Open Channel Flow : Numerical Methods and Computer Applications book cover
1st Edition

Open Channel Flow
Numerical Methods and Computer Applications

ISBN 9781439839751
Published November 9, 2010 by CRC Press
1258 Pages 447 B/W Illustrations

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Book Description

A comprehensive treatment of open channel flow, Open Channel Flow: Numerical Methods and Computer Applications starts with basic principles and gradually advances to complete problems involving systems of channels with branches, controls, and outflows/ inflows that require the simultaneous solutions of systems of nonlinear algebraic equations coupled with differential equations. The book includes downloadable resources that contain a program that solves all types of simple open channel flow problems, the source programs described in the text, the executable elements of these programs, the TK-Solver and MathCad programs, and the equivalent MATLAB® scripts and functions.

The book provides applied numerical methods in an appendix and also incorporates them as an integral component of the methodology in setting up and solving the governing equations. Packed with examples, the book includes problems at the end of each chapter that give readers experience in applying the principles and often expand upon the methodologies use in the text. The author uses Fortran as the software to supply the computer instruction but covers math software packages such as MathCad, TK-Solver, MATLAB, and spreadsheets so that readers can use the instruments with which they are the most familiar. He emphasizes the basic principles of conservation of mass, energy, and momentum, helping readers achieve true mastery of this important subject, rather than just learn routine techniques.

With the enhanced understanding of the fundamental principles of fluid mechanics provided by this book, readers can then apply these principles to the solution of complex real-world problems. The book supplies the knowledge tools necessary to analyze and design economical and properly performing conveyance systems. Thus not only is the book useful for graduate students, but it also provides professional engineers the expertise and knowledge to design well performing and economical channel systems.

Table of Contents

Dimensions, Terminology, and Review of Basic Fluid Mechanics
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

Energy and Its Dissipation in Open Channels
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
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

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
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

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

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

Numerical Solution of the St. Venant Equations
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

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

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