Index

Absolute pressure 46 Atmosphere Borda–Carnot head loss 262 Absolute viscosity 24–6 equilibrium of 46–8, 79 Bore 428, 482 Acceleration81, 89 stability of 79 Boundary-element method convective 90 (unit) 14 (BEM) 356, 358 of fluid particle 89–90 Atmospheric properties Boundary layer 298–352 substantial 89 670–1 control 338–9 temporal 90 Attitude angle definition 298 Acoustic velocity 493, 496 (of bearing) 234 descriptionof 299 Actuator disc 151 Avogadro’s hypothesis 18 displacement thickness Added mass 393 Axial-flow machine 596 301 Adhesion28 Axial-flow pumps 634–5 laminar 300, 306–9 Adiabatic flow inpipe 531–7 Axial-flow turbine 596, 607 momentum equation Adiabatic frictionless Axi-symmetric flow 33 303–6 conditions 522 momentum integral Adiabatic process 19, 488 Backward difference 356 equation306 Adiabatic temperature lapse Backward-facing blades 629 momentum thickness 302 rate 79–80 Backwater curve 457, 462 inopenchannels 423–4 Aerofoils 403–9 Bar (unit) 9, 14 transition region 299 definitions 403 Barometer 49–50 see also Laminar boundary finite span 406–9 Bearings layer; Turbulent boundary inhigh-speed flow 544–6 inclined slipper 222–8 layer infinite span 404–6 of infinite length 231 Bourdongauge 55–6 separation335–8 journal 230–9 Boyle’s Law 490 spanof 403 very short 235 Broad-crested weir 444–7 vortex starting 405 Bend-meter 290 Bulk modulus of elasticity 20 Affinity laws for pumps 640 Bends, losses in 266–8 Buoyancy 69–71 Air cavitation620 Bernoulli constant 381 centre of 70, 72 Air locks 107 Bernoulli’s equation 92–6, Airy waves 467 107, 391 Calorically perfect gas 18 Alternative depths 432 applications 109–30 Capillary depression, Anemometer 288 significance of terms in capillary rise 29 Aneroid barometer 50 95–6 Capillary waves 183, 469 Angle of attack 403 Bingham plastic 197 Cascade 267 Angle of heel 72 Blade element theory 637 Cauchy number 166 Angle of incidence 403 Blasius’s formula (frictionin Cauchy–Riemann equations Angular velocity 9 smooth pipes) 254 400 Antinodes 478 Blasius’s solutionfor laminar Cavitation16, 107, 619–22 Archimedes, Principle of 70 boundary layer 308–9 incentrifugalpumps Area coefficient 580 Bluff body 325 643–4 Aspect ratio 403 Boiling 16 damage 619–20

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Cavitationlimits for reaction Compressor 591 Dimensional analysis 170–9 turbines 621 Computational fluid application179–82 Cavitationnumber 170, 622 dynamics (CFD) methods 172 Celerity 563–4 353–8 process 172–3 Centipoise 26 Conformal transformation Dimensional formulae 11–2, Centistokes 26 404 679–83 Central difference 356 Conjugate depths 440 Dimensional Centred expansion 514–5 conjugate functions 399 homogeneity 12 Centre of buoyancy 70 Conservation of energy 95, Dipole 390 Centre of pressure 61 96–101 Discharge 114, 123 Centrifugal pumps 626–7 Conservation of matter 90 measurement of 290–1 basic equations 627–32 Continuity 90–2 Discretization diffuser-type 627 Continuity equation 354, errors 356–7 volute-type 627 458, 576 Dispersive waves 468 Centroid 57, 59 Continuum 4 Displacement thickness of Centroidal axis 57 Contraction, loss at abrupt boundary layer 301–2 Changes of state 19–20 262–4 Displacement work 95–6 Characteristic curve (of Control volume 139, 419 Double suctionmachine 627 pump) 631, 646 , free 79 Doublet 390–1, 402 Characteristic equations Convective acceleration 90 Downdrop curve 457 577–8 Convergent-divergent nozzle Downwash velocity 407 Characteristics 578 522, 524–9 Conversion factors 663–6 Draft tube 608 method of 577–80 Drag 324–35 Chézy equation419–23 Corresponding velocity 180 Couette flow 205 form 324 Chézy’s coefficient 421, 459 induced 408 Chézy’s formula 459 Creeping motion 331 Choking 107, 525, 535, 541 Critical depth 432, 437 normal pressure 324 Chord (of aerofoil) 403 Critical flow 416 profile 324 Chord line 403 