كتاب Mechanics of Fluids
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 كتاب Mechanics of Fluids

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كتاب Mechanics of Fluids Empty
مُساهمةموضوع: كتاب Mechanics of Fluids   كتاب Mechanics of Fluids Emptyالثلاثاء 06 أكتوبر 2020, 11:26 am

أخوانى فى الله
أحضرت لكم كتاب
Mechanics of Fluids
Eighth edition
Bernard Massey
Reader Emeritus in Mechanical Engineering
University College, London
Revised by
John Ward-Smith
Formerly Senior Lecturer in Mechanical Engineering
Brunel University  

كتاب Mechanics of Fluids M_o_f_10
و المحتوى كما يلي :


Contents
Preface to the eighth edition ix
1 Fundamental Concepts 1
1.1 The characteristics of fluids 1
1.2 Notation, dimensions, units and
related matters 4
1.3 Properties of fluids 12
1.4 The perfect gas: equation of state 17
1.5 Compressibility 20
1.6 Viscosity 21
1.7 Surface tension 28
1.8 Basic characteristics of fluids in motion 30
1.9 Classification and description of fluid flow 33
1.10 The roles of experimentation and theory
in fluid mechanics 38
1.11 Summary 41
Problems 41
2 Fluid Statics 43
2.1 Introduction 43
2.2 Variation of pressure with position in a fluid 43
2.3 The measurement of pressure 48
2.4 First and second moments of area 57
2.5 Hydrostatic thrusts on submerged surfaces 59
2.6 Buoyancy 69
2.7 The stability of bodies in fluids 71
2.8 Equilibrium of moving fluids 80
Problems 84
3 The Principles Governing Fluids in Motion 89
3.1 Introduction 89
3.2 Acceleration of a fluid particle 89
3.3 The continuity equation 90
3.4 Bernoulli’s equation 92
3.5 General energy equation for steady flow of any fluid 96vi Contents
3.6 Pressure variation perpendicular
to streamlines 107
3.7 Simple applications of Bernoulli’s equation 109
Problems 131
4 The Momentum Equation 134
4.1 Introduction 134
4.2 The momentum equation for steady flow 134
4.3 Applications of the momentum equation 138
Problems 156
5 Physical Similarity and Dimensional Analysis 159
5.1 Introduction 159
5.2 Types of physical similarity 160
5.3 Ratios of forces arising in dynamic similarity 162
5.4 The principal dimensionless groups of fluid dynamics 167
5.5 Other dimensionless groups 167
5.6 Dimensional analysis 170
5.7 The application of dynamic similarity 179
5.8 Ship resistance 182
Problems 188
6 Laminar Flow Between Solid Boundaries 191
6.1 Introduction 191
6.2 Steady laminar flow in circular pipes:
the Hagen–Poiseuille law 191
6.3 Steady laminar flow through an annulus 198
6.4 Steady laminar flow between parallel planes 199
6.5 Steady laminar flow between parallel planes,
one of which is moving 204
6.6 The measurement of viscosity 210
6.7 Fundamentals of the theory of
hydrodynamic lubrication 220
6.8 Laminar flow through porous media 239
Problems 242
7 Flow and Losses in Pipes and Fittings 245
7.1 Introduction 245
7.2 Flow in pipes of circular cross section 245
7.3 Variation of friction factor 249
7.4 Distribution of shear stress in a circular pipe 257
7.5 Friction in non-circular conduits 259
7.6 Other losses in pipes 260
7.7 Total head and pressure lines 271
7.8 Pipes in combination 277
7.9 Conditions near the pipe entry 283
7.10 Quasi-steady flow in pipes 284
7.11 Flow measurement 287
Problems 292Contents vii
8 Boundary Layers, Wakes and Other Shear Layers 298
8.1 Introduction 298
8.2 Description of the boundary layer 299
8.3 The thickness of the boundary layer 301
8.4 The momentum equation applied to the boundary layer 303
8.5 The laminar boundary layer on a flat plate with zero
pressure gradient 306
8.6 The turbulent boundary layer on a smooth flat plate
with zero pressure gradient 313
8.7 Friction drag for laminar and turbulent boundary
