Introductory fluid mechanics for physicists and mathematicians:
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Chichester
Wiley
2013
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| Edition: | 1. publ. |
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| Physical Description: | XX, 468 S. graph. Darst. |
| ISBN: | 9781119944850 9781119944843 |
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| 100 | 1 | |a Pert, Geoffrey J. |e Verfasser |0 (DE-588)133390411 |4 aut | |
| 245 | 1 | 0 | |a Introductory fluid mechanics for physicists and mathematicians |c Geoffrey J. Pert |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2013 | |
| 300 | |a XX, 468 S. |b graph. Darst. | ||
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| adam_text | Titel: Introductory fluid mechanics for physicists and mathematicians
Autor: Pert, Geoffrey J
Jahr: 2013
Contents
Preface
xvii
1 Introduction 1
1.1 Fluids as a State of Matter.................... 1
1.2 The Fundamental Equations for Flow of a Dissipationless Fluid 3
1.3 Lagrangian Frame......................... 4
1.3.1 Conservation of Mass................... 6
1.3.2 Conservation of Momentum-Euler s Equation..... 7
1.3.3 Conservation of Angular Momentum.......... 8
1.3.4 Conservation of Energy.................. 8
1.3.5 Conservation of Entropy................. 8
1.4 Eulerian Frame.......................... 8
1.4.1 Conservation of Mass-Equation of Continuity..... 8
1.4.2 Conservation of Momentum............... 9
1.4.3 Conservation of Angular Momentum.......... 10
1.4.4 Conservation of Energy.................. 11
1.4.5 Conservation of Entropy................. 11
1.5 Hydrostatics............................ 12
1.5.1 Isothermal Fluid-Thermal and Mechanical Equilibrium 12
1.5.2 Adiabatic Fluid-Lapse Rate............... 12
1.5.3 Stability of an Equilibrium Configuration........ 15
1.6 Streamlines ............................ 16
1.7 Bernoulli s Equation: Weak Form................ 16
1.8 Polytropic Gases ......................... 17
1.8.1 Applications of Bernoulli s Theorem .......... 19
1.8.1.1 Vena Contraeta................. 19
1.8.1.2 Flow of gas along a pipe of varying cross-section 20
Case study 1.1 Munroe Effect -Shaped Charge Explosive . . 22
2 Flow of Ideal Fluids 25
2.1 Introduction............................ 25
2.2 Kelvin s Theorem......................... 26
vn
VÜi Contents
2.2.1 Vorticity and Helmholtz s Theorems .......... 27
2.2.1.1 Simple or rectilinear vortex.......... 29
2.2.1.2 Vortex sheet................... 29
2.3 Irrotational Flow......................... 31
2.3.1 Crocco s Equation..................... 31
2.4 Irrotational Flow-Velocity Potential and the Strong Form of
Bernoulli s Equation ....................... 32
2.5 Incompressible Flow-Streamfunction.............. 33
2.5.1 Planar Systems...................... 33
2.5.2 Axisymmetric Flow-Stokes Streamfunction...... 34
2.6 Irrotational Incompressible Flow................. 35
2.6.1 Simply and Multiply Connected Spaces......... 37
2.7 Induced Velocity.......................... 38
2.7.1 Streamlined Flow around a Body Treated
as a Vortex Sheet..................... 41
2.8 Sources and Sinks......................... 42
2.8.1 Doublet Sources...................... 43
2.8.1.1 Doublet sheets................. 45
2.8.2 Flow Around a Body Treated as a Source Sheet .... 45
2.8.3 Irrotational Incompressible Flow Around a Sphere ... 48
Case study 2.1 Rankine Ovals................. 49
2.9 Two-Dimensional Flow...................... 51
2.9.1 Irrotational Incompressible Flow............. 51
2.10 Applications of Analytic Functions in Fluid Mechanics .... 52
2.10.1 Flow from a Simple Source and a Simple Vortex .... 52
2.10.1.1 Free vortex................... 53
2.10.1.2 Two-dimensional doublets and vortex loops . 55
2.10.2 Flow Around a Body Treated as a Sheet of Complex
Sources and Doublets................... 55
Case study 2.II Application of Complex Function Analysis to
the Flow around a Thin Wing.............. 59
2.10.3 Flow Around a Cylinder with Zero Circulation..... 62
2.10.4 Flow Around a Cylinder with Circulation ....... 64
2.10.5 The Flow Around a Corner ............... 66