inopenchannel 432–5, vortex 407–9 Circulation364–7 443–7 wave 340 Classical hydrodynamics 361 Critical pressure Drag coefficient 325, 637 Closed conduits only partly ratio 524 of bodies of revolution full 426–7 Critical 341 Coanda effect 108–9 247, 317 effect of compressibility Coefficient of contraction Critical slope 435, 462 544–6 114, 116 Critical velocity of three-dimensional Coefficient of discharge 114, inopenchannel 435 bodies 331–5 168–70 Current meters 288 of two-dimensional bodies for orifice 117 329–31 for venturi-meter 120 d’Alembert’s Paradox 392 Drag force 290, 314, 325 Coefficient of friction 227 Darcy’s equation248, 531 Drain-hole vortex 379 Coefficient of velocity 114 Darcy’s Law (flow through Drowned weir 448–9 Coefficient of viscosity 23 porous media) 239 Dynamic pressure 110 Cohesion28 Dashpot 207–9 Dynamic similarly 161–7 Colebrook’s equation351 Deflectionangle 506, 508 application179–82 Complex potential 400 de Laval nozzle 523–4 flow with elastic forces Complex variables 399–402 Density 12 acting 166–7 Compressibility (quantity) 20 at a point 12 flow with gravity forces Compressibility effects Designpressure ratio 527 acting 164–5 aerofoils 544 Deviationangle 633 flow with surface tension drag 340–1 Differential equations, of forces acting 165–6 elastic forces 166 fluid dynamics 354–6 flow with viscous forces Compressibility factor 518 Diffuser 264–5 acting 163–4 Compressible flow of gases incentrifugalpump 626 principal ratios 167 487–550 Diffuser pump 627 ratios of forces arising in Compressible fluids 20, Dilatancy 27 162–7 487, 517 Dilatant liquids 197 Dynamic viscosity 23–6

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Eccentricity 230 Finite-difference methods Fluid machines 591–657 Eccentricity ratio 230 356 effect of size onefficiency Eddy-making resistance 182 Finite-element methods 656–7 Eddy viscosity 341–3 357–8 Fluid motion, principles of Effective surface area 241 Finite-volume methods 358 89–130 Efficiency First Law of Fluid particle, accelerationof of fluid machines, effect of Thermodynamics 97, 89–90 size 656–7 488 Fluids Froude, of propeller 153 First moment of area 57–8 characteristics 1–4 hydraulic, of turbine 611 Floating bodies definition 1–2 manometric, of pump 629 containing a liquid 76–8 properties of 12–17, 667 overall, of pump 629 stability of 72–8 Fluid statics 43–83 Elastic forces 162, 166 Flow Force(s) 9 Elastic waves 493–7 in closed conduits only acting from outside fluid Elbow-meter 290 partly full 426–7 162 Electro-magnetic meters 291 compressible 487–550 applied to obstacles in Elliptical lift distribution cross-section530–43 stream 442–3 408–9 with free surface 346–7, caused by flow round Energy equation, steady flow 414–83 pipe–bend 141–4 91–100, 103 of inviscid fluid 361–409 caused by jet striking Energy gradient 418–9 to line sink 376 surface 138–9 Energy transformations, in from line source 375–6 controlling behaviour of constant-density fluid with variable fluids 162 105–7 density 346–7, due to surface tension 162 Energy transmission rate 487–550 at nozzle and reaction 473–4 with variable density in of jet 144–8 Enlargement, loss at abrupt pipes of constant resulting from action of 260–2 530–43 viscosity 162 Enthalpy 491 Flow direction, measurement onsolid body inflowing Entrainment 109, 352 291–2 fluid 148–50 Entropy, specific 489 Forced (rotational) vortex Flow field 30 381–2 Entry length 194, 283–4 Flowline 31 Entry loss 263 Form drag 251, 324 Flow measurement 287–92 Forward difference 356 Equationof motion Flow nets 370–3 oscillatory waves 464–71 Forward-facing blades 629 applied to real fluids Fourier’s theorem 465 Equationof state 17, 487 372–3 Equilibrium, relative 80 Francis turbine 596, 605–9 Flow nozzle 123–5 Free convection 79 Equilibrium of fluid 45 Flow parameters, variationin of constant density 45–6 Free discharge 