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| Batchelor G. — Introduction to Fluid Dynamics |
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| Предметный указатель |
'Stokeslet', flow due to 240
Acceleration of a material element 73
Acceleration of a material element in curvilinear co-ordinates 600
Acceleration, reaction on a moving body 405 407
Acoustic streaming 363
Acyclic flow 111
Adhesion, viscous 228
Adiabatic change of state 22
Aerofoil 435
Aerofoil, angle of incidence of 444
Aerofoil, approximate theory for thin 467
Aerofoil, generation of circulation round 438
Aerofoil, lift on 443
Aerofoil, obtained by conformal transformation of a circle 441
Air, physical properties of 594
Archimedes' theorem 16 177
Archimedes' theorem, analogue for rotating fluid 178
Aspect ratio of a wing 584
Atmosphere, equations for flow in a model 569
Atmosphere, the Standard 595
Avogadro's law 37
Axisymmetric flow 72
Axisymmetric flow with vorticity but no swirl in unbounded inviscid fluid 521
Axisymmetric flow, cylindrical 545
Axisymmetric flow, irrotational 449
Axisymmetric flow, steady with vorticity in inviscid fluid 543
Bernoulli surface 509
Bernoulli's theorem for steady motion 156 265 383 509
Bernoulli's theorem for steady motion, applications to irrotational flow 386
Bernoulli's theorem for steady motion, special forms of 161
Beta-plane approximation for motion on a rotating sphere 571
Blasius formulae for force and moment on a cylinder in steady irrotational flow 433
Body forces 7
Boltzmann distribution 40
Boltzmann's constant 43
Borda's mouthpiece 390 497
Boundary layer 302
Boundary layer at a free surface 364
Boundary layer at a free surface, attenuation of gravity waves due to 370
Boundary layer on a flat plate 308
Boundary layer on a yawed cylinder 377
Boundary layer, approximate form of equation of motion in 304
Boundary layer, displacement thickness of 311
Boundary layer, effect on flow due to moving body 336 342
Boundary layer, effects of acceleration and deceleration of the external stream 314
Boundary layer, growth of, in initially irrotational flow 321
Boundary layer, influence on shape of cavity behind a body moving through liquid 506
Boundary layer, momentum integral relation for 319
Boundary layer, momentum thickness of 320
Boundary layer, oscillatory 353
Boundary layer, oscillatory, steady streaming due to 358
Boundary layer, separation of 325
Boundary layer, similarity solution for stream velocity  316
Boundary layer, turbulent flow in 313
Bubbles in liquid, attraction due to oscillations in volume 455
Bubbles in liquid, rate of rise of spherical-cap 475
Bubbles in liquid, rising in a vertical tube 477
Bubbles in liquid, spherical, expanding 479
Bubbles in liquid, spherical, rising at large Reynolds number 367
Bubbles in liquid, spherical, rising at small Reynolds number 237
Bulk modulus of elasticity 24
Buoyancy force in a moving fluid 177
Buoyancy force on a body in fluid at rest 17
Camber of an aerofoil 446
Capillarity 67
Carnot's law 43
Cavitation 55 481
Cavitation in the tip vortex from a propeller 484
Cavitation, due to acceleration of liquid 485
Cavitation, number 483 491
Cavitation, sheet 491
Cavity in liquid, attached to a body in steady flow 502
Cavity in liquid, attached to a body in steady flow, air or vapour-filled 492
Cavity in liquid, attached to a body in steady flow, behind a flat plate, at ambient pressure 497
Cavity in liquid, attached to a body in steady flow, with non-zero cavitation number 503 505
Cavity in liquid, collapse of 486 488
Cavity in liquid, examples of formation in steady flow 482
Cavity in liquid, examples of formation in unsteady flow 485
Channel, steady flow in a converging or diverging 294
Chord of an aerofoil 445
Circle theorem 422
Circular cylinder in inviscid fluid rotating rigidly at infinity 540
Circular cylinder, circulation developed by rotation and translation of 427
Circular cylinder, damping force on oscillating 357
Circular cylinder, embedded in a simple shearing motion of inviscid fluid 542
Circular cylinder, flow due to rotation of 203
Circular cylinder, flow due to translation of assumed irrotational 424
Circular cylinder, flow due to translation of assumed irrotational at large Reynolds number 338 340 426
Circular cylinder, flow due to translation of assumed irrotational at Reynolds numbers between 1 and 100 257
Circular cylinder, flow due to translation of assumed irrotational at small Reynolds number 244
Circular cylinder, flow due to translation of assumed irrotational, development from rest 324 337
Circular streamlines, flow with 201
Circular tube, starting flow in 193
Circular tube, steady flow in 180