2.11 Force on a Body in Steady Two-Dimensional Incompressible
Ideal Flow............................. 66
2.12 Conformal Transforms ...................... 69
Appendix 2.A Drag in Ideal Flow .................. 70
2.A.1 Helmholtz s Flow and Separation............ 71
2.A.2 Lines of Vortices ..................... 72
2.A.2.1 Single infinite row of vortices......... 72
Contents ix
2.A.2.2 Two parallel Symmetrie rows of vortices ... 73
2.A.2.3 Two parallel alternating rows of vortices ... 73
3 Viscous Fluids 75
3.1 Basic Concept of Viscosity.................... 75
3.2 Differential Motion of a Fluid Element............. 76
3.3 Strain Rate ............................ 76
3.4 Stress................................ 77
3.5 Viscous Stress........................... 78
3.5.1 Momentum Equation................... 79
3.5.2 Energy Equation..................... 79
3.5.3 Entropy Creation Rate.................. 80
3.6 Incompressible Flow-Navier-Stokes Equation......... 80
3.6.1 Vorticity Diffusion .................... 81
3.6.2 Couette or Plane Poiseuille Flow ............ 81
3.7 Stokes or Creeping Flow..................... 82
3.7.1 Stokes Flow around a Sphere.............. 82
3.7.1.1 Oseen s correction............... 85
3.7.1.2 Proudman and Pearson s Solution....... 85
3.7.1.3 Lamb s Solution for a cylinder......... 86
3.8 Dimensionless Analysis and Similarity.............. 86
3.8.1 Similarity and Modelling................. 88
3.8.2 Self-similarity....................... 89
Appendix 3.A Buckingham s II Theorem and the Complete Set of
Dimensionless Products...................... 90
4 Waves and Instabilities in Fluids 93
4.1 Introduction............................ 93
4.2 Small-Amplitude Surface Waves................. 94
4.2.1 Surface Waves at a Free Boundary of a Finite Medium 96
4.2.1.1 Capillary waves................. 96
4.2.1.2 Gravity waves.................. 97
4.2.1.3 Transmission of energy............. 98
Case study 4.1 The Wake of a Ship-Wave Drag....... 99
4.1.1 Two-dimensional wake, Kelvin wedge..... 100
4.3 Surface Waves in Infinite fiuids ................. 102
4.3.1 Surface Wave at a Contact Discontinuity........ 102
4.3.2 Rayleigh-Taylor Instability............... 103
4.4 Surface Waves with Velocity Shear Across a
Contact Discontinuity....................... 104
4.5 Shallow Water Waves....................... 106
x Contents
4.6 Waves in a Stratified Fluid.................... 108
4.7 Stability of Laminar Shear Flow................. 112
4.8 Nonlinear Instability....................... 115
5 Turbulent Flow 117
5.1 Introduction............................ 117
5.1.1 The Generation of Turbulence.............. 119
5.2 Fully Developed Turbulence................... 121
5.3 Turbulent Stress-Reynolds Stresses............... 126
5.4 Similarity Model of Shear in a Turbulent Flow-von Karman s
Hypothesis............................. 127
5.5 Velocity Profile near a Wall in Fully Developed
Turbulence-Law of the Wall................... 127
5.6 Turbulent Flow Through a Duct................. 129
5.6.1 Prandtl s Distribution Law................ 130
5.6.2 Von Karman s Distribution Law............. 130
Case study 5.1 Turbulent Flow Through
a Horizontal Uniform Pipe................ 132
5.Li Blasius wall stress correlation......... 135
Appendix 5.A Prandtl s Mixing Length Model........... 136
6 Boundary Layer Flow 139
6.1 Introduction............................ 139
6.2 The Laminar Boundary Layer in Steady Incompressible
Two-Dimensional Flow-Prandtl s Approximation....... 141
6.3 Laminar Boundary Layer over an Infinite Fiat Plate-Blasius s
Solution.............................. 144
6.4 Laminar Boundary Layer-von Karman s Momentum Integral
Method............................... 146
6.4.1 Application to Boundary Layers with an Applied
Pressure Gradient..................... 149
6.5 Boundary Layer Instability and the Onset
of Turbulence-Tollmein-Schlichting Instability........ 151
6.6 Turbulent Boundary Layer on a Fiat Smooth Plate...... 152
6.6.1 Turbulent Boundary Layer-Power Law Distribution . 154
6.7 Boundary Layer Separation ................... 156
6.7.1 Viscous Flow Over a Cylinder.............. 159
6.8 Drag................................ 161
