1. F L U I D M E C H A N I C S FUNDAMENTALS AND APPLICATIONS
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2. McGRAW-HILL SERIES IN MECHANICAL ENGINEERING Alciatore and
Histand: Introduction to Mechatronics and Measurement Systems
Anderson: Computational Fluid Dynamics: The Basics with
Applications Anderson: Fundamentals of Aerodynamics Anderson:
Introduction to Flight Anderson: Modern Compressible Flow Barber:
Intermediate Mechanics of Materials Beer/Johnston: Vector Mechanics
for Engineers Beer/Johnston/DeWolf: Mechanics of Materials Borman
and Ragland: Combustion Engineering Budynas: Advanced Strength and
Applied Stress Analysis engel and Boles: Thermodynamics: An
Engineering Approach engel and Cimbala: Fluid Mechanics:
Fundamentals and Applications engel and Turner: Fundamentals of
Thermal-Fluid Sciences engel: Heat Transfer: A Practical Approach
Crespo da Silva: Intermediate Dynamics Dieter: Engineering Design:
A Materials & Processing Approach Dieter: Mechanical Metallurgy
Doebelin: Measurement Systems: Application & Design Dunn:
Measurement & Data Analysis for Engineering & Science EDS,
Inc.: I-DEAS Student Guide Hamrock/Jacobson/Schmid: Fundamentals of
Machine Elements Henkel and Pense: Structure and Properties of
Engineering Material Heywood: Internal Combustion Engine
Fundamentals Holman: Experimental Methods for Engineers Holman:
Heat Transfer Hsu: MEMS & Microsystems: Manufacture &
Design Hutton: Fundamentals of Finite Element Analysis
Kays/Crawford/Weigand: Convective Heat and Mass Transfer Kelly:
Fundamentals of Mechanical Vibrations Kreider/Rabl/Curtiss: The
Heating and Cooling of Buildings Mattingly: Elements of Gas Turbine
Propulsion Meirovitch: Fundamentals of Vibrations Norton: Design of
Machinery Palm: System Dynamics Reddy: An Introduction to Finite
Element Method Ribando: Heat Transfer Tools Schaffer et al.: The
Science and Design of Engineering Materials Schey: Introduction to
Manufacturing Processes Schlichting: Boundary-Layer Theory Shames:
Mechanics of Fluids Shigley/Mischke/Budynas: Mechanical Engineering
Design Smith: Foundations of Materials Science and Engineering
Stoecker: Design of Thermal Systems Suryanarayana and Arici: Design
and Simulation of Thermal Systems Turns: An Introduction to
Combustion: Concepts and Applications Ugural: Stresses in Plates
and Shells Ugural: Mechanical Design: An Integrated Approach
Ullman: The Mechanical Design Process Wark and Richards:
Thermodynamics White: Fluid Mechanics White: Viscous Fluid Flow
Zeid: Mastering CAD/CAM cen72367_fm.qxd 11/23/04 11:22 AM Page
ii
3. F L U I D M E C H A N I C S FUNDAMENTALS AND APPLICATIONS
YUNUS A. ENGEL Department of Mechanical Engineering University of
Nevada, Reno JOHN M. CIMBALA Department of Mechanical and Nuclear
Engineering The Pennsylvania State University cen72367_fm.qxd
11/23/04 11:22 AM Page iii
4. FLUID MECHANICS: FUNDAMENTALS AND APPLICATIONS Published by
McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc.,
1221 Avenue of the Americas, New York, NY 10020. Copyright 2006 by
The McGraw-Hill Companies, Inc. All rights reserved. No part of
this publication may be reproduced or distributed in any form or by
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prior written consent of The McGraw-Hill Companies, Inc.,
including, but not limited to, in any network or other electronic
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ancillaries, including electronic and print components, may not be
available to customers outside the United States. This book is
printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOW/DOW 0 9 8 7 6 5
4 ISBN 0072472367 Senior Sponsoring Editor: Suzanne Jeans Managing
Developmental Editor: Debra D. Matteson Developmental Editor: Kate
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Times Roman Printer: R. R. Donnelley Willard, OH Library of
Congress Cataloging-in-Publication Data engel, Yunus A. Fluid
mechanics : fundamentals and applications / Yunus A. engel, John M.
Cimbala.1st ed. p. cm.(McGraw-Hill series in mechanical
engineering) ISBN 0072472367 1. Fluid dynamics. I. Cimbala, John M.
II. Title. III. Series. TA357.C43 2006 620.1'06dc22 2004058767 CIP
www.mhhe.com cen72367_fm.qxd 11/23/04 11:22 AM Page iv
5. D e d i c a t i o n To all studentsIn hopes of enhancing
your desire and enthusiasm to explore the inner workings of our
marvelous universe, of which fluid mechanics is a small but
fascinating part; our hope is that this book enhances your love of
learning, not only about fluid mechanics, but about life.
cen72367_fm.qxd 11/23/04 11:22 AM Page v
6. Yunus A. engel is Professor Emeritus of Mechanical
Engineering at the University of Nevada, Reno. He received his B.S.
in mechanical engineer- ing from Istanbul Technical University and
his M.S. and Ph.D. in mechanical engineering from North Carolina
State University. His research areas are renewable energy,
desalination, exergy analysis, heat transfer enhancement, radiation
heat transfer, and energy conservation. He served as the director
of the Industrial Assessment Center (IAC) at the University of
Nevada, Reno, from 1996 to 2000. He has led teams of engineering
students to numerous manufacturing facilities in Northern Nevada
and California to do industrial assessments, and has prepared
energy conservation, waste minimization, and productivity
enhancement reports for them. Dr. engel is the coauthor of the
widely adopted textbook Thermodynam- ics: An Engineering Approach,
4th edition (2002), published by McGraw-Hill. He is also the author
of the textbook Heat Transfer: A Practical Approach, 2nd edition
(2003), and the coauthor of the textbook Fundamentals of Thermal-
Fluid Sciences, 2nd edition (2005), both published by McGraw-Hill.
Some of his textbooks have been translated to Chinese, Japanese,
Korean, Spanish, Turkish, Italian, and Greek. Dr. engel is the
recipient of several outstanding teacher awards, and he has
received the ASEE Meriam/Wiley Distinguished Author Award for
excel- lence in authorship in 1992 and again in 2000. Dr. engel is
a registered Professional Engineer in the State of Nevada, and is a
member of the American Society of Mechanical Engineers (ASME) and
the American Society for Engineering Education (ASEE). John M.
Cimbala is Professor of Mechanical Engineering at The Penn-
sylvania State Univesity, University Park. He received his B.S. in
Aerospace Engineering from Penn State and his M.S. in Aeronautics
from the California Institute of Technology (CalTech). He received
his Ph.D. in Aeronautics from CalTech in 1984 under the supervision
of Professor Anatol Roshko, to whom he will be forever grateful.
His research areas include experimental and com- putational fluid
mechanics and heat transfer, turbulence, turbulence modeling,
turbomachinery, indoor air quality, and air pollution control.