Circulation round a closed curve 93
Circulation round a closed curve, constancy in inviscid fluid 273
Circulation round a closed curve, effect of viscosity on 269
Collision between molecules 37 50
Complex potential for two-dimensional motion 107 409
Complex potential for two-dimensional motion, flow past a circular cylinder 421
Complex potential for two-dimensional motion, flow past an elliptic cylinder 429
Complex potential for two-dimensional motion, point vortex 111
Complex potential for two-dimensional motion, simple flow fields 410
Compressibility, coefficient of 24
Compressibility, coefficient of, of a liquid 56
Compressibility, coefficient of, of a perfect gas 43
Compressibility, coefficient of, of water 595
Conduction of heat 29
Conduction of heat in a moving fluid 136
Conformal transformation of two-dimensional irrotational flow 413
Conformal transformation of two-dimensional irrotational flow, use in free-streamline problems 494
Conical similarity of flow due to a highly swept wing 593
Conjugate functions 107
Conservation laws for a fluid in motion 135
Constitutive relations 32
Continuity equation 74
Continuum Hypothesis 4
Contraction coefficient for a jet from an orifice 388 497
Control surface 139
Convective rate of change 73
Coriolis force 140 555
Coriolis force, balance with frictional force in an Ekman layer 196
Coriolis force, effect on flow of dominance of 557 572
Coriolis force, modification of pressure to allow for 178
Coriolis force, restoring effect of 556
Corner, flow with negligible inertia forces near a 224
Critical point of a liquid-vapour system 54
Crocco's relation 160
Cyclic constant 110
Cyclonic flow system 572
D'Alembert's paradox 332 405
Darcy's law 224
Deviatoric stress tensor 142
Deviatoric stress tensor, relation to rate-of-strain tensor 144
Diffusion in a moving fluid 136
Diffusion of matter 29
Diffusion, coefficient of 33
Diffusion, coefficient of, for a perfect gas 49
Diffusion, coefficient of, for solutes in liquids 58 595
Diffusion, solution for an initial source 186
Diffusivity, thermal 35
Diffusivity, thermal, measured values of 597
Dispersion of vorticity distribution in two-dimensional unbounded flow 528 536
Displacement thickness 311
Dissipation of energy due to viscosity 153
Doubly-connected region, irrotational flow in 109
Downwash due to trailing sheet vortex from a wing 588
Drag on a body in a stream, with an attached cavity 500 503
Drag on a body moving steadily through fluid 331
Drag on a body moving steadily through fluid at high Reynolds number, with separation 339
| Drag on a body moving steadily through fluid at high Reynolds number, without separation 335
Drag on a body moving steadily through fluid, effect of transition to turbulence in the boundary layer 342
Drag on a body moving steadily through fluid, zero in an inviscid fluid 332
Drag on a circular cylinder or a sphere at large Reynolds number 341
Drag on a circular cylinder or a sphere at Reynolds numbers from 1 to 100 234 261
Drag on a circular cylinder or a sphere at small Reynolds number 233 246
Drag on a spherical gas bubble at large Reynolds number 367
Drag on a spherical gas bubble at small Reynolds number 237
Drag, form 332
Drag, induced, on a lifting body 331 582
Draining plate 263
Drift of fluid elements due to progressive wave 363
Dynamical similarity 213
Efflux from a circular orifice 387
Ekman layer in a rotating fluid 195
Ekman layer in a rotating fluid at a free surface 197
Ekman layer in a rotating fluid at a rigid plane boundary 199 293
Ellipsoid of revolution, irrotational flow due to motion of 455
Elliptic, co-ordinates 439 455
Elliptic, cylinder, irrotational flow due to motion of 427
Elliptic, loading of wing 587
Elliptic, tube, flow in an 182
Enthalpy 25
Enthalpy of a perfect gas 43
Enthalpy, stagnation 160
entropy 24
Entropy of a perfect gas 43
Equation of motion 137
Equation of motion for a Newtonian fluid 147 174
Equation of motion in cylindrical co-ordinates 602
Equation of motion in polar co-ordinates 600 602
Equation of motion, relative to moving axes 139
Equation of state 21
Equation of state for a perfect gas 43
Equation of state for water 56
Equilibrium of a fluid 4 20
Equipartition of energy, principle of 41
Eulerian specification of the flow field 71
Expansion viscosity 154
Expansion viscosity of a suspension of bubbles 253
Expansion, rate of 75
Fluid, Newtonian 146
Fluid, self-gravitating 18
Fluid, simple 1
Flux vector 31
force see also "Drag" "Lift
Force on a moving body in accelerating fluid 409
Force on a moving body in steady motion 331
Force on a moving body with irrotational flow 404
Force on a regular array of bodies in a stream 372 375
