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Index

Acoustic approximation 58, 269 attenuation 262, 269 energy 269 flux 269 pressure 270

Acceleration 19, 38, 39, 50, 61,109, 120,252,261,357,403

convective 39 Coriolis 84, 173 of gravity 63, 81, 84, 330 time dependent 39

Adiabatic 66,83,242 evolution 11,237,405,409,411 compression 67, 86 wall 203, 207, 208, 241, 242, 264, 265

Air, properties of 1, 6,8,18,20,23,24, 59,68, 192,228,233,239,243, 257-259,266,270

Airfoil 95, 96, 152 d'Alembert

operator 269 paradox 90

Angle of attack 419 Approximate method 6, 12, 29, 87, 89,

94,124,126,147,162,203,244, 248,250,263,275,329,368,419

Attenuation coefficient 262 of sound 269

Axisymmetric flow 100, 101, 120, 131, 151,155,157,162,166,168,169, 189,227,305,333,339,346,366, 422,423,441,442

Basic equations 37, 75, 98, 103, 144, 278,310,317,331

Bearing 12, 16, 136,246,275,278,280, 290,291,294,304,306,309,311-

313,315,367,368,372,377,412, 416

conical 276, 277, 281 foil 317, 320 hydrostatic 288, 305 journal 142, 275,277,278,290,292,

293,296-300,306,312,316,317,343 rheostatic 310 roller 30, 275, 276, 288, 320, 328 spherical 276, 277 spiral groove 301,302,317 step 295,314,384,386,401,414,417 thrust 276, 277, 281

Benard-Karman vortices 92 Bernoulli equation 68,378,386,387 Bifurcation 21, 77, 90, 367, 419 Biharmonic functions 330, 331, 333, 346 Bingham fluid 29, 127,307 Bipolar coordinates 343 Bluff body 93, 95 Body of revolution 95, 152,346 Boundary conditions 75-77, 81, 115,

121,137,145,151,153,156,159, 163,170,189,291,332,345,346, 360,361,390,399,422

for velocity 77,110,111,116,118, 128,131,134-136,139,141,147, 158,162,169,174,178,181,187, 193,200,208,238,248,265,282-284,309,355,358,368,370,371, 373,374,376,394,404,423,424, 433,434,436,440,442

for pressure 80, 84, 268, 286-288, 292-294,298,304,319,369,372,378, 383-387,395,396,406,413,415

thermal 79, 87, 203, 204, 206, 207, 209,210,218,222,225,228,230, 265,432

Boundary layer 19, 21, 44, 93, 97,135, 146,154-156,159,163,164,182,

480 Index

Boundary layer (Cont.) 183,201,203,224,226,238,252, 255,264,273,276,280,372-374, 387,388,390

concept 94, 96 equations 280

Brinckman number 86 Bulk viscosity 19, 55 Buoyancy 21,83,85,204,222,306

Capillary tube 192, 304 Cartesian coordinates 41,49,60,64,69,

121, 150, 172,281,360,368 Cauchy-Riemann conditions 115, 166,

332 Cavitation 3,84,288,291-293,310,

338,381,396 number 84

Cell model 2 Channel flow IlI-I13, Il9, 121, 131,

136,137,143,145-150,189,216-219,224,228,230,234,244,245, 360,388,389

Chaos 367,419 Choked flow 407-410, 413, 416 Circle

flow past 45, 89,91, 1I6, 139, 140, 166, 195, 197,296,334,339,360, 362-366,433,436,438,439

theorem 362 Circular pipe 88, 120, 122-124, 132,

171,190,192,227,228 Circulation 46, 47, 90, 95, 100, 142,

198,275 Coaxial cylinders 141,225,344,345 Coefficient of viscosity 13, 14, 17, 18,

54,55,57,58,61,65,251,252, 257,264,272,273

Combustion 9, 107, 116, 300 Complex

function 1I5, 173,366 potential 115, 116, 1I9, 193,304,

362,363 pressure resultant 332 velocity 115, 336, 364

Concentrated contact 9, 16,27,30,31, 291,321-326,328

Concentration 2, 8, 24-26

Concentric annulus 124 circles 45, 1I6, 139, 140, 166, 195,

197,339 spheres 341

Conductivity 2,3, 13,21,24,63,66,67, 79,86,204,212,227,238,239, 242,243,268

coefficient 22, 208 of gases 23 of liquids 22

Conical bearing 276, 277, 281, 302, 304 nozzle 144, 151, 152, 169, 171, 172,

329 Contact melting lubrication 328 Convergent

channel 143, 145, 146, 148-150, 169, 172,224

film 286,291,293,395 Convergent-divergent film 291,293,395 Conservative form 98 Constant wall temperature 204,218-