During the aca- demic year 199394, Professor Cimbala took a
sabbatical leave from the Uni- versity and worked at NASA Langley
Research Center, where he advanced his knowledge of computational
fluid dynamics (CFD) and turbulence modeling. Dr. Cimbala is the
coauthor of the textbook Indoor Air Quality Engineer- ing:
Environmental Health and Control of Indoor Pollutants (2003),
published by Marcel-Dekker, Inc. He has also contributed to parts
of other books, and is the author or co-author of dozens of journal
and conference papers. More information can be found at
www.mne.psu.edu/cimbala. Professor Cimbala is the recipient of
several outstanding teaching awards and views his book writing as
an extension of his love of teaching. He is a member of the
American Institute of Aeronautics and Astronautics (AIAA), the
American Society of Mechanical Engineers (ASME), the American
Society for Engineering Education (ASEE), and the American Physical
Society (APS). A B O U T T H E A U T H O R S cen72367_fm.qxd
11/23/04 11:22 AM Page vi
7. B R I E F C O N T E N T S C H A P T E R O N E INTRODUCTION
AND BASIC CONCEPTS 1 C H A P T E R T W O PROPERTIES OF FLUIDS 35 C
H A P T E R T H R E E PRESSURE AND FLUID STATICS 65 C H A P T E R F
O U R FLUID KINEMATICS 121 C H A P T E R F I V E MASS, BERNOULLI,
AND ENERGY EQUATIONS 171 C H A P T E R S I X MOMENTUM ANALYSIS OF
FLOW SYSTEMS 227 C H A P T E R S E V E N DIMENSIONAL ANALYSIS AND
MODELING 269 C H A P T E R E I G H T FLOW IN PIPES 321 C H A P T E
R N I N E DIFFERENTIAL ANALYSIS OF FLUID FLOW 399 C H A P T E R T E
N APPROXIMATE SOLUTIONS OF THE NAVIERSTOKES EQUATION 471 C H A P T
E R E L E V E N FLOW OVER BODIES: DRAG AND LIFT 561 C H A P T E R T
W E L V E COMPRESSIBLE FLOW 611 C H A P T E R T H I R T E E N
OPEN-CHANNEL FLOW 679 C H A P T E R F O U R T E E N TURBOMACHINERY
735 C H A P T E R F I F T E E N INTRODUCTION TO COMPUTATIONAL FLUID
DYNAMICS 817 cen72367_fm.qxd 11/23/04 11:22 AM Page vii
8. Preface xv C H A P T E R O N E INTRODUCTION AND BASIC
CONCEPTS 1 11 Introduction 2 What Is a Fluid? 2 Application Areas
of Fluid Mechanics 4 12 The No-Slip Condition 6 13 A Brief History
of Fluid Mechanics 7 14 Classification of Fluid Flows 9 Viscous
versus Inviscid Regions of Flow 9 Internal versus External Flow 10
Compressible versus Incompressible Flow 10 Laminar versus Turbulent
Flow 11 Natural (or Unforced) versus Forced Flow 11 Steady versus
Unsteady Flow 11 One-, Two-, and Three-Dimensional Flows 12 15
System and Control Volume 14 16 Importance of Dimensions and Units
15 Some SI and English Units 16 Dimensional Homogeneity 18 Unity
Conversion Ratios 20 17 Mathematical Modeling of Engineering
Problems 21 Modeling in Engineering 21 18 Problem-Solving Technique
22 Step 1: Problem Statement 22 Step 2: Schematic 23 Step 3:
Assumptions and Approximations 23 Step 4: Physical Laws 23 Step 5:
Properties 23 Step 6: Calculations 23 Step 7: Reasoning,
Verification, and Discussion 23 19 Engineering Software Packages 24
Engineering Equation Solver (EES) 25 FLUENT 26 110 Accuracy,
Precision, and Significant Digits 26 Application Spotlight: What
Nuclear Blasts and Raindrops Have in Common 31 Summary 30
References and Suggested Reading 30 Problems 32 C H A P T E R T W O
PROPERTIES OF FLUIDS 35 21 Introduction 36 Continuum 36 22 Density
and Specific Gravity 37 Density of Ideal Gases 38 23 Vapor Pressure
and Cavitation 39 24 Energy and Specific Heats 41 25 Coefficient of
Compressibility 42 Coefficient of Volume Expansion 44 26 Viscosity
46 27 Surface Tension and Capillary Effect 51 Capillary Effect 53
Summary 55 References and Suggested Reading 56 Application
Spotlight: Cavitation 57 Problems 58 C H A P T E R T H R E E
PRESSURE AND FLUID STATICS 65 31 Pressure 66 Pressure at a Point 67
Variation of Pressure with Depth 68 32 The Manometer 71 Other
Pressure Measurement Devices 74 33 The Barometer and Atmospheric
Pressure 75 34 Introduction to Fluid Statics 78 C O N T E N T S
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9. CONTENTS ix 35 Hydrostatic Forces on Submerged Plane
Surfaces 79 Special Case: Submerged Rectangular Plate 82 36
Hydrostatic Forces on Submerged Curved Surfaces 85 37 Buoyancy and
Stability 89 Stability of Immersed and Floating Bodies 92 38 Fluids
in Rigid-Body Motion 95 Special Case 1: Fluids at Rest 96 Special
Case 2: Free Fall of a Fluid Body 97 Acceleration on a Straight
Path 97 Rotation in a Cylindrical Container 99 Summary 102
References and Suggested Reading 103 Problems 103 C H A P T E R F O
U R FLUID KINEMATICS 121 41 Lagrangian and Eulerian Descriptions
122 Acceleration Field 124 Material Derivative 127 42 Fundamentals
of Flow Visualization 129 Streamlines and Streamtubes 129 Pathlines
130 Streaklines 132 Timelines 134 Refractive Flow Visualization
Techniques 135 Surface Flow Visualization Techniques 136 43 Plots
of Fluid Flow Data 136 Profile Plots 137 Vector Plots 137 Contour
Plots 138 44 Other Kinematic Descriptions 139 Types of Motion or
Deformation of Fluid Elements 139 Vorticity and Rotationality 144
Comparison of Two Circular Flows 147 45 The Reynolds Transport
Theorem 148 Alternate Derivation of the Reynolds Transport Theorem
153 Relationship between Material Derivative and RTT 155
Application Spotlight: Fluidic Actuators 157 Summary 156 References
and Suggested Reading 158 Problems 158 C H A P T E R F I V E MASS,
BERNOULLI, AND ENERGY EQUATIONS 171 51 Introduction 172
Conservation of Mass 172 Conservation of Momentum 172 Conservation
of Energy 172 52 Conservation of Mass 173 Mass and Volume Flow
Rates 173 Conservation of Mass Principle 175 Moving or Deforming
Control Volumes 177 Mass Balance for Steady-Flow Processes 177
Special Case: Incompressible Flow 178 53 Mechanical Energy and
Efficiency 180 54 The Bernoulli Equation 185 Acceleration of a
Fluid Particle 186 Derivation of the Bernoulli Equation 186 Force
Balance across Streamlines 188 Unsteady, Compressible Flow 189
Static, Dynamic, and Stagnation Pressures 189 Limitations on the
