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Index

Absolute pressure, 13, 41 Angular momentum flow, 174, video V5.12 restrictions on use of, 106–110, 222, Absolute Annulus, flow in, 257–258 video V3.12 in British Gravitational (BG) System, 7 Apparent viscosity, 16 unsteady flow, 107–108 in English Engineering (EE) System, 8 Aqueducts, 454 use of, video V3.2 in ideal gas law, 12 Archimedes, 27, 28, 62 Best efficiency points, 564 in International System (SI), 7 Archimedes’ principle, 61–64, video V2.7 Best hydraulic cross section, 460–461 Absolute velocity Area BG units. see British Gravitational (BG) System in centrifugal pumps, 558–561 centroid, 51–53 of units defined, 154, 551 with change in, 507–522 Bingham plastic, 16–17 in rotating sprinkler example, 176–177 isentropic flow of ideal gas with change in, Birds, wings of, 429 in turbo machine example, 551–554 510–516 Blades vs. relative velocity, 141–142 and , 511–513 curved and radia, 561, 562 Absolute viscosity moment of inertia, 52 radial, 561 of air, 620–621 Aspect ratio rotor, 575, 591 of common gases, 617 air foil, 435 stator, 575, 591 of common liquids, 617 plate, 271 turbo machine, 549 defined, 15 Assemblies, 603 Blade velocity, 551–554, 558–559 of U.S. Standard Atmosphere, 622–623 Atmosphere, standard. see Standard Blasius, H., 29, 285, 389 of water, 619 atmosphere Blasius formula, 285, 339 Acceleration Atmospheric pressure, 13, 39–40, 43, Blasius solution, 390–392 along streamline, 123–124 video V2.2 Blood pressure, measuring, 2, 36, 43, centrifugal, 129, video V3.4 Available energy, 190–191, 195, 482–483 video V2.3 convective, 125, 129, 250 Available net positive suction head, Blowers, 549, 577 defined, 121 564–565 Blunt bodies, 377, video V9.2 as field, 121, 206 Average velocity, in mass flowrate, 147–148 Body forces, 33, 160, 217 gravitational, 7, 8, 622–623 Axial-flow impulse turbines, 585 Boiling, 23–24, 96–97 local, 124 Axial-flow machines Boosters, 577 normal, 75, 127–129, video V3.4 compressors, 590–592 Bottom slope, 448–449, 454 particle, 75, 121, 206 defined, 550, 551 Boundary conditions role of material derivative, 121–124, 206 pumps, 574–577 in Bernoulli equation, 79 streamwise, 75, 129, video V5.3 Axisymmetric flow, 377 inviscid flow, 236, 237 Accessibility of flow, 451 no-slip, 14, 238, 251, video V1.4, Acoustic velocity, 22 Backward curved blades, 561, 562 video V6.12, video V6.13 Actual head rise, 560–562 Backward difference, 600, 602 in solving CFD simulation problems, 607 Adaptive grids, 607 Bar (unit), 43 Boundary element method, 603–604 Adiabatic flow, 183, 482, 507, 527–534 Barometers, 43 Boundary layer, 384–408 with friction. see aneroid, 47 concept in history of fluid mechanics, reversible. see Isentropic flow mercury, 42 27–28 Adverse pressure gradient, 241, 404 Basic dimensions, 4, 265 concept of, 223–224, 382, video V1.4, Aerodynamics, in history of fluid Bats, 431 video V6.12, video V9.12 mechanics, 28 COPYRIGHTEDBellows meters, 372 MATERIALdisplacement thickness, 386–387 Affinity laws, pump, 573 Bends, 345 effect of surface roughness, 420 Air, table of properties, 620–621 Bernoulli, D., 27, 28, 79 effects of pressure gradient, 403–407, Air bridges, 119 Bernoulli equation video V9.10 Air foils, 430, 435, video V9.21, video V9.23, cautions on use of, 79 equations, 388–392 video V9.24 derivation from Euler’s equations, flat plate, 384–388 Alternate depths, 450 221–222 and flow separation, 382 Andrade’s equation, 18 derivation from first law of thermodynamics, laminar flow Aneroid barometers, 47 189–195 approximate solution, 396–397 Angle of attack, 278, 406, 434, 436 derivation from F = ma, 79, 220–221 Blasius solution, 390–392 Angle of contact, 25 examples of use, 89–103 Prandtl solution, 388–390 Angular deformation, 205, 207–210, extended, 191 momentum integral equation for, 392–397, video V6.3 for incompressible flow, 505–506 407–408 Angular momentum. see Moment-of- irrotational flow, 109, 224 momentum thickness, 388 momentum physical interpretation, 82–85 pipe, 311

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I-2 Index

Boundary layer (continued) Composite body drag, 423–427 Control surfaces, 130 thickness, 385–388, video V9.6 Compressibility of fluids, 20–23, 37–39, Control volume, 129–131, video V4.14 transition from laminar to turbulent flow, 419–420 defined, 130 385, 397–398, video V9.7 Compressible flow, 479–547, video V11.2, deforming, 131, 158–160 turbulent flow, 385, 399–402 video V11.5 in derivation of continuity equation, 146–147 velocity profiles, 398, 404, 405, video V9.4 analogy with open-channel flow, 532–533 and first law of thermodynamics, 182–183 vorticity, 385 effect on use of Bernoulli equation, 106–107 fixed, 130–131, 148–154 Boundary layer separation, 404–405, video V6.8 with friction, 522–534 guidelines for selection, 142–143, 156–158 Bound vortex, 435, video V4.6 graphs of, 624, 626, 628, 630 infinitesimal, 204 Bourdon pressure gage, 47, video V2.4 with heating or cooling, 535–541 moving, 141–142, 154–156, 172–174 Boussinesq, J., 329 ideal gas thermodynamics, 480–485 velocity, 154 Bow thrusters, 170 introduction, 479–480 Control volume statement, 199–200 Brake horsepower, 563 isentropic, 501–507 Convective acceleration, 125, 129, 250 British Gravitational (BG) System of units, 7–8 Mach number and , 487–492 Convective derivative, 124–125 Broad-crested weirs, 472–474, video V10.14 regimes, 492–496 Converging channel, 599–603 Buckingham, E., 29, 266 as reversible process, 106–107 Converging-diverging duct flow, 510, 512–513, Buckingham pi theorem, 265–266 shock waves, 496–501 video V11.6, video V11.7 Buick Dynaflow, 557 stagnation properties, 485–487 Converging-diverging nozzles, 509, 518–522, Bulk modulus, video V1.7 two-dimensional supersonic, 543–544 video V11.6, video V11.7 characterizing compressibility, 20, 21 in variable area duct, 507–522, video V11.6, Converging duct flow, 508–509 defined, 20 video V11.7 Converging nozzles, 516–518, 521–522 Bulk modulus of elasticity, 489 Compressible flow passage, 515–516 Conversion factors, for units of measure, 9 Buoyant force, 61–64, video V2.7, video V2.9, Compressible flow turbines, 593–595 Cooling, 535–541 video V11.5 Compressible flow turbomachines, 589–595 Corrected compressor mass flowrate, 593 Compressors, 589–593, video V12.6 Cotton candy, 91 Canals, 452 axial-flow, 590–592 Couette flow, 252–254 Capacity, pump, 563 defined, 577, 589 Creeping flow, 259, 279 Capillary action, 25 multi-stage, 589–590 Critical depth, 450 Casings, 557, 558 as pumps, 549 Critical flow, open-channel, 443, 447 Cauchy, A., 28, 280 radial-flow, 590 Critical pressure ratios, 520, 521 Cauchy number, 278, 280 Compressor stall, 591 Critical properties, 506 Cavitation, 588 Compressor surge, 591 Critical Reynolds number, 385, 397 defined, 24, 96 Computational fluid dynamics (CFD), 333, Critical state, compressible flow, 506–507 producing in flowing liquid, 97 598–615, video V2.11, video V6.2, Cross, H., 366 Cavitation number, 280, 294, 303 video V6.16, video V11.6 Crystal Rapid, 466 Ceiling fans, hi-tech, 578 advantages for flow simulation studies, 614 Curl operator, 209 Center of buoyancy, 62–63, video V2.12 boundary conditions, 607 Curved shock waves, 496, 497 Center of pressure, 53 computational grid, 605–607 Curved surfaces, forces on, 59–61 Centrifugal acceleration, 129 converging channel example, 599–603 Cylinders Centrifugal pumps, 557–570, 577, video V12.3 difficulties in using, 611–613, 615 circular, 241–244 net positive suction head, 564–566 discretization, 603–605 drag coefficient for, 416–417, video V9.13 performance characteristics, 562–564 overview, 205, 259, 598–599 inviscid flow around, 242, video V6.6 performance curves, 562, 567–570 solving equations, 609–611 large vs. low Reynolds number flow around, system curve, 566–567 turbulence models, 607–609 382–383, video V6.8, video V6.16 theoretical considerations, 558–562 verification and validation, 613 pressure distribution on surface, 242, Centroid, 51–53 Computational grids. see Grids 406–407 CFD. see Computational fluid dynamics (CFD) Conservation of energy. see First law of rotating, 244–246, 436 Chaos, 333 thermodynamics separation location, 382, 404–405 Chezy, A., 28, 454 Conservation of linear momentum, 216–220, Cylindrical coordinates, 68–69 Chezy coefficient, 454 video V5.4, video V5.5, video V5.6 Cylindrical polar coordinates, 213, 225, 249 Chezy equation, 453–454 Conservation of mass, 92, 145–158, 210–216 Choked flow Conservative form, 611 D’Alembert, J., 27, 28, 243 Fanno, 525, 530–532 Contact angle, 25, video V1.11 D’Alembert’s paradox, 243, 404, 405 Rayleigh, 537 Continuity equation, 146–158. see also Darcy, H., 28, 320 in variable area duct, 514–515, 518 Conservation of mass Darcy friction factor, 320 Chord length, 430, 435 cylindrical polar coordinates, 213 Darcy-Weisbach equation, 336 Circulation defined, 211–212 DaVinci, L., 27, 28 flow past air foils, 434–436 derivation of, 146–148 Deepwater pipelines, 362 flow past cylinders, 436 differential form, 210–212 Deepwater waves, 446 flow past spheres, 436–438 finite control volume, 92–93 Deformation and vortex motion, 233 incompressible flow, 153, 154, angular, 205, 207–210, video V6.3 Closure problem, 608 video V5.1, video V5.2 linear, 205, 206–207 Coefficients, 281. see also specific coefficients unsteady flow, 147, 212 rate of, 207 Colebrook formula, 338 rectangular coordinates, 210–211 Deforming control volume, 131, 156–158 Combustion chamber, 530–531 Continuum hypothesis, 4 Degree of reaction, turbine, 578 Completely turbulent flow, 336–337 Contraction coefficient, 91, 92, 101, 475 Del (gradient) operator, 34 BBMIndx.inddMIndx.indd PagePage I-3I-3 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