220,224,230,234,235,238 Constitutive relation 2, 13, 14, 26, 27,

32-34,47,52,54,57,59,75,76,127 Continuity equation 47, 48, 60, 62, 67,

69,72,75,98,100, 101, 104,110, 135, 139, 143, 144, 150, 153, 156, 158, 162, 177,251,260,261,264, 279,280,283,289,329,333,339, 355,371,373,375,376,378,396, 398,399,403-405,409,413,420, 421,440

Continuum 1, 2, 5, 37,40,43, 52, 75, 258,267

Control surface 37, 47,102,103,106 volume 37,47,98, 102-107, 387, 391,

400 Control volume formulation 102 Convective

acceleration 39,75,77,82,90,96, 109,151,245,329,334,335,367

derivative 39 heat transfer 21

Cooling 25, 79, 203 Core 29, 97,127,129,131,192,307-

309

Coriolis acceleration 84, 173 Couette flow 78, 110-115, 127, 129,

142,178,187,188,204,205, 207,208,210,213,214,220,221, 238,242-245,248-250,275,281, 282

Couette-Poiseuille flow 114, 127,220, 221,245,248,249,281,282

Creeping flow 329 Curl 41, 45, 47, 52, 66, 69, 99, 330, 331,

420,421 Cylinder

drag 90, 91, 93, 343, 435, 437 flow past 46, 89, 92-94, 109, 116-

118,121,141,142,193,196,197, 225,275,321,322,324,343-345, 358,360,361,433,438-440

theorem 366 torque 141, 343, 345

Cylinder-plane configuration 117, 321, 322

Cylindrical coordinates 69, 70, 101, 120, 139, 143, 155, 158, 189,225, 227,270,276,281,333,339,346, 422

Darcy law 134, 136 Damping 310, 397 Dead water 92, 93 Decibel scale 270 Deformation rate 28, 40, 42, 43, 52 Density 2-5, 11, 13, 24, 25, 60, 61, 67,

83,86,237,250,256,264,269, 288,353,367,403-405,413,414

Diffusion 13, 24, 26, 196 Diffusivity coefficient 26 Dilatant fluid 28, 29 Dimensionless parameters 80 Directional viscosity 29 Discontinuity 90, 182, 185, 186, 188,

250,411,442 Dissipation 21,67,86,99,100,225,

226,228,237,242,246,250,432 of heat 11,13,21,66,216,224,228,

250,271 function 64,65,71,74,204,267 of a discontinuity surface 185 of a vortex 198

Divergence 50,69, 103,420 Divergent

channel 143, 145-150 film 287, 291-293, 395 nozzle 169, 172,410

Index 481

Drag coefficient 90-93, 351, 429, 430, 437,438,440,446,447

Duct flow I, 76, 87, 89, 112, 120, 121, 123-

126,131,132,134,136,137,139, 189,190,193,195,199,227,228, 234,235

in parallel 127 in series 127

Duhamel's relation 179 Dynamic pressure 6, 82, 112, 126,

378

Eccentric cylinders 116,117,122-124, 343

Eccentricity 291, 297, 342 Eccentricity ratio 291, 297, 316 Eckert number 85,86,205,206,241 Ekman

effect 172, 174, 184 number 84 spiral 175

Elasticity 3, 42, 121, 324, 325, 359 Elasto-hydrodynamic lubrication 320,

328 Elliptic

equation 76, 285 functions 145 integrals 145

Ellipsoid 342, 343, 353, 354, 357,430, 431

Energy balance 9, 37, 62, 63, 79, 106, 206,

271 equation 62,65-67,69,71,74,76,

80,85,86,106,107,126,203,204, 208,209,215,216,218,220,222, 223,225-227,229,230,233,237, 238,246,251,253,257,261,264, 267,281,285,291,391,395,400, 432,438

