A First Course in Fluid Dynamics

By: A. R. Paterson

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Paperback | 9 January 1984

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540 Pages

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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 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.

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"It is interesting to browse through the book and see from the selection and arrangement of the material the skeleton of an interesting course evolving..." Physics in Canada

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Non-Fiction Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Science Physics Classical Mathematics Fluid Mechanics Mathematics Applied Mathematics

Preface	p. ix
Introduction	p. 1
Fluid dynamics	p. 1
Structure of the text	p. 3
Method of working	p. 4
Reference	p. 5
Mathematical preliminaries	p. 7
Background knowledge	p. 7
Polar coordinate systems	p. 10
The vector derivative, [down triangle, open]	p. 13
Cartesian tensor methods	p. 14
Integration formulae	p. 17
Formulae in polar coordinates	p. 19
Exercises	p. 22
References	p. 24
Physical preliminaries	p. 25
Background knowledge	p. 25
Mathematical modelling	p. 25
Properties of fluids	p. 27
Dimensional reasoning	p. 29
Exercise	p. 30
Observational preliminaries	p. 32
The continuum model	p. 32
Fluid velocity and particle paths	p. 34
Definitions	p. 37
Streamlines and streaklines	p. 39
Exercises	p. 42
References	p. 43
Mass conservation and stream functions	p. 45
The continuity equation	p. 45
The convective derivative	p. 46
The stream function for two-dimensional flows	p. 48
Some basic stream functions	p. 53
Some flow models and the method of images	p. 58
The (Stokes) stream function for axisymmetric flows	p. 62
Models using the Stokes stream function	p. 64
Exercises	p. 68
References	p. 70
Vorticity	p. 71
Analysis of the motion near a point	p. 71
Simple model flows	p. 77
Models for vortices	p. 80
Definitions and theorems for vorticity	p. 83
Examples of vortex lines and motions	p. 89
Exercises	p. 92
References	p. 94
Hydrostatics	p. 95
Body forces	p. 95
The stress tensor	p. 96
The form of the stress tensor	p. 99
Hydrostatic pressure and forces	p. 102
Exercises	p. 108
References	p. 110
Thermodynamics	p. 111
Basic ideas and equations of state	p. 111
Energy and entropy	p. 115
The perfect gas model	p. 118
The atmosphere	p. 122
Exercises	p. 125
References	p. 126
The equation of motion	p. 127
The fundamental form	p. 127
Stress and rate of strain	p. 128
The Navier-Stokes equation	p. 131
Discussion of the Navier-Stokes equation	p. 133
Exercises	p. 138
References	p. 139
Solutions of the Navier-Stokes equations	p. 140
Flows with only one coordinate	p. 140
Some flows with two variables	p. 148
A boundary layer flow	p. 157
Flow at high Reynolds number	p. 160
Exercises	p. 165
References	p. 168
Inviscid flow	p. 169
Euler's equation	p. 169
The vorticity equation	p. 170
Kelvin's theorem	p. 177
Bernoulli's equation	p. 180
Examples using Bernoulli's equation	p. 186
A model for the force on a sphere in a stream	p. 197
Exercises	p. 201
References	p. 204
Potential theory	p. 205
The velocity potential and Laplace's equation	p. 205
General properties of Laplace's equation	p. 209
Simple irrotational flows	p. 214
Solutions by separation of variables	p. 216
Separation of variables for an axisymmetric flow: Legendre polynomials	p. 221
Two unsteady flows	p. 228
Bernoulli's equation for unsteady irrotational flow	p. 232
The force on an accelerating cylinder	p. 236
D'Alembert's paradox	p. 240
Exercises	p. 243
References	p. 247
Sound waves in fluids	p. 248
Background	p. 248
The linear equations for sound in air	p. 249
Plane sound waves	p. 253
Plane waves in musical instruments	p. 261
Plane waves interacting with boundaries	p. 264
Energy and energy flow in sound waves	p. 272
Sound waves in three dimensions	p. 278
Exercises	p. 285
References	p. 288
Water waves	p. 289
Background	p. 289
The linear equations	p. 290
Plane waves on deep water	p. 293
Energy flow and group velocity	p. 297
Waves at an interface	p. 300
Waves on shallower water	p. 305
Oscillations in a container	p. 310
Bessel functions	p. 317
Exercises	p. 322
References	p. 324
High speed flow of air	p. 325
Subsonic and supersonic flows	p. 325
The use of characteristics	p. 331
The formation of discontinuities	p. 339
Plane shock waves	p. 350
Exercises	p. 359
References	p. 362
Steady surface waves in channels	p. 363
One-dimensional approximation	p. 363
Hydraulic jumps or bores	p. 370
Changes across a hydraulic jump	p. 377
Solitary waves	p. 382
Exercises	p. 392
References	p. 395
The complex potential	p. 396
Simple complex potentials	p. 396
More complicated potentials	p. 402
Potentials for systems of vortices	p. 410
Image theorems	p. 413
Calculation of forces	p. 422
Exercises	p. 432
References	p. 434
Conformal mappings and aerofoils	p. 435
An example	p. 435
Mappings in general	p. 439
Particular mappings	p. 448
A sequence of mappings	p. 459
The Joukowski transformation of an ellipse	p. 462
The cambered aerofoil	p. 468
Further details on aerofoils	p. 476
Exercises	p. 479
References	p. 482
Hints for exercises	p. 483
Answers for exercises	p. 508
Books for reference	p. 519
Index	p. 521
Table of Contents provided by Syndetics. All Rights Reserved.

A First Course in Fluid Dynamics

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