كتاب Fluid Mechanics
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 كتاب Fluid Mechanics

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Fluid Mechanics - in SI Units 2nd Edition
R. C. Hibbeler
Second Edition in SI Units
SI Conversion by
Kai Beng Yap

كتاب Fluid Mechanics R_c_h_14
و المحتوى كما يلي :


Chapter Objectives 19
1.1 Introduction 19
1.2 Characteristics of Matter 21
1.3 The International System of Units 22
1.4 Calculations 25
1.5 Problem Solving 27
1.6 Some Basic Fluid Properties 29
1.7 Viscosity 34
1.8 Viscosity Measurement 39
1.9 Vapor Pressure 43
1.10 Surface Tension and Capillarity 44
1
Fundamental
Concepts 19
Chapter Objectives 61
2.1 Pressure 61
2.2 Absolute and Gage Pressure 64
2.3 Static Pressure Variation 66
2.4 Pressure Variation for Incompressible
Fluids 67
2.5 Pressure Variation for Compressible Fluids 69
2.6 Measurement of Static Pressure 72
2.7 Hydrostatic Force on a Plane Surface—
Formula Method 80
2.8 Hydrostatic Force on a Plane Surface—
Geometrical Method 86
2.9 Hydrostatic Force on a Plane Surface—
Integration Method 91
2.10 Hydrostatic Force on an Inclined Plane or
Curved Surface Determined by Projection 94
2.11 Buoyancy 101
2.12 Stability 104
2.13 Constant Translational Acceleration of
a Liquid 107
2.14 Steady Rotation of a Liquid 112
2
Fluid Statics 61
Chapter Objectives 189
4.1 Volumetric Flow, Mass Flow, and Average
Velocity 189
4.2 Finite Control Volumes 194
4.3 The Reynolds Transport Theorem 196
4.4 Conservation of Mass 200
4
Conservation of
Mass 189
Chapter Objectives 153
3.1 Types of Fluid Flow 153
3.2 Graphical Descriptions of Fluid Flow 157
3.3 Fluid Flow Descriptions 161
3.4 Fluid Acceleration 168
3.5 Streamline Coordinates 175
3
Kinematics
of Fluid Motion 153
CONTENTSChapter Objectives 359
7.1 Differential Analysis 359
7.2 Kinematics of Differential Fluid
Elements 360
7.3 Circulation and Vorticity 364
7.4 Conservation of Mass 369
7.5 Equations of Motion for a Fluid
Particle 371
7.6 The Euler and Bernoulli Equations 373
7.7 Potential Flow Hydrodynamics 377
7.8 The Stream Function 377
7.9 The Potential Function 383
7.10 Basic Two-Dimensional Flows 387
7.11 Superposition of Flows 396
7.12 The Navier–Stokes Equations 409
7.13 Computational Fluid Dynamics 414
7
Differential Fluid
Flow 359
Chapter Objectives 435
8.1 Dimensional Analysis 435
8.2 Important Dimensionless Numbers 438
8.3 The Buckingham Pi Theorem 441
8.4 Some General Considerations
Related to Dimensional Analysis 450
8.5 Similitude 451
8
Dimensional
Analysis and
Similitude 435
Chapter Objectives 301
6.1 The Linear Momentum Equation 301
6.2 Applications to Bodies at Rest 304
6.3 Applications to Bodies Having Constant
Velocity 313
6.4 The Angular Momentum Equation 318
6.5 Propellers and Wind Turbines 326
6.6 Applications for Control Volumes Having
Accelerated Motion 331
6.7 Turbojets and Turbofans 332
6.8 Rockets 333
6
Fluid Momentum 301
Chapter Objectives 231
5.1 Euler’s Equations of Motion 231
5.2 The Bernoulli Equation 235
5.3 Applications of the Bernoulli
Equation 238
5.4 Energy and Hydraulic Grade
Lines 251
5.5 The Energy Equation 260
5
Work and Energy
of Moving Fluids 231
14 contentsChapter Objectives 475
9.1 Steady Laminar Flow between Parallel
Plates 475
9.2 Navier–Stokes Solution for Steady Laminar
Flow between Parallel Plates 481
9.3 Steady Laminar Flow within a Smooth
Pipe 486
9.4 Navier–Stokes Solution for Steady
Laminar Flow within a Smooth Pipe 490
9.5 The Reynolds Number 492
9.6 Fully Developed Flow from an
Entrance 497
9.7 Laminar and Turbulent Shear Stress within
a Smooth Pipe 499
9.8 Steady Turbulent Flow within a Smooth
Pipe 502
9
Viscous Flow within
Enclosed Conduits 475
Chapter Objectives 575
11.1 The Concept of the Boundary Layer 575
11.2 Laminar Boundary Layers 581
11.3 The Momentum Integral Equation 590
11.4 Turbulent Boundary Layers 594
11.5 Laminar and Turbulent Boundary
Layers 596
11.6 Drag and Lift 602
11.7 Pressure Gradient Effects 604
11.8 The Drag Coefficient 609
11.9 Drag Coefficients for Bodies Having
Various Shapes 613
11.10 Methods for Reducing Drag 620
11.11 Lift and Drag on an Airfoil 624
11
Viscous Flow over
External Surfaces 575
Chapter Objectives 655
12.1 Types of Flow in Open Channels 655
12.2 Open-Channel Flow Classifications 657
12.3 Specific Energy 658
12.4 Open-Channel Flow over a Rise or
Bump 666
12.5 Open-Channel Flow under a Sluice
Gate 670
12.6 Steady Uniform Channel Flow 674
12.7 Gradually Varied Flow 681
12.8 The Hydraulic Jump 688
12.9 Weirs 693
12
Open-Channel Flow 655
Chapter Objectives 521
10.1 Resistance to Flow in Rough Pipes 521
10.2 Losses Occurring from Pipe Fittings and
Transitions 535
10.3 Single-Pipeline Flow 541
10.4 Pipe Systems 548
10.5 Flow Measurement 554
10
Analysis and Design
for Pipe Flow 521
contents 1516 contents
Chapter Objectives 715
13.1 Thermodynamic Concepts 715
13.2 Wave Propagation through a
Compressible Fluid 724
13.3 Types of Compressible Flow 727
13.4 Stagnation Properties 731
13.5 Isentropic Flow through a Variable
Area 738
13.6 Isentropic Flow through Converging and
Diverging Nozzles 743
13.7 The Effect of Friction on Compressible
Flow 752
13.8 The Effect of Heat Transfer on
Compressible Flow 762
13.9 Normal Shock Waves 768
13.10 Shock Waves in Nozzles 771
13.11 Oblique Shock Waves 776
13.12 Compression and Expansion
Waves 781
13.13 Compressible Flow Measurement 786
13
Compressible Flow 715
Chapter Objectives 807
14.1 Types of Turbomachines 807
14.2 Axial-Flow Pumps 808
14.3 Radial-Flow Pumps 815
14.4 Ideal Performance for Pumps 818
14.5 Turbines 824
14.6 Pump Performance 831
14.7 Cavitation and the Net Positive Suction
Head 834
14.8 Pump Selection Related to the Flow
System 836
14.9 Turbomachine Similitude 838
Appendix
A Physical Properties of Fluids 856
B Compressible Properties of a
Gas (k = 1.4) 859
Fundamental Solutions 870
Answers to Selected Problems 886
Index 899
14
Turbomachines 807
INDEX
A
Absolute pressure, 32, 58, 64–65, 150
ideal gas law and, 32, 58
standard atmospheric
pressure and, 64–65, 150
zero, 64
Absolute temperature, 23, 32, 58
Absolute viscosity, 36
Accelerated motion, 331–335, 357
control volume with, 331, 357
fluid momentum and, 331–335, 357
rockets, 333–335
turbojets and turbofans, 332
Accelerated nonuniform
open-channel flow, 656
Acceleration of fluids, see Fluid
acceleration; Streamline
coordinates
Acceleration of liquid, 107–111, 151
Adhesion, 44
Adiabatic process, 720, 803
Adverse pressure gradient, 605
Air, properties of, 858
Airfoils, 620–621, 624–632, 652
angle of attack, 620, 627, 629
circulation and, 625–626
design of, 621
drag coefficients for, 621
drag on, 624–632
drag reduction for, 620–621, 652
