three-dimensional irrotational flows, 228-229 two-dimensional irrotational flows, 220-222 Units. abbreviations, 5832 conversion, 577-580r[r]
(1)I - :
THE INTERNATIONAL STUDENT EDlTlOlij
+JoJk !
W I? Graebel Professor Emeritus Dept of Mechanical Engineering
and Applied Mechanics The University of Michigan
(2)Published in 2001 by Taylor & Francis 29 West 35th Street New York, NY 10001
Published in Great Britain by Taylor & Francis 11 New Fetter Lane London EC4P 4EE
Copyright 2001 by Taylor & Francis
Printed in the United States of America on acid-free paper
All right reserved No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying and recording or in any information storage or retrieval system without permission in writing from the publisher
Library of Congress Cataloging-in-Publication Data Graebel, W P
Engineering fluid mechanics / by W.P Graebel.-International student ed p c m
Includes bibliographical references and index ISBN l-56032-733-2 (alk paper)
1 Fluid mechanics I Title
TA357.G692 2000
(3)Contents
Preface xiii 1 Introduction to Fluid Mechanics
Chapter Overview and Goals Introduction Definition of a Fluid The Continuum Hypothesis Systems of Units
a British gravitational system of units b.SIsystemofunits Stress and Pressure Fluid Properties a Mass and weight densities b Bulk modulus and coefficient of compressibility c Vapor pressure d Surface tension e No-slip condition f Absolute viscosity g Kinematic viscosity Non-Newtonian Fluids Problem -solving Approach Suggestions for Further Reading Problems for Chapter 2 Hydrostatics and Rigid-Body Motions
Chapter Overview and Goals The Hydrostatic Equation Manometers Rise of Liquids Due to Surface Tension Forces on Surfaces
a Plane surfaces b Forces on circular cylindrical surfaces c Buoyancy forces
d Stability of submerged and floating bodies 1
1 6 10 13 13 14 16 18 25 26 27 28 31 33 34 41 41 41 50 55 61 63 67 70 73
(4)v i c o n t e n t s
5 Rigid-Body Acceleration 78
6 Rigid-Body Rotation 80
Suggestions for Further Reading 83
Problems for Chapter 84
3 Fluid Dynamics . 109
Chapter Overview and Goals 109
1 Flow Properties and Characteristics 109
2 Acceleration and the Material Derivative 120
3 Control Volume and Control Surface Concepts 123
4 Conservation of Mass-the Continuity Equation 126
5 Newton’s Law-the Linear Momentum Equation 130
6 Balance of Energy Equation 133
7 The Entropy Inequality 137
8 Applications 138
a Applications for flow measurement 138
b Fans, propellers, windmills, and wind turbines 143
c Forces on vanes 148
d Miscellaneous applications 15 Unsteady Flows and Translating Control Volumes 156
a Unsteady flows 157
b Approximately unsteady flows 159
10 Conservation of Moment-of-Momentum and Rotating Control Volumes 163
a Moment-of-momentum equations for stationary control volumes 163
b Moment-of-momentum equations for rotating control volumes 163
11 Path Coordinates-the Euler and Bernoulli Equations 168
a Application-pitot tubes 170
Suggestions for Further Reading 17 Problems for Chapter 17 4 Differential Analysis 193
Chapter Overview and Goals 193
1 The Local Continuity Equation 193
2 The Stream Function 197
a Two-dimensional flows-Lagrange’s stream function 197
b Three-dimensional flows 20 Equations Governing Inviscid Flows 204
4 Vorticity and Circulation 209
5 Irrotational Flows and the Velocity Potential 15 a Intersection of velocity potential lines and streamlines 18 b Simple two-dimensional irrotational flows 19 c Hele-Shaw flows 227
d Simple three-dimensional irrotational flows 228
(5)Contents vii
6 Rates of Deformation Stress Constitutive Relations Equations for Newtonian Fluids 10 Boundary Conditions 11 Some Solutions to the Navier -Stokes Equations When Convective
Acceleration Is Absent a Stokes’ first problem-impulsive motion of a plate b Stokes’ second problem-oscillation of a plate Suggestions for Further Reading Problems for Chapter
