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A First Course in Fluid Dynamics - A. R. Paterson

A First Course in Fluid Dynamics

Paperback

Published: 9th January 1984
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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.

"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

Prefacep. ix
Introductionp. 1
Fluid dynamicsp. 1
Structure of the textp. 3
Method of workingp. 4
Referencep. 5
Mathematical preliminariesp. 7
Background knowledgep. 7
Polar coordinate systemsp. 10
The vector derivative, [down triangle, open]p. 13
Cartesian tensor methodsp. 14
Integration formulaep. 17
Formulae in polar coordinatesp. 19
Exercisesp. 22
Referencesp. 24
Physical preliminariesp. 25
Background knowledgep. 25
Mathematical modellingp. 25
Properties of fluidsp. 27
Dimensional reasoningp. 29
Exercisep. 30
Observational preliminariesp. 32
The continuum modelp. 32
Fluid velocity and particle pathsp. 34
Definitionsp. 37
Streamlines and streaklinesp. 39
Exercisesp. 42
Referencesp. 43
Mass conservation and stream functionsp. 45
The continuity equationp. 45
The convective derivativep. 46
The stream function for two-dimensional flowsp. 48
Some basic stream functionsp. 53
Some flow models and the method of imagesp. 58
The (Stokes) stream function for axisymmetric flowsp. 62
Models using the Stokes stream functionp. 64
Exercisesp. 68
Referencesp. 70
Vorticityp. 71
Analysis of the motion near a pointp. 71
Simple model flowsp. 77
Models for vorticesp. 80
Definitions and theorems for vorticityp. 83
Examples of vortex lines and motionsp. 89
Exercisesp. 92
Referencesp. 94
Hydrostaticsp. 95
Body forcesp. 95
The stress tensorp. 96
The form of the stress tensorp. 99
Hydrostatic pressure and forcesp. 102
Exercisesp. 108
Referencesp. 110
Thermodynamicsp. 111
Basic ideas and equations of statep. 111
Energy and entropyp. 115
The perfect gas modelp. 118
The atmospherep. 122
Exercisesp. 125
Referencesp. 126
The equation of motionp. 127
The fundamental formp. 127
Stress and rate of strainp. 128
The Navier-Stokes equationp. 131
Discussion of the Navier-Stokes equationp. 133
Exercisesp. 138
Referencesp. 139
Solutions of the Navier-Stokes equationsp. 140
Flows with only one coordinatep. 140
Some flows with two variablesp. 148
A boundary layer flowp. 157
Flow at high Reynolds numberp. 160
Exercisesp. 165
Referencesp. 168
Inviscid flowp. 169
Euler's equationp. 169
The vorticity equationp. 170
Kelvin's theoremp. 177
Bernoulli's equationp. 180
Examples using Bernoulli's equationp. 186
A model for the force on a sphere in a streamp. 197
Exercisesp. 201
Referencesp. 204
Potential theoryp. 205
The velocity potential and Laplace's equationp. 205
General properties of Laplace's equationp. 209
Simple irrotational flowsp. 214
Solutions by separation of variablesp. 216
Separation of variables for an axisymmetric flow: Legendre polynomialsp. 221
Two unsteady flowsp. 228
Bernoulli's equation for unsteady irrotational flowp. 232
The force on an accelerating cylinderp. 236
D'Alembert's paradoxp. 240
Exercisesp. 243
Referencesp. 247
Sound waves in fluidsp. 248
Backgroundp. 248
The linear equations for sound in airp. 249
Plane sound wavesp. 253
Plane waves in musical instrumentsp. 261
Plane waves interacting with boundariesp. 264
Energy and energy flow in sound wavesp. 272
Sound waves in three dimensionsp. 278
Exercisesp. 285
Referencesp. 288
Water wavesp. 289
Backgroundp. 289
The linear equationsp. 290
Plane waves on deep waterp. 293
Energy flow and group velocityp. 297
Waves at an interfacep. 300
Waves on shallower waterp. 305
Oscillations in a containerp. 310
Bessel functionsp. 317
Exercisesp. 322
Referencesp. 324
High speed flow of airp. 325
Subsonic and supersonic flowsp. 325
The use of characteristicsp. 331
The formation of discontinuitiesp. 339
Plane shock wavesp. 350
Exercisesp. 359
Referencesp. 362
Steady surface waves in channelsp. 363
One-dimensional approximationp. 363
Hydraulic jumps or boresp. 370
Changes across a hydraulic jumpp. 377
Solitary wavesp. 382
Exercisesp. 392
Referencesp. 395
The complex potentialp. 396
Simple complex potentialsp. 396
More complicated potentialsp. 402
Potentials for systems of vorticesp. 410
Image theoremsp. 413
Calculation of forcesp. 422
Exercisesp. 432
Referencesp. 434
Conformal mappings and aerofoilsp. 435
An examplep. 435
Mappings in generalp. 439
Particular mappingsp. 448
A sequence of mappingsp. 459
The Joukowski transformation of an ellipsep. 462
The cambered aerofoilp. 468
Further details on aerofoilsp. 476
Exercisesp. 479
Referencesp. 482
Hints for exercisesp. 483
Answers for exercisesp. 508
Books for referencep. 519
Indexp. 521
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521274241
ISBN-10: 0521274249
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 540
Published: 9th January 1984
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.71 x 15.19  x 3.28
Weight (kg): 0.84