induced drag, 621, 628–629
lift and, 624–632
race cars with, 627
split-scimitar winglets on, 628
vortex trail, 628
Andrade’s equation, 38
Anemometer, 556
Angle of attack, 620, 627, 629
Angle valve, 539
Angular distortion, 363, 431
Angular momentum, 318–325, 357, 809, 816
axial-flow pumps, 809
control volumes for, 318–319, 357
procedure for analysis of, 319
radial-flow pumps, 816
representation of, 318–325
steady flow, 319
Apparent shear stress, 500–501
Apparent viscosity, 37
Area of flow, 674
Average angular velocity, 362
Average pressure, 61
Average velocity, 191
Axial-flow machines, 807,
808–814, 855
angular momentum and, 809
continuity equation for, 809
flow categorization of, 807
flow kinematics, 810–811, 855
fluid flow through, 808–809
power by, 810
procedure for analysis of, 811
pumps, 808–814, 855
B
Backpressure, 743–751, 771–772, 804
Barometer, 72
Bends, losses from, 538
Bernoulli equation, 235–252, 298–299, 327,
374–376
differential fluid flow and, 374–376
energy (EGL) and hydraulic grade lines
(HGL) from, 251–252
flow work from, 236
fluid flow applications, 238–250
limitations, 237
procedure for analysis using, 244
propeller fluid momentum
and, 327
streamline applications,
235–237, 243
Best hydraulic cross section, 676–677
Betz’s law, 329
Bluff body, 604
Bodies at rest, fluid momentum of, 304–313
Bodies with constant velocity, fluid momentum of, 313–317
Body force, 372
Boundary layers, 237, 497, 575–601, 651–652
development of, 575–576
displacement thickness, 578, 582
disturbance thickness, 577, 582, 595
drag and, 584, 595, 596–601
external surfaces, 575–601, 651
flat plate analysis for combined layers,
596–601
friction drag, 584, 596–601
fundamental equations for, 653
laminar, 577, 581–589, 596–601, 651–652
momentum integral equation for,
590–593, 652
momentum thickness, 579, 583
pipe fluid flow and, 237
Prandtl’s one-seventh power law for, 594
regions of, 576–577
shear stress, 583–584, 595
thickness of, 577–579
transitional flow, 577
turbulent, 577, 594–601, 651–652
viscous fully developed flow and, 497
Bourdon gage, 76
Broad-crested weir, 696
Brookfield viscometer, 39
Buckingham Pi theorem,
441–449, 473
Bulk modulus, 31, 58
Bump, open-channel flow over, 666–669
Buoyancy, 101–105, 151
center of, 101, 105
hydrometer measurement of, 102
principle of, 101, 151
stability and, 104–105
Buoyant force, 101
Butterfly valve, 539
C
Calculations for fluid mechanics, 25–26
Canals, 655
Capacity factor, 329
Capillarity, 46–47, 59
Casing, flow through, 817
Cavitation, 43, 59, 834–835, 855
Centerline, pipe flow and, 252
Centrifugal pump, 815
Centroid (C), 80, 86, 150
Channel cross sections, 659, 674,
676–677, 682
best hydraulic, 676–677
geometric properties of channel
shapes, 674
gradually varied flow and, 681
nonrectangular, 661
rectangular, 659–661, 682
specific energy and, 659–661
Chézy equation, open-channel flow
and, 675
Choked nozzles, 744, 804
Circulation (Г), 364–365, 367, 392, 432,
625–626
free-vortex flow, 392
Kutta-Joukowski theorem for, 625–626
lift and, 625–626
rotational flow and, 364–365,
367, 432
Closed conduits, fluid flow in, 240–241
Coanda effect, 606
899900 Index
Cohesion, 44
Colebrook equation, 527
Compressible flow, 715–805
continuity equation for, 725, 738, 752,
762, 768, 777
energy equation for, 754, 763, 769,
777–779
expansion and compression waves,
781–785
friction effect on, 752–761, 804
fundamental equations of, 805
heat transfer effect on,
762–767, 804
hypersonic flow, 728
ideal gas law and, 716, 754, 763, 769
isentropic flow analysis, 738–751
linear momentum equation
for, 725–726, 738–739, 753,
762, 768, 777
Mach cone, 729
Mach number (M) for, 727–730, 755,
769–771, 803
measurement of, 786–787, 804
nozzles, 740, 743–751, 771–775, 804
shock waves, 728, 768–780, 804
sonic flow, 728
stagnation properties, 731–737, 803
subsonic flow, 727, 739, 786
supersonic flow, 728, 739, 787
thermodynamic concepts for, 715–723, 803
variable areas with, 738–743
wave propagation through, 724–726
Compressible fluids, 69–71, 265
Compression waves, 781
Compressor, 332
Computational fluid dynamics (CFD), 160,
414–416
Conduits, 475–519, 528, 655–713. See also
Parallel plates; Pipes
enclosed conduits, 475–519
hydraulic diameter, 528
noncircular conduits, 528
open channels, 653–713
Connections, losses from, 538
Conservation of energy, 262–263
Conservation of mass, 189–229, 369–370, 432
average velocity, 191
continuity equation for, 200–201, 229,
369–370, 432
control volume change and, 196–198, 229
differential fluid flow, 369–370, 432
finite control volume for,
194–195, 229
mass flow, 192, 229
procedure for analysis of, 202
Reynolds transport theorem for,
196–200, 229
special cases for, 201
volumetric flow, 190–191, 229
Constant-pressure process, 717–718
Constant temperature, compressible fluids
and, 69
Constant-volume process, 717
Continuity equation, 200–201, 229, 369–370,
432, 590, 688, 725, 738, 752, 762, 768, 777,
809, 816
axial-flow pumps, 809
compressible flow and, 725, 738,
752, 762, 768, 777
cylindrical coordinates, 370
differential fluid flow,
369–370, 432
fluid flow change and,
200–201, 229
friction effects on flow and, 752
heat transfer effects on flow
and, 762
hydraulic jump and, 688
momentum integral equation and, 590
radial-flow pumps, 816
shock waves and, 768, 777
two-dimensional flow, 370
wave propagation using, 725
Continuum, 21
Control surface, 162, 194–195
Control volume, 162, 168–169, 187, 194–198,
229, 302–305, 318–319, 331, 357
accelerated motion of, 331, 357
angular momentum equation and,
318–319, 357
approach to fluid flow, 162, 187
convective and local change,
198, 229
finite, 194–195
fluid acceleration and, 168–169
fluid momentum and, 302–305, 318–319,
331, 357
linear momentum equation and,
301–304, 357
open control surfaces, 195
Reynolds transport theorem
and, 196–199, 229
steady flow and, 195, 229, 303
time rate of change, 196–198, 229
velocity of flow for, 195
Convective acceleration, 169, 176
Convective control volume change, 198, 229
Converging–diverging nozzle, 745
Converging nozzle, 744
Cord, wing measurement of, 620
Critical depth, 660–661
Critical flow, 658
Critical pressure, 744
Critical Reynolds number, 493
Critical slope of open channels, 677
Critical suction head, 834
Critical zone, 526
Culverts, 655
Curved boundary, fluid flow around, 239
Curved surfaces, hydrostatic
force on, 94–100, 151
horizontal component, 94–95, 151
liquid below plate, 96
resultant forces on, 94–96
vertical component, 95, 151
Cylinders, 402–405, 605–607, 610–611
drag coefficient for, 610–611
ideal flow around, 605
pressure gradient effects, 605–607
real flow, 606–607
superposition of flow around, 402–405
Cylindrical coordinates, continuity