Index I-3

Density Distorted models, 290–291, video V7.8, EE units. see English Engineering (EE) System of air, 620–621 video V7.11, video V7.12, video V7.17, of units as fluid characteristic, 11, video V2.10 video V7.18 Efficiency ideal gas, 483–484 Diverging-converging duct flow, 510 fan performance example, 198 mass flow, 523–524, 535 Diverging duct flow, 508–509 hydraulic, 563 stagnation, 486 Donor cell differencing, 612 isentropic, 592 of U.S. Standard Atmosphere, 622–623 Doppler effect, 494 mechanical, 563 of water, 11, 619 Double-suction impellers, 558 overall, pump, 563 Dental drills, 584–585 Doublet, 234–236 polytropic, 592 Depth ratio, 465–466 Drag, 408–427 pumps vs. turbines, 587–588 Derivative on circular cylinder, 243 volumetric, 563 convective, 124–125 defined, 377–378 Elbows, losses in, 345–346 local, 124 example, 378–379 Elevation head, 83, 104 material, 121–124, 126–127, 138–139, 206 form, 410–412, video V7.2, video V9.11 Enclosed impellers, 558 substantial, 121–124, 206 friction, 409–410 Energy Design flowrate, 564 friction coefficient, 401–402 available, 190–191 Differential analysis, 204–261 overview, 408–409 internal, 182, 480–481, 483–484 and conservation of linear momentum, pressure, 410–412 kinetic, 83, 182 216–220 on rotating cylinder, 245 per unit mass, 182 and conservation of mass, 210–216 Drag coefficient per unit volume, 193 determination of pi terms by example, air foil, 435 per unit weight. see Head 273–274 automobile, 424–425 potential, 83, 182 determination of pi terms by inspection, composite body, 423–427 specific, 449–452 275–276 cylinder, 416–417, video V9.13 stored, 182 and fluid element kinematics, 205–210 defined, 380 Energy balance, 448–449 introduction, 205–206 as dimensionless group in fluid mechanics, Energy equation, 182–198 and inviscid flow, 220–227 278 application to nonuniform flows, 195–198 and plane potential flows, 227–246 effect of compressibility on, 419–420, 492 application to one-dimensional flows, Differential equations. see Differential analysis effect of Froude number on, 422–423, 185–189 Diffuser pumps, 557 video V8.13 video V9.18 combined with moment-of-momentum Diffusers, 344 effect of Mach number on, 419–420 equation, 198 Dimensional analysis, 262–285 effect of shape on, 412–413, 418, comparison with Bernoulli equation, and Buckingham pi theorem, 265–271 video V9.11, video V9.19 189–195 common dimensionless groups, 277–282 effect of surface roughness on, 420–422 defined, 185 concept of dimensions, 4–5 ellipse, 412–413 derivation, 182–185 correlation of experimental data in, flat plate normal to flow, 412, 414, 415, 418, semi-infinitesimal control volume statement 282–285 video V7.2 of, 199 defined, 262–263 flat plate parallel to flow, 401–402, 412–415, Energy line, 354–355, 448–449 determination of pi terms by inspection, 418 Energy line (EL), 103–105 275–276 form, 410–412 English Engineering (EE) System of units, 8–9 determination of reference dimensions, friction, 396, 401, 409–410 Enthalpy, 186, 481, 483–484, 486 273–274 in model studies of flow around bodies, 295 Entrance length, 312, video V8.12 of ducts, 349–352 pressure, 410–412 Entrance loss, 341, 342 for fully developed laminar pipe flow, Reynolds number dependence, 414–419 Entrance region, 224, 311, 341 319–321 selected three-dimensional objects, 425 Entropy, 199–200, 482–484 overview, 263–265 selected two-dimensional objects, 425–427 and Fanno flow, 524–525 of pipe flow, 333–352 sphere, 297, 414–417, 420–421, 436, 437, and normal shock, 500 selection of variables, 271–273 video V9.17 of Rayleigh flow, 536 Dimensional homogeneity, 4–4, 266 streamlined body, 413 T–s diagrams, 505 Dimensionless groups Drag friction coefficient, 396 Equation of state, 12–13, 480 common in fluid mechanics, 277–282 Drooping head curve, 563 Equations. see also specific equations defined, 264–265 Ducts general homogeneous, 5 Dimensionless products dimensional analysis, 349–352 of motion, 219–220 defined, 264–265 vs. pipes, 307 restricted homogeneous, 5 pi terms as, 266 Dynamic pressure, 85 Equipotential lines, 228 Dimensions Dynamic similarity, 288 Equivalent length, 340, 341 basic, 4, 267 Dynamic viscosity Euler, L., 27, 28, 220, 280 of common physical quantities, 5 of air, 620–621 Eulerian description of flow, 115–116 reference, 266, 273–274 of common gases, 617 Eulerian description of motion, video V6.2 Discharge coefficient of common liquids, 617 Euler number, 278, 280, 303 nozzle, 368 defined, 15 Euler’s equations, 74 orifice, 367 of U.S. Standard Atmosphere, 622–623 Euler’s equations of motion, 220 underflow gates, 475 of water, 619 Euler turbo machine equation, 555 Venturi meter, 369 Exhausters, 577 Discretization, 603–605 Eddies, 327, 607 Exit pipe loss, 342, video V8.12 Displacement thickness, 386–387 Eddy viscosity, 329, 608–609, video V8.7 Expansion waves, 543, video V11.9 BBMIndx.inddMIndx.indd PagePage I-4I-4 8/13/188/13/18 5:275:27 PMPM f-512f-512 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I-4 Index

