Yamaguchi H. Engineering Fluid Mechanics (Fluid Mechanics and Its Applications)

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Index 565

Fiber-spinning, 434

Finger tensor, 40, 457, 458, 484

First law of thermodynamics, 52, 53, 57

First normal

stress coefficient, 419, 427, 465–472

stress difference, 419, 428–430, 484

Flow

coefficient, 135

curve, 400–403, 444, 445

instability, 305

measurement, 129–140

meters, 135

separation, 155

work, 265

Flows

of films, 310, 311

of jet, 168, 176, 177, 208

Fluid-fluid interface, 87–90

Fluid particle, 7, 23, 26

Fluid static, 73–77

Flux, 36, 44, 46, 52, 55

Forced vortex, 85

Fourier’s law, 61

Francis turbine, 181, 185, 186

Free surface, 85–87

Friction

factor (coefficient), 211, 259, 302,

326–328, 399, 412

velocity, 372, 389

Froude number, 289, 290

Fully developed flow, 321–330

Gas constant, 93, 227

Gauge pressure, 76, 99

Gauss’s divergence (integral) theorem, 13,

26, 45, 49, 55, 68, 122, 523, 532

Generalized Bernoulli equation,

521, 522

Generalized Newtonian fluid, 400,

406–408

Generalized Reynolds number, 408

Geometric similarity, 287, 288

Giesekus model (equation), 461, 462,

471, 472

Glassy modulus, 427

Goddard-Miller equation, 460

Grashof number (gravitational), 293

Gravitational

acceleration, 47, 283

potential, 68, 92, 121, 295, 521

Guide vanes, 189–191

Hagen-Poiseuille flow, 321, 323, 324,

330–334

Harmonic function, 116, 118

Head

coefficient, 197

loss, 186, 205

manometric, 185

piezometric, 75

potential, 124

pressure, 124

pump, 185–187

theoretical, 185, 186, 218

total, 124

turbine, 189–195

velocity, 124

Heat

conduction, 61, 297, 337–339

flux vector, 55

generated, 55

input, 53

transfer, 55, 61, 264–267, 295, 296,

353, 355, 359–361,

381–385, 388

transfer coefficient, 296, 384

Hele-Shaw flow, 311, 312

Hencky strain, 435, 481

Hook’s law, 405

Hydraulic

efficiency, 194, 195

radius, 320

Hydrostatic

paradox, 92, 93

pressure, 73

stress, 29, 73

Hydrostatics, see Fluid static

Ideal gas law, 225, 227

Immiscible fluid, 87, 90

566 Index

Impeller

radial flow, 181, 182

of turbo-pump, 181, 182

Impulse

function, 244

turbine, 172, 209

Inclined tube manometer, 75, 76

Incompressible (fluid) flow, 30, 44,

280–283

Inertia damper, 524

Inertial reference frame, 16–19, 73,

74, 85

Initial conditions, 331, 354, 451,

473–475

Instability

dynamics of development, 303

of thermal equilibrium, 297

thermomagnetic, 527–532, 535

Interface, 73, 87–90

Internal

angular momentum, 51

energy, 53, 57, 265, 508

flow, 225, 230, 243, 527

Intrinsic

angular momentum, 497, 510

rotation, 510

Invariant of tensors, 37, 38, 406

Inviscid

core length, 319, 320

flow, 115–122, 343, 344

Irrotational flows, 116

Isentropic

flow, 228, 255

process, 237

Isotropic fluid (flow), 37, 44

Jacobian, 24, 25, 31, 32

Jaumann (time) derivative, 21, 459

Jeffreys

element, 449, 452, 453

Joukowski

airfoil, 160–168

transformation, 120, 161

Journal bearing, 310

Kaplan turbine, 214

Kàrmàn integral equation, 349

Kàrmàn-Trefftz airfoil, 164, 178

K-BKZ model (equation), 464, 465

Kelvin

circulation theorem, 152–160

element, 449–451

force density, 510, 521

k-İ model, 378–380

Kinematic

similarity, 286–288

viscosity, 198, 277, 369, 476

Kinetic energy of turbulence, 370

Knudsen number, 6

Kolmogorov (micro) scales, 369, 370