Use of the Bernoulli Equation 190 Hydraulic Grade Line (HGL) and
Energy Grade Line (EGL) 192 55 Applications of the Bernoulli
Equation 194 56 General Energy Equation 201 Energy Transfer by
Heat, Q 202 Energy Transfer by Work, W 202 57 Energy Analysis of
Steady Flows 206 Special Case: Incompressible Flow with No
Mechanical Work Devices and Negligible Friction 208 Kinetic Energy
Correction Factor, a 208 Summary 215 References and Suggested
Reading 216 Problems 216 C H A P T E R S I X MOMENTUM ANALYSIS OF
FLOW SYSTEMS 227 61 Newtons Laws and Conservation of Momentum 228
62 Choosing a Control Volume 229 63 Forces Acting on a Control
Volume 230 cen72367_fm.qxd 11/23/04 11:22 AM Page ix
10. 64 The Linear Momentum Equation 233 Special Cases 235
Momentum-Flux Correction Factor, b 235 Steady Flow 238 Steady Flow
with One Inlet and One Outlet 238 Flow with No External Forces 238
65 Review of Rotational Motion and Angular Momentum 248 66 The
Angular Momentum Equation 250 Special Cases 252 Flow with No
External Moments 253 Radial-Flow Devices 254 Summary 259 References
and Suggested Reading 259 Problems 260 C H A P T E R S E V E N
DIMENSIONAL ANALYSIS AND MODELING 269 71 Dimensions and Units 270
72 Dimensional Homogeneity 271 Nondimensionalization of Equations
272 73 Dimensional Analysis and Similarity 277 74 The Method of
Repeating Variables and the Buckingham Pi Theorem 281 Historical
Spotlight: Persons Honored by Nondimensional Parameters 289 75
Experimental Testing and Incomplete Similarity 297 Setup of an
Experiment and Correlation of Experimental Data 297 Incomplete
Similarity 298 Wind Tunnel Testing 298 Flows with Free Surfaces 301
Application Spotlight: How a Fly Flies 304 Summary 305 References
and Suggested Reading 305 Problems 305 C H A P T E R E I G H T FLOW
IN PIPES 321 81 Introduction 322 82 Laminar and Turbulent Flows 323
Reynolds Number 324 83 The Entrance Region 325 Entry Lengths 326 84
Laminar Flow in Pipes 327 Pressure Drop and Head Loss 329 Inclined
Pipes 331 Laminar Flow in Noncircular Pipes 332 85 Turbulent Flow
in Pipes 335 Turbulent Shear Stress 336 Turbulent Velocity Profile
338 The Moody Chart 340 Types of Fluid Flow Problems 343 86 Minor
Losses 347 87 Piping Networks and Pump Selection 354 Piping Systems
with Pumps and Turbines 356 88 Flow Rate and Velocity Measurement
364 Pitot and Pitot-Static Probes 365 Obstruction Flowmeters:
Orifice, Venturi, and Nozzle Meters 366 Positive Displacement
Flowmeters 369 Turbine Flowmeters 370 Variable-Area Flowmeters
(Rotameters) 372 Ultrasonic Flowmeters 373 Electromagnetic
Flowmeters 375 Vortex Flowmeters 376 Thermal (Hot-Wire and
Hot-Film) Anemometers 377 Laser Doppler Velocimetry 378 Particle
Image Velocimetry 380 Application Spotlight: How Orifice Plate
Flowmeters Work, or Do Not Work 383 Summary 384 References and
Suggested Reading 385 Problems 386 C H A P T E R N I N E
DIFFERENTIAL ANALYSIS OF FLUID FLOW 399 91 Introduction 400 92
Conservation of MassThe Continuity Equation 400 Derivation Using
the Divergence Theorem 401 Derivation Using an Infinitesimal
Control Volume 402 Alternative Form of the Continuity Equation 405
Continuity Equation in Cylindrical Coordinates 406 Special Cases of
the Continuity Equation 406 93 The Stream Function 412 The Stream
Function in Cartesian Coordinates 412 The Stream Function in
Cylindrical Coordinates 419 The Compressible Stream Function 420 x
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11. 94 Conservation of Linear MomentumCauchys Equation 421
Derivation Using the Divergence Theorem 421 Derivation Using an
Infinitesimal Control Volume 422 Alternative Form of Cauchys
Equation 425 Derivation Using Newtons Second Law 425 95 The
NavierStokes Equation 426 Introduction 426 Newtonian versus
Non-Newtonian Fluids 427 Derivation of the NavierStokes Equation
for Incompressible, Isothermal Flow 428 Continuity and NavierStokes
Equations in Cartesian Coordinates 430 Continuity and NavierStokes
Equations in Cylindrical Coordinates 431 96 Differential Analysis
of Fluid Flow Problems 432 Calculation of the Pressure Field for a
Known Velocity Field 432 Exact Solutions of the Continuity and
NavierStokes Equations 437 Summary 455 References and Suggested
Reading 456 Problems 456 C H A P T E R T E N APPROXIMATE SOLUTIONS
OF THE NAVIERSTOKES EQUATION 471 101 Introduction 472 102
Nondimensionalized Equations of Motion 473 103 The Creeping Flow
Approximation 476 Drag on a Sphere in Creeping Flow 479 104
Approximation for Inviscid Regions of Flow 481 Derivation of the
Bernoulli Equation in Inviscid Regions of Flow 482 105 The
Irrotational Flow Approximation 485 Continuity Equation 485
Momentum Equation 487 Derivation of the Bernoulli Equation in
Irrotational Regions of Flow 487 Two-Dimensional Irrotational
Regions of Flow 490 Superposition in Irrotational Regions of Flow
494 Elementary Planar Irrotational Flows 494 Irrotational Flows
Formed by Superposition 501 CONTENTS xi 106 The Boundary Layer
Approximation 510 The Boundary Layer Equations 515 The Boundary
Layer Procedure 520 Displacement Thickness 524 Momentum Thickness
527 Turbulent Flat Plate Boundary Layer 528 Boundary Layers with
Pressure Gradients 534 The Momentum Integral Technique for Boundary
Layers 539 Application Spotlight: Droplet Formation 549 Summary 547
References and Suggested Reading 548 Problems 550 C H A P T E R E L
E V E N FLOW OVER BODIES: DRAG AND LIFT 561 111 Introduction 562
112 Drag and Lift 563 113 Friction and Pressure Drag 567 Reducing
Drag by Streamlining 568 Flow Separation 569 114 Drag Coefficients
of Common Geometries 571 Biological Systems and Drag 572 Drag
Coefficients of Vehicles 574 Superposition 577 115 Parallel Flow
over Flat Plates 579 Friction Coefficient 580 116 Flow over
Cylinders and Spheres 583 Effect of Surface Roughness 586 117 Lift
587 End Effects of Wing Tips 591 Lift Generated by Spinning 594
Application Spotlight: Drag Reduction 600 Summary 598 References
and Suggested Reading 599 Problems 601 C H A P T E R T W E L V E