Experimental data, 282–285 rotameter, 370, video V8.15 Fountains, 352 Explicit method, 605 turbine meter, 370–371 Francis, J., 586 Extended Bernoulli equation, 191 ultrasonic flowmeter, 371 Francis turbine, 586, 587 Extensive property, 131–132 Venturi meter, 99, 100, 366, 368–369, Free jets, 90–92, video V3.9 External flow, 375–439 video V3.10 Free-stream velocity, 403 background, 375–376 open-channel flow Free surface, 50 boundary layer characteristics, 384–408 sluice gate, 100–102, 475–476 Free-surface flow, 298–299 drag, 408–427 uniform, 452–454 Free vortex, 81, 232, 234 general characteristics, 376–384 weir, 102–103, 460–474, video V10.13 Frequency parameter, 281 lift, 426–438 Flow meters. see Flow measurement Friction, 522–534 Eyes, in pump casings, 557 Flow net, 228 Friction coefficient, 278, 395–396 Eyes, pressure of, 86 Flowrate Friction drag. see Drag mass, 92, 147 Friction drag coefficient, 401 Falling (drooping) head curve, 563 normal (design), 564 Friction factor Fan laws, 578 of toilets, 154 data correlation for, 337 Fanning friction factor, 320 volume, 92, 147 in dimensional analysis of laminar pipe flow, Fanno flow, 523–534 Flow separation, 382, 406–407, video V9.9, 319–321 basic equations of, 523–526 video V9.19 for Fanno flow, 532–534 choked vs. non-choked, 528, 530–532 Flow visualization, 116, 117–121, video V4.1, Moody chart, 336–338 defined, 523 video V4.6, video V4.9, video V7.16, noncircular conduits, 350 duct sizing in, 532–534 video V9.19, video V11.5 smooth pipe, 337 for ideal gas, 628–629 Flow work, 184 in wholly turbulent flow, 336–337 of ideal gas, 527–529 Fluid dynamics vs. fluid statics, 11 Frictionless flow, 507 supersonic, 534 Fluid machines, videos V12.1–V12.5 compressible adiabatic. see Isentropic flow Fanno line, 523–526, 529–530, 541 Fluid mechanics compressible with heat transfer. see Rayleigh Fans, 549, 552, 577–578 defined, 1 flow Favorable pressure gradient, 404 flow parameters, 1–2 with heating or cooling, 535–541 Field representation, 112–113, video V4.2 history of, 27–29 incompressible, 79, 222 Finite control volume analysis, 145–203, 199–201 Fluids open channel. see Open-channel flow Finite difference method, 604 defined, 3 in variable area duct, 507–522 Finite element method, 603–604 describing characteristics, 3–4 Friction slope, 448, 462–463 Finite volume method, 605 flow parameters, 1–2 Fricton velocity, 330 First law of thermodynamics, 145, 182–198, ideal, 222 Frontal area, 380, 413 200–201, video V5.15, video V5.16 inviscid, 220–227, 223 Frontinus, S., 27, 28 First moment of area, 51 molecular structure, 3–4 Froude, W., 28, 279 First Tds equation, 199 Newtonian, 15 Froude number, 278, 279, 299–300, 303, 443, Fittings, losses in, 345–346 non-Newtonian, 16 446–448, video V7.4, video V10.5 Fixed control volume, 130–131, 148–154 properties, 11, 14, 617–620 and drag coefficient, 422–423 Flaps, air foil, 432, video V9.23, video V9.24 viscous, 15 and Mach number, 542 Flat plate drag coefficient, 401–402 Fluid speed Fuel pumps, 567 Flat plates in Fanno flow, 525 Fully developed flow Blasius solution, 390–392, 391 of Rayleigh flow, 536 applying Navier-Stokes equations, 318–319 drag coefficient Fluid statics laminar, 313–322, video V8.10 normal to flow, 412, 414, 415, 418, equilibrium in, 31 in pipes, 311–312 video V7.2 forces in, 50–55 turbulent, 323–333 parallel to flow, 412–413, 414, 415, 418 pressure height relation, 34–35, 37–41 Fully developed region, 224 momentum integral equation, 392–397 vs. fluid dynamics, 11 laminar flow, 393 Force Gc, 9 turbulent flow, 399 body, 33, 160, 217 Gage fluid, 44 relative roughness on, 401 buoyant, 61–64, video V2.7, video V2.9 Gage pressure, 13, 41 Flettner, A., 246 compressibility, 280 Galilei, G., 27, 28 Floating ball water fountains, 252 drag, 243, 377–380, 408–427 “Galloping Gertie,” 290 Floating bodies, video V2.7 hydrostatic Gas constants Archimedes’ principle, 61–64 on curved surfaces, 59–61, video V2.6 defined, 14 stability, 64–65 on plane surfaces, 50–55, video V2.5 in ideal gas equation of state, 12, 480 Flow, in converging channel, 599–603 lift, 243, 377–378 universal, 480 Flow coefficient, 571, 587 pressure, 46, 57 Gas dynamics. see Compressible flow Flow measurement, 98–103 shear, 14 Gas turbine engines, 593–595 external flow surface, 33–34, 160, 217–219 Gas turbines, 495 Pitot tube, 86–87, 104, video V3.8 surface tension, 24–26 Gauss-Sidel iteration, 601 internal flow as unit of measure, 7–9 General homogeneous equations, 5 bellows meter, 584 viscous, 15 Geometric similarity, 288 magnetic flowmeter, 583 Forced vortex, 232 Glass wool, 91 nozzle meter, 99, 366–370 Form drag, 410–412 Grade line nutating disk meter, 371–372, video V8.16 Forward curved blades, 561 energy, 103–105, 448–449 orifice meter, 99, 366, 367 Forward difference, 600 hydraulic, 103–105 BBMIndx.inddMIndx.indd PagePage I-5I-5 26/10/1826/10/18 5:425:42 PMPM f-0157f-0157 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Index I-5