Case study 6.1 Control of Separation in Aerodynamic
Structures......................... 163
6.9 Laminar Wake........................... 163
Contents xi
6.10 Separation in the Turbulent Boundary Layer.......... 166
6.10.1 Turbulent Wake...................... 168
Appendix 6.A Singular Perturbation Problems and the Method of
Matched Asymptotic Expansion................. 169
7 Convective Heat Transfer 175
7.1 Introduction............................ 175
7.2 Forced Convection......................... 176
7.2.1 Empirical Heat Transfer Rates from a Flowing Fluid . 178
7.2.1.1 Heat transfer from a fluid flowing along a pipe 178
7.2.1.2 Heat transfer from a fluid flowing across a pipe 179
7.2.1.3 Heat exchanger design............. 180
7.2.1.4 Logarithmic mean temperature........ 181
7.2.2 Friction and Heat Transfer Analogies in Turbulent Flow 182
7.2.2.1 Reynolds analogy................ 182
7.2.2.2 Prandtl-Taylor correction........... 183
7.2.2.3 Von Karman s correction ........... 184
7.2.2.4 Martinelli s correction............. 186
7.2.2.5 Colburn s modification............. 188
7.3 Heat Transfer in a Laminar Boundary Layer.......... 189
7.3.1 Boundary Integral Method................ 190
7.4 Heat Transfer in a Turbulent Boundary Layer on a Smooth
Fiat Plate............................. 193
7.5 Free or Natural Convection.................... 194
7.5.1 Boussinesq Approximation................ 196
7.5.2 Free Convection from a Vertical Plate.......... 198
7.5.2.1 Similarity analysis............... 198
7.5.2.2 Boundary layer integral approximation .... 199
7.5.3 Free Convection from a Heated Horizontal Plate .... 201
7.5.4 Free Convection between Parallel Horizontal Plates . . 202
7.5.4.1 Ray leigh-Benard instability.......... 204
7.5.5 Free Convection around a Heated Horizontal Cylinder 206
Case study 7.1 Positive Column of an Are .......... 206
8 Compressible Flow and Sound Waves 209
8.1 Introduction............................ 209
8.2 Propagation of Small Disturbances............... 211
8.2.1 Plane Waves........................ 212
8.2.2 Energy of Sound Waves.................. 213
8.3 Reflection and Transmission of a Sound Wave at an Interface . 214
8.4 Spherical Sound Waves...................... 215
xii Contents
8.5 Cylindrical Sound Waves..................... 217
9 Characteristics and Rarefactions 219
9.1 Mach Lines and Characteristics................. 219
9.2 Characteristics........................... 221
9.2.1 Uniqueness Theorem................... 222
9.2.2 Weak Discontinuities................... 223
9.2.3 The Hodograph Plane .................. 223
9.2.4 Simple Waves....................... 223
9.3 One-Dimensional Time-Dependent Expansion......... 224
9.3.1 The Centred Rarefaction................. 226
9.3.2 Reflected Rarefaction................... 228
9.3.3 Isothermal Rarefaction.................. 230
9.4 Steady Two-Dimensional Irrotational Expansion........ 231
9.4.1 Characteristic Invariants................. 232
9.4.2 Expanding Supersonic Flow around a Corner ..... 235
9.4.3 Flow around a Sharp Corner-Centred Rarefaction . . 235
9.4.3.1 The complete Prandtl-Meyer flow...... 238
9.4.3.2 Weak rarefaction................ 239
10 Shock Waves 241
10.1 Introduction............................ 241
10.2 The Shock Transition and the Rankine-Hugoniot Equations . 242
10.2.1 Rankine-Hugoniot Equations for a Polytropic Gas . . 243
10.2.1.1 Strong shocks.................. 244
10.3 The Shock Adiabat........................ 245
10.3.1 Weak Shocks and the Entropy Jump.......... 248
10.4 Shocks in Real Gases....................... 250
10.5 The Hydrodynamic Structure of the Shock Front ....... 254
10.5.1 Polytropic Gas Shocks.................. 256
10.5.1.1 Shocks supported by heat transfer...... 260
10.5.2 Weak Shocks ....................... 261
10.6 The Shock Front in Real Gases ................. 264
10.7 Shock Tubes............................ 267
10.7.1 Shock Tube Theory.................... 269
10.8 Shock Interaction......................... 271
10.8.1 Planar Shock Reflection at a Rigid Wall........ 271
10.8.1.1 Collision between two planar shocks..... 274
10.8.2 Overtaking Interactions.................. 275