flux (acoustical) 269, 270 internal 3, 9, 11,62,63,65,271

482 Index

Energy (Cont.) kinetic 5, 6, 9,13,63,66,67,106,

241,385 Enthalpy 10-12,24,67,251,253 Entrance (see also inlet)

boundary conditions 246,338, 391 effect 88,113,120,121,217,230,

232,233 length 230, 233, 387-391

Entry flow 392 Entropy 10-12,66,68,107,251,253,

256,260,271 Equation of continuity (see continuity

equation) Equation of state 3, 4, 9, 15,51,69, 76,

237,251-253,258,259,261,285 Equation of vorticity (see vorticity) Equations of motion 47, 49-51, 61, 64,

69,173,226,237,276,280,281,391 cartesian coordinates 48, 50-52, 55 cylindrical coordinates 70, 71 noninertial frame 62 spherical coordinates 72, 73 under integral form 102,104-106

Euler number 82, 90 Eulerian 38-40, 47, 60, 77, 98, 99, 336,

346,360 Exit effect 88,217,387,395,401,406-

410,413,416 External flow 21,76,80,89,96,97 External solution 96 Externally pressurized bearings 285,

288,304,319,377,404

Falling sphere 351 Far field 424, 428, 429 Film attached to a moving surface 391,

393 Film thickness 2, 212, 280-285, 287,

290,291,294,296,299,302,304, 305,312,313,316,318,321,323, 325-328,337,368,369,373,378, 380,382,384,396,398,403,404, 406,414

First principle of thermodynamics 9, 1I, 37, 62, 66

Fluid compressible 2,3,5,18,37,55,57,

60,61,67,69,76,83,86,101,107, 179,182,237,238,258,261,263, 264,284,285,287,290,309,311-313,317,320,403,409,410

incompressible 2, 3, 5, 25, 37, 48, 54, 56,57,60,61,65,73,75,76,81, 85,99,100,109,139,177,199, 203,204,237,238,244,245,263, 265,266,283,285,310,312-314, 318,321,329,367,403,404,408-410,419

inviscid 2, 13, 37, 46, 49, 51, 60, 67, 68,76,77,82,83,90,92-97,99, 1I0, 112, 115, 116, 121, 139, 143, 146,153-155,166,179,180,185, 237,252,254,258,260,271,273, 280,334,336,342,343,347-353, 358,362,363,366,378,391,405, 406, 41I, 419, 444

Flow impulsive 178,181,182,188,192,263 isothermal 243, 248, 250, 285, 288,

311,326,403,405,407,409,413 leffery-Hamel143, 144, 147,166,

223, 375 oscillating 183, 184, 193, 195,344,

345, 357 pattern 75,87,92,93,135,152,166,

167,237,334,348,351,361,362, 364,419,442

upon concentric circles 1I6, 139, 140, 166,195,197,339

upon concurrent lines 143, 144, 150, 166,428,436

Foil bearing 317,318,320,326 Free convection 83,84,203,206,222 Free energy 12 Free enthalpy 12 Free surface 3, 79, 80, 113, 121, 172,

174,184,185,223 Free volumes model 2 Forced convection 21, 204, 206 Forced heat transfer 21, 204, 214 Froude number 82 Fully developed flow 88, Ill, 120, 217,

228,230,232,388,390

Galilean frame of reference 61

Gas constant 7, 8, 24, 252, 320 Gas lubrication 243,287,304,309 Gas mixture 6, 12, 24 Gas properties 5,8, 19,20,23 General Couette flow 115 Grashof number 83, 222 Gravity 63,81-84,105,109,110,113,

140,158,178,193,330,339,351 Grease 27,29, 127, 304, 307,308 Gumbel's conditions 293

Hagen-Poiseuille flow (see also pipe flow) 88,120,151,171,190,191,230

Half Sommerfeld solution 293 Heat

conduction 21, 62, 67, 86, 217, 227, 432

flux 63, 68, 79, 204-208, 216-219, 226,228,229

specific at constant pressure 9 specific at constant volume 9 specific (liquids) 3, 4, 65 transfer 9,13,21,24,62,66,67,86,