Gradient, pressure. see Pressure gradient Hydraulic diameter, 257, 350 Irreversible flow, 199–201 Gradient operator, 122, 206, 225 Hydraulic efficiency, 563 Irrotational flow, 109, 209–210, 222–227 Gradually varied flow (GVF), 442, 461–463 Hydraulic grade line (HGL), 103–105 Irrotational vortex, 231–232 Grand Canyon, 466 Hydraulic jumps, 464–469, video V10.11, Isentropic efficiency, 592 Gravity, acceleration of, 7, 8, 622–623 video V10.12 Isentropic flow, 501–507 Grids, 600, 604–607, 611–612, video VA.2 classification of, 468–469 with area change, 510–516 Guide vanes, 345, 575, 591 depth ratio across, 465–466 basic equations for, 502–503 GVF. see Gradually varied flow as example of rapidly varied flow, 464 and Bernoulli’s equation, 505–506 head loss across, 465–466 and compressible flow condition, 106–107 Hagen, G., 28, 254, 316–317 Hydraulic loss, 563 critical state, 506–507 Hagen-Poiseuille flow, 254, 316–317, video V6.14 Hydraulic radius, 454 defined, 485 Half-body, 315–318, video V6.5 Hydraulics, in history of fluid mechanics, 27 ideal gas, 502–505 Head Hydrodynamics, in history of fluid mechanics, 27 for ideal gas, 624–625 elevation, 83, 104 Hydrometers, 63, video V2.8 Mach number in, 490 in energy line concept, 103–104 Hydrostatic force Isentropic process, 21, 482, 485 loss. see Head loss on curved surfaces, 59–61, video V2.6 Isentropic stagnation properties, 487 piezometric, 104 on plane surfaces, 50–55, video V2.5 Isothermal atmosphere, 38–39 pressure, 36, 83, 84, 104 Hydrostatic pressure, 85 Isothermal process, 21 pump, 560–562, 564–566 Hydrostatic pressure distribution, 35–38 shaft, 193 Hydrostatic pressure forces, 54 Jacobi method, 610 shaft work head, 193 Hypersonic flow, 495 Jet exit pressure, 90–91 shutoff, 563 Joule, 7 total, 83, 104 Ideal fluid, 222 Jumps, hydraulic. see Hydraulic jumps velocity, 83, 104 Ideal gases weir, 469–473 compressible flow functions for, 624–631 Kaplan, V., 586 Head coefficient, 570, 587 isentropic flow of, 510–516 Kaplan turbines, 586–587 Head curve speed of sound, 489 Kármán vortex street, 281 falling (drooping), 563 thermodynamics of, 480–485 Kármán vortex trail, video V4.12, video V6.16, rising, 563 Ideal gas flow, 480, video V11.1 video V9.12 Head loss with area change, 510–516 Kilogram, 7 defined, 193 Fanno, 527–534 Kinematic similarity, 288 in diffusers, 344 isentropic, 502–505 Kinematics of fluid flow, 112–144, 205–210 in enlargements and contractions, 342–345 Rayleigh, 537–541 Kinematic viscosity in entrances, 341, 342, video V8.12 Ideal gas law, 12–13, 480, video V11.1 of air, 620–621 in exits, 342, video V8.12 Ideal head rise, 560–562 of common gases, 618 in gradual contractions, 344 Impellers, 549, 557, 558 of common liquids, 618 in hydraulic jumps, 465–466, video V10.11, Implicit method, 605 defined, 20 video V10.12 Impulse function, 535 of water, 619 major, 334–339 Impulse turbines, video V12.5 Kinetic energy minor, 334, 339–349, video V8.14 axial-flow, 585 in first law of thermodynamics, 182 in mitered bends, 345 defined, 578 turbulence, 609 in nozzles, 344–345 dental drills as, 584–585 in work-energy principle, 82 in open-channel flow, 449 Pelton wheel example, 578–584 Kinetic energy coefficient, 195–198 in pipe bends, 345–346 vs. reaction turbines, 578 Knudsen number, 282 in pipe entrances, 341 Inclined tube manometer, 46–47 Kutta-Joukowski law, 246 in pipes, 321, 344–346 Incompressible flow, 79, 212, 222 in sudden area changes, 341 Bernoulli’s equation for, 505–506 Lagrangian description of flow, 115–116, in valves and fittings, 345–346 constant-area duct flow with friction vs., video V4.4, video V4.5 Head loss coefficient, 339–342 522–523 Lake Nyos, 64 Head rise coefficient, 570 Incompressible fluids, 20, 21, 35–39, video V1.7 Laminar boundary layer Heat exchangers, 325 Induced drag, 435 Blasius solution, 390–392 Heating, 535–541 Inertial control volume, 160 description of, 385, video V9.4 Heat transfer Infinitesimal control volume, 204 effect of pressure gradient, 403–407 net rate, 182 Inhalers, 95 friction drag coefficient for, 396 rate, expressed in first law of Inlet guide vanes, 591 Prandtl solution, 388–390 thermodynamics, 182 Inlet velocity, 561 thickness, video V9.4 Hilsch, Rudolph, 485 Intensity of turbulence, 326 Laminar flow, video V4.7 Hilsch tube, 485 Intensive property, 131–132 in an annulus, 257–258 History of fluid mechanics, 27–29 Internal energy, 182, 480–481, 483–484 applying dimensional analysis, 319–321 Homogeneous flow, 442 International System (SI) of units, 7 in boundary layers, 385 Horseshoe vortex, 435, video V4.6, video V9.1, Inviscid core, 311 between parallel plates, 250–254 video V9.25 Inviscid flow past cylinders, 405 Housings, pump, 557 applying differential analysis, 220–227 past spheres, 416–417 Hurricanes, 232 applying Newton’s second law, 74–75 in pipes, 254–256, 309–311, 313–322, Hybrid grids, 607 defined, 74, 220 video V6.14, video V8.2 Hydraulically smooth wall, 337 Inviscid fluids, 77, 223 vs. turbulent flow, 117 BBMIndx.inddMIndx.indd PagePage I-6I-6 26/10/1826/10/18 5:425:42 PMPM f-0157f-0157 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

I-6 Index

Laplace’s equation, 225, 227 Manometer rule, 44, 45 for inviscid flow, 220–227 Laplacian operator, 225 Manometers and wheel brake design, 161 Lapse rate, 40 defined, 43 Momentum flux, 169, 170, video V5.7 Large eddy simulation models, 609, 614–615 differential, 45–46 Momentum integral equation Law of the wall, 330 inclined tube, 46–47 boundary layer flow on flat plate, 392–397 Length ratio, 278 piezometer tube, 42–43, 85, video V2.3 boundary layer with nonzero pressure Length scale, 290 U-tube, 43–46 gradient, 407–408 Lift, 243, 245–246, 377–380, 426–438 Mass. see Conservation of mass boundary layer with zero pressure gradient, Lift coefficient Mass, units of 393 air foil, 430 in British Gravitational (BG) System, 8 Momentum thickness, 388 defined, 380 in English Engineering (EE) System, 8 Moody, L., 29, 336 as dimensionless group in fluid in International System (SI), 7 Moody chart, 336–338 mechanics, 278 Mass flow density, 523–524, 535 Motorized surfboard, 165 rotating cylinder or sphere, 436–438 Mass flow function, dimensionless, 514, 515, Moving grids, 607 writing, 428 518 Multigrid methods, 611 Lift-drag polar diagram, 431 Mass flowrate, 92, 147 Multiple pipe system. see Pipe systems Lift to drag ratio, 431 Mass flow rate Multi-stage compressors, 589–590 Linear deformation, 205–207 for converging nozzle, 517–518 Multi-stage pumps, 558 Linear momentum. see Newton’s second law of in duct, 514–515 Multistage turbines, 567 motion Mass vs. weight, 7, 89 Linear momentum equation, 159–174 Material derivative, 121–124, 126–127, Nanoscale, 310 application, 160–164 138–139, 206 Nappe, 472 derivation, 159–160 Maximum flowrate, 454 Navier, L., 28, 249 Linear momentum flow, 159, video V5.4, Measurement, flow. see Flow measurement Navier-Stokes equation video V5.5, video V5.6, video V5.8, Mechanical efficiency, 563 applying to laminar flow, 250–252, 318–319 video V5.9 Mechanical energy equation, 191 cautions on use of, 259 Linear partial differential equations. see Mechanical heart assist devices, 577 cylindrical polar coordinates, 249 Laplace’s equation Mechanical loss, 563 defined, 248–249, 259 Liquid-jet scalpels, 117 Meniscus, 43 rectangular coordinates, 248–249 Liquid knife, 516 Mesh. see Grids Net positive suction head, 564–566 Liquid mirror telescope (LMT), 70 Meters, flow. see Flow measurement Newton (unit), 7 Local acceleration, 124 Method of repeating variables, 266–268, Newton, I., 27, 28 Local derivative, 124 270–271 Newtonian fluids, 15, 247–249 Local friction coefficient, 395–396 Method of superposition, video V6.5 Newton’s law of viscosity, 327 Logarithmic velocity profile, 330 Minor loss, 334, 339–349 Newton’s second law of motion, 32, 73–82, Loss, major and minor. see Head loss Minor loss coefficient, 339–342 145, 159–182, 217 Loss coefficient, 330, 339–342 Mixed-flow machines, 550 along a streamline, 76–80 Loss of available energy, 190–191, 195, Mixed-flow pumps, 574–577 and Bernoulli equation, 189 482–483 Mixing length, 329 normal to a streamline, 80–82 Low Reynolds number flow, 380–384, 414–416, Model design conditions, 286 Nikuradse, J., 336 video V1.3, video V7.7, video V8.6 Modeling laws, 286 Nodes, 603 Models Noncircular conduits, 349–352 Mach, E., 28, 280 defined, 286 Nonconservative form, 611 Mach cone, 493–496, video V1.8, video V11.3, distorted, 290–291, video V7.8, video V7.12, Noninertial reference frame, 160 video V11.4 video V7.17, video V7.18 Non-Newtonian fluids, 16 Machine Mach number, 593 practical use of, 263 Nonuniform flow, 194–198, 442 Mach number, 23, 278, 280, 303, 487–492 scales for, 289–290 Normal acceleration, 75, 127–129, video V3.4 and area for isentropic flow, 511–513 similitude concept, 262 Normal depth, 456 and drag coefficient, 419–420, 492 theory of, 286–289 Normal flowrate, 564 for Fanno flow, 527–529 true, 290, 291 Normal shock flow and Froude number, 542 typical studies with, 292–301, video V7.1, for ideal gas, 626–628 in isentropic flow, 503 video V7.9, video V7.18, video V7.19, Normal shock waves, 496–500, video V11.7 and isentropic flow pressure, 506 video V7.20 basic equations, 497–500 and Mach cone angle, 494–495 Moment of inertia, 52 defined, 496 and normal shock, 498–500 Moment-of-momentum, 555–557 examples, 500–501 and stagnation properties, 489–492 application of equation, 175–182, video V5.13 and Rayleigh/Fanno lines, 536, 541 Mach number tables, 491–492 derivation, 174–175 Normal stress Mach waves, 494, 543–544, video V1.8, turbo machine considerations, 179, 555–557 in conservation of linear momentum, 217 video V11.3 Moment-of-momentum equation, 198 in Newtonian fluids, 15, 247, 248 Magnetic flowmeter, 371 Momentum and work transfer, 183–184 Magnus, H., 436 angular. see Moment-of-momentum No-slip condition, 14, 238, 251, video V1.4, Magnus effect, 246, 436 linear. see Newton’s second law of motion video V6.12, video V6.13 Major loss. see Head loss Momentum coefficient, 169 Nozzle discharge coefficient, 368 Manning, R., 28, 454 Momentum equation. see also Linear Nozzle meters, 99, 366–371 Manning coefficient, 454–456 momentum equation Nozzles Manning equation, 454–456 for control volume, 159, 171, 217 converging, 516–518, 521–522 BBMIndx.inddMIndx.indd PagePage I-7I-7 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