COMPRESSIBLE FLOW 611 121 Stagnation Properties 612 122 Speed of
Sound and Mach Number 615 123 One-Dimensional Isentropic Flow 617
Variation of Fluid Velocity with Flow Area 620 Property Relations
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12. 124 Isentropic Flow through Nozzles 624 Converging Nozzles
625 ConvergingDiverging Nozzles 629 125 Shock Waves and Expansion
Waves 633 Normal Shocks 633 Oblique Shocks 640 PrandtlMeyer
Expansion Waves 644 126 Duct Flow with Heat Transfer and Negligible
Friction (Rayleigh Flow) 648 Property Relations for Rayleigh Flow
654 Choked Rayleigh Flow 655 127 Adiabatic Duct Flow with Friction
(Fanno Flow) 657 Property Relations for Fanno Flow 660 Choked Fanno
Flow 663 Application Spotlight: Shock-Wave/ Boundary-Layer
Interactions 667 Summary 668 References and Suggested Reading 669
Problems 669 C H A P T E R T H I R T E E N OPEN-CHANNEL FLOW 679
131 Classification of Open-Channel Flows 680 Uniform and Varied
Flows 680 Laminar and Turbulent Flows in Channels 681 132 Froude
Number and Wave Speed 683 Speed of Surface Waves 685 133 Specific
Energy 687 134 Continuity and Energy Equations 690 135 Uniform Flow
in Channels 691 Critical Uniform Flow 693 Superposition Method for
Nonuniform Perimeters 693 136 Best Hydraulic Cross Sections 697
Rectangular Channels 699 Trapezoidal Channels 699 137 Gradually
Varied Flow 701 Liquid Surface Profiles in Open Channels, y(x) 703
Some Representative Surface Profiles 706 Numerical Solution of
Surface Profile 708 138 Rapidly Varied Flow and Hydraulic Jump 709
139 Flow Control and Measurement 714 Underflow Gates 714 Overflow
Gates 716 Summary 723 References and Suggested Reading 724 Problems
725 C H A P T E R F O U R T E E N TURBOMACHINERY 735 141
Classifications and Terminology 736 142 Pumps 738 Pump Performance
Curves and Matching a Pump to a Piping System 739 Pump Cavitation
and Net Positive Suction Head 745 Pumps in Series and Parallel 748
Positive-Displacement Pumps 751 Dynamic Pumps 754 Centrifugal Pumps
754 Axial Pumps 764 143 Pump Scaling Laws 773 Dimensional Analysis
773 Pump Specific Speed 775 Affinity Laws 777 144 Turbines 781
Positive-Displacement Turbines 782 Dynamic Turbines 782 Impulse
Turbines 783 Reaction Turbines 785 145 Turbine Scaling Laws 795
Dimensionless Turbine Parameters 795 Turbine Specific Speed 797 Gas
and Steam Turbines 800 Application Spotlight: Rotary Fuel Atomizers
802 Summary 803 References and Suggested Reading 803 Problems 804 C
H A P T E R F I F T E E N INTRODUCTION TO COMPUTATIONAL FLUID
DYNAMICS 817 151 Introduction and Fundamentals 818 Motivation 818
Equations of Motion 818 Solution Procedure 819 Additional Equations
of Motion 821 Grid Generation and Grid Independence 821 Boundary
Conditions 826 Practice Makes Perfect 830 xii FLUID MECHANICS
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13. 152 Laminar CFD Calculations 831 Pipe Flow Entrance Region
at Re 500 831 Flow around a Circular Cylinder at Re 150 833 153
Turbulent CFD Calculations 840 Flow around a Circular Cylinder at
Re 10,000 843 Flow around a Circular Cylinder at Re 107 844 Design
of the Stator for a Vane-Axial Flow Fan 845 154 CFD with Heat
Transfer 853 Temperature Rise through a Cross-Flow Heat Exchanger
853 Cooling of an Array of Integrated Circuit Chips 855 155
Compressible Flow CFD Calculations 860 Compressible Flow through a
ConvergingDiverging Nozzle 861 Oblique Shocks over a Wedge 865 156
Open-Channel Flow CFD Calculations 866 Flow over a Bump on the
Bottom of a Channel 867 Flow through a Sluice Gate (Hydraulic Jump)
868 Application Spotlight: A Virtual Stomach 869 Summary 870
References and Suggested Reading 870 Problems 871 A P P E N D I X 1
PROPERTY TABLES AND CHARTS (SI UNITS) 885 TABLE A1 Molar Mass, Gas
Constant, and Ideal-Gas Specfic Heats of Some Substances 886 TABLE
A2 Boiling and Freezing Point Properties 887 TABLE A3 Properties of
Saturated Water 888 TABLE A4 Properties of Saturated
Refrigerant-134a 889 TABLE A5 Properties of Saturated Ammonia 890
TABLE A6 Properties of Saturated Propane 891 TABLE A7 Properties of
Liquids 892 TABLE A8 Properties of Liquid Metals 893 TABLE A9
Properties of Air at 1 atm Pressure 894 TABLE A10 Properties of
Gases at 1 atm Pressure 895 CONTENTS xiii TABLE A11 Properties of
the Atmosphere at High Altitude 897 FIGURE A12 The Moody Chart for
the Friction Factor for Fully Developed Flow in Circular Pipes 898
TABLE A13 One-dimensional isentropic compressible flow functions
for an ideal gas with k 1.4 899 TABLE A14 One-dimensional normal
shock functions for an ideal gas with k 1.4 900 TABLE A15 Rayleigh
flow functions for an ideal gas with k 1.4 901 TABLE A16 Fanno flow
functions for an ideal gas with k 1.4 902 A P P E N D I X 2
PROPERTY TABLES AND CHARTS (ENGLISH UNITS) 903 TABLE A1E Molar
Mass, Gas Constant, and Ideal-Gas Specific Heats of Some Substances
904 TABLE A2E Boiling and Freezing Point Properties 905 TABLE A3E
Properties of Saturated Water 906 TABLE A4E Properties of Saturated
Refrigerant-134a 907 TABLE A5E Properties of Saturated Ammonia 908
TABLE A6E Properties of Saturated Propane 909 TABLE A7E Properties
of Liquids 910 TABLE A8E Properties of Liquid Metals 911 TABLE A9E
Properties of Air at 1 atm Pressure 912 TABLE A10E Properties of
Gases at 1 atm Pressure 913 TABLE A11E Properties of the Atmosphere
at High Altitude 915 Glossary 917 Index 931 cen72367_fm.qxd
11/23/04 12:13 PM Page xiii
14. cen72367_fm.qxd 11/23/04 11:22 AM Page xiv
15. B A C K G R O U N D Fluid mechanics is an exciting and
fascinating subject with unlimited practi- cal applications ranging
from microscopic biological systems to automobiles, airplanes, and
spacecraft propulsion.Yet fluid mechanics has historically been one
of the most challenging subjects for undergraduate students. Unlike
ear- lier freshman- and sophomore-level subjects such as physics,
chemistry, and engineering mechanics, where students often learn
equations and then plug and chug on their calculators, proper
analysis of a problem in fluid mechan- ics requires much more.