452 time and space 30–1 Free jet 113 Equilibrium of moving Flow patterns 31–2 fluids 80–3 Free outfall 448–9 basic 373–82 Free surface 45, 414–83 Equipotential lines 368 combinations of basic Equivalent grain size 252 Free surface energy 472 384–99 Free turbulence 352–3 Euler head 629 combining 383–4 Euler’s equation94, 524 Free-vortex machines 611 Flow types 33–8 Friction drag for laminar and for steady, frictionless Reynold’s demonstration flow 522 turbulent boundary 33–5, 245–8 layers together Euler’s equation(energy Flow visualization548–50 transfer in 317–20 Flow work 95–6 Frictionfactor 248–9, 534 machines) 610 Fluid coupling 652–4 Exit loss 262 for rough pipes 349–51 , differential for smooth pipes 348–9 equations of 354–6 variation249–55 Falling sphere method 212–3 Fluid flow, basic Frictioninnon-circular Fanno flow 531–7 characteristics 30–3 conduits 259–60 Fans 591, 625, 650 Fluid flywheel 654 Frictionlosses 568 Filament line 32 Fluidization241–2 Frictionvelocity 344

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Froude efficiency of Hydrostatic thrusts 60–7 Kozeny–Carman equation propeller 153 oncurved surfaces 65–7 241 165, 167, horizontal component 65 Kozeny constant 241 183, 416, 435 onplanesurface 60–3 Kutta–Joukowski condition Froude’s theorem resultant thrust 66–7 405 (for propeller) 152 onsubmerged surfaces Kutta–Joukowski law 337, Fully developed flow 192, 59–69 396 246, 283 vertical component 66 Laminar boundary layer 17–8 Ideal fluid 28 approximate velocity Gases Impellers 592 distributions 312 characteristics 2 free vortex design635 compressible flow Blasius’s solution308, 309 mixed-flow pump 634 onflat plate with zero 487–548 Impulse turbines 597 Gas flow functions 672–9 pressure gradient Inclined slipper 306–12 Gate valve 570 bearings 222–8 Gauge pressure 13, 45 predicting separation in Incompressible fluid 38 322–3 General energy equation, Induced drag 408 with variable density thickness 309–11 Induced mass 393 Laminar flow 33–5 491–2 Inertia force 162–3 Geometric similarity 160 betweenparallel planes Inertia head 555 199–209 Gibson’s inertia-pressure Inertia pressure 555–7 method 557 betweensolid boundaries Inertia-pressure method 557 191–242 Gradually varied flow Interfacial tension 28 456–63 incircular pipe 191–8, Interferometer technique 549 543 equations 457–61 International standard Gravitational energy 472 distinguishing features 35 atmosphere 670–1 fully developed 193–5 Gravity forces 164–5 Invert 419 Group velocity 474–6 non-Newtonian liquid in Irrotational flow 366 circular pipe 196–8 Irrotational vortex 376–9, Hagen–Poiseuille formula inpipes 191–8 401 through circular annulus 191–4 Isentropic bulk modulus 20 Half body 386 198–9 Isentropic process 489, 522 through porous media Head, definition 45, 105 Isobar 44 Head, manometric 629 239–42 Isothermal bulk modulus 20 Laminar sub-layer 251, 300, Head losses inpipes 260–71 Isothermal flow inpipe Head lost to friction103, 347 539–42 Laplace’s equation368, 400 248–9 Isothermal process 19 Homologous series Laser–Doppler anemometer (of machines) 614 289 Hot-film anemometer 288 Jet Laval nozzle 523–4 Hot-wire anemometer 288 force due to, striking Laws of thermodynamics Hydraulic efficiency 611 surface 138–41 487–91 Hydraulic grade line 106, free 352 Lift 403 272 reactionof 144–8 Lift coefficient 403, 544, 637 Hydraulic jumps 438–42 Jet propulsion145–6 Line of flow 31 types inrectangular Journal bearing 230–9 Line sink 376 channels 441–2 Line source 375, 401 Hydraulic meandepth 259 Kaplanturbine 596, 607, Liquids, characteristics 2 Hydraulic radius 260 615 Local acceleration89 Hydrodynamic lubrication Kinematic eddy viscosity 342 Logarithmic profile 346–7 220–39 Kinematic similarity 160–1 Lower critical Reynolds Hydrodynamic mass 393 Kinematic viscosity 26, 669 number 247 Hydrodynamic transmissions Kinetic energy 472 Lower critical velocity 247 651–6 Kinetic energy correction Lubrication Hydrostatic forces 419 factor 100, 352 hydrodynamic 220–39 Hydrostatic lubrication220 Kingsbury bearing 224 hydrostatic 220