Force on a semi-infinite axisymmetric body with irrotational flow 462
Force on a steadily moving cylinder with irrotational flow 433
Force on sharp edge of a plate due to irrotational flow round it 412
Force, buoyancy 17 177
Force, damping, on oscillating body 355
Force, surface or contact 7
Force, volume or body 7
Free shear layers at large Reynolds number 346
Free streamline theory for steady two-dimensional flow 493
Free surface of liquid, conditions at 150
Geostrophic flow in a rotating fluid 572
Gradient wind 573
Growth rate of disturbance to a sheet vortex 516
Harmonics, circular 127
Harmonics, spherical 121
Hele-Shaw cell 222
Helmholtz free energy 25
Helmholtz free energy, contribution of surface tension to 61
Homenergic flow 160
Homentropic flow 156 166
Impact of a body on a free surface of liquid 473
Impulse, fluid 408 518 529
Impulsive motion of a fluid 471
Incompressible fluid 75 147
Incompressible fluid, conditions for behaviour as 167
Indicator diagram 23
Indicator diagram for liquid-vapour system 54
Induced drag on a lifting body 331 582
Inertia, force 241
Inertia, waves in a rotating fluid 564
Internal energy 21
Internal energy of a perfect gas 43
Internal energy, changes in, in a moving fluid 151
Internal energy, contribution from rotational and vibrational modes to 45
Internal energy, equation 153
Irrotational motion of fluid in a rotating ellipsoid 506
Irrotational motion of fluid in the angle between two plane walls 411
Irrotational motion of fluid, axisymmetric 449
Irrotational motion of fluid, due to a moving rigid body 398
Irrotational motion of fluid, due to a plate with an attached cavity in a stream 497
Irrotational motion of fluid, due to translation of a body simulated by sources on the axis 458 464
Irrotational motion of fluid, due to translation of a circular cylinder 129 424
Irrotational motion of fluid, due to translation of a cylinder of given shape 421
Irrotational motion of fluid, due to translation of a ellipsoid of revolution 455
Irrotational motion of fluid, due to translation of a elliptic cylinder 427
Irrotational motion of fluid, due to translation of a flat plate 431 432 436
Irrotational motion of fluid, due to translation of a semi-infinite body 460
Irrotational motion of fluid, due to translation of a slender body 463 466
Irrotational motion of fluid, due to translation of a sphere 123 452
Irrotational motion of fluid, expression for pressure in 383
Irrotational motion of fluid, general properties of 380
Irrotational motion of fluid, kinetic energy of 383
Irrotational motion of fluid, made steady by a choice of rotating axes 396
Irrotational motion of fluid, persistence of 276
Irrotational motion of fluid, regarded as due to a layer of sources or doublets 130
Irrotational vector, definition of 81
Isentropic change of state 24
Isentropic flow 156 165
Isotropic medium, diffusion and heat conduction in 32
Jeffery — Hamel flow 294
Jet from a steady point source of momentum 205
Jet in two dimensions, at large Reynolds number 344
Jet of liquid from an orifice in two dimensions 495
Jet of liquid impinging on a plane wall 392 501
Jet, adjoining a rigid wall 377
Jets of liquid impinging to form a sheet 506
Joukowski transformation and aerofoils 444
Joukowski's hypothesis for circulation round an aerofoil in steady motion 437 438
Kelvin's circulation theorem 273 380
Kelvin's minimum energy theorem 384
Kinematic viscosity 37 175
Kinetic energy of irrotational flow due to a moving body 402
Kinetic energy of unbounded fluid in motion with vorticity 520
Kinetic energy of unbounded fluid in motion with vorticity in two dimensions 529
Kinetic theory of gases 37
Kundt's dust tube 363
Lagrangian specification of flow field 71
Laplace's equation 101
Laplace's equation, in orthogonal curvilinear co-ordinates 599
Lift force on a body moving through fluid 331 580
Lift force on a wing 586
Lift force, due to circulation round a moving cylinder 406 434
Lift force, due to circulation round a moving cylinder for a Joukowski aerofoil 446 447
Lift force, due to circulation round a moving cylinder for a thin aerofoil 470
Lift force, due to circulation round a moving cylinder for any aerofoil 443
Lifting-line theory for wings of large aspect ratio 583
Line vortex 93
Line vortex, being extended and diffused 272
Line vortex, circular 511 521
Line vortex, self-induced movement of 509
Line vortex, spreading due to viscosity 204
Loschmidt's number 37
Lubrication theory 219
Mach number 168
Magnus effect 427
Mass-conservation equation 74
Material, boundary, conditions at a 148
Material, derivative 73
Material, elements 71
Material, elements, rates of change of 131
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