Index I-7

converging-diverging, 509, 518–522, Particle image velocimeter (PIV), 113 Poiseuille, J., 28, 254, 316–317 video V11.6, video V11.7 Pascal (unit), 13 Poiseuille flow, 254, 256, 316–31, video V6.14 defined, 90 Pascal, B., 28, 32 Poiseuille’s law, 256, 317 for inhalers, 95 Pascal’s law, 32 Polar coordinates, 68 loss coefficients, 344–345 Pathlines, 119–121, video V4.11 Polar diagram, lift-drag, 431 overexpanded flow, 520, video V11.6, Pelton wheels, 578–584, video V5.6, Polytropic efficiency, 592 video V11.7 video V12.2, video V12.4 Position vector, 113 rocket, 521 Perfect gas law. see Ideal gas law Potential energy, 83, 182 thrust, video V5.11 Perfect guiding assumption, 551 Potential flow theory, video V6.9, video V6.10 underexpanded flow, 520, video V11.7 Perfectly expanded flow, 520 basic plane flows, 227–228, 236, video V6.6, Numerical methods, 259, video V6.15 Physical properties of fluids video V6.7, video V6.11 Nutating disk meters, 371–372, video V8.16 of air, 620–621 doublet, 234–236 of common gases, 617–618, 620–621 sink, 229–231 Oblique shock waves, 496, 544, video V1.8, of common liquids, 617–618 source, 229–230 video V11.6, video V11.7, of U.S. Standard Atmosphere, 622–623 uniform flow, 228–229 videos V11.9–V11.11 of water, 619 vortex motion, 231–234 One-dimensional compressible flow Piezometers, 43–44, 85, video V2.3 defined, 225 in constant-area duct with friction, 522–534 Piezometric head, 104, video V2.3 finding solutions to problems, 246–246 in constant-area duct with heating or cooling, Pipes, 307–373 singularity, 230 535–541 aging, 336–337 superposition of basic plane flows, 236–246, in variable area duct, 507–522 compressible adiabatic flow in. see Fanno flow video V6.5 One-dimensional flow, 116–117 deepwater, 362 flow past circular cylinder, 241–244 One-equation model, 333 dimensional analysis of flow in, 333–352 flow past half-body, 236–239, video V6.5 Open-channel flow, 441–477 fittings, 345–346 flow past Rankine oval, 239–241 analogy with compressible flow, 542–543 flow characteristics, 308–313 flow past rotating cylinder, 244–246 critical flow, 443, 447 flow meters, 366–371 Potential function, 225 defined, 441 flow rate, 366–371 Pound, 8 energy considerations with, 448–452 fully developed flow in, 254–257, 311–322 Power gradually varied flow, 461–463 head loss. see Head loss as expression of work transfer rate, 183 gradually varying, 442 heat transfer in. see Rayleigh flow and lift for flight, 429–430 hydraulic jump, 464–469, video V10.11, hydraulically smooth, 337 shaft, 556, 559 video V10.12 laminar flow in, 254–257, 309–311, units of, 7 laminar, 442 video V6.14 Power coefficient, 570, 587 Manning equation for, 454–456 laminar vs. turbulent flow in, 311–312 Power-law velocity profile, 330 normal depth, 456 noncircular, 349–352 Power specific speed, 587–589 rapidly varied flow, 463–476 pressure and shear stress in, 312–313 Prandtl, L., 27–29, 329, 382 rapidly varying, 442 relative roughness of, 335–338 Prandtl boundary layer equations, 388–390 surface wave propagation, 443–448 smooth, 337 Prediction equation, 286 transitional, 442 standard components, 345–347 Pressure turbulent, 442 transitional flow in, 309, 323–325, absolute, 13, 41 uniform flow, 442, 452–461 video V8.2, video V8.3, video V8.9 atmospheric, 13, 43, 622–623 varied flow, video V10.6, video V10.8 turbulent flow in, 309–311, 323–333, center of, 53 Open channels video V8.2, video V8.3 defined, 12–13, 31 best hydraulic cross sections, 460–461 typical system components, 307, 309 and drag, 378–379 characteristics of, 441–443, video V10.6 vs. ducts, 307 dynamic, 85 geometric properties of, 452–456, Pipe systems, video V6.15 gage, 13, 41 video V10.7 loop, 363–364 hydrostatic, 35–38, 85 shear stress in, 453–454 multiple pipes, 362–366 and ideal gas law, 12–13 velocity contours in, 453 networks, 365–366 in isentropic flow, 502, 503, 505–506 Open impellers, 558 parallel, 362, 363 isentropic stagnation. see Isentropic Operating point, 567 series, 362–363 stagnation properties Orifice discharge coefficient, 367 single pipes, 352–361 and lift, 429–430 Orifice meters, 99, 366, 367 Pi terms measurement of, 41–42, 86, 89, video V2.3, Orifices, flow through, 91 defined, 266 video V2.4 Outer layer, turbulent pipe flow, 328, 329 determination by inspection, 275–276 and normal shock, 498–499 Outlet velocity, 561 determination by method of repeating at a point, 31–32, 75, video V3.7 Overall efficiency, pump, 563 variables, 266–267 and raindrops, 78 Overexpanded flow, 520, video V11.6, determination example, 273–274 and shear stress in pipes, 312–313 video V11.7 problems with, 282–285 stagnation. see Overlap layer, turbulent pipe flow, 328, 329 uniqueness of, 274–275 static, 85 Pi theorem, 265–266 suction, 41 Panel method, 604 Pitot, H., 28 thermodynamic, 85 Parachutes, 288 Pitot tubes, 86–87, 104, 501, video V3.8 of tires, 49 Parallel plates Plane Poiseuille flow, 256 total, 86 Couette flow, 252–254 Planform area, 380, 413, 430 vacuum, 41 steady laminar flow between, 250–252 Poise, 20 vapor, 23–24 BBMIndx.inddMIndx.indd PagePage I-8I-8 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