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Mach angle 498 Net Positive SuctionHead Orifice intersection 510–1 (NPSH) 644 flow through sharp-edged reflection510 Neutral equilibrium 71 112–9, 268–9 Mach cone 497–8 Newtonian fluid 24 quasi-steady flow through Mach line 498 Newton’s First Law 92 119 21, 166, 496, Newton’s Law of Universal submerged 118–9 501, 518 Gravitation12 Orifice meter 123–5 Mach waves 508 Newton’s laws of motion Oscillatory waves Mach–Zehnder 138 see Waves interferometer 550 Newton’s Law 14, Oseen’s formula 331 Magnus effect 395 95, 134 Overturning couple 73 Manning’s formula 422–3 Newton’s Third Law 22, Manning’s roughness 136, 440 Parabolic velocity profile coefficient 422 Nikuradse’s experiments 193 Manometers 50–5 250–2 Parallel axes theorem 59 Manometric efficiency 629 Nodes 478–9 Particle mechanics 332 head 629 Non-Newtonian liquids Pascal (unit) 7, 9, 14 Mass flow parameter 521 26–7 Pascal’s Law 15 Meandensity 12 laminar flow in circular Path-line 31 Meansteady flow 37 pipe 196–8 Peltonwheel 598–605 Metacentre 72 Non-uniform flow 30 Percentage slip 596 Metacentric height 73 Non-uniform velocity Perfect gas 18, 489 Metacentric radius 75 distributioneffects Period of oscillation77 Michell bearing 224 100, 138, Perpendicular axes Micro-manometers 54 632–4 theorem 59 Micropoise 26 Normal depth 419 Petroff’s law 233 Mild slope 435 Normal flow 419 Phase velocity 468 Millibar 14 Normal shock Physical constants 667 Minor losses 260 waves 500–5 Physical similarity 159–70 Mixed-flow machines 596 Notches 126–30 see also specific types Mixed-flow pump 634, 645 rectangular 127 Piezo–electric gauges 56 Mixing length 343 V 129 Piezometer tube 45–6 Molecular structure 3 Nozzle, force at 144–8 Piezometric head 46 Moment of inertia 59 Numeric 5 Piezometric pressure 46 Momentum correction factor Pipe bend 138 Oblique shock waves force caused by flow Momentum equation 134–54 505–12 round 141–4 applications 138–54 intersection 510–2 head loss due to 266 boundary layer 303–6 reflection510–2 Pipe fittings, losses in 267–8 Momentum integral One-dimensional flow 32 Pipe networks 280–1 equation, boundary with negligible friction Pipe with side tappings layer 306 522–4 281–2 Momentum theory Open channels 414 Pipes propeller 150–4 boundary layer in 423–4 branched 278–80 wind turbine 154 occurrence of inparallel 277–8 Momentum thickness of critical conditions inseries 277 boundary layer 302 443–54 Pi theorem 172 Moody diagram 252 optimum cross-section Pitometer 112 Moving fluids, equilibrium of 425–6 Pitot-static tube 110–2, 519 80–3 simple waves and Pitot tube 110–2 Multi-stage pumps 639 surges in427–31 inflow with variable specific energy and density 517–20 Nappe 126–7 alternative depths of Plasticity 27 Navier–Stokes equations flow 431–7 Plastic solids 2 354–6 steady-flow energy Poise 26 numerical procedures for equationfor 416–8 Poiseuille (unit) 25 solving 356–8 types of flow 415–6 Poiseuille’s equation194

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Polar diagram 337 Quasi-steady flow Secondary flow, losses due Porosity 239, 270 through orifice 119 to 266 Positive-displacement through pipes 284–6 Second Law of machines 591 Thermodynamics 441 Potential flow 368 Second moment of area 58–9 Prandtl-Meyer angle 515 Radial blades 629 Seiches 479 Prandtl-Meyer expansion Radial-flow machine 596 Semi-perfect gas 19 515 Radial-flow turbine 605 Separation320–1 Prandtl-vonKármántheory Rankine–Hugoniot from aerofoil 335–7 343 relation502 positionof 339 Pressure 13–6 Rankine oval 389 predicting in laminar absolute 13, 46, 49 Rapid flow 416 boundary layer centre of 61–3 approaching weir 