Kronecker delta, 15

Kutta condition (hypothesis), 156

Kutta-Joukowski

hypothesis, 156

theorem, 160

Lagrangian

derivative, 8

specification, 7, 26

Laminar entrance flow, 320–322

Laminar flow

between concentric pipes, 339

between parallel plates, 299

between rotating cylinders,

302–306, 318

in a pipe, 319–334

Langevin

argument, 500, 501, 504

function, 499

Laplace’s equation, 116, 150, 312, 337

Lapse rate, 93, 96

Larmor frequency, 502

Laval tube (nozzle), 232

Law of wall, 372, 388, 389

Leading edge, 154, 155

Level meter, 524

Levitation of magnets, 497, 524

Index 567

Lewis number, 536

Lift

on an airfoil, 156, 160, 166, 192

coefficient, 166, 192

Limiting length, 262

Linear

elastic material (body), 405

momentum conservation, 44–47

momentum flux, 46

sublayer, 372–375

viscoelasticity, 425, 454

Linearly accelerating containers, 86, 87,

108, 109

Load-bearing capacity, 309

Local

heat transfer coefficient, 361, 384

Nusselt number, 361, 385

Lodge network (rubberlike) liquid

(model), 457, 463

Logarithmic velocity distribution, 374

Loss coefficient, 143–145, 205

Loss modulus, 425, 426, 440, 441

Lower convective

derivative, 21, 459

Maxwell model, 459

Lubrication

equation, 306, 307

rotating shaft, 305

Mach

angle, 230

corn, 230

correction, 131

number, 131, 230, 289, 290

Magnetic

boundary condition, 532–534

dimension, 527

force (Kelven force density), 497,

521, 530

materials, 502, 503

normal traction, 523

particles, 498, 502

permeability, 506, 508

polarization, 508, 517

pressure jump, 523, 525, 532–535

Rayleigh number, 531

susceptibility, 501, 506

Magnetic fluids, 2, 497

dynamics, 507–514

properties, 497–498

shaft seals, 525

Magnetite, 497

Magnetization

of saturation, 498, 499

Magnetocaloric effect, 497, 514, 517

Magnetostatic buoyant force, 524

Magnetoviscous effect, 498, 503, 512

Manometers, 90, 91, 130, 131

Manometric head, 185

Mapping function, 119, 120

Mass

conservation, 43, 44

diffusion, 536

flow rate, 123

flux, 44, 241

transfer, 532

Material

derivative, 7, 20, 152

functions, 417, 422, 423, 425

line (element), 9, 21, 23, 24

objectivity, 19–22, 33–35, 459, 460

Maxwell

element, 448–453

equation, 58, 516

model of viscoelastic fluid, 447, 448

model of viscosity, 280

stress tensor, 507–509, 511

Maxwell model (CRM), 455, 463–473

Mean free path, 5

Mechanical

efficiency, 195

loss angle, 425, 441

Memory function, 455, 458, 463

Metacenter, 101

Metacentric height, 101

Metric tensor, 23

Micromanometer, 90, 91

Minor losses, 140–145

Mises airfoil, 164

Mixed flow pumps, 202

Mixing length, 371

Mobility factor, 461

568 Index

Modulus, 405, 425–427, 440, 441,

448–454, 463

Molecular Prandtl number, 383

Moment, 160

Moment of inertia (of surface), 79

Moment of momentum, 128, 183–188

Momentum

flux, 126, 243

thickness, 350–356, 386

Nappe, 137

Natural convection, 295, 297

Navier-Stokes equations, 282–285

Néel relaxation, 502, 505

Net positive suction head (NSPH), 206

coefficient, 205

Neumann energy equation, 56

Newton’s law of viscosity, 279

Newton’s second law, 43, 64, 126, 289

Newtonian fluid, 279, 280, 440

Non-Newtonian fluid, 399, 400

Normal

instability, 520

shock (wave), 236, 237, 246, 248

stress, 29, 88

No-slip condition, 311, 336, 337, 341,

358, 472

Nozzle, 176, 177

Numbers (nondimensional)