97,180,199,203,214,218-220, 229,233-235,241,246,248,250, 356,433,438,439

Hele Shaw analogy 334, 335, 337-339, 397, 398 flow 334

Helicoidal groove bearings and seals 302

Hertzian contact 324, 327 High speed sliding motions 412 Homentropic 11 Hydraulic radius 122, 124-126 Hydrodynamic lubrication 114, 120,

139, 142, 275 elastohydrodynamic 320 equations 276 gas 309 liquid 294 mechanisms 285

Hydrostatic 222, 288, 304, 305, 309, 319,320,329

Hyperbolic equations 75

Ideal gas 7, 12, 28

Index 483

Impact point 348 Impulsive motion 178, 181, 263 Incipient motion 265-268 Incompressible flow 139, 177,203,263,

265,266,285,367 Incompressible fluid 48, 56, 57, 60, 62,

65,81,99,100,110,177,199,204, 237,238,244,263,266,283,285, 312,313,318,329,367,403,409, 419

Indicial notation 40,41,49,56 Inertia forces 19-21,26,49,82,87,88,

100,109,120,127,144,147,171, 244,245,280,281,284,329,334, 335,339,367,371,374,380,382, 384,395,397,398,402,403,407,417

Inertial frame of reference 61 Inertialess 148,281,329,367,369,371,

381,383,395,397-399,401,403, 409,410,416,420

Inherent restrictor 307 Initial conditions 77,80,81,178,181,

197,268,355 Inlet boundary conditions 80, 286, 292,

320,328,379,385,387,388,391, 406,412

Inner solution 443,445 Integral relations 102,103,237,331,

360,372-374,387,391,404,411 Internal energy 3, 9, lI, 61, 63, 65, 67,

106,271 Inviscid fluid 2, 13, 37, 46, 49, 51, 67,

68, 77, 82, 90, 94, 143, 179, 180, 185,334,347,362,363,419,444

Inviscid flow 76, 77, 82, 83, 90, 94, 99, 115, 166,336,342,343,347-353, 358,363,366,378,405,406

Irrotational flow 99, 101, 142,429, 437, 439

Isentropic evolution 11, 237 Isothermal evolution 243,285,288,

311,326,403,405,407,409,413 Isothermal flow 243 Isotropy 53, 54

Jeffery-Hamel flow 147, 166, 223 Jet 97, 166-168 Journal bearing (see bearing)

484 Index

Kinematics of fluid flow 37, 290 Kinematic viscosity 14, 15,60, 175, 185,

201,280,367 Kinetic Reynolds number 194 Kinetic theory of gases 5, 9, 17, 18,22,

26 Knudsen number 1, 5,13,77,78 Krakatoa 273 Kronecker's symbol 51

Lagrangian description 38 Laminar flow 20,93,96,110,111,113,

125,126,134,175,185,192,194 Laplace equation 166 Laplace operator 60, 101, 102,269,333,

347,399,421 Line contact 326 Liquid

cavitation 3,84,288,291-293,310, 338, 381, 396

equation of state 3, 4, 237, 251-253, 258,259,261,285

lubrication 83, 114, 120, 140, 142, 276,280,288,290-294,309,310, 312,317,391

properties 1-4, 34, 367 viscosity 3, 4

Liquid film lubrication 30 Lubrication 83, 114, 120, 140, 142, 150,

243,275,276,280,285,287,288, 291,292,294,299,301,304,307, 309,310,320,321,323,324,328, 329,334,367,368,372,375,391

Longitudinal flow 96, 305, 306, 308, 320,378-380,404,406,408-410

Mach number 67,68,83,243,256,261, 265,267,403,405-407,409,413, 414,416,417

Mass transfer 13,24,25,97 Mass flux 25, 47, 79, 244, 245, 248, 251,

317,320 Material

acceleration 38, 39, 61, 84 derivative 39, 42, 48, 61, 69, 104 volume 38,39,47,49-51,62,63,66,