Oftentimes, students must first assess the problem, make and
justify assumptions and/or approximations, apply the relevant phys-
ical laws in their proper forms, and solve the resulting equations
before ever plugging any numbers into their calculators. Many
problems in fluid mechan- ics require more than just knowledge of
the subject, but also physical intuition and experience. Our hope
is that this book, through its careful explanations of concepts and
its use of numerous practical examples, sketches, figures, and
photographs, bridges the gap between knowledge and proper
application of that knowledge. Fluid mechanics is a mature subject;
the basic equations and approxima- tions are well established and
can be found in numerous introductory fluid mechanics books. The
books are distinguished from one another in the way the material is
presented. An accessible fluid mechanics book should present the
material in a progressive order from simple to more difficult,
building each chapter upon foundations laid down in previous
chapters. In this way, even the traditionally challenging aspects
of fluid mechanics can be learned effectively. Fluid mechanics is
by its very nature a highly visual subject, and students learn more
readily by visual stimulation. It is therefore imperative that a
good fluid mechanics book also provide quality figures,
photographs, and visual aids that help to explain the significance
and meaning of the mathematical expressions. O B J E C T I V E S
This book is intended for use as a textbook in the first fluid
mechanics course for undergraduate engineering students in their
junior or senior year. Students are assumed to have an adequate
background in calculus, physics, engineering mechanics, and
thermodynamics. The objectives of this text are To cover the basic
principles and equations of fluid mechanics To present numerous and
diverse real-world engineering examples to give students a feel for
how fluid mechanics is applied in engineering practice To develop
an intuitive understanding of fluid mechanics by emphasiz- ing the
physics, and by supplying attractive figures and visual aids to
reinforce the physics P R E F A C E cen72367_fm.qxd 11/23/04 11:22
AM Page xv
16. The text contains sufficient material to give instructors
flexibility as to which topics to emphasize. For example,
aeronautics and aerospace engineer- ing instructors may emphasize
potential flow, drag and lift, compressible flow, turbomachinery,
and CFD, while mechanical and civil engineering instructors may
choose to emphasize pipe flows and open-channel flows,
respectively. The book has been written with enough breadth of
coverage that it can be used for a two-course sequence in fluid
mechanics if desired. P H I L O S O P H Y A N D G O A L We have
adopted the same philosophy as that of the texts Thermodynamics: An
Engineering Approach by Y. A. engel and M. A. Boles, Heat Transfer:
A Practical Approach byY. A. engel, and Fundamentals of
Thermal-Fluid Sci- ences by Y. A. engel and R. H. Turner, all
published by McGraw-Hill. Namely, our goal is to offer an
engineering textbook that Communicates directly to the minds of
tomorrows engineers in a sim- ple yet precise manner Leads students
toward a clear understanding and firm grasp of the basic principles
of fluid mechanics Encourages creative thinking and development of
a deeper understand- ing and intuitive feel for fluid mechanics Is
read by students with interest and enthusiasm rather than merely as
an aid to solve problems It is our philosophy that the best way to
learn is by practice. Therefore, spe- cial effort is made
throughout the book to reinforce material that was pre- sented
earlier (both earlier in the chapter and in previous chapters). For
example, many of the illustrated example problems and
end-of-chapter prob- lems are comprehensive, forcing the student to
review concepts learned in pre- vious chapters. Throughout the
book, we show examples generated by computational fluid dynamics
(CFD), and we provide an introductory chapter on CFD. Our goal is
not to teach details about numerical algorithms associated with
CFDthis is more properly presented in a separate course, typically
at the graduate level. Rather, it is our intent to introduce
undergraduate students to the capabilities and limitations of CFD
as an engineering tool. We use CFD solutions in much the same way
as we use experimental results from a wind tunnel test, i.e., to
reinforce understanding of the physics of fluid flows and to
provide quality flow visualizations that help to explain fluid
behavior. C O N T E N T A N D O R G A N I Z AT I O N This book is
organized into 15 chapters beginning with fundamental concepts of
fluids and fluid flows and ending with an introduction to
computational fluid dynamics, the application of which is rapidly
becoming more common- place, even at the undergraduate level.
Chapter 1 provides a basic introduction to fluids, classifications
of fluid flow, control volume versus system formulations,
dimensions, units, sig- nificant digits, and problem-solving
techniques. xvi FLUID MECHANICS cen72367_fm.qxd 11/23/04 11:22 AM
Page xvi
17. Chapter 2 is devoted to fluid properties such as density,
vapor pressure, specific heats, viscosity, and surface tension.
Chapter 3 deals with fluid statics and pressure, including
manometers and barometers, hydrostatic forces on submerged
surfaces, buoyancy and stability, and fluids in rigid-body motion.
Chapter 4 covers topics related to fluid kinematics, such as the
differ- ences between Lagrangian and Eulerian descriptions of fluid
flows, flow patterns, flow visualization, vorticity and
rotationality, and the Reynolds transport theorem. Chapter 5
introduces the fundamental conservation laws of mass, momentum, and
energy, with emphasis on the proper use of the mass, Bernoulli, and
energy equations and the engineering applications of these
equations. Chapter 6 applies the Reynolds transport theorem to
linear momentum and angular momentum and emphasizes practical
engineering applica- tions of the finite control volume momentum
analysis. Chapter 7 reinforces the concept of dimensional
homogeneity and intro- duces the Buckingham Pi theorem of
dimensional analysis, dynamic similarity, and the method of
repeating variablesmaterial that is useful throughout the rest of
the book and in many disciplines in science and engineering.
Chapter 8 is devoted to flow in pipes and ducts. We discuss the
differ- ences between laminar and turbulent flow, friction losses
in pipes and ducts, and minor losses in piping networks. We also
explain how to properly select a pump or fan to match a piping
network. Finally, we dis- cuss various experimental devices that
are used to measure flow rate and velocity. Chapter 9 deals with
differential analysis of fluid flow and includes derivation and
application of the continuity equation, the Cauchy equa- tion, and
the NavierStokes equation. We also introduce the stream function
and describe its usefulness in analysis of fluid flows. Chapter 10
discusses several approximations of the NavierStokes equa- tions
and provides example solutions for each approximation, including
creeping flow, inviscid flow, irrotational (potential) flow, and
boundary layers. Chapter 11 covers forces on bodies (drag and
lift), explaining the dis- tinction between friction and pressure
drag, and providing drag coeffi- cients for many common geometries.
This chapter emphasizes the practical application of wind tunnel
measurements coupled with dynamic similarity and dimensional
analysis concepts introduced earlier in Chapter 7. Chapter 12
extends fluid flow analysis to compressible flow, where the
behavior of gases is greatly affected by the Mach number, and the
con- cepts of expansion waves, normal and oblique shock waves, and
choked flow are introduced. Chapter 13 deals with open-channel flow
and some of the unique fea- tures associated with the flow of
liquids with a free surface, such as sur- face waves and hydraulic
jumps. PREFACE xvii cen72367_fm.qxd 11/23/04 11:22 AM Page
xvii
18. Chapter 14 examines turbomachinery in more detail,
including pumps, fans, and turbines. An emphasis is placed on how
pumps and turbines work, rather than on their detailed design. We
also discuss overall pump and turbine design, based on dynamic
similarity laws and simplified velocity vector analyses. Chapter 15
describes the fundamental concepts of computational fluid dynamics
(CFD) and shows students how to use commercial CFD codes as a tool
to solve complex fluid mechanics problems. We emphasize the
application of CFD rather than the algorithms used in CFD codes.