layers together 317
8.8 Effect of pressure gradient 320
8.9 Boundary layer control 338
8.10 Effect of compressibility on drag 340
8.11 Eddy viscosity and the mixing length
hypothesis 341
8.12 Velocity distribution in turbulent flow 344
8.13 Free turbulence 352
8.14 Computational fluid dynamics 353
Problems 358
9 The Flow of an Inviscid Fluid 361
9.1 Introduction 361
9.2 The stream function 362
9.3 Circulation and vorticity 364
9.4 Velocity potential 367
9.5 Flow nets 370
9.6 Basic patterns of flow 373
9.7 Combining flow patterns 383
9.8 Combinations of basic flow patterns 384
9.9 Functions of a complex variable 399
9.10 An introduction to elementary
aerofoil theory 403
Problems 410
10 Flow with a Free Surface 414
10.1 Introduction 414
10.2 Types of flow in open channels 415
10.3 The steady-flow energy equation for open channels 416
10.4 Steady uniform flow – the Chézy equation 419
10.5 The boundary layer in open channels 423
10.6 Optimum shape of cross-section 425
10.7 Flow in closed conduits only partly full 426
10.8 Simple waves and surges in open channels 427
10.9 Specific energy and alternative depths
of flow 431
10.10 The hydraulic jump 438
10.11 The occurrence of critical conditions 443
10.12 Gradually varied flow 456viii Contents
10.13 Oscillatory waves 464
10.14 Tsunamis 480
10.15 Conclusion 482
Problems 483
11 Compressible Flow of Gases 487
11.1 Introduction 487
11.2 Thermodynamic concepts 487
11.3 Energy equation with variable density: static and
stagnation temperature 491
11.4 The speed of sound 493
11.5 Shock waves 499
11.6 Supersonic flow round a corner 512
11.7 The Pitot tube in compressible flow 517
11.8 Some general relations for one-dimensional flows 520
11.9 One-dimensional flow through nozzles 522
11.10 Compressible flow in pipes of constant cross-section 530
11.11 High-speed flow past an aerofoil 544
11.12 Analogy between compressible flow and flow with
a free surface 546
11.13 Flow visualization 548
Problems 550
12 Unsteady Flow 554
12.1 Introduction 554
12.2 Inertia pressure 555
12.3 Pressure transients 558
12.4 Surge tanks 583
Problems 588
13 Fluid Machines 591
13.1 Introduction 591
13.2 Reciprocating pumps 592
13.3 Turbines 596
13.4 Rotodynamic pumps 625
13.5 Hydrodynamic transmissions 651
13.6 The effect of size on the efficiency of fluid machines 656
Problems 657
Appendix 1 Units and Conversion Factors 663
Appendix 2 Physical Constants and Properties of Fluids 667
Appendix 3 Tables of Gas Flow Functions 672
Appendix 4 Algebraic Symbols 679
Answers to Problems 685
Index 68
Index
Absolute pressure 46
Absolute viscosity 24–6
Acceleration 81, 89
convective 90
of fluid particle 89–90
substantial 89
temporal 90
Acoustic velocity 493, 496
Actuator disc 151
Added mass 393
Adhesion 28
Adiabatic flow in pipe 531–7
Adiabatic frictionless
conditions 522
Adiabatic process 19, 488
Adiabatic temperature lapse
rate 79–80
Aerofoils 403–9
definitions 403
finite span 406–9
in high-speed flow 544–6
infinite span 404–6
separation 335–8
span of 403
vortex starting 405
Affinity laws for pumps 640
Air cavitation 620
Air locks 107
Airy waves 467
Alternative depths 432
Anemometer 288
Aneroid barometer 50
Angle of attack 403
Angle of heel 72
Angle of incidence 403
Angular velocity 9
Antinodes 478
Archimedes, Principle of 70
Area coefficient 580
Aspect ratio 403
Atmosphere
equilibrium of 46–8, 79
stability of 79
(unit) 14
Atmospheric properties
670–1
Attitude angle
(of bearing) 234
Avogadro’s hypothesis 18
Axial-flow machine 596
Axial-flow pumps 634–5
Axial-flow turbine 596, 607
Axi-symmetric flow 33
Backward difference 356
Backward-facing blades 629
Backwater curve 457, 462
Bar (unit) 9, 14
Barometer 49–50
