows
Problems
References

Appendix A: Open Channel Geometry and Properties
Appendix B: Numerical Methods
Appendix C: ODESOL: Subroutine to Solve ODEs
Index

Biography

Roland Jeppson is Professor Emeritus of civil and environmental engineering in the Utah Water Research Laboratory (UWRL) at Utah State University in Logan.