10.8.2.1 Shock overtaking a shock........... 276
10.8.2.2 Shock-rarefaction overtaking......... 276
Contents xiii
10.8.2.3 Shock interaction with a contact surface . . . 276
10.9 Oblique Shocks.......................... 277
10.9.1 Large Mach Number................... 281
10.9.2 The Shock Polar ..................... 282
10.9.3 Supersonic Flow Incident on a Body .......... 285
10.10 Adiabatic Compression...................... 287
Appendix 10.A An Alternative Approach to the General Conserva-
tion Law Form of the Fluid Equations ............. 290
10.A.1 Hyperbolic Equations................... 290
10.A.2 Formal Solution...................... 291
10.A.3 Discontinuities....................... 292
10.A.4 Weak Solutions...................... 293
11 Aerofoils in Low-Speed Incompressible Flow 295
11.1 Introduction............................ 295
11.1.1 Aerofoils.......................... 296
11.2 Two-Dimensional Aerofoils.................... 298
11.2.1 Kutta Condition ..................... 299
11.3 Generation of Lift on an Aerofoil................ 301
11.4 Pitching Moment about the Wing................ 302
11.5 Lift from a Thin Wing...................... 304
11.6 Application of Conformal Transforms to the Properties
of Aerofoils............................. 309
11.6.1 Blasius s Equation .................... 309
11.6.2 Conformal Mapping of a Circular Cylinder....... 310
11.6.3 The Lift and Pitching Moment of Aerofoils Generated
by Transformations of a Circle.............. 312
11.7 The Two-Dimensional Panel Method.............. 314
11.8 Three-Dimensional Wings .................... 315
11.8.1 Velocity at the Wing Surface............... 318
11.8.2 The Force on the Wing.................. 319
11.8.3 Prandtl s Lifting Line Model-Downwash Velocity ... 320
11.8.4 Lift and Drag as Properties of the Wake........ 323
Case study 11.1 Calculation of Lift and Induced Drag for
Three-Dimensional Wings................ 327
ll.I.i Wingloading.................. 327
ll.I.ii Elliptic loading................. 329
11.9 Three-Dimensional Panel Method................ 330
Appendix ll.A Evaluation of the Principal
Value Integrals........................... 331
Appendix ll.B The Zhukovskii Family of Transformations..... 332
xiv Contents
ll.B.l Zhukovskii Transformation................ 333
ll.B.1.1 Transformation of a circle to a streamlined
Symmetrie body................. 333
11.B.l.2 Transformation of a circle to a streamlined
asymmetric body................ 333
ll.B.2 Karman-Treffetz Transformation............ 334
ll.B.3 Von Mises Transformation................ 336
ll.B.4 Theodorsen s Solution for an Arbitrary Profile..... 338
12 Aerofoils in High-Speed Compressible Fluid Flow 341
12.1 Introduction............................ 341
12.2 Linearised Theory for Two-Dimensional Flows:
Subsonic Compressible Flow around a Long Thin
Aerofoil - Prandtl-Glauert Correction............. 344
12.2.1 Improved Compressibility Corrections.......... 347
12.3 Linearised Theory for Two-Dimensional Flows:
Supersonic Flow about an Aerofoil - Ackeret s Formula .... 347
12.4 Drag in High-Speed Compressible Flow............. 350
12.4.1 Swept Wings ....................... 350
12.4.2 Drag in Supersonic Flow................. 351
12.4.3 Transonic Flow...................... 351
12.5 Linearised Theory of Three-Dimensional Supersonic Flow -
von Karman Ogives and Sears-Haack Bodies ......... 354
12.5.1 Whitcomb Area Rule................... 358
Case study 12.1 Hypersonic Wing................ 359
13 Deflagrations and Detonations 363
13.1 Introduction............................ 363
13.1.1 Deflagrations ....................... 363
13.1.1.1 Propagating burn................ 364
13.1.1.2 Deflagration propagating in a closed tube . . 367
13.1.2 Detonations........................ 367
13.2 Detonations, Deflagrations and the Hugoniot Plot....... 368
13.2.1 The Structure of a Deflagration............. 373
13.2.1.1 The Shvab-Zel dovich model of a deflagration 374
13.2.1.2 Detonations as deflagrations initiated
by a shock.................... 375
13.2.2 Chapman-Jouget Hypothesis.............. 376
Case study 13.1 Deflagrations and Detonations in
Laser-Matter Breakdown................ 377