of Brinkman, 294

of Deborah, 489

of Eckert, 293

of Euler, 289

of Froude, 289

of Grashof, 293

of Lewis, 536

of Mach, 289

of Nusselt, 296

of Peclet, 294

of Prandtl, 294, 360, 378, 383

of Rayleigh, 297

of Reynolds, 289, 290, 302, 312, 408,

412, 415

of Stanton, 296, 362

of Strouhal, 292, 352, 408, 489

of Taylor, 305, 306

of Weber, 289

of Weissenberg, 489

Numerical solutions, 334, 474, 475

Oblique shock, 237, 251–255, 274

Oil feeding reservoir, 108–110

Oldroyd’s equations, 460, 461, 485–487

One equation models, 370–377

Open channel flow, 137

broad-crested wire choked flow, 176

Orifice meter, 132–135

Oscillatory rheometric flow, 424–427

Outer layer, 372–374

Over-expanded condition, 237, 238

Overlap layer, 372

Overshooting, 475

Paraboloid of revolution, 108

Parallel plates, 299

Peclet number, 294

Pelton wheel, 172, 173, 208–211, 219

Perfect fluid, 30, 115, 154

Performance curves, 198, 199

Phan-Thien and Tanner model, 463

parameter, 196, 291

Phase-shift, 425, 441

Piezometric head, 75

Piezotropic (fluid), 152

Pitot probe (tube), 129–132, 255–258

Planar elongational flow, 422

Plane flow, 301, 334

Poiseuille

flow, 301, 321–325, 328–332

paraboloid, 324, 412

Polar (material) fluid, 48, 51, 52, 507

Polarization of magnetic fluid, 517

Polyadic (alternator), 15, 49

Polymeric fluid (solution), 2, 424,

460, 489

Polytropic change, 93–96

Potential

flow, 115–121

function, 92, 116

vortex, 119

Index 569

Power

coefficient, 197

law fluid, 401–403, 412–414, 444, 445

law profile, 329, 330, 387, 409

Prandtl

boundary layer equation, 343

number, 294, 360, 378, 382, 388

relation, 250

universal law of friction, 327

Pressure, 29

(loss) coefficient, 142–146, 197, 321

drop (loss), 145, 325, 409, 436

dynamic, 130

at elbow channel, 140, 141, 145

equation, 124

function, 122, 152, 233

head, 124, 185, 192

jump, 523, 525, 532–535

recovery (factor), 144

stagnation, 130

total, 124, 322

vessel, 106

Principal axes (of stress), 37, 38

Principal stress, 280

Principle of Archimedes, 82

Principle of frame invariance, 19, 20

Product of surface area (inertia), 79

Profile development region, 320, 321

Propeller, 142, 146

efficiency, 147–149

Pseudoplastic fluids, 401

Pseudovector, 14, 16, 33, 49, 128,

509, 513

Pump

efficiency, 194, 195

head, 185

Pumps

axial flow, 182, 183

mixed flow, 182, 183, 213

performance curve, 198, 199

radial flow, 181

Pyromagnetic coefficient, 501, 530

Quasi-linear, 457

Quasi-stationary, 497, 507, 516, 521

Rabinowitsch

correction, 444

equation, 443

procedure, 441–445

Radial flow pumps, 183, 188

Rankine-Hugoniot relationship, 248, 252

Rankine ovoid (oval), 173, 174

Rate of

deformation tensor, 10, 34

heat transfer, 264, 265, 267

strain tensor, 11, 280, 381, 406, 456,

478–483

Rayleigh line (curve), 241–246, 264–270

Rayleigh number, 297, 298, 527–532

Rayleigh-Plesset equation, 149–152

Reaction turbine, 208

Rectilinear acceleration, 18

Relative

acceleration, 74, 85

strain tensors, 23, 453, 478–483

velocity, 74

Relaxation

model, 505

modulus, 454

time, 448–457, 502, 505, 506

Retardation time, 452, 453

Retarded elasticity, 452

Reversible, 228

Reynolds

decomposition, 365

equation for lubrication, 307

equation for turbulent flow, 368

number, 289, 302, 312, 408, 412, 415

stress, 367, 368, 372

Reynolds’ analogy, 361, 362, 381–385

Reynolds’ transport theorem, 23–26, 35,

36, 45, 48, 65, 68, 128

Rheometric flow, 418, 419, 424–427

Rheopectic fluid, Rheopexy, 404

Rigid body rotation, 16, 82

Rosensweig equation, 516–519

Rotating

blade, 140–142

containers, 85, 108

cylinders, 119, 299–306, 415

570 Index

reference frame, 16–19, 73, 85, 124, 125

spheres, 412–415

Rotational

Reynolds number, 305

viscosity, 517–519

Rotation tensor, 16–35

Roughness, 287, 298

Runner, 185

Saturation magnetization, 501

Scale effect, 202, 203

Shafts seals, 525

Second

coefficient of viscosity, 291

moment of surface area (inertia), 79,

81, 103

normal stress coefficient, 419, 467

normal stress difference, 419,

484, 485

Self-levitating effect, 524

Semi-vertex angle, 251, 274

Separated

point, 350

region, 350–353

Shaft power, 195

Sharp-crested weir, 137–140

Shear

stress, 29, 418–421, 476

thickening fluid, 403

thinning fluid, 401

velocity, 421

work, 439, 440

Shearfree flow, 421–424

Shliomis magnetic relaxation