Bearings
inclined slipper 222–8
of infinite length 231
journal 230–9
very short 235
Bend-meter 290
Bends, losses in 266–8
Bernoulli constant 381
Bernoulli’s equation 92–6,
107, 391
applications 109–30
significance of terms in
95–6
Bingham plastic 197
Blade element theory 637
Blasius’s formula (friction in
smooth pipes) 254
Blasius’s solution for laminar
boundary layer 308–9
Bluff body 325
Boiling 16
Borda–Carnot head loss 262
Bore 428, 482
Boundary-element method
(BEM) 356, 358
Boundary layer 298–352
control 338–9
definition 298
description of 299
displacement thickness
301
laminar 300, 306–9
momentum equation
303–6
momentum integral
equation 306
momentum thickness 302
in open channels 423–4
transition region 299
see also Laminar boundary
layer; Turbulent boundary
layer
Bourdon gauge 55–6
Boyle’s Law 490
Broad-crested weir 444–7
Bulk modulus of elasticity 20
Buoyancy 69–71
centre of 70, 72
Calorically perfect gas 18
Capillary depression,
capillary rise 29
Capillary waves 183, 469
Cascade 267
Cauchy number 166
Cauchy–Riemann equations
400
Cavitation 16, 107, 619–22
in centrifugal pumps
643–4
damage 619–20690 Index
Cavitation limits for reaction
turbines 621
Cavitation number 170, 622
Celerity 563–4
Centipoise 26
Centistokes 26
Central difference 356
Centred expansion 514–5
Centre of buoyancy 70
Centre of pressure 61
Centrifugal pumps 626–7
basic equations 627–32
diffuser-type 627
volute-type 627
Centroid 57, 59
Centroidal axis 57
Changes of state 19–20
Characteristic curve (of
pump) 631, 646
Characteristic equations
577–8
Characteristics 578
method of 577–80
Chézy equation 419–23
Chézy’s coefficient 421, 459
Chézy’s formula 459
Choking 107, 525, 535, 541
Chord (of aerofoil) 403
Chord line 403
Circulation 364–7
Classical hydrodynamics 361
Closed conduits only partly
full 426–7
Coanda effect 108–9
Coefficient of contraction
114, 116
Coefficient of discharge 114,
168–70
for orifice 117
for venturi-meter 120
Coefficient of friction 227
Coefficient of velocity 114
Coefficient of viscosity 23
Cohesion 28
Colebrook’s equation 351
Complex potential 400
Complex variables 399–402
Compressibility (quantity) 20
Compressibility effects
aerofoils 544
drag 340–1
elastic forces 166
Compressibility factor 518
Compressible flow of gases
487–550
Compressible fluids 20,
487, 517
Compressor 591
Computational fluid
dynamics (CFD)
353–8
Conformal transformation
404
Conjugate depths 440
conjugate functions 399
Conservation of energy 95,
96–101
Conservation of matter 90
Continuity 90–2
Continuity equation 354,
458, 576
Continuum 4
Contraction, loss at abrupt
262–4
Control volume 139, 419
Convection, free 79
Convective acceleration 90
Convergent-divergent nozzle
522, 524–9
Conversion factors 663–6
Corresponding velocity 180
Couette flow 205
Creeping motion 331
Critical depth 432, 437
Critical flow 416
in open channel 432–5,
443–7
Critical pressure
ratio 524
Critical Reynolds number
247, 317
Critical slope 435, 462
Critical velocity
in open channel 435
Current meters 288
d’Alembert’s Paradox 392
Darcy’s equation 248, 531
Darcy’s Law (flow through
porous media) 239
Dashpot 207–9
Deflection angle 506, 508
de Laval nozzle 523–4
Density 12
at a point 12
Design pressure ratio 527
Deviation angle 633
Differential equations, of
fluid dynamics 354–6
Diffuser 264–5
in centrifugal pump 626
Diffuser pump 627
Dilatancy 27
Dilatant liquids 197
Dimensional analysis 170–9
application 179–82
methods 172
process 172–3
Dimensional formulae 11–2,
679–83
Dimensional
homogeneity 12
Dipole 390
Discharge 114, 123
measurement of 290–1
Discretization
errors 356–7
Dispersive waves 468
Displacement thickness of
boundary layer 301–2
Displacement work 95–6