13-I.i Solid targets................... 378
Contents XV
13.1.i.a High-intensity irradiation -
deflagration model......... 379
13.1.i.b Low-intensity irradiation -
self-regulating model........ 380
13.I.Ü Gaseous targets................. 381
14 Self-similar Methods in Compressible Gas Flow
and Intermediate Asymptotics 383
14.1 Introduction............................ 383
14.2 Homogeneous Self-similar Flow of a Compressible Fluid .... 386
14.2.1 General Homogeneous Expansion of a Compressible
Gas............................. 386
14.2.1.1 Adiabatic flow ................. 389
14.2.1.2 Isothermal flow................. 389
14.2.2 Homogeneous Adiabatic Compression.......... 390
14.2.2.1 Homogeneous collapse of spheres....... 390
14.2.2.2 Homogeneous collapse of shells........ 393
14.3 Centred Self-similar Flows.................... 395
14.4 Flow Resulting from a Point Explosion in Gas - Blast Waves . 397
14.5 Adiabatic Collapse of a Sphere.................. 402
14.6 Convergent Shock Waves - Guderley s Solution........ 407
14.6.1 Compression of a Shell and Collapse of Fluid
into a Void......................... 412
Case study 14.1 The Fluid Dynamics of Inertial Confinement
Fusion........................... 414
14.Li Basic principles................. 414
14.1.i.a Hydrodynamic compression .... 415
Problems 417
Solutions 427
Bibliography 455
Index 463
|
| any_adam_object | 1 |
| author | Pert, Geoffrey J. |
| author_GND | (DE-588)133390411 |
| author_facet | Pert, Geoffrey J. |
| author_role | aut |
| author_sort | Pert, Geoffrey J. |
| author_variant | g j p gj gjp |
| building | Verbundindex |
| bvnumber | BV041067350 |
| classification_rvk | UF 4000 |
| classification_tum | PHY 220f |
| ctrlnum | (OCoLC)847063980 (DE-599)HBZHT017573142 |
| dewey-full | 532 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532 |
| dewey-search | 532 |
| dewey-sort | 3532 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV041067350 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:38:52Z |
| institution | BVB |
| isbn | 9781119944850 9781119944843 |
| language | English |
| lccn | 2013004480 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026044338 |
| oclc_num | 847063980 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-11 DE-29T |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-11 DE-29T |
| physical | XX, 468 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley |
| record_format | marc |
| spelling | Pert, Geoffrey J. Verfasser (DE-588)133390411 aut Introductory fluid mechanics for physicists and mathematicians Geoffrey J. Pert 1. publ. Chichester Wiley 2013 XX, 468 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Strömungsmechanik (DE-588)4077970-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 http://catalogimages.wiley.com/images/db/jimages/9781119944843.jpg Cover HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026044338&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pert, Geoffrey J. Introductory fluid mechanics for physicists and mathematicians Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4155620-3 (DE-588)4123623-3 |
| title | Introductory fluid mechanics for physicists and mathematicians |
| title_auth | Introductory fluid mechanics for physicists and mathematicians |
| title_exact_search | Introductory fluid mechanics for physicists and mathematicians |
| title_full | Introductory fluid mechanics for physicists and mathematicians Geoffrey J. Pert |
| title_fullStr | Introductory fluid mechanics for physicists and mathematicians Geoffrey J. Pert |
| title_full_unstemmed | Introductory fluid mechanics for physicists and mathematicians Geoffrey J. Pert |
| title_short | Introductory fluid mechanics for physicists and mathematicians |
| title_sort | introductory fluid mechanics for physicists and mathematicians |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Strömungsmechanik Mathematische Methode Lehrbuch |
| url | http://catalogimages.wiley.com/images/db/jimages/9781119944843.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026044338&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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