equation for, 370
D
d’Alembert’s paradox, 405
Darcy friction factor, 523, 573
Darcy-Weisbach equation, 524, 573
Density, 29, 58, 732, 756, 764
compressible flow and, 732,
756, 764
property of, 29, 58
friction effect on flow and, 756
heat transfer effects on flow
and, 764
Derived units, 22
Differential fluid flow, 359–433
analysis for, 359–360
angular distortion of, 363, 431
Bernoulli equation for, 374–376
circulation, 364–365, 367, 392, 432
computational fluid dynamics (CFD),
414–416
conservation of mass, 369–370, 432
continuity equation for,
369–370, 432
dilatation of, 361, 431
equations of motion for fluid
particles, 371–376
Euler equations for, 373, 375–376
hydrodynamics, 377–386
ideal fluid flow, 366, 370,
377–386, 431
irrotational flow, 366
kinematics of elements, 360–363
linear distortion of, 361, 431
Navier-Stokes equations for, 409–413
potential function, 383–386, 432
rotation of, 362, 431
rotational flow, 364–368Index 901
stream function, 377–382, 432
superposition of flows, 396–408, 433
translation of, 360–361, 431
two-dimensional flow,
387–395, 433
velocity components, 378, 383–384
vorticity, 365, 368, 432
Differential manometer, 75
Dilatant fluids, 37
Dilatation, 361, 431
Dimensional analysis, 434–473
Buckingham Pi theorem,
441–449, 473
dimensionless numbers for, 438–440, 473
flow considerations for, 450–451
principle of dimensional
homogeneity, 436–437
procedure for analysis, 442
similitude and, 451–462, 473
Dimensional homogeneity, 25, 436–437
Dimensionless groups, 435
Dimensionless numbers,
438–440, 473
Euler number (Eu), 438, 473
Froude number (Fr), 439, 473
Mach number (Ma), 440, 473
Reynolds number (Re), 439, 473
Weber number (We), 440, 473
Dimensionless ratio, 503
Discharge, see Mass flow;
Volumetric flow
Discharge coefficients, 535, 554–555, 671,
694–695
flow measurement adjustment
using, 554–555
losses and, 535, 671
nozzles, 555
orifice, 555
Venturi, 554
weirs, 694–695
Displacement thickness, boundary layers,
578, 582
Distortion, 361, 363, 431
Disturbance thickness, boundary layers,
577, 582
Dot product, 191
Doublet, 398–399
Drag, 456–457, 584, 595, 596–608, 624–632,
651–652
airfoils, 621, 624–632, 652
angle of attack, 620
boundary layers and, 584, 595, 596–601
components of, 602–604
direction of, 602
flat plate with, 595
friction drag, 584, 596–601, 604
fundamental equations for, 653
induced, 621, 628–629
lift and, 602–604, 624–632
pressure drag, 604–608
pressure gradient effects, 604–608
reduction of, 620–623
section, 621
similitude for, 456–457
skin friction coefficient, 584
spinning ball trajectory and, 630
streamline the body for, 620
vehicles, 622–623
vortex trail and, 628
Drag coefficient, 609–619,
621, 623, 629, 651
airfoils, 621
cylinders, 610–611
Froude number (Fr) and, 612
geometric shapes, applications
for, 613–619
Mach number (M), 612–613
Reynolds number (Re) and,
610–611
spheres, 611
vehicles, 623
Dynamic fluid devices, 808. See
also Turbomachines
Dynamic force, 304
Dynamic pressure, 239
Dynamic similitude, 453
Dynamic viscosity, 36
E
Eddy viscosity of flow, 502
Effective angle of attack, 629
Efficiency, 265, 328–329, 819,
829, 833
fluid momentum and, 328–329
hydraulic, 819
manufacturer performance
curves, 833
power and, 265, 328–329
propellers, 328
turbomachines, 819, 829, 833
wind turbines, 329
Elevation head, 251
Empirical solutions for resistance in
rough pipes, 527–528
Enclosed conduits, viscous flow in,
475–519
fully developed flow from an entrance,
497–498
Navier-Stokes solution for flow in,
481–485, 490–491
procedures for analysis of, 482, 494
Reynolds number for, 492–496
shear stress in a smooth pipe, 499–502
steady laminar flow between
parallel plates, 475–485
steady laminar flow in smooth pipes,
486–491
steady turbulent flow in smooth pipes,
502–507
Energy equation, 260–273, 299,
690, 754, 763, 769, 777–779
compressible flow, 265
conservation of energy, 262–263
flow work, 261, 262–263
friction effects on flow and, 754
gravitational potential
energy, 260
heat energy, 261–262
heat transfer effects on flow
and, 763
hydraulic jump and, 690
incompressible flow, 263–264
internal energy, 260
kinetic energy, 260
mechanical efficiency, 265
nonuniform velocity, 266
power, 265
procedure for analysis using, 267
shaft work, 261, 262–263
shear work, 261
shock waves and, 769,
777–779
system energy, 260
work, 261–263
Energy grade line (EGL),
251–260, 299
Enthalpy, 265, 717
Entrance length, 497
Entropy, 718–719, 803
Equations of motion for fluid
particles, 371–376
Equilibrium, stability and,
104–106, 151
Equivalent-length ratio, 540
Euler number (Eu), 438, 473
Eulerian description of fluid
flow, 162, 187
Euler’s equations of motion,
231–234, 298, 373, 375–376
differential fluid flow and,
373, 375–376
differential forms of, 231–232
inviscid fluids, 232–233, 298
n and s directions, 232
steady horizontal flow of ideal
fluid, 233
two-dimensional steady flow, 373
Expansion and contraction, losses
from, 537
Expansion factor, 787902 Index
Expansion waves, 781
Extensive fluid properties, 196
External surfaces, 575–653
airfoils, 621, 624–632, 652
boundary layers, 575–601, 651
drag and lift effects, 602–604, 624–632
drag coefficient for, 609–619, 621,
623, 629, 651
drag reduction, 620–623
fundamental equations for, 653
laminar boundary layers, 577, 581–589,
596–601, 651
momentum integral equation for, 590–593
pressure gradient effects, 604–608
turbulent boundary layers, 577, 594–601, 652
vehicles, 622–623
viscous flow over, 575–653
F
Fanno flow, gas properties and, 864
Fanno line, 757, 804
Favorable pressure gradient, 605
Finite control volume, 194–195, 229, 415
Finite difference method, CFD, 415
Finite element method, CFD, 415
Flat plate analysis, 594–601
combined boundary layers, 596–601
drag on, 595
shear stress along, 595
turbulent boundary layers, 594–595
Floatation, see Buoyancy; Stability
Flow coefficients, 535
Flow kinematics, see Kinematics of fluid
motion
Flow meters, 554–558, 573. See also
Measurement tools
Flow net, 384
Flow systems, 836–837
Flow work, 236, 261–263
Bernoulli equation and, 236
energy equation and, 261–263
pressure and, 261
rate of, 262
Fluid acceleration, 168–174, 187
control volume and, 168–169
convective acceleration, 169, 176
local acceleration, 169, 175
resultant acceleration, 176
streamline coordinates for, 175–177
time rate change in velocity, 168–169, 187
three-dimensional flow, 170
Fluid flow, 153–167, 186–187, 190–193,
235–260, 298–299, 538
See also Differential fluid flow; Pipe flow
around a curved boundary, 239
Bernoulli equation for, 235–242
closed conduits, 240–241
computational fluid dynamics (CFD), 160
dimension basis of classification, 155
energy equation, 260–273, 299