I-8 Index

Pressure at a jet exit, 90–91 stages in, 575 obtaining for moving control volume, Pressure coefficient, 278, 280, 411 system equation, 566 141–142 Pressure correction algorithm, 613 vs. fans, 577–578 physical interpretation, 138 Pressure distribution vs. turbines, 554–555 relationship to material derivative, 138–139 air foils, 376 role in selection of control volume, 142–143 automobile, 428, video V2.1 Quasi-steady flow, 108 steady effects, 139 cylinder, inviscid flow, 242 unsteady effects, 140–141 cylinder, viscous effects, 406–407 Radial blades, 561 Rheology, 3 entrance of pipe, 312, 341 Radial-flow compressors, 590 Right-hand rule, 177 hydrostatic, 35–38 Radial-flow machines, defined, 550, 551 Rigid-body motion of fluids, 65–70 in rigid-body motion, 65–70 Raindrops, 77 Ripple tank, comparison of compressible and in rotating fluids, 68–69 Rankine ovals, 239–241 open-channel flows, 542 standard atmosphere, 39–41 Ranque, George, 485 Rising head curve, 563 Pressure drag. see Drag Ranque vortex tube, 485 Rocket nozzles, 521 Pressure drag coefficient, 410–412 Rapidly varied flow (RVF), 442, 463–476, Rogue waves, 443 Pressure forces, 32–34 video V10.9, video V10.10 Rotameters, 370, video V8.15 Pressure gradient Rate of angular deformation, 210, video V6.3 Rotation, 109, 205, 207–210 adverse, 241, 404 Rate of heat transfer, 182 Rotor blades, 575, 591 effect on surface forces, 34 Rate of shearing strain, 15, 210 Rotors, turbo machine, 176, 180, 550, 552 effects on boundary layer, 403–407, Rayleigh, Lord, 29 Roughness video V9.10 Rayleigh flow, 535–541 effect on models, 292, 298, 299, video V7.13 favorable, 404 basic equations for, 535–537 on flat plates, 401 Pressure head, 36, 83, 84, 104 in combustion chamber, 540–541 in open channels, 454–456, 459–460 Pressure prism, 56–59 defined, 535 in pipes, 335–338 Pressure recovery coefficient, 344 for ideal gas, 630–631 relative, 335–338 Pressure-sensitive paint, 378 of ideal gas, 537–541 typical values of, 336 Pressure tap, 88, 89, 104 normal in, 541 Round-off errors, 614 Pressure transducers, 48–50 Rayleigh line, 535–537, 539–541 Runners, 549 defined, 48 Reaction turbines, 578, 586–588 illustrated, 48, 50 Rectangular weirs, 102–103, 471 Scales role of strain gages, 49–50 Reentrant entrance, 341 length, 290 Pressure-velocity coupling, 612, 613 Reference dimensions, 266, 273–274 types for models, 289–290 Pressure vessels, 61 Relation parameters, 611 Scales, turbulence model, 607 Pressure waves, 493–495 Relative roughness, 278, 335–338, 401 Scaling laws for pumps, 571–573 Primary quantities, 4 Relative velocity Schlieren visualization, of flow, 494–495 Primitive variable equation, for mass flowrate, in centrifugal pumps, 558–559 Secondary flow, in pipes, 345 514 defined, 148, 551 Secondary quantities, 4 Primitive variables, 599 and Reynolds transport theorem, 142 Second law of thermodynamics, 145, 199–201 Product of inertia, 52 in rotating sprinkler example, 177 combination of first and, 200–201 Profile, velocity. see Velocity profile as turbo machine energy consideration, semi-infinitesimal control volume statement Propeller pumps, 575 551–554 of, 199–200 Properties vs. absolute velocity, 141–142 Second moment of area, 52 of air, 620–621 Relaxation, 611 Semi-infinitesimal control volume statement of common gases, 617–618, 620–621 Repeating variable method, 266–268, 270–271 of energy equation, 199 of common liquids, 617–619 Required net positive suction head, 564, 565 of second law of thermodynamics, 199–200 of U.S. Standard Atmosphere, 40, 622–623 Residuals, 603, 611 Separation, video V6.8, video V9.9, of water, 619 Resistance coefficient, Manning, 454–456 video V9.16, video V9.19 Prototype, 286 Restricted homogeneous equations, 5 in boundary layers, 224, 382, 404–406 Pump affinity laws, 573 Reversible procesess, 482 in pipes, 341, 345 Pump performance curves, 562, 567–570 Reynolds, O., 29, 279, 396, 328 Separation location Pumps Reynolds averaged Navier-Stokes equations, 608 on air foils, 406–407 axial-flow, 574–577 Reynolds number on cylinders, 382, 404–405 centrifugal, 557–570, 577, video V12.3 critical. see Transition to turbulence defined, 404 defined, 549 defined, 18, 279 illustrated, 383 dimensionless parameters, 570–571 as dimensionless group in fluid mechanics, 278 Shaft power, 178, 556, 559 efficiency, 194 and drag coefficient, 492 Shaft torque, 178, 555, 559 geometrically similar, 570–571 large vs. low, properties of flows, 380–384, Shaft work, 178, 185, 191, 193, 556–557 head, 560, 564–565 video V1.1, video V1.2, video V7.3, Shaft work head, 193, 560, 562 ideal vs. actual head rise, 560–562 video V7.7, video V9.15 Shallow water waves, 446 mixed-flow, 574–577 similarity, 303 Sharp-crested weirs, 102–103, 469–472, parallel, 569–570 Reynolds pipe flow experiment, 396, video V8.2 video V10.13 performance characteristics, 561–564 Reynolds stress, 328, 329 Shearing strain propeller, 575 Reynolds transport theorem, 132–143 defined, 14 scaling laws, 572–573 defined, 131 rate of, 15, 210, video V6.3 series, 569 derivation, 134–138 Shearing stress similarity laws, 570–572 example of use, 135 defined, 3 specific speed, 573–574 general form, 138 distribution in pipes, 315, 321 BBMIndx.inddMIndx.indd PagePage I-9I-9 26/10/1826/10/18 5:435:43 PMPM f-0157f-0157 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