449–51 322–3 gauge 13, 45, 49 inopenchannel 435 Separationpoint 321 measurement of 48–57 Rapidly varied flow 456 Separationstreamline 321 Rate of shear 23 piezometric 46 Shadowgraph method 548 Rayleigh step 228–9 variationwith positionin Shear rate 23 fluid 43–8 Reactionturbine 597 Shear stress 1, 22, 191 Pressure coefficient 168 cavitationlimits for 621 distributionincircular pipe net head across 607–9 Pressure diagrams 565 257–8 Reciprocating pump 592–6 Pressure drag 324 Ship resistance 182–8 Rectilinear flow 374, 400–1 Pressure forces 162, 168 Shock 499 Region of influence 497–8 Shock losses 631 Pressure gauges 55–7 Relative density 13 Pressure gradient 320–2 Shock phenomena 340 Relative equilibrium 80 Shock stall 546 adverse 321 Restoring couple 72 favourable 320–1 Shock wave 499–511 Reversible adiabatic process definition 499–500 Pressure head 46 503 Pressure line 271–5 intersection of 510–12 Reversible process 488 normal 499–505 Pressure losses 245–55, 259, Reynolds number 35 oblique 505–11 260–71 local 137 reflectionof 510–12 Pressure transducer 57 significance of 163–4 Shooting flow 435 Pressure transients 558–80 Reynolds stress 342–3 SI units 6 Pressure variation Rheology 28 perpendicular to Rheopectic liquids 27 internationally agreed names 6–7 streamlines 107–8 Rigid-body rotation381 prefixes for multiples and Pressure waves 560 Ripples 469 magnitude 560–4 submultiples 8 Robins effect 396 Similarity 160 velocity 560–4 Rocket propulsion146–8 Principle of conservation of chemical 162 Rotameter 303 dynamic 161–7 mass 90–2 Rotational flow 366, 381 geometric 160 Profile drag 324 Rotodynamic machines 592 kinematic 160–1 three-dimensional bodies basic equations 609–13 of machines 639–40 331–5 Rotodynamic pumps 625–51 physical 159–60 two-dimensional bodies Rotor 592 329–31 Rough zone of flow 251 thermal 161 Propeller, momentum theory Runner 592 Similarity laws 150–4 pumps 639–40 Propeller turbine 607 turbines 613–7 Pseudo-plastic liquids Salt-dilutionmethod 291 Single suction pump 627 27, 197 Salt-velocity method 290 Singular point 375 Pumps 591, 625–51 Saturationpressure 16 Sink 376 characteristic curves for Saturationvapour pressure Siphon272 644–5 of water 667 Skinfriction 307 performance characteristics Scale effect 182 Skin-friction coefficient 168, 644–6 Scale factor 160 307–8 selection650–1 Schlierenmethod 549 Slant depth 61

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Slip Stall torque 654 Tail race 606 influid couplings 652 Standing wave 478–9 Temperature 9 inreciprocatingpumps Stanton diagram 250 Temperature difference 10 596 Starting vortex 405 Temperature lapse rate 47 Slip coupling 652 Steady flow 36 Temporal acceleration89 Slip surface 511 Steady-flow energy equation Terminal velocity 213, 333 Slope 461–3 derivation97–100 Thermally perfect gas 17–8, Smooth zone of flow 251 for open channels 416–9 489 Solidity practical application Thermodynamic concepts of axial runner 628 103–4 487–91 of wire gauze 270 Steady-flow momentum Thermodynamic effects 487 Sommerfeld boundary equation134, 428 Thixotropic liquids 27 condition 232–3 Steady uniform flow 415, Thoma’s Sommerfeld condition, half 419–23 parameter 620 237 Steep slope 435, 462–3 Thomson’s theorem 407 Sommerfeld number 234 Stokes (unit) 26 Three-dimensional flow 32, Sonic velocity 493–6 Stokes’s Law 212, 391 331–5 Source 375–6, 401 Straight-line closure 570 Thrust coefficient 153 Source and sink of Streak-line 32 Thwaites’s method 322–3 numerically equal Stream filament 31 Töpler system 549 strength 387–9 Stream function 362–4 Torque coefficient 654 Span(of aerofoil) 403 Streamlined body 325 Torque converter 654–6 Specific-energy curve in Streamlines 31, 362–3, 370 Torricellianvacuum 49 dimensionless form pressure variation Torricelli’s formula 114 436–7 perpendicular to Total energy line 106, Specific energy in open 107–9 