Double suction machine 627
Doublet 390–1, 402
Downdrop curve 457
Downwash velocity 407
Draft tube 608
Drag 324–35
form 324
induced 408
normal pressure 324
profile 324
vortex 407–9
wave 340
Drag coefficient 325, 637
of bodies of revolution
341
effect of compressibility
544–6
of three-dimensional
bodies 331–5
of two-dimensional bodies
329–31
Drag force 290, 314, 325
Drain-hole vortex 379
Drowned weir 448–9
Dynamic pressure 110
Dynamic similarly 161–7
application 179–82
flow with elastic forces
acting 166–7
flow with gravity forces
acting 164–5
flow with surface tension
forces acting 165–6
flow with viscous forces
acting 163–4
principal ratios 167
ratios of forces arising in
162–7
Dynamic viscosity 23–6Index 691
Eccentricity 230
Eccentricity ratio 230
Eddy-making resistance 182
Eddy viscosity 341–3
Effective surface area 241
Efficiency
of fluid machines, effect of
size 656–7
Froude, of propeller 153
hydraulic, of turbine 611
manometric, of pump 629
overall, of pump 629
Elastic forces 162, 166
Elastic waves 493–7
Elbow-meter 290
Electro-magnetic meters 291
Elliptical lift distribution
408–9
Energy equation, steady flow
91–100, 103
Energy gradient 418–9
Energy transformations, in
constant-density fluid
105–7
Energy transmission rate
473–4
Enlargement, loss at abrupt
260–2
Enthalpy 491
Entrainment 109, 352
Entropy, specific 489
Entry length 194, 283–4
Entry loss 263
Equation of motion
oscillatory waves 464–71
Equation of state 17, 487
Equilibrium, relative 80
Equilibrium of fluid 45
of constant density 45–6
Equilibrium of moving
fluids 80–3
Equipotential lines 368
Equivalent grain size 252
Euler head 629
Euler’s equation 94, 524
for steady, frictionless
flow 522
Euler’s equation (energy
transfer in
machines) 610
Exit loss 262
Falling sphere method 212–3
Fanno flow 531–7
Fans 591, 625, 650
Filament line 32
Finite-difference methods
356
Finite-element methods
357–8
Finite-volume methods 358
First Law of
Thermodynamics 97,
488
First moment of area 57–8
Floating bodies
containing a liquid 76–8
stability of 72–8
Flow
in closed conduits only
partly full 426–7
compressible 487–550
cross-section 530–43
with free surface 346–7,
414–83
of inviscid fluid 361–409
to line sink 376
from line source 375–6
with variable
density 346–7,
487–550
with variable density in
pipes of constant
530–43
Flow direction, measurement
291–2
Flow field 30
Flowline 31
Flow measurement 287–92
Flow nets 370–3
applied to real fluids
372–3
Flow nozzle 123–5
Flow parameters, variation in
time and space 30–1
Flow patterns 31–2
basic 373–82
combinations of basic
384–99
combining 383–4
Flow types 33–8
Reynold’s demonstration
33–5, 245–8
Flow visualization 548–50
Flow work 95–6
Fluid coupling 652–4
Fluid dynamics, differential
equations of 354–6
Fluid flow, basic
characteristics 30–3
Fluid flywheel 654
Fluidization 241–2
Fluid machines 591–657
effect of size on efficiency
656–7
Fluid motion, principles of
89–130
Fluid particle, acceleration of
89–90
Fluids
characteristics 1–4
definition 1–2
properties of 12–17, 667
Fluid statics 43–83
Force(s) 9
acting from outside fluid
162
applied to obstacles in
stream 442–3
caused by flow round
pipe–bend 141–4
caused by jet striking
surface 138–9
controlling behaviour of
fluids 162
due to surface tension 162
at nozzle and reaction
of jet 144–8
resulting from action of
viscosity 162
on solid body in flowing
fluid 148–50
Forced (rotational) vortex
381–2
Form drag 251, 324
Forward difference 356
Forward-facing blades 629
Fourier’s theorem 465
Francis turbine 596, 605–9
Free convection 79
Free discharge 452
Free jet 113
Free outfall 448–9
Free surface 45, 414–83
Free surface energy 472
Free turbulence 352–3
Free-vortex machines 611