103-107

Mechanisms of lubrication 285,291 Melting lubrication 328 Metal

cutting lubrication 320, 328 working lubrication 27, 320, 328

Mixture of fluids 6, 12,24, 26, 58, 256, 261

Molecular collisions 1, 5, 6, 13,25,267 Molecular mean free path 1,5,17,18,

78 Moment of momentum 106 Momentum

balance 13,17,22,24,27,38,47,49, 79,270

equation 26,59,60,67-69,75,77, 86,96,104,105,110,112,113, 120,131,135,140,144,150,151, 153,156,167,168,196,220,223, 237,238,240,246,251,253,258, 261,264,273,281,282,340,369-371,373-375,377,378,380,383, 387,389,390,392,396,397,400, 404,409,412

theorem 105, 106,351,391 Moving

reference frame 61, 354 surface 29, 37, 57, 80, 102, 104-106,

283,295,308,346,348,351,352, 357,358,361,383,391,393,428, 431

wall 78, 1I0, 129, 183,205-207,215, 239,241,242,244,334,337

Navier-Stokes equations 59, 61, 62, 70-73,76,77,80-83,85,90,96,99, 101,110,120,122,139,140,143, 144,152,153,158,162,164,177, 178,199,208,237,248,251,279, 280,329,334,339,359,367,372, 376,385,403,411,419,420,440, 441

Newtonian fluid 8, 13, 14, 18,26-30, 32,34,52,55,57-60,75,109,127, 129-132,308,420

No slip condition 13,56,76,77,79,93, 95,143,337,341,348

Noninertial coordinate system 61, 84, 172,173,200

Non-Newtonian fluids 26-30,34,291 Nonparallel walls 121, 144,223,375 Nonuniform translation 181,182,354 Normal stress 3,13,18,27,49,51-53,

55 Normal unit vector 22, 56, 103, 120, 332 Nozzle 144,151,152,169,171,172,

329,405,406,410 Nusselt number 87,218,219,228,230,

232-235,432,438

One-dimensional flow 2, 126, 134, 135, 251,270,271,273,285

Open channel flow 113 Oscillating cylinder 344, 345 Outer solution 443, 445

Parabolic equation 76, 179 Parabolic vessel 168 Paradox

d' Alembert 90 Stokes 358, 360, 361,433,442 Whitehead 441,442

Parallel flow 26, 44,89,109,110,112-114,

120, 127, 128, 134, 139, 166, 177, 179,189,199,208,215,220,238, 243,244,250,263,276,281,282, 329

plates 13, 14,78, 110, 119,238,245, 247,406

walls 119, 135, 144, 146, 150, 187, 188,222,223,243,276,278,288, 289,301,334,337,339,375,395, 407,408,412,414,415

Pathline 38,39,44, 109, 177, 199,200 Peclet number 86, 432 Perimeter 124 Permeability coefficient 134 Pi theorem 80 Pipe flow 120, 124, 125, 190, 192,228,

230, 231, 237 Plane flow 100,110,111,115,127,128,

140, 144, 146, 151-154, 156, 165, 172,179,184,199,200,204,205, 213,215,223,226,227,238,263, 264,331,334,336,343,358,362

Index 485

Plane slider 294, 296, 307, 308, 313, 315,414-416,422,423,433,440

Plastic 26-29 Point contact 323,328 Poiseuille flow 88,111-114,120,127,

129,130,135,146,147,150,151, 172, 190, 191,215,220,221,230, 244,245,248,249,275,281,282, 288,304,384,387,388,390

Porous surfaces 79, 134 walls 80, 135-137

Potential flow 76, 99, 139, 143, 334, 336,429,

440 force 62, 115,330 velocity 47, 99, 142, 269, 337

Prandtl number 24,79,85,86,205, 218,224,237,239,246,262,265

Pressure coefficient 82, 348 Pressure drop 112, 304, 306, 340, 378,

380,385-387,401 Pressure-dependent viscosity 15, 16, 18-

20,29-31,33,34,291,320,324 Pressure equation 126,238,282-285,

289,291-295,300,304,311,313, 314,316-321,323,327,369,378, 413,414

Pressure loss 88,89, 121, 124-126, 131-134

Properties of fluids 1-5,7,8,12,13, 21,24,26,27,29,30,32,34,37, 52,60,61,65,66,69,71,73,75, 76,81,85,86,99-101,126,203, 204,208,215,223,225,237,252, 261,263,266,272,273,285,291, 310,328,367,419