271–5 channels 431–5 Stream-tube 31 Total head 96 Specific entropy 489 Strength of source 375 Total head line 106, 271–5 Specific heat capacity 489 Strength of vortex 377 Tranquil flow 416, 435 Specific gravity 13 Stress 1, 9, 15 Transitionregionof Specific speed Strickler’s formula 422 boundary layer 299 power 616 328 Transition zone of flow 251 pumps 639–40 Submerged bodies, Transpiration methods turbines 616 stability of 71–2 210–1 Speed of sound 493–6 Subsonic flow 522, 524, Tsunamis 480–2 Speed ratio of Peltonwheel 526–7 Turbines 591, 596–625 603 Subsonic velocity 496 performance characteristics Spiral vortex 398–9 Substantial acceleration 89 623–5 Stability Super-cavitating machines types 596–7 of atmosphere 79 644 Turbulence 35 of bodies influids 71–8 Supersonic flow 502, 527 free 352–3 of body subject to betweentwo boundaries Turbulent boundary layer, on additional force 78 516–7 smooth flat plate with of floating bodies 72–8 over concave boundary zero pressure gradient of fluid itself 79–80 516 313–6 of submerged bodies 71–2 round corners 512–6 Turbulent flow 35 Stable equilibrium 71 Supersonic velocity 497 inpipes 246–8 Stagnation enthalpy 492 Surface profiles 457, 459 velocity distributionin Stagnation hypothesis 405 classification461–3 344–52 Stagnation point 110, 384, Surface tension 28–30, 469 Two-dimensional flow 32–3 517 Surface tension forces 165–6 Stagnation pressure 110, 503 Surface waves 464–9 Stagnation temperature 492, Surge tanks 583–6 Undular jump 441–2 502 Surges inopenchannels Uniform flow 30 Stall 337 427–31 Uniform rectilinear flow Stalled flow 337 Système International 374, 384 Stalling angle 337 d’Unités (SI units) 6 Unit flow 624

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Unit power 624 Redwood 211 Water hammer 558 Units 4–10 rotary 215–8 Wave drag 340 prefixes 8 Saybolt 211 Wave energy 472–3 Unit speed 624 Searle 231 Wave formation480 Universal gas constant 18 Viscometry 210 Wave-making resistance Unstable equilibrium 71 Viscosimeter see Viscometer 182–3 Unsteady flow 36–7 Viscosity 21–8 Wave propagation, finite Upper (or higher) critical absolute 23 waves 498–9 velocity 247 basic SI unit 25 Waves U-tube manometers 50–5 causes of 24–5 Airy 467–8 dynamic 23, 668 capillary 469 Vacuum 48–9 eddy 341–2 deep water 468 Valve closure 569–74 influence on flow 37 dispersive 468 Valve opening factor 570 kinematic 26, 669 elastic 493–7 Vapour pressure 16 measurement of 210 gravity 468 Varied flow 416 quantitative definition moving into shallow water Velocity 21–4 477–8 of flow 630 variationwith temperature inopenchannels 427–31 of sound 496 668–9 oscillatory 464–79 of whirl 601 Viscous forces 163–4 reflection564–9 Velocity defect 345 Viscous resistance 191–2 standing 478–9 Velocity defect law 345 Viscous stresses 199 166–7 Velocity diagrams 609–10, Viscous sub-layer 251–2, Weir 612 347 broad-crested 444–7 Velocity distribution Voidage 240 drowned 447–8 inrough pipes 349–50 Volute 605, 626 rapid flow approaching insmooth pipes andover Vortex 449–51 smooth plates forced 381–2 sharp-crested 126–30 345–8 free 376–9 suppressed 128 inturbulentflow 344–52 spiral 398–9 Whirl 609 Velocity gradient 22 starting (on aerofoil) 405 Whirl slip 633 Velocity head 96 Vortex drag 407–9 Wicket gates 606 Velocity measurement Vortex pair 396–8 Windage 603 288–90 Vortex shedding 328 Wind turbine, momentum Velocity potential 367–9 Vortex sheet 511–2 theory 154 Velocity profile 22 Vortex street (or trail) Wings, aerodynamics of Vena contracta 113 326–8 403–9, 544–6 Venturi flume 451–4 Vortex strength 377 Vorticity 365–6 Venturi-meter 119–22 Yaw meter 291 Virtual mass 392–3 Yield stress 198 Viscoelastic materials 27 Wake Viscometer 211 definition 325 Engler 211 flow pattern326 Zone of action 498 Ostwald 211 width 328 Zone of silence 498

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