Friction drag for laminar and
turbulent boundary
layers together
317–20
Friction factor 248–9, 534
for rough pipes 349–51
for smooth pipes 348–9
variation 249–55
Friction in non-circular
conduits 259–60
Friction losses 568
Friction velocity 344692 Index
Froude efficiency of
propeller 153
Froude number 165, 167,
183, 416, 435
Froude’s theorem
(for propeller) 152
Fully developed flow 192,
246, 283
Gas constant 17–8
Gases
characteristics 2
compressible flow
487–548
Gas flow functions 672–9
Gate valve 570
Gauge pressure 13, 45
General energy equation,
with variable density
491–2
Geometric similarity 160
Gibson’s inertia-pressure
method 557
Gradually varied flow
456–63
equations 457–61
Gravitational energy 472
Gravity forces 164–5
Group velocity 474–6
Hagen–Poiseuille formula
191–4
Half body 386
Head, definition 45, 105
Head, manometric 629
Head losses in pipes 260–71
Head lost to friction 103,
248–9
Homologous series
(of machines) 614
Hot-film anemometer 288
Hot-wire anemometer 288
Hydraulic efficiency 611
Hydraulic grade line 106,
272
Hydraulic jumps 438–42
types in rectangular
channels 441–2
Hydraulic mean depth 259
Hydraulic radius 260
Hydrodynamic lubrication
220–39
Hydrodynamic mass 393
Hydrodynamic transmissions
651–6
Hydrostatic forces 419
Hydrostatic lubrication 220
Hydrostatic thrusts 60–7
on curved surfaces 65–7
horizontal component 65
on plane surface 60–3
resultant thrust 66–7
on submerged surfaces
59–69
vertical component 66
Ideal fluid 28
Impellers 592
free vortex design 635
mixed-flow pump 634
Impulse turbines 597
Inclined slipper
bearings 222–8
Incompressible fluid 38
Induced drag 408
Induced mass 393
Inertia force 162–3
Inertia head 555
Inertia pressure 555–7
Inertia-pressure method 557
Interfacial tension 28
Interferometer technique 549
International standard
atmosphere 670–1
Invert 419
Irrotational flow 366
Irrotational vortex 376–9,
401
Isentropic bulk modulus 20
Isentropic process 489, 522
Isobar 44
Isothermal bulk modulus 20
Isothermal flow in pipe
539–42
Isothermal process 19
Jet
force due to, striking
surface 138–41
free 352
reaction of 144–8
Jet propulsion 145–6
Journal bearing 230–9
Kaplan turbine 596, 607,
615
Kinematic eddy viscosity 342
Kinematic similarity 160–1
Kinematic viscosity 26, 669
Kinetic energy 472
Kinetic energy correction
factor 100, 352
Kingsbury bearing 224
Kozeny–Carman equation
241
Kozeny constant 241
Kutta–Joukowski condition
405
Kutta–Joukowski law 337,
396
Laminar boundary layer
approximate velocity
distributions 312
Blasius’s solution 308, 309
on flat plate with zero
pressure gradient
306–12
predicting separation in
322–3
thickness 309–11
Laminar flow 33–5
between parallel planes
199–209
between solid boundaries
191–242
in circular pipe 191–8,
543
distinguishing features 35
fully developed 193–5
non-Newtonian liquid in
circular pipe 196–8
in pipes 191–8
through circular annulus
198–9
through porous media
239–42
Laminar sub-layer 251, 300,
347
Laplace’s equation 368, 400
Laser–Doppler anemometer
289
Laval nozzle 523–4
Laws of thermodynamics
487–91
Lift 403
Lift coefficient 403, 544, 637
Line of flow 31
Line sink 376
Line source 375, 401
Liquids, characteristics 2
Local acceleration 89
Logarithmic profile 346–7
Lower critical Reynolds
number 247
Lower critical velocity 247
Lubrication
hydrodynamic 220–39
hydrostatic 220Index 693
Mach angle 498
intersection 510–1
reflection 510
Mach cone 497–8
Mach line 498
Mach number 21, 166, 496,
501, 518
Mach waves 508
Mach–Zehnder
interferometer 550
Magnus effect 395
Manning’s formula 422–3
Manning’s roughness
coefficient 422
Manometers 50–5
Manometric efficiency 629
head 629
Mass flow parameter 521
Mean density 12