energy (EGL) grade lines, 251–260, 299
Eulerian description of, 162, 187
frictional effects and, 154
gases, compression and, 237
graphical descriptions of, 157–160
hydraulic (HGL) grade lines, 251–260, 299
Lagrangian description of, 161, 187
laminar flow, 154, 186
mass flow, 192, 229
measurement of, 240–242
open channels, 240, 298
optical methods of visualization, 160
pathlines, 159, 186
pipes, 240–242, 251–260, 299
reservoirs, 238
secondary, 538
space and time basis of classification, 156
steady flow, 156, 186
streaklines, 159, 186
streamlines, 157, 186–187, 231–237, 243, 298
systems and particle behavior,
161–167, 187
transitional flow, 154
turbulent flow, 154, 186
uniform flow, 156, 186
velocity profile, 154–155, 190–193
volumetric flow, 190–191, 229
Fluid mechanics, 18–59
branches of, 20
calculations, 25–26
capillarity, 46–47, 59
characteristics of matter, 21, 58
historical development of, 20
international systems of units, 22–24, 58
problem solving, 27–29
procedure for analysis of, 27
properties of fluids, 29–34, 58
surface tension (s), 44–47, 59
vapor pressure, 43, 59
viscosity measurement, 39–42
viscosity, 34–42, 58–59
Fluid momentum, 301–357
accelerated motion and, 331, 357
angular momentum equation,
318–325, 357
bodies at rest, 304–313
bodies with constant velocity, 313–317
control volumes for, 302–305, 318–319,
331, 357
Froude’s theorem for, 327, 329
linear momentum equation, 301–317,
326–327, 357
procedures for analysis of, 305, 319
propellers, 326–329, 330, 357
rockets, 333–335
steady flow and, 303, 319
turbofans, 332
turbojets and turbofans, 332
wind turbines, 329
Fluid motion, see Kinematics
of fluid motion
Fluid particles, 161–167, 371–376
Bernoulli equation for, 374–376
behavior in fluid systems, 161–167
body and surface forces, 372
equations of motion for, 371–376
Euler equations for, 373, 374–375
normal and shear stresses, 371
stress field, 371
Fluid properties, 29–38
bulk modulus, 31
density, 29–30
ideal gas law, 32
incompressibility of liquids, 29
specific gravity, 30
specific weight, 30
viscosity, 34–38
Fluid statics, 61–151
absolute pressure, 64–65, 150
acceleration of a liquid,
107–111, 151
buoyancy, 101–103, 151
compressible fluids, 69–71
curved surfaces, 94–100, 151
formula method, 80–85
gage pressure, 64, 150
geometrical method, 86–90
hydrostatic force, 80–100, 150
inclined surfaces, 94–100, 151
incompressible fluids, 67–68
integration method, 91–93
Pascal’s law, 62
plane surfaces, 80–93, 150
pressure, 61–79, 150
rotation of a liquid, 112–115, 151
stability, 104–106, 151
static pressure, 66, 72–79, 150
Fluid system particle behavior, 161–167, 187
Eulerian description of, 162, 187
Lagrangian description of, 161, 187
region of, 161
surroundings of fluid particles, 161
velocity of, 161–167
Fluids, 34, 37, 231–299, 856–858
Bernoulli equation for, 235–250, 298–299
classification of liquids and gases
as, 34
dilatant, 37
energy equation for, 260–273, 299
energy grade line (EGL), 251–260, 299Index 903
Euler’s equations of motion for,
231–234, 298
hydraulic grade line (HGL), 251–260
ideal, 37, 233, 235–236, 298
inviscid, 37, 232–233, 298
measurement of flow of, 240–242, 298
movement of, 231–299
physical properties of, 856–858
procedures for analysis of, 244, 267
pseudo-plastic, 37
viscous, 237, 264, 299
work by, 236, 261–269, 299
Flume, 655
Forced vortex, 112–113, 151, 393
Forces, similitude corresponding to, 458
Formula method for plane surfaces,
80–93, 150
Francis turbine, 827, 855
Free-body diagrams, 304
Free-vortex flow, 392, 404–405, 817
Friction, 752–761, 804
compressible flow, effect on, 752–761, 804
continuity equation and, 752
density and, 756
energy equation and, 754
Fanno line and, 757, 804
ideal gas law and, 754
linear momentum equation and, 753
pipe length vs. Mach number, 755
pressure and, 756
temperature and, 756
Friction drag, 584, 596–601, 604
Friction factor, 752
Friction loss, 264, 522–523
Friction slope, 681
Froude number (Fr), 439, 473, 612, 658, 711
dimensional analysis using, 439, 473
drag coefficient and, 612
open-channel flow and, 658, 711
Froude’s theorem, 327, 329
Fully developed flow from an entrance,
497–498
Fused quartz force-balance Bourdon tube, 76
G
Gage pressure, 64, 150
Gas, 21, 30–32, 34, 58, 237, 265, 856–857,
859–869
bulk modulus of, 31
classification as fluid, 34
compressible flow of, 265
compressible properties of, 859–869
density of, 30
energy equation for, 265
enthalpy of, 265
Fanno flow, 864
hydrostatic force of, 96
ideal gas law, 32, 58
incompressible flow of, 237
isentropic relations of, 859–863
normal shock relations, 866–868
physical properties of, 856–857
Prandtl-Meyer expansion, 869
Rayleigh flow, 865
Gate valve, 539
Geometric shapes, drag coefficients for,
613–619
Geometric similitude, 452
Geometrical method for plane surfaces,
86–90
Globe valve, 539
Gradual expansion and contraction, 537
Gradually varied open-channel flow, 681–687
Gravitational potential energy, 236, 260
H
Haaland equation, 527
Hagen-Poiseuille equation, 489
Half body, superposition of flow around,
396–397
Hazen-Williams equation, 528
Head datum for flow analysis, 251–252
Head-discharge curve, 819
Head loss, 264. See also Losses
Heat energy, 261–263
Heat transfer, 762–767
compressible flow affected by, 762–767, 804
continuity equation for, 762
density, 764
energy equation for, 763
ideal gas law and, 763
linear momentum equation for, 762
pressure, 764
Rayleigh line and, 765, 804
stagnation temperature and pressure,
764–765
temperature, 764
velocity, 763–764
Hydraulic diameter, 528
Hydraulic efficiency, 819
Hydraulic grade line (HGL),
251–260, 299
Hydraulic head, 251
Hydraulic jump, 656, 688–692, 712
continuity equation for, 688
energy equation for, 690
momentum equation for, 689
Hydraulic radius, 674
Hydraulics, 20
Hydrodynamics, 20, 377–386
ideal fluid flow, 366, 370, 377–386, 431
potential flow, 377–386
potential function, 383–386, 432
stream function, 377–382, 432
velocity components, 378, 383–384
Hydrometer, 102
Hydrostatic force, 80–100, 150–151
curved surfaces, 94–100, 151
formula method for, 80–85
gas, effects of, 96
geometrical method for, 86–90
inclined surfaces, 94–100, 151
integration method for, 91–93
plane surfaces, 80–93, 150
resultant forces of, 80–82, 86–87, 91
Hypersonic flow, 728
I
Ideal fluid flow, 366, 370, 377–386, 431
irrotational flow of, 366
rotational flow of, 366
viscous flow compared to, 366
Ideal fluids, 37, 233, 235–237, 298
Bernoulli equation for, 235–237, 298
Euler’s equations of motion for horizontal flow of, 233
low viscosity and compressibility of, 37
streamlines of, 235–236, 298
Ideal gas law, 32, 58, 716, 754, 763, 769, 803
absolute pressure and temperature
of, 32, 58
