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How can the drag coefficient of a car be reduced? What factors govern the variation in the shape of the Earth's magnetosphere? What is the basis of weather prediction? These are examples of problems that can only be tackled with a sound knowledge of the principles and methods of fluid dynamics. This important discipline has applications which range from the study of the large-scale properties of the galaxies to the design of high precision engineering components. This book introduces the subject of fluid dynamics from the first principles. The first eleven chapters cover all the basic ideas of fluid mechanics, explaining carefully the modelling and mathematics needed. The last six chapters… More illustrate applications of this material to linearised sound and water waves, to high speed flow of air, to non-linear water waves on channels, and to aerofoil theory. Over 350 diagrams have been used to illustrate key points. Exercises are included to help develop and reinforce the reader's understanding of the material presented. References at the ends of each chapter serve not only to guide readers to more detailed texts, but also list where alternative descriptions of the salient points in the chapter may be found. This book is an undergraduate text for second or third year students of mathematics or mathematical physics, who are taking a first course in fluid dynamics.Less

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Book details

List price: $89.99 Copyright year: 1983 Publisher: Cambridge University Press Publication date: 11/10/1983 Binding: Paperback Pages: 540 Size: 6.25" wide x 9.25" long x 1.00" tall Weight: 1.584 Language: English

AuthorTable of Contents

Preface

Introduction

Fluid dynamics

Structure of the text

Method of working

Reference

Mathematical preliminaries

Background knowledge

Polar coordinate systems

The vector derivative, [down triangle, open]

Cartesian tensor methods

Integration formulae

Formulae in polar coordinates

Exercises

References

Physical preliminaries

Background knowledge

Mathematical modelling

Properties of fluids

Dimensional reasoning

Exercise

Observational preliminaries

The continuum model

Fluid velocity and particle paths

Definitions

Streamlines and streaklines

Exercises

References

Mass conservation and stream functions

The continuity equation

The convective derivative

The stream function for two-dimensional flows

Some basic stream functions

Some flow models and the method of images

The (Stokes) stream function for axisymmetric flows

Models using the Stokes stream function

Exercises

References

Vorticity

Analysis of the motion near a point

Simple model flows

Models for vortices

Definitions and theorems for vorticity

Examples of vortex lines and motions

Exercises

References

Hydrostatics

Body forces

The stress tensor

The form of the stress tensor

Hydrostatic pressure and forces

Exercises

References

Thermodynamics

Basic ideas and equations of state

Energy and entropy

The perfect gas model

The atmosphere

Exercises

References

The equation of motion

The fundamental form

Stress and rate of strain

The Navier-Stokes equation

Discussion of the Navier-Stokes equation

Exercises

References

Solutions of the Navier-Stokes equations

Flows with only one coordinate

Some flows with two variables

A boundary layer flow

Flow at high Reynolds number

Exercises

References

Inviscid flow

Euler's equation

The vorticity equation

Kelvin's theorem

Bernoulli's equation

Examples using Bernoulli's equation

A model for the force on a sphere in a stream

Exercises

References

Potential theory

The velocity potential and Laplace's equation

General properties of Laplace's equation

Simple irrotational flows

Solutions by separation of variables

Separation of variables for an axisymmetric flow: Legendre polynomials

Two unsteady flows

Bernoulli's equation for unsteady irrotational flow

The force on an accelerating cylinder

D'Alembert's paradox

Exercises

References

Sound waves in fluids

Background

The linear equations for sound in air

Plane sound waves

Plane waves in musical instruments

Plane waves interacting with boundaries

Energy and energy flow in sound waves

Sound waves in three dimensions

Exercises

References

Water waves

Background

The linear equations

Plane waves on deep water

Energy flow and group velocity

Waves at an interface

Waves on shallower water

Oscillations in a container

Bessel functions

Exercises

References

High speed flow of air

Subsonic and supersonic flows

The use of characteristics

The formation of discontinuities

Plane shock waves

Exercises

References

Steady surface waves in channels

One-dimensional approximation

Hydraulic jumps or bores

Changes across a hydraulic jump

Solitary waves

Exercises

References

The complex potential

Simple complex potentials

More complicated potentials

Potentials for systems of vortices

Image theorems

Calculation of forces

Exercises

References

Conformal mappings and aerofoils

An example

Mappings in general

Particular mappings

A sequence of mappings

The Joukowski transformation of an ellipse

The cambered aerofoil

Further details on aerofoils

Exercises

References

Hints for exercises

Answers for exercises

Books for reference

Index

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