Mean steady flow 37
Metacentre 72
Metacentric height 73
Metacentric radius 75
Michell bearing 224
Micro-manometers 54
Micropoise 26
Mild slope 435
Millibar 14
Minor losses 260
Mixed-flow machines 596
Mixed-flow pump 634, 645
Mixing length 343
Molecular structure 3
Moment of inertia 59
Momentum correction factor
138
Momentum equation 134–54
applications 138–54
boundary layer 303–6
Momentum integral
equation, boundary
layer 306
Momentum theory
propeller 150–4
wind turbine 154
Momentum thickness of
boundary layer 302
Moody diagram 252
Moving fluids, equilibrium of
80–3
Multi-stage pumps 639
Nappe 126–7
Navier–Stokes equations
354–6
numerical procedures for
solving 356–8
Net Positive Suction Head
(NPSH) 644
Neutral equilibrium 71
Newtonian fluid 24
Newton’s First Law 92
Newton’s Law of Universal
Gravitation 12
Newton’s laws of motion
138
Newton’s Second Law 14,
95, 134
Newton’s Third Law 22,
136, 440
Nikuradse’s experiments
250–2
Nodes 478–9
Non-Newtonian liquids
26–7
laminar flow in circular
pipe 196–8
Non-uniform flow 30
Non-uniform velocity
distribution effects
100, 138,
632–4
Normal depth 419
Normal flow 419
Normal shock
waves 500–5
Notches 126–30
rectangular 127
V 129
Nozzle, force at 144–8
Numeric 5
Oblique shock waves
505–12
intersection 510–2
reflection 510–2
One-dimensional flow 32
with negligible friction
522–4
Open channels 414
boundary layer in 423–4
occurrence of
critical conditions
443–54
optimum cross-section
425–6
simple waves and
surges in 427–31
specific energy and
alternative depths of
flow 431–7
steady-flow energy
equation for 416–8
types of flow 415–6
Orifice
flow through sharp-edged
112–9, 268–9
quasi-steady flow through
119
submerged 118–9
Orifice meter 123–5
Oscillatory waves
see Waves
Oseen’s formula 331
Overturning couple 73
Parabolic velocity profile
193
Parallel axes theorem 59
Particle mechanics 332
Pascal (unit) 7, 9, 14
Pascal’s Law 15
Path-line 31
Pelton wheel 598–605
Percentage slip 596
Perfect gas 18, 489
Period of oscillation 77
Perpendicular axes
theorem 59
Petroff’s law 233
Phase velocity 468
Physical constants 667
Physical similarity 159–70
see also specific types
Piezo–electric gauges 56
Piezometer tube 45–6
Piezometric head 46
Piezometric pressure 46
Pipe bend
force caused by flow
round 141–4
head loss due to 266
Pipe fittings, losses in 267–8
Pipe networks 280–1
Pipe with side tappings
281–2
Pipes
branched 278–80
in parallel 277–8
in series 277
Pi theorem 172
Pitometer 112
Pitot-static tube 110–2, 519
Pitot tube 110–2
in flow with variable
density 517–20
Plasticity 27
Plastic solids 2
Poise 26
Poiseuille (unit) 25
Poiseuille’s equation 194694 Index
Polar diagram 337
Porosity 239, 270
Positive-displacement
machines 591
Potential flow 368
Prandtl-Meyer angle 515
Prandtl-Meyer expansion
515
Prandtl-von Kármán theory
343
Pressure 13–6
absolute 13, 46, 49
centre of 61–3
gauge 13, 45, 49
measurement of 48–57
piezometric 46
variation with position in
fluid 43–8
Pressure coefficient 168
Pressure diagrams 565
Pressure drag 324
Pressure forces 162, 168
Pressure gauges 55–7
Pressure gradient 320–2
adverse 321
favourable 320–1
Pressure head 46
Pressure line 271–5
Pressure losses 245–55, 259,
260–71
Pressure transducer 57
Pressure transients 558–80
Pressure variation
perpendicular to
streamlines 107–8
Pressure waves 560
magnitude 560–4
velocity 560–4
Principle of conservation of
mass 90–2
Profile drag 324
three-dimensional bodies
331–5
two-dimensional bodies
329–31
Propeller, momentum theory
150–4
Propeller turbine 607
Pseudo-plastic liquids
27, 197
Pumps 591, 625–51
characteristic curves for
644–5
performance characteristics
644–6
selection 650–1
Quasi-steady flow
through orifice 119