compressible flow and, 716, 754, 763,
769, 803
friction effects on flow and, 754
gas behavior and, 32, 716, 803
heat transfer effects on flow and, 763
shock waves and, 769
Ideal pump head, 818
Ideal turbine head, 829
Impeller, 808
Impulse turbine, 824–826
Inclined surfaces, hydrostatic force on,
94–100, 151
gas effects on, 96
horizontal component, 94–95, 151
liquid below plate, 96
resultant forces on, 94–96, 151
vertical component, 95, 151
Inclined-tube manometer, 79
Incompressibility of liquids, 29, 31
Incompressible fluids, 67–68, 237, 263–264
energy equation for flow of, 263–264
fluid flow of gas, 237
pressure head, 68
pressure variation of, 67–68
Induced drag, 621, 628–629
Inlet and exit transitions, losses from, 536
Integration method, 91–93904 Index
Intensive fluid properties, 196
Internal energy, 260, 716, 803
Inviscid fluids, 37, 232–233, 298
Irrotational flow, 366
Isentropic flow, compressible flow
analysis of, 738–751
area ratios for, 740–741
backpressure, 743–751
continuity equation for, 738
converging nozzles, 744
converging-diverging nozzles, 745
Laval nozzle, 740, 745
linear momentum equation for, 738–739
subsonic flow, 739
supersonic flow, 739
variable areas of, 738–743
Isentropic process, 720, 725, 803
Isentropic relations of gas, 859–863
K
Kaplan turbine, 827, 855
Kinematic similitude, 452
Kinematic viscosity (n), 38, 59
Kinematics of differential fluid elements,
360–363
angular distortion, 363, 431
dilatation, 361, 431
linear distortion, 361, 431
rotation, 362, 431
translation, 360–361, 431
Kinematics of fluid motion, 153–187,
810–811, 815–816, 828
axial-flow pumps, 810–811
computational fluid dynamics (CFD), 160
control volume, 162, 168–169, 187
Eulerian description for, 162, 187
fluid acceleration, 168–174, 187
fluid flow, 153–167, 186
fluid particles, 161–167
Lagrangian description for, 161, 187
pathlines, 159, 186
radial-flow pumps, 815–816
reaction turbines, 828
schlieren photography, 160
shadowgraphs, 160
streaklines, 159, 186
streamlines, 157–158, 175–178, 186–187
Kinetic energy, 236, 260
Kinetic energy coefficient, 266
Kinetic head, 251
Kutta-Joukowski theorem, 625–626
L
Lagrangian description of fluid flow, 161, 187
Laminar boundary layers, 577, 581–589,
596–601, 651–652
Blasius solution for, 581–582
boundary layer region, 577
displacement thickness, 582
disturbance thickness, 582
flat plate analysis for combined layers,
596–601
friction drag, 584, 596–601
fundamental equations for, 652
momentum thickness, 583
shear stress, 583–584
skin friction coefficient for, 584
Laminar flow, 154, 186, 475–499, 519,
522–523, 526, 573, 656
between parallel plates,
475–485, 519
Darcy friction factor for, 523, 573
fully developed flow from an entrance,
497–498
Moody diagram for, 526
Navier-Stokes solution for, 481–485,
490–491
open channels, 656
procedures for analysis of,
482, 494
resistance in rough pipes, 522–523,
526, 573
Reynolds number for, 492–496
shear stress in a smooth pipe, 499
smooth pipes with, 486–491
viscous fluids, 475–499, 519
viscous shear stress, 499
Laminar (viscous) sublayer,
500, 577
Laplace’s equation, 387
Laser Doppler flow meter, 558
Laval nozzle, 740, 745, 804
Law of the wall, 503
Lift, 602–604, 624–632, 652
airfoils, 624–632
angle of attack and, 620, 627, 629
circulation and, 625–626
components of, 602–604
drag and, 602–604, 624–632
force of, 602
fundamental equations for, 652
Kutta-Joukowski theorem for,
625–626
Magnus effect of, 630
spinning ball trajectory and, 630
Lift coefficient, 627
Line sink flow, 391, 398–399
Line source flow, 390–391, 398–399
Linear distortion, 361, 431
Linear momentum equation, 301–317,
326–327, 357, 725–726, 738–739, 753, 762,
768, 777
bodies at rest, 304–313
bodies with constant velocity, 313–317
compressible flow and, 725–726, 738–739,
753, 762, 768, 777
control volumes for, 302–305, 357
free-body diagram for, 304
friction effects on flow and, 753
heat transfer effects on flow and, 762
procedure for analysis of, 305
propeller fluid momentum and,
326–327
representation of, 301–304
shock waves and, 768, 777
steady flow, 303
wave propagation using, 725–726
Liquid droplets, 45
Liquids, 21, 29–31, 34, 43–47, 59, 107–115,
151, 856
acceleration of, 107–111, 151
bulk modulus of, 31
capillarity of, 46–47, 59
density of, 29
forced vortex formation,
112–113, 151
incompressibility of, 29, 31
nonwetting, 46
paraboloid surface of, 113, 151
physical properties of, 856
pressure variations in,
107–111, 151
rotation of, 112–115, 151
saturation of, 43
specific gravity of, 30
surface tension, 44–47, 59
wetting, 46
Local acceleration, 169, 175
Local control volume change, 198, 229
Losses, 522–523, 574, 535–541, 573,
818–819, 829
bends causing, 538
Darcy friction factor for, 523, 573
Darcy-Weisbach equation, 524, 573
equivalent-length ratio, 540
expansion and contraction
causing, 537
friction loss, 522–523
head loss, 522–524, 573, 818–819, 829
hydraulic efficiency and, 819
inlet and exit transitions
causing, 536
major head loss, 522–524, 541, 573
minor head loss, 535–537, 541, 573
pipe connections causing, 538
pipe fittings and transitions
causing, 535–541
pumps, 818–819
resistance in rough pipes and,
522–523, 573Index 905
resistance (loss) coefficient, 535
turbines, 829
valves causing, 539
M
Mach cone, 729
Mach number (M), 440, 473, 612–613,
727–730, 755, 769–771, 803
compressible flow and, 727–730, 755,
769–771, 803
dimensional analysis using, 440, 473
drag coefficient and, 612–613
flow classification using, 727–730
friction effect on flow and, 755
pipe length vs., 755
shock waves, relationships and, 769–771
Mach wave fans, 781–786
Magnetic flow meter, 558
Magnus effect, 630
Major head loss, 522–524, 541, 573. See also
Losses
Manning equation, 676, 712
Manometer rule, 74
Manometers, 73–75, 79, 241
Mass, see Conservation of mass
Mass flow, 191, 229
Material derivative, 169
Matter, characteristics of, 21, 58
Mean steady flow, 500
Measurement tools, 39–42, 72–79, 102, 150,
240–242, 554–558, 573, 786–787, 804
anemometer, 556
barometer, 72
Bourdon gage, 76
Brookfield viscometer, 39
buoyancy, 102
compressible flow, 786–787, 804
differential manometer, 75
flow meters, 554–558, 573
fluid flow, 240–242
fused quartz force-balance
Bourdon tube, 76
hydrometer, 102
magnetic flow meter, 558
manometer rule, 74
manometers, 73–75, 241
nozzle meter, 555
nutating disk flow meter, 557
orifice meter, 555
Ostwald viscometer, 40
piezoelectric gages, 76
piezometer, 240, 786
pipe flow, 554–558, 573
pitot (stagnation) tube, 240,
298, 786
pitot-static tube, 241
positive displacement flow
meter, 557
pressure transducers, 76, 241
rotational viscometer, 39
static pressure, 72–79, 150
subsonic flow, 786
supersonic flow, 787