Each chapter contains a large number of end-of-chapter homework
prob- lems suitable for use by instructors. Most of the problems
that involve calcu- lations are in SI units, but approximately 20
percent are written in English units. Finally, a comprehensive set
of appendices is provided, giving the ther- modynamic and fluid
properties of several materials, not just air and water as in most
introductory fluids texts. Many of the end-of-chapter problems
require use of the properties found in these appendices. L E A R N
I N G T O O L S EMPHASIS ON PHYSICS A distinctive feature of this
book is its emphasis on the physical aspects of the subject matter
in addition to mathematical representations and manipulations. The
authors believe that the emphasis in undergraduate education should
remain on developing a sense of underlying physical mechanisms and
a mas- tery of solving practical problems that an engineer is
likely to face in the real world. Developing an intuitive
understanding should also make the course a more motivating and
worthwhile experience for the students. EFFECTIVE USE OF
ASSOCIATION An observant mind should have no difficulty
understanding engineering sci- ences. After all, the principles of
engineering sciences are based on our every- day experiences and
experimental observations. Therefore, a physical, intuitive
approach is used throughout this text. Frequently, parallels are
drawn between the subject matter and students everyday experiences
so that they can relate the subject matter to what they already
know. SELF-INSTRUCTING The material in the text is introduced at a
level that an average student can fol- low comfortably. It speaks
to students, not over students. In fact, it is self- instructive.
Noting that the principles of science are based on experimental
observations, most of the derivations in this text are largely
based on physical arguments, and thus they are easy to follow and
understand. EXTENSIVE USE OF ARTWORK Figures are important learning
tools that help the students get the picture, and the text makes
effective use of graphics. It contains more figures and illus-
trations than any other book in this category. Figures attract
attention and stimulate curiosity and interest. Most of the figures
in this text are intended to serve as a means of emphasizing some
key concepts that would otherwise go unnoticed; some serve as page
summaries. xviii FLUID MECHANICS cen72367_fm.qxd 11/23/04 11:22 AM
Page xviii
19. CHAPTER OPENERS AND SUMMARIES Each chapter begins with an
overview of the material to be covered.A summary is included at the
end of each chapter, providing a quick review of basic con- cepts
and important relations, and pointing out the relevance of the
material. NUMEROUS WORKED-OUT EXAMPLES WITH A SYSTEMATIC SOLUTIONS
PROCEDURE Each chapter contains several worked-out examples that
clarify the material and illustrate the use of the basic
principles. An intuitive and systematic approach is used in the
solution of the example problems, while maintaining an informal
conversational style. The problem is first stated, and the
objectives are identified. The assumptions are then stated,
together with their justifica- tions. The properties needed to
solve the problem are listed separately. Numerical values are used
together with their units to emphasize that numbers without units
are meaningless, and unit manipulations are as important as
manipulating the numerical values with a calculator. The
significance of the findings is discussed following the solutions.
This approach is also used con- sistently in the solutions
presented in the instructors solutions manual. A WEALTH OF
REALISTIC END-OF-CHAPTER PROBLEMS The end-of-chapter problems are
grouped under specific topics to make prob- lem selection easier
for both instructors and students. Within each group of problems
are Concept Questions, indicated by C, to check the studentslevel
of understanding of basic concepts. The problems under Review
Problems are more comprehensive in nature and are not directly tied
to any specific section of a chapter in some cases they require
review of material learned in previ- ous chapters. Problems
designated as Design and Essay are intended to encourage students
to make engineering judgments, to conduct independent exploration
of topics of interest, and to communicate their findings in a pro-
fessional manner. Problems designated by an E are in English units,
and SI users can ignore them. Problems with the are solved using
EES, and com- plete solutions together with parametric studies are
included on the enclosed DVD. Problems with the are comprehensive
in nature and are intended to be solved with a computer, preferably
using the EES software that accompa- nies this text. Several
economics- and safety-related problems are incorpo- rated
throughout to enhance cost and safety awareness among engineering
students. Answers to selected problems are listed immediately
following the problem for convenience to students. USE OF COMMON
NOTATION The use of different notation for the same quantities in
different engineering courses has long been a source of discontent
and confusion. A student taking both fluid mechanics and heat
transfer, for example, has to use the notation Q for volume flow
rate in one course, and for heat transfer in the other. The need to
unify notation in engineering education has often been raised, even
in some reports of conferences sponsored by the National Science
Foundation through Foundation Coalitions, but little effort has
been made to date in this regard. For example, refer to the final
report of the Mini-Conference on Energy Stem Innovations, May 28
and 29, 2003, University of Wisconsin. In this text we made a
conscious effort to minimize this conflict by adopting the familiar
PREFACE xix cen72367_fm.qxd 11/23/04 11:22 AM Page xix
20. thermodynamic notation V . for volume flow rate, thus
reserving the notation Q for heat transfer. Also, we consistently
use an overdot to denote time rate. We think that both students and
instructors will appreciate this effort to promote a common
notation. A CHOICE OF SI ALONE OR SI/ENGLISH UNITS In recognition
of the fact that English units are still widely used in some
industries, both SI and English units are used in this text, with
an emphasis on SI. The material in this text can be covered using
combined SI/English units or SI units alone, depending on the
preference of the instructor. The property tables and charts in the
appendices are presented in both units, except the ones that
involve dimensionless quantities. Problems, tables, and charts in
English units are designated by E after the number for easy
recognition, and they can be ignored easily by the SI users.
COMBINED COVERAGE OF BERNOULLI AND ENERGY EQUATIONS The Bernoulli
equation is one of the most frequently used equations in fluid
mechanics, but it is also one of the most misused. Therefore, it is
important to emphasize the limitations on the use of this idealized
equation and to show how to properly account for imperfections and
irreversible losses. In Chapter 5, we do this by introducing the
energy equation right after the Bernoulli equation and
demonstrating how the solutions of many practical engineering
problems differ from those obtained using the Bernoulli equation.
This helps students develop a realistic view of the Bernoulli
equation. A SEPARATE CHAPTER ON CFD Commercial Computational Fluid
Dynamics (CFD) codes are widely used in engineering practice in the
design and analysis of flow systems, and it has become exceedingly
important for engineers to have a solid understanding of the
fundamental aspects, capabilities, and limitations of CFD.
Recognizing that most undergraduate engineering curriculums do not
have room for a full course on CFD, a separate chapter is included
here to make up for this defi- ciency and to equip students with an
adequate background on the strengths and weaknesses of CFD.
APPLICATION SPOTLIGHTS Throughout the book are highlighted examples
called Application Spotlights where a real-world application of
fluid mechanics is shown. A unique feature of these special
examples is that they are written by guest authors. The Appli-
cation Spotlights are designed to show students how fluid mechanics
has diverse applications in a wide variety of fields. They also
include eye-catching photographs from the guest authors research.