through pipes 284–6
Radial blades 629
Radial-flow machine 596
Radial-flow turbine 605
Rankine–Hugoniot
relation 502
Rankine oval 389
Rapid flow 416
approaching weir 449–51
in open channel 435
Rapidly varied flow 456
Rate of shear 23
Rayleigh step 228–9
Reaction turbine 597
cavitation limits for 621
net head across 607–9
Reciprocating pump 592–6
Rectilinear flow 374, 400–1
Region of influence 497–8
Relative density 13
Relative equilibrium 80
Restoring couple 72
Reversible adiabatic process
503
Reversible process 488
Reynolds number 35
local 137
significance of 163–4
Reynolds stress 342–3
Rheology 28
Rheopectic liquids 27
Rigid-body rotation 381
Ripples 469
Robins effect 396
Rocket propulsion 146–8
Rotameter 303
Rotational flow 366, 381
Rotodynamic machines 592
basic equations 609–13
Rotodynamic pumps 625–51
Rotor 592
Rough zone of flow 251
Runner 592
Salt-dilution method 291
Salt-velocity method 290
Saturation pressure 16
Saturation vapour pressure
of water 667
Scale effect 182
Scale factor 160
Schlieren method 549
Secondary flow, losses due
to 266
Second Law of
Thermodynamics 441
Second moment of area 58–9
Seiches 479
Semi-perfect gas 19
Separation 320–1
from aerofoil 335–7
position of 339
predicting in laminar
boundary layer
322–3
Separation point 321
Separation streamline 321
Shadowgraph method 548
Shear rate 23
Shear stress 1, 22, 191
distribution in circular pipe
257–8
Ship resistance 182–8
Shock 499
Shock losses 631
Shock phenomena 340
Shock stall 546
Shock wave 499–511
definition 499–500
intersection of 510–12
normal 499–505
oblique 505–11
reflection of 510–12
Shooting flow 435
SI units 6
internationally agreed
names 6–7
prefixes for multiples and
submultiples 8
Similarity 160
chemical 162
dynamic 161–7
geometric 160
kinematic 160–1
of machines 639–40
physical 159–60
thermal 161
Similarity laws
pumps 639–40
turbines 613–7
Single suction pump 627
Singular point 375
Sink 376
Siphon 272
Skin friction 307
Skin-friction coefficient 168,
307–8
Slant depth 61Index 695
Slip
in fluid couplings 652
in reciprocating pumps
596
Slip coupling 652
Slip surface 511
Slope 461–3
Smooth zone of flow 251
Solidity
of axial runner 628
of wire gauze 270
Sommerfeld boundary
condition 232–3
Sommerfeld condition, half
237
Sommerfeld number 234
Sonic velocity 493–6
Source 375–6, 401
Source and sink of
numerically equal
strength 387–9
Span (of aerofoil) 403
Specific-energy curve in
dimensionless form
436–7
Specific energy in open
channels 431–5
Specific entropy 489
Specific heat capacity 489
Specific gravity 13
Specific speed
power 616
pumps 639–40
turbines 616
Speed of sound 493–6
Speed ratio of Pelton wheel
603
Spiral vortex 398–9
Stability
of atmosphere 79
of bodies in fluids 71–8
of body subject to
additional force 78
of floating bodies 72–8
of fluid itself 79–80
of submerged bodies 71–2
Stable equilibrium 71
Stagnation enthalpy 492
Stagnation hypothesis 405
Stagnation point 110, 384,
517
Stagnation pressure 110, 503
Stagnation temperature 492,
502
Stall 337
Stalled flow 337
Stalling angle 337
Stall torque 654
Standing wave 478–9
Stanton diagram 250
Starting vortex 405
Steady flow 36
Steady-flow energy equation
derivation 97–100
for open channels 416–9
practical application
103–4
Steady-flow momentum
equation 134, 428
Steady uniform flow 415,
419–23
Steep slope 435, 462–3
Stokes (unit) 26
Stokes’s Law 212, 391
Straight-line closure 570
Streak-line 32
Stream filament 31
Stream function 362–4
Streamlined body 325
Streamlines 31, 362–3, 370
pressure variation
perpendicular to
107–9
Stream-tube 31
Strength of source 375
Strength of vortex 377
Stress 1, 9, 15
Strickler’s formula 422
Strouhal number 328
Submerged bodies,