thermal mass flow meter, 557
turbine flow meter, 556
venturi meter, 242, 554, 787
viscosity, 39–42
vortex flow meter, 556
Mechanical efficiency, 265
Meniscus, 46
Metacenter, 105
Minor head loss, 535–537, 541, 573
Mixed-flow machines, 807
Mixing-length hypothesis, 502
Models, 451, 456–457. See also Similitude
Momentum, see Angular
momentum; Fluid momentum; Linear
momentum equation
Momentum integral equation,
boundary layer analysis using,
continuity equation and, 590
hydraulic jump and, 689
velocity profile for, 591–592
Momentum thickness, boundary
layers, 579, 583
Moody diagram, 525–527
Motion, 231–299, 371–376. See also
Kinematics of fluid motion
Bernoulli equation for,
Euler’s equations of, 231–234, 298, 373,
375–376
fluid particles, 371–376
fluids, 231–299
N
Navier-Stokes equations,
Cartesian coordinate form, 409–410
cylindrical coordinate form, 411
laminar flow in parallel plates, 481–485
laminar flow in smooth pipes, 490–491
procedure for analysis using, 482
viscous flow solutions using,
Net positive suction head (NPSH), 834–835
Neutral equilibrium, 104
Newtonial fluids, 37, 59
Newton’s law of viscosity, 35, 36
Newton’s second law of motion, 168
No-slip condition, 35
Non-Newtonian fluids, 37
Noncircular conduits, 528
Nondimensional flow, 155
Nonuniform open-channel flow, 656, 712
Nonuniform velocity, 266
Nonwetting liquids, 46
Normal stresses, 371
Nozzle discharge coefficient, 555
Nozzle meter, 555
Nozzles, 740, 743–751, 771–775, 804
backpressure in, 743–751,
771–772, 804
choked, 744, 804
compressible flow and, 740, 743–751,
771–775
converging, 744, 803
converging-diverging, 745, 803
isentropic flow through, 740, 743–751
Laval, 740, 745, 804
shock waves in, 771–775, 804
underexpanded flow in, 772
Nutating disk flow meter, 557
O
Oblique shock waves, 776–780
One-dimensional flow, 155
Open-channel flow,
Bernoulli equation for, 240
canals, 655
Chézy equation for, 675
critical slope of, 677
cross sections,
culverts, 655
flume, 655
Froude number (Fr) for, 658, 711
fundamental equations for, 713
geometric properties of channel
shapes, 674
gradually varied, 681–687
hydraulic jump, 656, 688–692, 712
laminar, 656
Manning equation for, 676, 712
nonuniform, 656, 712
over a rise or bump, 666–669
pitot tube for measurement of, 240, 298
prismatic channel, 656
Reynolds number (Re) for, 674
similitude for, 455
slopes, 677, 681–684
specific energy and, 658–666, 711
steady, 656, 674–680
surface profile for, 682–684, 712
surface roughness coefficient for, 676906 Index
Open-channel flow (Continued)
turbulent, 656
under a sluice gate, 670–673
uniform, 656, 674–680
wave celerity, 657–658
weirs, 693–697, 712
Operating point, 836
Orifice discharge coefficient, 555
Orifice meter, 555
Ostwald viscometer, 40
P
Paraboloid liquid surface, 113, 151
Parallel-axis theorem, 81
Parallel pipe systems, 548, 549, 573
Parallel-plane theorem, 82
Parallel plates, 475–485, 519
horizontal flow from constant pressure
gradient, 478–479
horizontal flow from motion of
top plate, 480
Navier-Stokes solution for flow
in, 481–485
steady laminar flow between,
viscous fluid flow in, 475–485
Particle image velocimetry (PIV), 558
Pascal’s law, 62, 150
Pathlines, 159, 186
Pelton wheel, 824–826, 855
Piezoelectric gages, 76
Piezometer, 73, 240, 786
Piezometer rings, 554
Pipe flow, 521–573
analysis and design, 521–573
flow measurement, 554–558, 573
losses, 522, 535–541, 573
parallel systems for, 548, 549, 573
procedures for analysis,
relative roughness, 525
resistance in rough pipes, 521–534
series systems for, 548, 573
single pipelines, 541–547
surface roughness, 525
systems for, 548–553, 573
Pipes, 240–242, 251–260, 454, 486–507,
517, 521–534, 535–541
bends, 538
centerline, 252
connections, 538
energy grade line (EGL), 251–260, 299
entrance length, 497
expansion and contraction, 537
fittings and transitions, 535–541
fluid flow in, 240–242
fully developed flow from an entrance,
497–498
head datum for flow analysis, 251–252
horizontal flow through
circular, 489
hydraulic grade line (HGL), 251–260, 299
inlet and exit transitions, 536
laminar flow in, 486–499, 519
Navier-Stokes solution for flow in,
490–491
resistance in, 521–534
Reynolds number for flow through,
rough, 521–534
shear stress in, 499–502
similitude for flow in, 454
smooth, 486–491, 499–507, 517
turbulent flow in,
497–507, 517
valves, 539
viscous fluid flow in, 486–507, 517
Pitot (stagnation) tube, 240–241, 298, 786
Pitot-static tube, 241
Plane surfaces, hydrostatic force
on,
formula method for, 80–85
geometrical method for, 86–90
integration method for, 91–93
plates with constant width, 87
resultant force on,
symmetrical plates, 82
Planform, 621
Plates, see Plane surfaces
Poiseuille flow, 489
Positive displacement flow
meter, 557
Potential flow, see Hydrodynamics
Potential function (f), 383–386, 432
Power,
axial-flow pumps, 810
capacity factor, 329
efficiency and, 265, 328–329
fluid momentum and, 328–329
propeller output of, 328
radial-flow pumps, 817
rate of work, 265, 299
shaft, 810
turbines, 825, 829
wind turbine output of, 329
Power law approximation, 504–505
Prandtl-Meyer expansion, 783, 869
Prandtl’s one-seventh power law, 594
Pressure,
absolute, 32, 58, 64–65, 150
average, 61
backpressure, 743–751
center of, 81–82
compressible flow and, 732, 743–751, 756,
764–765
compressible fluids, 69–71
critical, 744
dynamic, 239
effects on viscosity, 38
flow work and, 261
fluid flow around curved boundary, 239
fluid statics and, 61–79
friction effect on flow and, 756
gage, 64
heat transfer effects on flow
and, 764
incompressible fluids, 67–68
isentropic flow through nozzles, 743–751
Pascal’s law, 62, 150
stagnation, 239, 732, 764–765
standard atmospheric, 64–65
static, 66, 72–79, 150, 233, 239, 732
total, 239
variation of, 66–71
Pressure coefficient, 438
Pressure drag, 604–607
Pressure gradient effects, 604–608
adverse and favorable, 605
Coanda effect, 606
ideal flow around a cylinder, 605
real flow around a cylinder, 606–607
vortex shedding, 608
Pressure head, 68, 251
Pressure transducers, 76, 241
Prismatic channel, 656
Problem solving, 27–29
Propeller turbine, 828
Propellers, fluid momentum of, 326–329,
330, 357
Bernoulli equation for, 327
Froude’s theorem for, 327
linear momentum equation for, 326–327
power output and efficiency of, 328
Prototype, 451. See also Similitude
Pseudo-plastic fluids, 37
Pump head, 264, 818
Pump scaling laws, 839
Pumps, 261–263, 807, 808–823, 831–837, 855
axial-flow, 808–814, 855
cavitation and, 834–835, 855
flow system and selection of, 836–837
head-discharge curve, 819
head loss, 818–819
hydraulic efficiency, 819
ideal performance for, 818–823
manufacturer performance
curves, 833
