ISBN-10:
0521254167
ISBN-13:
9780521254168
Pub. Date:
01/01/1984
Publisher:
Cambridge University Press
A First Course in Fluid Dynamics

A First Course in Fluid Dynamics

by A. R. Paterson

Hardcover

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Product Details

ISBN-13: 9780521254168
Publisher: Cambridge University Press
Publication date: 01/01/1984
Pages: 544
Product dimensions: 5.98(w) x 8.98(h) x (d)

Table of Contents

Prefaceix
Introduction1
1Fluid dynamics1
2Structure of the text3
3Method of working4
Reference5
IMathematical preliminaries7
1Background knowledge7
2Polar coordinate systems10
3The vector derivative, [down triangle, open]13
4Cartesian tensor methods14
5Integration formulae17
6Formulae in polar coordinates19
Exercises22
References24
IIPhysical preliminaries25
1Background knowledge25
2Mathematical modelling25
3Properties of fluids27
4Dimensional reasoning29
Exercise30
IIIObservational preliminaries32
1The continuum model32
2Fluid velocity and particle paths34
3Definitions37
4Streamlines and streaklines39
Exercises42
References43
IVMass conservation and stream functions45
1The continuity equation45
2The convective derivative46
3The stream function for two-dimensional flows48
4Some basic stream functions53
5Some flow models and the method of images58
6The (Stokes) stream function for axisymmetric flows62
7Models using the Stokes stream function64
Exercises68
References70
VVorticity71
1Analysis of the motion near a point71
2Simple model flows77
3Models for vortices80
4Definitions and theorems for vorticity83
5Examples of vortex lines and motions89
Exercises92
References94
VIHydrostatics95
1Body forces95
2The stress tensor96
3The form of the stress tensor99
4Hydrostatic pressure and forces102
Exercises108
References110
VIIThermodynamics111
1Basic ideas and equations of state111
2Energy and entropy115
3The perfect gas model118
4The atmosphere122
Exercises125
References126
VIIIThe equation of motion127
1The fundamental form127
2Stress and rate of strain128
3The Navier-Stokes equation131
4Discussion of the Navier-Stokes equation133
Exercises138
References139
IXSolutions of the Navier-Stokes equations140
1Flows with only one coordinate140
2Some flows with two variables148
3A boundary layer flow157
4Flow at high Reynolds number160
Exercises165
References168
XInviscid flow169
1Euler's equation169
2The vorticity equation170
3Kelvin's theorem177
4Bernoulli's equation180
5Examples using Bernoulli's equation186
6A model for the force on a sphere in a stream197
Exercises201
References204
XIPotential theory205
1The velocity potential and Laplace's equation205
2General properties of Laplace's equation209
3Simple irrotational flows214
4Solutions by separation of variables216
5Separation of variables for an axisymmetric flow: Legendre polynomials221
6Two unsteady flows228
7Bernoulli's equation for unsteady irrotational flow232
8The force on an accelerating cylinder236
9D'Alembert's paradox240
Exercises243
References247
XIISound waves in fluids248
1Background248
2The linear equations for sound in air249
3Plane sound waves253
4Plane waves in musical instruments261
5Plane waves interacting with boundaries264
6Energy and energy flow in sound waves272
7Sound waves in three dimensions278
Exercises285
References288
XIIIWater waves289
1Background289
2The linear equations290
3Plane waves on deep water293
4Energy flow and group velocity297
5Waves at an interface300
6Waves on shallower water305
7Oscillations in a container310
8Bessel functions317
Exercises322
References324
XIVHigh speed flow of air325
1Subsonic and supersonic flows325
2The use of characteristics331
3The formation of discontinuities339
4Plane shock waves350
Exercises359
References362
XVSteady surface waves in channels363
1One-dimensional approximation363
2Hydraulic jumps or bores370
3Changes across a hydraulic jump377
4Solitary waves382
Exercises392
References395
XVIThe complex potential396
1Simple complex potentials396
2More complicated potentials402
3Potentials for systems of vortices410
4Image theorems413
5Calculation of forces422
Exercises432
References434
XVIIConformal mappings and aerofoils435
1An example435
2Mappings in general439
3Particular mappings448
4A sequence of mappings459
5The Joukowski transformation of an ellipse462
6The cambered aerofoil468
7Further details on aerofoils476
Exercises479
References482
Hints for exercises483
Answers for exercises508
Books for reference519
Index521

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