240 243 246 250 251 253 253 256 259 260
5 Dimensional Analysis .
Chapter Overview and Goals Introduction Buckingham’s Pi Theorem Introductory Example Algebraic Approach for the Formulation of Dimensionless Parameters Interpretation of Dimensionless Parameters as Force Ratios Summary of Steps Involved in Forming Dimensionless Parameters Some Common Dimensionless Parameters Examples of the Use of Dimensionless Parameters Model Studies-Similitude 10 Experimental Facilities
a Froude number facilities b Mach number facilities c Cavitation number facilities
Suggestions for Further Reading Problems for Chapter
265 265 265 266 268 270 274 275 276 278 281 284 284 285 285 287 288 6 Laminar Viscous Flow 295
Chapter Overview and Goals Flow between Parallel Plates a Solid plates at both boundaries b Solid plate plus a free surface Lubrication Flow in a Circular Tube or Annulus
a Circular tube b Circular annulus Stability of Tube Flow Boundary Layer Theory Flow Separation
Suggestions for Further Reading Problems for Chapter
(6)Index 675 U
u See Specific internal energy
U.S standard atmosphere, properties, 592-593r Uniform flow description, 422
Uniform stream
three-dimensional irrotational flows, 228-229 two-dimensional irrotational flows, 220-222 Units
abbreviations, 5832 conversion, 577-580r
Universal gas constant, definition, 459 Unsteady drag, description, 381 Unsteady flow
description 110 open channels 418-420 problems, 186
V
Vacuum pressure, description, 12-13 Vanes
forces, 148-151 problems, 17% 180 Vapor pressure
description, 16 examples, 16- I8 problems, 37 saturation line, 16, 17f vaporization line 16, l?f
Vaporization line, description, 16, 17j Vectors, description, 11
Vehicle drag example, 386-387 formula, 385-386 Velocity
conversion factors, 58Of integration of measurements, 17 Velocity measuring devices
hot-wire and hot-film anemometers, 503-504 laser Doppler velocimeter, 504-507 pitot tubes, 501-503
Velocity potential calculation, 216
irrotational flows, 215-240 problems, 262-263
Velocity-to-discharge measurements, problem, 53 Vena contracta
definition, 141 description, 509
Venturi, Giovanni Battista, role in fluid mechan-ics, 617
Venturi meter
advantages and disadvantages, 508
design 507-508
measurement of flow, 138-140 operation, 508
problems, 176-177, 53 Vibrations study problem , 567-568 Vis viva, description, 613
Viscoelastic, description, 29 Viscoelastic fluids
description, straining, 248 Viscometry, problems, 530 Viscosity
concept, 26-27 conversion factors, 580r definition, 247 pressure effect, 27 problems, 38-39 temperature effect, 28 units, 27
Viscosity-measuring devices falling-body viscometer, 525
Oswald-Cannon-Fenske viscometer, 523,524f rotating cylinder viscometer, 522-523 Saybolt viscometer, 523
Viscous, associated quantities, 274 viscous flow
laminar See Laminar viscous flow turbulent See Turbulent viscous flow Viscous sublayer, description, 370 Volume, conversion factors, 580r Volume per unit mass, 13 Volume rate-measuring devices
Doppler-acoustic flow meter, 14 elbow meter, O -5 11
integration of velocity measurements, 17-5 18 magnetic flow meter, 15
nozzles, 509-510 orifice plate, 509
positive displacement meter, 51 l-512 rotameter, 12-5 13
turbine meter, 13 venturi meter, 507-508
vortex shedding flow meter, 14-5 15 weirs, 15-5 17
Volume/time, conversion factors, 580t Volume viscosity, description, 248
van Helmholtz, Hermann Ludwig Ferdinand, role in fluid mechanics, 620
von KArmBn, Theodore, role in fluid mechanics, 114-115,623
Vortex flow, particle position, 113 Vortex generators, description, 335-336 Vortex line, definition, 212
(7)676 I n d e x
Vortex motion circulation, 214 rate of deformation, 243 vorticity calculation, 211-212
Vortex near walls, superposition of irrotational flows, 231-235
Vortex shedding flow meter advantages and disadvantages, 514 design, 514-515
operation, 14
Vortex sheets, definition, 212 Vortex tubes, definition, 212 Vorticity
change, 214-215 circulation, 212-215 derivation, 209-212 description, 114
examples, 114-116,118-119f, 211-212 problems, 262-263
velocity component variations, 209 visualization, 114, 115-l 18f Vorticity equation, description, 25 Vorticity vector, definition, 211
W
Wake, description, 115
Walhs, John, role in fluid mechanics, 615 Water
physical properties, 590t sonic speed, 449 Water hammer
analysis, 455-457 description, 454 example, 458-459 occurrence, 454-455 pipe closed-ended, 457
pipe constrained from changing length, 457 pipe open-ended, 458
Water power, description, 538
Water tunnel, use for dimensional analysis, 285-287
Wave drag, description, 380
Wave motion, study problem , 568-569 Wave tank, use for dimensional analysis, 284 We See Weber number
Weak shock wave, description, 485 Weber number, description, 278 Weight density See Specific weight Weirs
advantages and disadvantages, 516-517 design, 515-516
operation, 515-517 problems, 532
Weissenberg effect, example of non-Newtonian fluid, 29
Welland Canal, role in history, 403 Whistling, use of vortices, 116 Wicket gates, description, 559
Wind-driven power generator, efficiency, 147-148 Wind musical instruments, use of vortices, 116 Wind tunnel , use for dimensional analysis, 285 Wind turbines
calculation of fluid dynamics, 144-148 use, 143-144
W i n d m i l l s
calculation of fluid dynamics, 144-148 use, 143-144
Wine tears, role of surface tension, 19,2Of Wing lift and drag, dimensionless parameters,
279-280
Wobble plate type positive displacement pump, description, 534,546
Work, conversion factors, 580r Work/mass, conversion factor, 580r
Wren, Christopher, role in fluid mechanics, 615 Wright, Wilbur, use of fluid mechanics,
Y Young, Thomas , research, 568
Z