stability of 71–2
Subsonic flow 522, 524,
526–7
Subsonic velocity 496
Substantial acceleration 89
Super-cavitating machines
644
Supersonic flow 502, 527
between two boundaries
516–7
over concave boundary
516
round corners 512–6
Supersonic velocity 497
Surface profiles 457, 459
classification 461–3
Surface tension 28–30, 469
Surface tension forces 165–6
Surface waves 464–9
Surge tanks 583–6
Surges in open channels
427–31
Système International
d’Unités (SI units) 6
Tail race 606
Temperature 9
Temperature difference 10
Temperature lapse rate 47
Temporal acceleration 89
Terminal velocity 213, 333
Thermally perfect gas 17–8,
489
Thermodynamic concepts
487–91
Thermodynamic effects 487
Thixotropic liquids 27
Thoma’s cavitation
parameter 620
Thomson’s theorem 407
Three-dimensional flow 32,
331–5
Thrust coefficient 153
Thwaites’s method 322–3
Töpler system 549
Torque coefficient 654
Torque converter 654–6
Torricellian vacuum 49
Torricelli’s formula 114
Total energy line 106,
271–5
Total head 96
Total head line 106, 271–5
Tranquil flow 416, 435
Transition region of
boundary layer 299
Transition zone of flow 251
Transpiration methods
210–1
Tsunamis 480–2
Turbines 591, 596–625
performance characteristics
623–5
types 596–7
Turbulence 35
free 352–3
Turbulent boundary layer, on
smooth flat plate with
zero pressure gradient
313–6
Turbulent flow 35
in pipes 246–8
velocity distribution in
344–52
Two-dimensional flow 32–3
Undular jump 441–2
Uniform flow 30
Uniform rectilinear flow
374, 384
Unit flow 624696 Index
Unit power 624
Units 4–10
prefixes 8
Unit speed 624
Universal gas constant 18
Unstable equilibrium 71
Unsteady flow 36–7
Upper (or higher) critical
velocity 247
U-tube manometers 50–5
Vacuum 48–9
Valve closure 569–74
Valve opening factor 570
Vapour pressure 16
Varied flow 416
Velocity
of flow 630
of sound 496
of whirl 601
Velocity defect 345
Velocity defect law 345
Velocity diagrams 609–10,
612
Velocity distribution
in rough pipes 349–50
in smooth pipes and over
smooth plates
345–8
in turbulent flow 344–52
Velocity gradient 22
Velocity head 96
Velocity measurement
288–90
Velocity potential 367–9
Velocity profile 22
Vena contracta 113
Venturi flume 451–4
Venturi-meter 119–22
Virtual mass 392–3
Viscoelastic materials 27
Viscometer 211
Engler 211
Ostwald 211
Redwood 211
rotary 215–8
Saybolt 211
Searle 231
Viscometry 210
Viscosimeter see Viscometer
Viscosity 21–8
absolute 23
basic SI unit 25
causes of 24–5
dynamic 23, 668
eddy 341–2
influence on flow 37
kinematic 26, 669
measurement of 210
quantitative definition
21–4
variation with temperature
668–9
Viscous forces 163–4
Viscous resistance 191–2
Viscous stresses 199
Viscous sub-layer 251–2,
347
Voidage 240
Volute 605, 626
Vortex
forced 381–2
free 376–9
spiral 398–9
starting (on aerofoil) 405
Vortex drag 407–9
Vortex pair 396–8
Vortex shedding 328
Vortex sheet 511–2
Vortex street (or trail)
326–8
Vortex strength 377
Vorticity 365–6
Wake
definition 325
flow pattern 326
width 328
Water hammer 558
Wave drag 340
Wave energy 472–3
Wave formation 480
Wave-making resistance
182–3
Wave propagation, finite
waves 498–9
Waves
Airy 467–8
capillary 469
deep water 468
dispersive 468
elastic 493–7
gravity 468
moving into shallow water
477–8
in open channels 427–31
oscillatory 464–79
reflection 564–9
standing 478–9
Weber number 166–7
Weir
broad-crested 444–7
drowned 447–8
rapid flow approaching
449–51
sharp-crested 126–30
suppressed 128
Whirl 609
Whirl slip 633
Wicket gates 606
Windage 603
Wind turbine, momentum
theory 154
Wings, aerodynamics of
403–9, 544–6
Yaw meter 291
Yield stress 198
Zone of action 498
Zone of silence 498


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