Basic Hydrodynamics

Basic Hydrodynamics explores the application of computers to problem solving involved in fluid flow. This book contains 5 chapters that cover the use of BASIC programming language in hydrodynamic problems and some programs with graphic output, as well as some simple finite difference, finite element and boundary element programs. After a brief introduction to BASIC programming, this book goes discussing the fundamentals of potential flow theory that will be used to calculate flows, which can be regarded as frictionless. These topics are followed by a presentation of some analytical expressions for potential flows. Chapter 3 outlines the computer based methods for solving problems within these flows, while Chapter 4 highlights some potential flow methods to the solution of groundwater flows. Exact solutions are also provided for comparison with the computer methods. Lastly, Chapter 5 considers free surface flows, such as linear waves and flows from jets.
This work will be of value to engineers, designers, and computer programmers and scientists who are interested in computer application to hydrodynamics field.

Preface

1 Introduction to BASIC

1.1 The BASIC Philosophy

1.2 Elementary BASIC

1.3 Checking Programs

1.4 Versions of BASIC and Different Computers

1.5 Bibliography

2 Potential Flow Fundamentals

Essential Theory

2.1 Stream Function

2.2 Velocity Potential

2.3 Flow Nets

2.4 Sketching Flow Nets

2.5 Combining Simple Solutions

2.6 Mapping

2.7 Bernoulli's Equation

2.8 Application of Bernoulli's Equation

2.9 Pressure in a Circular Passage

2.10 Forces on a Circle with a Circulation

2.11 Expressions for Pressures and Forces

2.12 Boundary Layer on a Flat Plate

2.13 Bibliography

Worked Examples

2.1 XYSP1: Stream Function and Potential in a Source

2.2 SPLOT: Streamlines of Sources and a Stream

2.3 TRANC1: Transforms Circle Flow and Plots Shape

2.4 TRANC2: Forces on a Transformed Circle

2.5 FDBL: Boundary Layer on a Flat Plate

Problems

3 Numerical Solutions to Potential Flows

Essential Theory

3.1 General Approach

3.2 Finite Difference Method — Principles

3.3 Finite Difference Equations

3.4 Finite Differences — Boundary Value

3.5 Solution of Finite Difference Equations

3.6 Finite Element Method

3.7 Boundary Element Methods

3.8 Bibliography

Worked Examples

3.1 FDIT1: Finite Difference Solution for Flow through a Channel

3.2 FEM2: Finite Element Program for Potential Flow Past a Circle

3.3 BEM2: Boundary Element Program Applied to Circle Flow

3.4 BEM3: Circle Flow as an 'External' BEM Problem

Problems

4 Seepage Flows

Essential Theory

4.1 Introduction

4.2 Confined Flow under a Dam

4.3 Confined Flow into Excavations

4.4 Flows with Variable Permeability

4.5 Free Surface Flow on a Shallow Foundation

4.6 Horizontal Seepage Flow

4.7 Flow in Confined and Unconfined Aquifers

4.8 Well near a Boundary

4.9 Time Varying Seepage

4.10 Bibliography

Worked Examples

4.1 SPXY2: Flow under a Dam

4.2 XYSP2: Flow to Wells on an Island

4.3 FDIT3: Flow to Wells — Finite Differences

4.4 FDIT10: Flow under a Dam — Finite Differences

4.5 FDIT12: Seepage with Varying Permeability — Finite Differences

4.6 FDIT4: Free Surface Flows — Finite Differences

Problems

5 Free Surface Flows

Essential Theory

5.1 Water Surface Waves

5.2 Reflection of Waves

5.3 Complex Potential for waves

5.4 The Boundary Element Method and Waves

5.5 Reflected and Transmitted Waves

5.6 Forces on Large 2D Objects Fixed in Waves

5.7 Wave Forces on Vertical Cylinders

5.8 Wave Forces on Large Vertical Cylinders

5.9 Other Free Surface Flows

5.10 The x-ψ Coordinate System

5.11 Flows from an Orifice

5.12 Sluice Gates

5.13 Weirs and Spillways

5.14 Bibliography

Worked Examples

5.1 WAVE1: Wave Length and Celerity

5.2 WAVE2: Surface and Water Movement in Waves

5.3 BEM4: Waves and Obstacles

5.4 FDSX4: Jets and Weirs

Problems

Index