Index I-9

drag from, 378–379 Specific heat ratio Steady flow, video V4.7 effect on fluids, 3, 14, 15–17, 19 of air, 620–621 defined, 117 as force acting on differential element, defined, 21, 482 fluid particles, 74 218 Specific speed and Reynolds transport theorem, 139 in laminar flow, 326–327 for pumps, 573–574 streaklines in, 119 lift from, 429–430 and turbine efficiency, 587–589 streamlines in, 118 in Newtonian fluid, 248 Specific volume, 11 Steam tables, 187 in open-channel flow, 453–454 Specific weight Steel wool, 91 and pressure in pipes, 312–313 of air, 620–621 Stoke, 20 in turbulent flow, 325–329 of water, 619 Stokes, G., 28, 249, 415 in work transfer, 184 Speed of sound, video V11.3 Stokes’ law, 283 Shear thickening fluids, 16 defined, 22–23 Stratified flow, 442 Shear thinning fluids, 16 ideal gas, 22, 489 Stratosphere, 40 Ships, 246 and Mach number, 487–492 Streaklines, 119–121, video V4.10, video V7.14 Shock absorbers, 195 table of values for air at standard atmospheric Stream function, 213–216 Shock regime, 520 pressure, 620–621 Streamline bodies, video V2.1, video V9.2, Shock waves, 496–501, videos V11.6–V11.11 table of values for water at standard video V9.20 curved, 496, 497 atmospheric pressure, 619 Streamline coordinates, video V4.13 in gas turbines, 495 Spheres Streamline curvature, 74–75 normal, 496–500. see Normal shockwaves drag coefficient for, 297, 414–517, 420–421, Streamlined bodies, 377 oblique, 496, 544, video V11.6, video V11.7, 436, 437, video V9.17 Streamlines, video V4.9 videos V11.9–V11.11 effect of surface roughness, 420–421 defined, 74 Shrouded impellers, 558 low Reynolds number flow past, 414 equation, 214 Shutoff head, 563 rotating, 436–438 and Newton’s second law of motion, 76–82 Similarity laws, pump, 571–573 Spillways, 466, video V10.15, video V10.16 use of coordinate systems, 127–129 Similarity requirements, 286–288 Stability, 64–65, video V2.11, video V2.12 in visualization and analysis of flow fields, Similarity variable, 390, 391 Staggered grid, 611–612 118–121 Similitude Stagnation density, 486 Streamtube, 185–186 based on differential equations, Stagnation enthalpy, 486 Streamwise acceleration, 75 301–304 Stagnation point, 85, video V3.7 Stress as concept in experimentation, 262 Stagnation pressure, 86, video V3.8 Newtonian fluid, 15, 247–248 Single-stage pumps, 558 across normal shock waves, 500 normal, 183–184, 217, 248 Single-suction impellers, 558 and critical state, 507 notation, 218 Sink flow defined, 486 shearing. see Shearing stress defined, 230 in Fanno flow, 529 sign convention, 218 example, 230–231 isentropic. see Isentropic stagnation tangential, 184 strength of, 230 properties turbulent, 325–329 Sinusoidal waves, 445–446 in isentropic flow, 502 Strouhal, V., 29, 281 Siphon, 97–98 and Mach number, 490 Strouhal number, 278, 280–281, 386, SI (International System) units, 7 in Rayleigh flow, 539 video V7.5 Slip, in experimental data, 282 Stagnation pressure probe. see Pitot tubes Structured grids, 606 Slope Stagnation properties, 485–487. see Isentropic Strutt, J. W., 535 of channel bottom, 448–449, 454 stagnation properties Subcritical flow, 443, 447–448, 450, energy line, 103–105, 448–449 in isentropic flow, 502 video V10.5 friction, 448, 462–463 and Mach number, 489–492 Submerged area, forces on, 50–53 Slug, 8 mass flow rate in terms of, 514 Subsonic flow, 23, 494 Sluice gates and normal shock, 499 in coverging/diverging duct, 508–509 discharge coefficient, 475 Stagnation streamline, 86, video V3.7, Fanno, 525 flow rate under, 100–102, 475–476 video V4.9 Rayleigh, 536, 538 force on, 170–171 Substantial derivative, 121–124, 206 free outflow, 475 across normal shock waves, 499 Suction, 41 submerged, 475–476 and critical state, 506 Suction specific speed, 574–575 Smooth pipe, 337 defined, 486 Sudden contraction, 343 Sonar systems, 327 in isentropic flow, 502 Sudden expansion, 343 Sonic flow, 494 and Mach number, 489–490 Supercritical flow, 443, 447–448, 450, Sonification, 489 in Rayleigh flow, 538–539 video V10.5 Sound, speed of. see Speed of sound Stall condition, 407, 435, video V9.21 Superposition, 236–246, video V6.5 Sound waves, patterns in, 489 Standard atmosphere Supersonic flow, 23, 494, video V1.8, Source flow, 229–230, video V6.5 defined, 40 video V11.6, video V11.7 Space shuttle, fuel pump of, 567 pressure variation, 39–41 in coverging/diverging duct, 508–509 Specific energy, 449–452 properties of, 40, 622–623 Fanno, 525, 534 Specific energy diagram, 449–450 State, equation of, 12–13, 480 in gas turbines, 495 Specific gravity, 12, 26 Static fluids, pressure variation in, 34–39 in pitot tube, 501 Specific head. see Specific energy Static pressure, 85 Rayleigh, 538 Specific heat Static pressure tap, 88, 89, 104 two-dimensional, 543–544 constant pressure, 21, 481–482, 485 Static properties, 485–487, 499, 514 Surface forces, 33–34, 160, 217–219 constant volume, 21, 480–482, 485 Stator blades, 575, 591 Surface pressure, 378 BBMIndx.inddMIndx.indd PagePage I-10I-10 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

I-10 Index

Surface tension, video V7.6, video V10.3 in fully developed flows, 323–325 Turbulent jet, video V8.1 defined, 24–26 in open-channels, 442 Turbulent pipe flow, video V8.2, video V8.3, effect on models, 298–299 in pipe flows, 396, 323–325, video V8.2, video V8.9 and oil spills, 26 video V8.3 fully developed, 323–333 of water, 619 Translation, in fluid element flow, 205–207 general characteristics, 396–398 Surface waves, 443–448, video V7.4, Transonic flow, 495 logarithmic, 330 video V9.18, videos V10.1–V10.5 Triangular weirs, 103, 471–472, video V10.13 mean vs. fluctuating velocity, 325–326 Sutherland equation, 18 Troposphere, 40–41 overlap layer, 328, 329 System curve, 566–567 True models, 290, 291 power law, 330 System equation, 566 Truncation, 604 shear stress distribution, 315, 326, 328 Systems, 129–131 Truncation errors, 614 velocity profile, 329–331, video V8.2 Systems of units, 7–9 Tsunamis, 446 viscous sublayer, 328–329 Turbine flow meters, 370–371 Turbulent stresses, 325–329 Tacoma Narrows Bridge, 290 Turbines, 578–589 Two-dimensional flow, 116 Tangential stress work, 184 axial-flow, 551 Two-dimensional objects, 376–377, 425 T ds equations, 483 compressible flow, 589, 593–595 Two-dimensional supersonic flow, 543–544 Temperature defined, 578 Two-equation model, 333 absolute, 7, 8 Francis, 586, 587 Celsius, 7 gas, 593–595 Ultrasonic flowmeter, 371 centigrade, 7 impulse, 578–585, video V12.4, video V12.5 Unchoked flow, 518, 530–532 Fahrenheit, 7 Kaplan, 586–587 Underexpanded flow, 520, video V11.7 in isentropic flow, 502, 503 multistage, 567 Underflow gates, 475–476 Kelvin, 7 Pelton wheel, 578–584, video V5.6, Underrelaxed calculations, 611 and normal shock, 498–499 video V5.14, video V12.4 Uniform flow Rankine, 7 performance maps, 595 in open channels, 442, 453–461 of Rayleigh flow, 537 radial-flow, 551 potential, 228–229 stagnation. see Stagnation temperature reaction, 578, 586–588 in sections, 195 of U.S. Standard Atmosphere, 622–623 vs. pumps, 554–555 Uniform flow field, 222 Temperature–entropy (T–s) diagrams, 505, 524 wind, 553 Units Terminal velocity, of falling object, 418–419 Turbomachines, 549–596 conversion factors, 9 Thermal choking, 537 angular momentum considerations, 555–557 defined, 4 Thermodynamic pressure, 85. see Pressure axial-flow, 550, 575–577, 590–592 need for consistency, 9–11 Thermodynamics basic energy considerations, 551–555 systems of, 6–9 for Fanno flow, 527–529 centrifugal pumps, 557–570, video V12.3 Universal gas constant, 480 first law, 145, 182–198 compressible flow, 589–595 Unsteady Bernoulli equation, 107 of ideal gases, 480–485 defined, 549–550 Unsteady flow, 107–108, 117–119, 124, second law, 145, 199–201 dimensionless parameters, 570–571 140–141, 152–153, video V3.11, static properties, 485 fans, 577–578 video V4.7, video V5.10 Three-dimensional flow, 116 mixed-flow, 550, 575–577 Unstructured grids, 606 Three-dimensional objects, 377, 425–427 pump scaling laws, 571–573 Upstream velocity, 376 Three Gorges Dam, 54 radial-flow, 550, 590 Upwind differencing, 612 Three-point difference, 602 rotary sprinkler, 176–179, video V4.11, U.S. standard atmosphere. see Standard Three-reservoir problem, 364–365 video V5.12, video V12.2 atmosphere Throat, duct, 509, 510 suction specific speed, 574–575 Useful energy. see Available energy Thrust, 169–170, video V5.11 turbines, 578–589 U-tube manometers, 44–45 Tidal waves. see Tsunamis Turbopumps, 567 Time-averaged equations, 333 Turbulence Time-averaged velocity, 324–326 chaos, 333 Vacuum pressure, 41 Tire pressure, 49 characteristics of, 117, 325–327, video V1.1, Valve losses, 346 Toilets, 148 video V8.1, video V8.7, video V8.8, Valves, 340, 346–347 Torque video V8.11 Vanes, 557. see also Guide vanes in moment-of-momentum equation, 174–180 intensity of, 326 Vapor pressure shaft, 178, 555, 559 mixing in, 325, 327, video V1.1, video V8.4, in barometer tubes, 42 Torque converter, 557 video V8.5, video V8.7 boiling, 23–24 Torricelli, E., 28, 42, 90 modeling, 333 defined, 23–24 Torricelli’s formula, 90 Reynolds stress in, 328 effect on cavitation, 24 Total head, 83, 104 sensitivity of bats to, 431 of water, 619 Total pressure, 86 spots in, 397 Variable area duct Total pressure ratio, 589 Turbulence kinetic energy, 609 one-dimensional compressible flow in, Total properties, 487 Turbulence models, 607–609 507–522 Trailing vortex, 435, video V4.6, video V9.1, Turbulent boundary layer Varied flow. see Gradually varied flow (GVF); video V9.25 approximate solution for flat plate, 399–401 Rapidly varied flow (RVF) Tranquil flow, 443 effect on separation, 406–407 Velocity Transition to turbulence, video V9.5 properties, 399–401, video V9.8 absolute, 148, 176–177, 551–554, 558–559 in boundary layer flows, 385, 397–398, transition from laminar boundary layer, 385 absolute vs. relative, 141–142 video V9.7 velocity profiles in, 398 average, 147–148 BBMIndx.inddMIndx.indd PagePage I-11I-11 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s

