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 MECH: “index” — 2005/8/29 — 17:52 — page 689 — #1 690 Index 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 Convection, 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 Reynolds number 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 MECH: “index” — 2005/8/29 — 17:52 — page 690 — #2 Index 691 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 Fluid dynamics, 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 MECH: “index” — 2005/8/29 — 17:52 — page 691 — #3 692 Index Froude efficiency of Hydrostatic thrusts 60–7 Kozeny–Carman equation propeller 153 oncurved surfaces 65–7 241 Froude number 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 Gas constant 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