Protuberance 337, 360, 398-403 Pseudo-plane flow 172, 200, 334,

339 Pseudo-plastic 28, 29 Pure shear flow 52, 54, 58, 110, 363 Pure viscous flow 87

Quasi-parallel flow 134,281

Radiation 21, 24, 63, 270

486 Index

Radial flow 144, 158, 162, 302, 305, 306,308,320,378,380,388,409, 410,412

Rarefied gas 1, 5, 77, 79 Rate of flow 108, 1l0, 122, 127, 136,

192,242,306,309,326,384,388, 428

Rayleigh's problem 181 Real gas 6-8 Recovery factor 242 Relaxation process 57 Restrictor 304, 306, 307 Reynolds

analogy 240, 253 boundary conditions 51, 299, 300 number 19-21,82-84,86-89,91, 110,

113, 114, 126, 146, 194,218,223, 224,244,250,279,280,329,334, 339,342,348,358,367,368,372, 374,378,380,388,390,391,398, 401,419,424,430,434,437,438, 441-443,446,447

transfer theorem 103 Rheology 26 Rheopectic 30 Rheostatic

bearing 310 film 308, 309 regime 130, 134

Riaboushinski flow 166 Ricati equation 167 Richardson annular effect 195 Rossby number 84 Rotating

cone 27 cylinder 141,142,196,225,275,343-

345 disk 119, 157, 158, 161, 162,343 ellipsoid 342, 343 sphere 341, 432

Rotation of fluid 44, 61, 121, 162-165, 339,439

Rupture, boundary conditions 288, 291-293,299,310,326

Seal 246, 275-277, 280, 281, 285, 291, 292,294,300-302,304,309,312, 320,368,372,377,391,412

Second principle of thermodynamics 12,38,69

Self-acting effect 285,288,295,307, 310-312

Self-acting film 294 Self-acting lubrication 285 Self-diffusion 24 Self-similar solution 137,147,152,153,

157,179,181,187-189,192,198, 223,389

Semi plane theorem 366 Separation flow 149,292 Separation of boundary layer 93,95,

387 Shear flow 44,45, 52, 77, 110, 240, 358,

363-365 Shear stress 13, 14, 18, 22, 26, 28-30,

34,35,51,79,88,92, 1l0, 112-115, 124, 127, 129, 141, 146, 155, 172,182-184,192,212,213,219, 221,249,283,286,289,341,375, 394,441

Shear viscosity 55 Shock wave 9, 16,31,250,252-258,261-

263,271,273,320,406,410,411 structure 55, 58, 249, 252 thickness 249, 255, 257-260

Short bearing 294, 300 Similarity criteria 80 Slender body 95,420,431 Sliding bearing (motion) 285,290,312,

321,328,391,392,403,412-414 Slip velocity 5, 13,78, 79 Slow plane flow 331,358,433 Slow rotation 339, 341 Slow viscous flow 19, 82, 89, 134,214,

216,220,238,246,275,321,330-332,334,339,342,353,358,359, 362,365,419,420,423,441

Small perturbations 83,269,371,415, 419,439

Sommerfeld condition 293, 298, 300 number 83, 295, 299 solution 293,310

Sound attentuation of 269, 272 speed 8, 83,243,252,253,260,269,

270,403,405

Source 12, 22, 47,104,107,116,117, 143, 146, 167, 180,214,273,364, 365,428,436,444,445

Specific heat of gases 8-10 of liquids 3, 4

Specific volume 3, 5, 7,66 Speed of propagation 59, 83, 269 Sphere, flow past 91, 329, 346, 347,

349-352,423,432,436,441,447 Sphere in translation 89, 91, 93, 94,

348,350-352,354,357,358,429, 432

Sphere-plane configuration 321, 323 Spherical bearing 276, 277, 281 Spherical coordinates 69, 71, 72, 10 1,

144,166,281,333,340,346,355, 424,445

Spin tensor 41 Spiral groove bearings and seals 301,

302,317 Squeeze effect 285, 289, 290, 311, 312,

397 Stability of laminar flow 20, 21, 113,

222 Stagnation point 68,152,153,155,157,

226,227,348,419,420 Stanton number 87, 219, 227 Starting flow 190, 192 State variables 11, 12,76 Static pressure 6, 49, 51, 387 Static stiffness 306, 307 Steady flow 39, 45, 48, 65-67, 82, 87,