equation, 515

Shock

strength, 249

wave, 241, 246–255, 281

Shroud, 181

Similarity rules, 194–203,

Similarity solution, 344–346

Similitude, 195, 196, 286–294

Simple

(shearfree) extensional flow, 11, 12,

421–424, 478–483

shear flow, 11, 12, 415, 472–478

Sink, 118, 119

Siphon, 174, 423

Skew-symmetric tensor (anti-symmetric

tensor), 14, 15, 18, 49, 50, 52, 55,

509–511

Skin friction coefficient, 326

Slip factor, 188

Slipper-pad bearing, 306–312, 318

Slipstream, 142

Soft magnet approximation, 529

Solenoidal velocity field, 44

Sonic

line, 255

velocity, 225

Sound

velocity (speed), 131, 132,

225–230

wave, 229

Source, 118, 119

Specific

energy, 59, 185

gravity, 524

heat, 59

heat ratio, 131, 228

speed, 201, 202, 207

volume, 57, 227

Speed

factor, 210

of sound, 225, 229

Spherical gap flow, 412–415

Spin

energy, 56

flux, 52

tensor, 10, 21, 55

viscosity, 512

Sprinkler, 179, 180

Squeeze film, 308, 423

Stability of floating object, 100–104

Stagnation

hole, 130, 131

point, 130, 155, 156

pressure, 130, 255

quantities, 232

Stall, 167

Standard

atmosphere, 76, 93–96

flow, 417, 418, 478–483

temperature, 93–96

Index 571

Stanton number, 296, 362, 385

Starting vortex, 155, 156

Static hole, 130, 131

Static pressure, 130, 151

Steric repulsion, 498

Stokes

equation, 322, 323, 335

flow, 310–316

law, 316

Stokes’ hypothesis, 281, 282

Stopping vortex, 156

Storage module, 425, 426, 440, 441

Stratosphere, 110

Stream function, 116, 117, 312, 345

Stream lines, 122, 125, 130, 138

Stream tube, 122, 123, 125, 127, 128

Stress

of force, 27, 28

ratio, 420, 421

tensor, 26, 30, 279, 418

vector, 27

Strong shock, 249

Strouhal number, 292, 352, 408, 489

Sturm-Liouville problem, 338

Submerged surface, body, 80–82,

100–104

Subsonic flow, 229, 236, 255, 269

Substantial derivative, 7, 47

Sudden

contraction, 140, 141

expansion, 140, 141, 272

Supercritical, 520

Superparamagnetism, 501, 502

Supersonic

flow, 230, 257

nozzle, 232

Surface

couple, 49, 51, 512

force, 26, 45

shape, 344

tension, 87, 104, 105, 151, 152, 499

Surfactant, 88, 498

System International, 2, 3

Tab-orifice, 136–140

Tank-orifice, 136, 138

Taylor

microscale, 369, 370

number, 305, 306

vortex, 305

Theoretical specific energy, 185

Thermal

boundary layer, 351–353

chocking, 268

conductivity, 61, 62, 293

diffusivity, 62, 360, 513, 537

expansion, coefficient, 60, 61, 292, 529

similarity, 293, 294

Thermodynamic relations, 56–62

first law, 52, 53

Maxwell equation, 58

pressure, 29, 57, 59, 73

second law, 57, 58

Thermomagnetic natural convection

(Thermoconvective), 520, 527–532

Thixotropic fluid, thixotropy, 404

Thrust

bearing, 309

function, 244

Time average, 364

Torque, 65, 66, 128, 304, 305

coefficient, 305, 414

Torricelli’s theorem, 138, 139

Total

drag force, 309

efficiency, 194

energy, 122

enthalpy, 354

head, 124

pressure, 432, 510

stress tensor, 37, 74, 87, 279, 280,

418–420, 431, 438, 456,

507, 509

Trailing

edge, 155, 156, 162

vortex (stopping vortex), 156

Transducer, 439

Transport equation, 375

Troposphere, 96, 110

Trouton viscosity, 423

Turbine

axial flow, 183

Francis, 185

impulse, 172, 208

572 Index

Kaplan, 189, 213–217

mixed flow, 182, 183

Pelton wheel, 208–211, 219

radial flow, 181

reaction, 208

Turbomachines, 180–183

of efficiencies, 194, 195

Turbulent

boundary layer, 346, 370–385

diffusion, 287

entrance flow, 320–322

flow, 364–389

heat flux coefficient, 382

intensity (relative), 366

models, 368, 370–380

pipe flow, 327–328

Prandtl number, 382, 383, 388

transport, 281

velocity profile, 328, 329, 373–375

Two equation models, 378–380

Uniaxially stretching, 422, 433, 466

Unidirectional flow, 299–306

Unitary matrix, 16

Units, 2, 3

Unit tensor, 14, 15

Upper convective

derivative, 21, 33–35, 459, 478

Maxwell model (UCM), 33, 457,

465–478, 484–487

U-tube manometer, 75, 129

Vane, 189, 193

Velocimetry, 129–132, 255–258

Velocity

coefficient, 134, 210

defect (volume flow rate), 124

diagram, 125, 183–188

gradient tensor, 10, 13

head, 124

measurement, 257

potential, 116, 118, 312

Vena contracta, 133, 271, 272

Venturi meter (tube), 135, 136

Viscoelastic

boundary layer, 475–478

fluid, 23, 405–406

linear, 454

Viscometer, see Rheometric flow

Viscometric

flow, 417, 418, 428–437

function, 419, 420