GLOSSARY OF FLUID MECHANICS TERMS Throughout the chapters, when an
important key term or concept is introduced and defined, it appears
in black boldface type. Fundamental fluid mechanics terms and
concepts appear in blue boldface type, and these fundamental terms
also appear in a comprehensive end-of-book glossary developed by
Professor James Brasseur of The Pennsylvania State University. This
unique glossary is an excellent learning and review tool for
students as they move forward in xx FLUID MECHANICS cen72367_fm.qxd
11/23/04 11:22 AM Page xx
21. their study of fluid mechanics. In addition, students can
test their knowledge of these fundamental terms by using the
interactive flash cards and other resources located on our
accompanying website (www.mhhe.com/cengel). CONVERSION FACTORS
Frequently used conversion factors, physical constants, and
frequently used properties of air and water at 20C and atmospheric
pressure are listed on the front inner cover pages of the text for
easy reference. NOMENCLATURE A list of the major symbols,
subscripts, and superscripts used in the text are listed on the
inside back cover pages of the text for easy reference. S U P P L E
M E N T S These supplements are available to adopters of the book:
STUDENT RESOURCES DVD Packaged free with every new copy of the
text, this DVD provides a wealth of resources for students
including Fluid Mechanics Videos, a CFD Animations Library, and EES
Software. ONLINE LEARNING CENTER Web support is provided for the
book on our Online Learning Center at www.mhhe.com/cengel. Visit
this robust site for book and supplement infor- mation, errata,
author information, and further resources for instructors and
students. ENGINEERING EQUATION SOLVER (EES) Developed by Sanford
Klein and William Beckman from the University of WisconsinMadison,
this software combines equation-solving capability and engineering
property data. EES can do optimization, parametric analysis, and
linear and nonlinear regression, and provides publication-quality
plotting capabilities. Thermodynamics and transport properties for
air, water, and many other fluids are built-in and EES allows the
user to enter property data or functional relationships. FLUENT
FLOWLAB SOFTWARE AND TEMPLATES As an integral part of Chapter 15,
Introduction to Computational Fluid Dynam- ics, we provide access
to a student-friendly CFD software package developed by Fluent Inc.
In addition, we provide over 40 FLUENT FLOWLAB templates to
complement the end-of-chapter problems in Chapter 15. These
problems and templates are unique in that they are designed with
both a fluid mechanics learn- ing objective and a CFD learning
objective in mind. INSTRUCTORS RESOURCE CD-ROM (AVAILABLE TO
INSTRUCTORS ONLY) This CD, available to instructors only, offers a
wide range of classroom prepa- ration and presentation resources
including an electronic solutions manual with PDF files by chapter,
all text chapters and appendices as downloadable PDF files, and all
text figures in JPEG format. PREFACE xxi cen72367_fm.qxd 11/23/04
11:22 AM Page xxi
22. COSMOS CD-ROM (AVAILABLE TO INSTRUCTORS ONLY) This CD,
available to instructors only, provides electronic solutions
delivered via our database management tool. McGraw-Hills COSMOS
allows instruc- tors to streamline the creation of assignments,
quizzes, and tests by using prob- lems and solutions from the
textbookas well as their own custom material. A C K N O W L E D G M
E N T S The authors would like to acknowledge with appreciation the
numerous and valuable comments, suggestions, constructive
criticisms, and praise from the following evaluators and reviewers:
xxii FLUID MECHANICS Mohammad Ali Kettering University Darryl Alofs
University of Missouri, Rolla Farrukh Alvi Florida A & M
University & Florida State University Ryoichi Amano University
of WisconsinMilwaukee Michael Amitay Rensselaer Polytechnic
Institute T. P. Ashokbabu National Institute of Technology, India
Idirb Azouz Southern Utah University Kenneth S. Ball University of
Texas at Austin James G. Brasseur The Pennsylvania State University
Glenn Brown Oklahoma State University John Callister Cornell
University Frederick Carranti Syracuse University Kevin W. Cassel
Illinois Institute of Technology Haris Catrakis University of
California, Irvine Louis N. Cattafesta III University of Florida
Soyoung Cha University of Illinois at Chicago Tiao Chang Ohio
University Young Cho Drexel University Po-Ya (Abel) Chuang The
Pennsylvania State University William H. Colwill American Hydro
Corporation A. Terrence Conlisk Jr. The Ohio State University
Daniel Cox Texas A&M University John Crepeau University of
Idaho Jie Cui Tennessee Technological University Lisa Davids
Embry-Riddle Aeronautical University Jerry Drummond The University
of Akron Dwayne Edwards University of Kentucky Richard Figliola
Clemson University Charles Forsberg Hofstra University Fred K.
Forster University of Washington cen72367_fm.qxd 11/23/04 11:22 AM
Page xxii
23. PREFACE xxiii Rong Gan The University of Oklahoma Philip
Gerhart University of Evansville Fred Gessner University of
Washington Sam Han Tennessee Technological University Mark J.
Holowach Ballston Spa, NY Neal Houze Purdue University Barbara
Hutchings Fluent Incorporated Niu Jianlei Hong Kong Polytechnic
University, Hong Kong David Johnson University of Waterloo Matthew
Jones Brigham Young University Zbigniew J. Kabala Duke University
Fazal Kauser California State Polytechnic University, Pomona Pirouz
Kavehpour University of California, Los Angeles Jacob Kazakia
Lehigh University Richard Keane University of Illinois at
UrbanaChampaign Jamil Khan University of South Carolina N. Nirmala
Khandan New Mexico State University Jeyhoon Khodadadi Auburn
University Subha Kumpaty Milwaukee School of Engineering James A.
Liburdy Oregon State University Chao-An Lin National Tsing Hua
University, Taiwan Kraemer Luks The University of Tulsa G.
Mahinthakumar North Carolina State University Saeed Manafzadeh
University of Illinois at Chicago Daniel Maynes Brigham Young
University James M. McDonough University of Kentucky Richard S.
Miller Clemson University Shane Moeykens Fluent Incorporated Joseph
Morrison NASA Langley Research Center Karim Nasr Kettering
University C. O. Ng University of Hong Kong, Hong Kong Wing Ng
Virginia Polytechnic Institute Tay Seow Ngie Nanyang Technological
University, Singapore John Nicklow Southern Illinois University at
Carbondale Nagy Nosseir San Diego State University Emmanuel Nzewi
North Carolina A&T State University Ali Ogut Rochester
Institute of Technology Michael Olsen Iowa State University
cen72367_fm.qxd 11/23/04 11:22 AM Page xxiii
24. xxiv FLUID MECHANICS The authors also acknowledge the guest
authors who contributed photographs and write-ups for the
Application Spotlights: Roger Pawlowski Lawrence Technological
University Bryan Pearce The University of Maine Blair Perot
University of Massachusetts Amherst Alexander Povitsky The
University of Akron Guy Riefler Ohio University Kurt Rosentrater
Northern Illinois University Subrata Roy Kettering University
Joseph Sai Texas A&M UniversityKingsville Gregory Selby Old
Dominion University Gary S. Settles The Pennsylvania State
University Winoto SH National University of Singapore, Singapore
Muhammad Sharif The University of Alabama Mark Stone Washington
State University Chelakara Subramanian Florida Institute of
Technology Constantine Tarawneh The University of TexasPan American
Sahnaz Tigrek Middle East Technical University Hsu Chin Tsau Hong
Kong University of Science and Technology, Hong Kong M. Erol
Ulucakli Lafayette College Oleg Vasilyev University of Missouri Zhi
Jian Wang Michigan State University Timothy Wei Rutgers, The State
University of New Jersey Minami Yoda Georgia Institute of
Technology Mohd Zamri Yusoff Universiti Tenaga Nasional, Malaysia
Michael L. Billet The Pennsylvania State University James G.
Brasseur The Pennsylvania State University Werner J. A. Dahm
University of Michigan Brian Daniels Oregon State University
Michael Dickinson California Institute of Technology Gerald C.