net positive suction head (NPSH), Index
performance characteristics, 831–833
positive suction head and, 834–835
procedure for analysis of, 811
radial-flow, 815–817, 855
shaft work by, 261–263
Q
Quasi-steady flow, 263
R
Race cars, airfoil effects on, 627
Radial-flow machines, 807, 815–817, 819, 855
angular momentum and, 816
casing, flow through, 817
centrifugal pump, 815
continuity equation for, 816
flow kinematics, 815–816, 855
head-discharge curve, 819
power by, 817
Rankine oval, superposition of flow around,
400–401
Rapid flow, 658
Rayleigh flow, gas properties and, 865
Rayleigh line, 765, 804
Reaction turbine, 827–830
Relative roughness, 525
Reservoirs, fluid flow from, 238
Resistance (loss) coefficient, 535
Resistance in rough pipes, 521–534
critical zone, 526
Darcy friction factor for, 523
Darcy-Weisbach equation for, 524
empirical solutions for, 527–528
Hazen-Williams equation
for, 528
head loss, 522–524
laminar flow, 522–523, 526, 577
losses and, 522–523
Moody diagram for, 525–527
noncircular conduits, 528
procedure for analysis of, 529
transitional flow and, 526
turbulent flow, 523–524, 527, 577
Resultant acceleration, 176
Resultant force,
center of pressure, 81–82
centroid (C) of, 80, 86, 150
curved and inclined surfaces, 94–96, 151
formula method and, 80–82
geometrical method and, 86–87
horizontal component, 94–95, 151
hydrostatic forces,
integration method and, 91
liquid below plate, 96
location of, 81–82, 86–87, 91
parallel-axis theorem for, 81
parallel-plane theorem for, 82
plane surfaces, 80–82, 86–87, 91, 150
plates with constant width, 87
symmetrical plates, 82
vertical component, 95, 151
x
p coordinate location, 82
yp coordinate location, 81
Retarded nonuniform open-channel
flow, 656
Reynolds number (Re),
critical, 493
dimensional analysis using, 439, 473
drag coefficient and, 610–611
laminar flow in pipes determined using,
open-channel flow and, 674
procedure for analysis using, 494
Reynolds stress, 501
Reynolds transport theorem, 196–200, 229
applications of, 198–199
control volume and, 196–198, 229
extensive and intensive fluid
properties, 196
time rate of change and, 196–198, 229
Ring elements, rotation of liquid in, 112–113
Rise, open-channel flow over, 666–669
Rotation of differential fluid elements,
362, 431
Rotation of liquid, 112–115, 151
Rotational flow, 364–368
circulation, 364–365, 367, 432
ideal vs. viscous behavior, 366
vorticity, 365, 368, 432
Rotational viscometer, 39
Rotor blades, 828
Roughness, pipe walls, 525. See also
Resistance in rough pipes
Rounding off numbers, 25
S
Saturation, 43
Scale ratio, 452
Schlieren photography, 160
Secondary flow, 538
Section drag, 621
Series pipe systems, 548, 573
Shadowgraphs, 160
Shaft head, 265
Shaft power, 810
Shaft work, 261–263
Sharp-crested weir, 693–695
Shear strain (∆r), 36, 363
Shear stress (t), 36, 371, 499–502, 583–584
apparent, 500–501
fluid particle motion and, 371
laminar boundary layers, 583–584
laminar pipe flow with, 499
Reynolds stress, 501
skin friction coefficient for, 584
turbulent pipe flow with, 499–502
viscosity and, 36
viscous, 499
Shear velocity, 503
Shear work, 261
Shedder bar, 556
Ship motion, similitude for, 456–457
Shock diamonds, 772
Shock waves, 728, 768–780, 804, 866–868
continuity equation for, 768, 777
energy equation for, 769, 777–779
gas, relations with, 866–868
ideal gas law and, 769
linear momentum equation for, 768, 777
Mach number relationships and, 769–771
normal, 768–771, 866–868
nozzles with, 771–775
oblique, 776–780
sonic and supersonic flow and, 728
standing, 768
S.I. units (International System), 58
Similitude,
dimensional analysis and,
dynamic, 453
forces corresponding to, 458
geometric, 452
kinematic, 452
models and, 451, 456–457
open-channel flow, 455
prototypes and, 451
pump scaling laws for, 839
ship motion and, 456–457
specific speed, 840
steady pipe flow, 454
turbomachines, 838–843
Single pipeline flow, 541–547
Skin friction coefficient, 584
Slopes, open channels, 677, 681–684
Sluice gate, open-channel flow under,
Solids, characteristics of, 21
Sonic flow, 728
Sonic velocity, 724–726, 803
Space, fluid flow and, 156
Specific energy, 658–666, 711
critical depth for, 660–661
nonrectangular cross section channels, 661
rectangular cross section channels,
659–661908 Index
Specific energy diagram, 659
Specific gravity, 30, 58
Specific heat, 717–718
Specific speed, 840
Specific weight, 30, 58
Speed of sound, 724–726
Spheres, drag coefficient for, 611
Spinning balls, drag and lift effects on, 630
Split-scimitar winglets, 628
Stability, buoyancy and, 104–106, 151
Stable equilibrium, 104
Stagnation point, 157, 239
Stagnation properties,
compressible flow and, 731–737,
764–765, 803
density, 732, 764–765, 803
heat transfer effects on flow and, 764–765
pressure, 239, 732
temperature, 731–732, 764–765, 803
Stagnation tube, 240
Stall condition, 627
Standard atmospheric pressure, 64–65, 150
Standing shock waves, 768
Static pressure, 66, 72–79, 150, 233, 239, 732
Euler’s equation of motion and, 233
fluid flow around curved boundary, 239
measurement tools for, 72–79, 150
stagnant pressure vs., 732
variation, 66
Static temperature, 731
Stationary waves, 661
Stator blades, 828
Stator vanes, 808
Steady flow,
angular momentum equation for, 319
Euler’s equations of motion for, 233, 373
finite control volume and, 195, 229
horizontal flow of ideal fluid, 233
linear momentum equation for, 303
open channel, 656, 674–680
two-dimensional, 373
Streaklines, 159, 186
Stream function (c), 377–383, 432
hydrodynamics and, 377–383, 432
velocity components, 378
volumetric flow, 379
Streamline coordinates, 175–178, 187
Streamlines,
Bernoulli equation applied to, 235–236,
243, 298
equation of, 158
Euler’s equations applied to,
231–234, 298
ideal flow and, 235–236, 298
inviscid flow and, 231–234, 298
stagnation point in, 157
velocity fields as, 157, 186
Streamtubes, 158
Stress field, 371
Stresses, fluid particle motion
and, 371
Strouhal number (St), 556, 608
Subcritical flow, 658, 711
Subsonic flow, 727, 739, 786
Suction heads, 834–835
Sudden expansion and
contraction, 537
Supercritical flow, 658, 711
Superposition of flows,
396–408, 433
around a cylinder, 402–405
around a Rankine oval, 400–401
doublet, 398–399
fundamental equations for, 433
free-vortex flow, 404–405
past a half body, 396–397
uniform flow, 396–397, 400–405
Supersonic flow, 728, 739, 787
Surface force, 371
Surface profile for open-channel flow,
682–684, 712
Surface roughness, 525, 676
Surface tension (σ), 44–47, 59
adhesion and, 44, 46
capillarity, 46–47
cohesion and, 44, 46
liquid droplets, 45
nonwetting and wetting liquids, 46
Surfaces, see Curved surfaces; External surfaces; Inclined surfaces; Plane surfaces