90,100,105,109,127,172,177, 188,191, 199,204,251,264,279, 285,331,340,341,343,357,359, 370,403,404,446

Steady rotation 341, 343 Step bearing 295,314,315,317,384,

386,401,414,416 Step slider 296,303,400 Stiffness coefficient 397 Stokes

flow 329, 341, 347-354,420,428,433 hypothesis 55, 58, 252 operator 101, 102 paradox 358, 360, 361, 442 postulates 52, 54 problem 181, 182

Index 487

theorem 46, 47, 197 Strain rate 40,42-45, 47, 52-54, 57, 69,

72 Stream function 100, 101, 136, 165,

166,169,170,199,264,331,333, 334,336,340-343,346,348,355, 359,360,362,363,368,375,386, 423,441,444,446

Stream line 26, 39,44,45, 67, 68, 88, 90,92,97,100,109,116,139,140, 143,144,160,166,167,172,177, 199,200,344

Stress tensor 47, 49-54, 56, 64 Strouhal number 82, 92, 279 Subsonic flow 76,250,405-409,411,

413 Substantial derivative 39, 61, 69 Superposition 114, 178, 354 Supersonic flow 76,250,403,405,406,

409-411, 413 Supersonic inlet conditions 320, 412 Supply system 126, 306, 320, 383 Surface deformation 285,291,324,325 Surface tension 80, 84, 85, 121,222,

292,293,353,394,395 System of ducts 126

Tangential viscosity 55 Taper-flat pad 314,315 Taylor

flow 199, 200 number 85

Temperature field 22,66,203,204,206, 210,215,223-226,234,237,240,432

Tension, on a solid surface 332,351, 353

Tensor41-45,47,49-54,56,64,103 Thermal

conductivity 2, 21-23, 79, 212, 239 effects 21, 25, 61, 203, 204, 212 entrance 230,232,233 expansion 83

Thermodynamic equilibrium 7, 8, 57, 58 notions 7 pressure 51, 54, 55 principles 7, 9, 11, 12, 37, 62, 66, 68,

69

488 Index

Thermohydrodynamics 203 Thin layer 243,246,275,276, 306, 329,

368,372,397 Thixotropic 30 Three-dimensional flow 157, 199,293,

397 Thrust bearing 276,277,281 Total derivative 39, 48, 104 Transfer properties 2, 12 Transition regime 21, 89 Translation of a semiplane 119 Transonic flow 76, 179 Transversal heat transfer 214, 220, 246 Tribology 275, 301, 307 Tunnel model 2 Turbulence 21, 77,89,90,93,223,419 Turbulent flow 240,367,373,388,419 Two circular cylinders 116 Two-dimensional flow 100, 136, 264,

285,288,293,294,307,312,317, 324,331,368,370,371,375,383, 387,391,395,396,400,406,412, 422,440,442

Uniform flow 44, 67, 86, 90, 97, 134, 164,251,346,348,353,354,364, 365,419,423,433,440

Unsteady effects 82, 395 Unsteady flow 39, 82, 105, 177-179,

181,190,195,199,263,284,290, 312,332,343,345,376,404,440

Variable viscosity 208, 213, 220, 221, 281

Vector 22,38-41,46-50,56,60-63,65, 69,71,78,98-100,103,104,120,

141,174,177,284,285,330,332, 351,420

Velocity field 38-40,115,117,118,143,172,

184,187,200,203,220,226,280, 330,336,364,421

potential 47, 99, 142,269,337 Viscoelastic fluids 29, 32-34 Visco-inertial flow 113, 199, 367 Viscoplastic media 27, 29, 127, 128,

130, 131 Viscosity

coefficient 14 laws 15-19 of gases 17, 19,20 of liquids 15

Viscous flow pattern 87 Viscous stresses 82, 420 Voids model 2 Voight model 33, 34 Vortex 21,45,92,93,100,116,142,

180,185,186,196,198,365 Vortex sheet 92, 185, 186 Vorticity 41, 44, 66, 99-101,141,186,

195,197-200,331,332,336,347, 361,398,399,420,422,429,436, 437

VVake80,9O,92-95,97,428,429,436, 437,439

Weak shock wave 257,258,261-263, 271

Weber law 270 number 85

Whitehead's paradox 441,442 Work 9,11,12,46,62-65,271