Index I-11

blade, 551–554, 558–559 Viscous flow, 247–249 gravity, video V10.4, video V11.4 friction, 330 Viscous fluids, 15 mach, 494, 543–544, video V1.8, inlet, 561 Viscous stresses, 248 video V11.3 outlet, 561 Viscous sublayer, turbulent pipe flow, pressure, 493–495 particle, 74, 113 328–329 rogue, 443 Pressure-velocity coupling, 612, 613 Visualization flow, 116, 117–121, video V4.6, role of gravity, 444–445 relative, 148, 177, 551–554, 558–559 video V4.9, video V7.16, video V9.19 shallow water, 446 time-averaged, 324–326 Volume flow meters, 371–372 shock. see Shock waves Velocity diagrams, 552–553, 556, 559, 585 Volume flowrate, 92 sinusoidal, 445–446 Velocity distribution. see Velocity profile Volumetric dilatation, 207 sound, 489 Velocity field, 112–121, 206, video V4.2, Volumetric efficiency, 563 surface, 443–448, video V9.18, video V4.3, video V6.1, video V6.2 Volumetric loss, 563 video V10.3, video V10.4, Velocity gradient, 14 Volutes, 557 video V10.5, video V11.4 Velocity head, 83, 104 Von Kármán, T., 29, 281, 393 Wave speed, 443–446, 543, video V11.3 Velocity measurement. see Flow measurement Vortex, 231–234 Weather, 43 Velocity potential, 224–225 bound, 435, video V4.6, video V9.25 Weber, M., 29, 281 combined, 232, video V4.8 Weber number, 278, 281, 303, video V7.6 Velocity profile defined, 231–232 Weight vs. mass, 7, 8, 9 in boundary layers forced, 232 Weir coefficient, 471–473 effect of pressure gradient on, 404, 405 free, 81, 232, 234, horseshoe, 435 Weir head, 469–473 laminar flow, 396 irrotational, 231–232 Weirs in transition from laminar to turbulent Kármán trail, video V6.16, video V9.14 broad-crested, 472–474, video V10.14 flow, 398 ring, video V4.1 defined, 102, 469 turbulent flow, 399–401 rotational, 232 rectangular, 102–103, 471 between flat plates, 250–252 strength of, 232 sharp-crested, 102–103, 469–472, in open channels, 453 tornado, video VA.3 video V10.13 in pipes trailing, 435, video V3.5, video V4.6, triangular, 103, 471–472, video V10.13 laminar flow, 255, 315–316, video V8.10 video V9.1, video V9.25 Weisbach, J., 28 power law, 330 Vortex shedding, 281, 288, video V4.12, Wetted perimeter, 257, 350, 452–453 turbulent flow, 329–331, video V8.10 video V7.5, video V7.10, video V9.14 Wheel brake design, 161 Velocity ratio Vortex street, video V6.16, video V7.5, Wheels, 549 as dimensionless group in fluid mechanics, video V9.12 Wholly turbulent flow, 336–337 278 Vorticity, 209–210, 222, 225, 385 Wicket gates, 586 in Fanno flow, 528 Windmills, 553, video V12.1 Velocity vector, 113 Wake, video V9.3, video V9.9 Wind tunnels, 348, video V3.3, video V7.15, Vena contracta, 91, 101, 341 and boundary layer, 224 video V9.11, video V9.22 Venturi, G., 28 streamlined object, 426 Wind turbines, 553 Venturi discharge coefficient, 369 vortex street, video V6.16, video V9.14 Winglets, 436 Venturi meters, 99, 100, 366, 368–369, Wake region Wing loading, 430 video V3.10 defined, 382 Wing tip vortices, 209, 435–436, video V3.5 Venturi regime, 520 flat plate, 382 Work Venturi tube, 510 Wall friction factor, 526 expressed in first law of thermodynamics, Viscosity Wall functions, 609 183 absolute or dynamic, 15 Wall shear stress, 315, 321, 392 flow, 184 of air, 620–621 Water, table of properties, 619 normal stress, 183–184 apparent, 16 Water horsepower, 563 rate of, 178, 183 of common gases, 617–618 Water jet, 20, 84 shaft, 178, 185, 191, 193, 556–557 of common liquids, 617–618 Water table, comparison of compressible and shear stress, 184 defined, 14 open-channel flows, 542 tangential stress, 184 eddy, 329, 608–609 Water tunnels, 288 and turbomachines, 555–557 effect of temperature on, 17–18 Watt, 7 unit of, 7 kinematic, 20 Wave motion, 445–446 Work-energy equation, 82–83 and oil spills, 26 Waves of U.S. Standard Atmosphere, 622–623 calculating speed, 443–446 Zeroequation model, 333, 609 of water, 619 deepwater, 446 Zone of action, 494 Viscous dissipation, 321 expansion, 543, video V11.9 Zone of silence, 494 BBMIndx.inddMIndx.indd PagePage I-12I-12 8/13/188/13/18 5:275:27 PMPM f-512f-512 //208/WB02304_EVALCS/9781119469582/bmmatter/text_s208/WB02304_EVALCS/9781119469582/bmmatter/text_s