Sutherland’s equation, 38
Swing check valve, 539
System approach to fluid flow, 161, 187
System energy, energy equation for, 260
T
Temperature,
absolute, 23, 32, 58
compressible flow and, 731–732, 756,
764–765
constant, 69
effects on viscosity, 38
friction effect on flow and, 756
heat transfer effects on flow
and, 764
ideal gas law and, 32
SI unit, 23
stagnation, 731–732, 764–765
static, 731
Theoretical discharge, 694
Thermal mass flow meter, 557
Thermodynamics, 715–723, 803
compressible flow, concepts for, 715–723
enthalpy and, 717
entropy and, 718–719, 803
first law of, 716, 803
ideal gas law, 716, 803
internal energy and, 716, 803
isentropic process, 720, 803
second law of, 718–719, 803
specific heat, 717–718
Three-dimensional flow, 155, 170
Time rate of change,
control volume and, 196–198, 229
convective and local change, 198, 229
Reynolds transport theorem and,
196–198, 229
velocity, 168–169, 187
Time, fluid flow and, 156, 157, 186
Torque, turbines and, 825, 829
Torricelli’s law, 238
Total head, 251
Total pressure, 239
Tranquil flow, 658
Transitional flow, 154, 526, 536, 577
Transitional flow region, 504
Translation of differential fluid
elements, 360–361, 431
Turbine efficiency, 829
Turbine flow meter, 556
Turbine head, 264
Turbines,
efficiency, 829
flow kinematics, 828
Francis, 827, 855
head loss, 829
impulse, 824–826
Kaplan, 827, 855
Pelton wheel, 824–826, 855
power by, 825, 829
propeller, 828
reaction, 827–830
shaft work by, 261–263
torque of, 825, 829
wind output, 329
Turbofan engine, fluid momentum and, 332
Turbojets, fluid momentum and, 332
Turbomachines, 807–855
axial-flow machines, 807, 808–814, 855
cavitation and, 834–835, 855
efficiency of, 819, 829, 833
flow systems for, 836–837
mixed-flow machines, 807
net positive suction head (NPSH),
Index
procedure for analysis of, 811
pumps, 807, 808–823, 831–837, 855
radial-flow machines, 807, 815–817, 855
similitude, 838–843
turbines, 807, 824–830, 855
Turbulent boundary layers,
boundary layer region, 577
disturbance thickness, 595
external surfaces, 577,
594–601, 651
flat plate analysis for combined layers,
fundamental equations for, 653
Prandtl’s one-seventh power law for, 594
viscous fluids, 577, 594–601
Turbulent flow, 154, 186, 497–507, 517,
523–524, 527, 573, 656
apparent shear stress, 500–501
Darcy-Weisbach equation for, 524, 573
fully developed flow from an entrance,
497–498
laminar viscous sublayer, 500
law of the wall, 503
mean steady flow, 500
Moody diagram for, 527
open channels, 656
power law approximation, 504–505
resistance in rough pipes, 523–524, 527, 573
shear stress in a smooth pipe, 499–502
shear velocity, 503
smooth pipes with, 502–507, 517
transitional flow region, 504
viscous fluids, 497–507, 517
viscous sublayer, 500, 503
Turbulent flow region, 504
Two-dimensional flow, 155, 370, 373,
387–395, 433
continuity equation for, 370
differential fluid flow, 370, 373,
387–395, 433
equipotential lines and, 389
Euler’s equations of motion for, 373
forced-vortex flow, 393
free-vortex flow, 392
fundamental equations for, 433
Laplace’s equation for, 387
line sink flow, 391
line source flow, 390–391
steady flow, 373
uniform flow, 388–389
U
U-tube manometer, 73
Ultrasonic flow meters, 558
Underexpanded flow, 772
Undulations, 661
Uniform flow, 156, 186, 388–389, 396–397,
400–405, 656, 674–680
around a cylinder, 402–405
around a Rankine oval, 400–401
open channel, 656, 674–680
past a half body, 396–397
superposition of, 396–397, 400–405
two-dimensional, 388–389
Uniform velocity, 191
Units, 22–24, 58
Unstable equilibrium, 104
Unsteady open-channel flow, 656
V
Valves, losses from, 539
Vapor pressure, 43, 59, 834
Vehicles, drag reduction for, 622–623
Velocity,
average, 191
flow classification and, 154–156
equation of the streamline
and, 158
finite control volume and, 195, 229
fluid systems, 161–167
heat transfer effects on flow and, 763–764
shear, 503
time rate change in, 168–169, 187
Velocity components of differential fluid
flow, 378, 383–384
Velocity field, 157, 162
Velocity gradient, 36
Velocity head, 251
Velocity kinematic diagrams, 810
Velocity profile,
average velocity, 191
flow classification using, 154–155
momentum integral equation
using, 591–592
nonuniform velocity, 266
paraboloid form, 487
volumetric flow from, 190–191
uniform velocity, 191
Vena contracta, 536, 693
Venturi discharge coefficient, 554
Venturi meter, 242, 554, 787
Viscosity, 34–42, 58–59
absolute, 36
apparent, 37
dynamic, 36
kinematic (n), 38, 59
measurement of, 39–42
Newtonian fluids, 37, 59
Newton’s law of, 35, 36
non-Newtonian fluids, 37
physical cause of, 35, 58
pressure and temperature effects, 38
shear stress and strain, 36
Viscous flow
boundary layers
drag and lift effects
drag coefficient for
drag reduction, 620–623
enclosed conduits and, 474–519
external surfaces and, 575–653
fully developed flow from an entrance,
irrotational vs. rotational, 366
laminar boundary layers,
laminar flow, 475–499, 519
momentum integral equation for, 590–593
Navier–Stokes solution for
pressure gradient effects, 604–608
procedures for analysis of, 482, 494
Reynolds number for, 492–496
shear stress in a smooth pipe, 499–502
steady laminar flow between parallel
plates, 475–485, 519
steady laminar flow in smooth pipes,
486–491
steady turbulent flow in smooth pipes,
502–507, 517
turbulent boundary layers, 577,
594–601, 652
turbulent flow, 497–507, 517
Viscous fluids, 237, 264, 299
Viscous shear stress, 499
Viscous sublayer, 500, 503, 577
Volume, 86, 162
Volumetric dilatation rate, 361
Volumetric flow, 190–191, 229, 379
Volute pump, 815
Von Kármán vortex street, 556, 608
Vortex flow, 112–113, 151, 392–393,
404–405, 817
forced-vortex (rotation), 112–113,
151, 393
free-vortex (circulation), 392,
404–405, 817
Vortex flow meter, 556
Vortex shedding, 608
Vortex trail, 628
Vorticity (z), 365, 368, 432
W
Water, physical properties
of, 857
Wave celerity, 657–658910 Index
Wave propagation, 724–726
Waves, 781–785. See also Shock waves
compression and expansion, 781
Mach wave fans, 781–786
Prandtl-Meyer expansion
function, 783
Weber number (We), 440, 473
Weirs, 693–697, 712
broad-crested, 696
discharge coefficient for, 694–695
rectangular openings, 694
sharp-crested, 693–695
triangular openings, 695
Wetted perimeter, 674
Wetting liquids, 46
Wind turbines, fluid momentum
of, 329
Wing vortex trail, 628
Work, 236, 261–269, 298
compressible flow, 265
conservation of energy, 262–263
energy equation and, 261–269, 298
flow work, 236, 261–263
incompressible flow,
263–264
power rate of, 265, 299
shaft work, 261–263
shear work, 261
Z
Zero absolute pressure, 64
Zero viscosity, 37


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