Lauchle The Pennsylvania State University James A. Liburdy Oregon
State University Anupam Pal The Pennsylvania State University
Ganesh Raman Illinois Institute of Technology Gary S. Settles The
Pennsylvania State University Lorenz Sigurdson University of
Alberta cen72367_fm.qxd 11/23/04 11:22 AM Page xxiv
25. Special thanks go to Professor Gary Settles and his
associates at Penn State (Lori Dodson-Dreibelbis, J. D. Miller, and
Gabrielle Tremblay) for creating the exciting narrated video clips
that are found on the DVD that accompanies this book. Similarly,
the authors acknowledge several people at Fluent Inc., who helped
to make available the wonderful CFD animations that are also found
on the DVD and the FLUENT FLOWLAB templates that are available for
downloading from the books website: Shane Moeykens, Barbara Hutch-
ings, Liz Marshall, Ashish Kulkarni, Ajay Parihar, and R. Murali
Krishnan. The authors also thank Professor James Brasseur of Penn
State for creating the precise glossary of fluid mechanics terms,
Professor Glenn Brown of Oklahoma State for providing many items of
historical interest throughout the text, Professor Mehmet Kanoglu
of Gaziantep University for preparing the solutions of EES
problems, and Professor Tahsin Engin of Sakarya University for
contributing several end-of-chapter problems. Finally, special
thanks must go to our families, especially our wives, Zehra engel
and Suzanne Cimbala, for their continued patience, understanding,
and support throughout the preparation of this book, which involved
many long hours when they had to handle family concerns on their
own because their husbands faces were glued to a computer screen.
Yunus A. engel John M. Cimbala PREFACE xxv cen72367_fm.qxd 11/23/04
11:22 AM Page xxv
26. INTRODUCTION AND BASIC CONCEPTS I n this introductory
chapter, we present the basic concepts commonly used in the
analysis of fluid flow. We start this chapter with a discussion of
the phases of matter and the numerous ways of classification of
fluid flow, such as viscous versus inviscid regions of flow,
internal versus external flow, compressible versus incompressible
flow, laminar versus turbulent flow, natural versus forced flow,
and steady versus unsteady flow. We also discuss the no-slip
condition at solidfluid interfaces and present a brief his- tory of
the development of fluid mechanics. After presenting the concepts
of system and control volume, we review the unit systems that will
be used. We then discuss how mathematical mod- els for engineering
problems are prepared and how to interpret the results obtained
from the analysis of such models. This is followed by a presenta-
tion of an intuitive systematic problem-solving technique that can
be used as a model in solving engineering problems. Finally, we
discuss accuracy, pre- cision, and significant digits in
engineering measurements and calculations. 1 CHAPTER 1 OBJECTIVES
When you finish reading this chapter, you should be able to I
Understand the basic concepts of fluid mechanics and recognize the
various types of fluid flow problems encountered in practice I
Model engineering problems and solve them in a systematic manner I
Have a working knowledge of accuracy, precision, and significant
digits, and recognize the importance of dimensional homogeneity in
engineering calculations cen72367_ch01.qxd 10/29/04 2:31 PM Page
1
27. 11 I INTRODUCTION Mechanics is the oldest physical science
that deals with both stationary and moving bodies under the
influence of forces. The branch of mechanics that deals with bodies
at rest is called statics, while the branch that deals with bodies
in motion is called dynamics. The subcategory fluid mechanics is
defined as the science that deals with the behavior of fluids at
rest (fluid sta- tics) or in motion (fluid dynamics), and the
interaction of fluids with solids or other fluids at the
boundaries. Fluid mechanics is also referred to as fluid dynamics
by considering fluids at rest as a special case of motion with zero
velocity (Fig. 11). Fluid mechanics itself is also divided into
several categories. The study of the motion of fluids that are
practically incompressible (such as liquids, especially water, and
gases at low speeds) is usually referred to as hydrody- namics. A
subcategory of hydrodynamics is hydraulics, which deals with liq-
uid flows in pipes and open channels. Gas dynamics deals with the
flow of fluids that undergo significant density changes, such as
the flow of gases through nozzles at high speeds. The category
aerodynamics deals with the flow of gases (especially air) over
bodies such as aircraft, rockets, and automo- biles at high or low
speeds. Some other specialized categories such as meteo- rology,
oceanography, and hydrology deal with naturally occurring flows.
What Is a Fluid? You will recall from physics that a substance
exists in three primary phases: solid, liquid, and gas. (At very
high temperatures, it also exists as plasma.) A substance in the
liquid or gas phase is referred to as a fluid. Distinction between
a solid and a fluid is made on the basis of the substances ability
to resist an applied shear (or tangential) stress that tends to
change its shape. A solid can resist an applied shear stress by
deforming, whereas a fluid deforms continuously under the influence
of shear stress, no matter how small. In solids stress is
proportional to strain, but in fluids stress is propor- tional to
strain rate. When a constant shear force is applied, a solid
eventu- ally stops deforming, at some fixed strain angle, whereas a
fluid never stops deforming and approaches a certain rate of
strain. Consider a rectangular rubber block tightly placed between
two plates. As the upper plate is pulled with a force F while the
lower plate is held fixed, the rubber block deforms, as shown in
Fig. 12. The angle of deformation a (called the shear strain or
angular displacement) increases in proportion to the applied force
F. Assuming there is no slip between the rubber and the plates, the
upper surface of the rubber is displaced by an amount equal to the
displacement of the upper plate while the lower surface remains
station- ary. In equilibrium, the net force acting on the plate in
the horizontal direc- tion must be zero, and thus a force equal and
opposite to F must be acting on the plate. This opposing force that
develops at the platerubber interface due to friction is expressed
as F tA, where t is the shear stress and A is the contact area
between the upper plate and the rubber. When the force is removed,
the rubber returns to its original position. This phenomenon would
also be observed with other solids such as a steel block provided
that the applied force does not exceed the elastic range. If this
experiment were repeated with a fluid (with two large parallel
plates placed in a large body of water, for example), the fluid
layer in contact with the upper plate would 2 FLUID MECHANICS
FIGURE 11 Fluid mechanics deals with liquids and gases in motion or
at rest. Vol. 16/Photo Disc. Contact area, A Shear stress t = F/A
Shear strain, a Force, F a Deformed rubber FIGURE 12 Deformation of
a rubber eraser placed between two parallel plates under the
influence of a shear force. cen72367_ch01.qxd 11/19/04 10:24 AM
Page 2
28. move with the plate continuously at the velocity of the
plate no matter how small the force F is. The fluid velocity
decreases with depth because of fric- tion between fluid layers,
reaching zero at the lower plate. You will recall from statics that
stress is defined as force per unit area and is determined by
dividing the force by the area upon which it acts. The normal
component of the force acting on a surface per unit area is called
the normal stress, and the tangential component of a force acting
on a surface per unit area is called shear stress (Fig. 13). In a
fluid at rest, the normal stress is called pressure. The supporting
walls of a fluid eliminate shear stress, and thus a fluid at rest
is at a state of zero shear stress. When the walls are removed or a
liquid container is tilted, a shear develops and the liquid
splashes or moves to attain a horizontal free surface. In a liquid,
chunks of molecules can move relative to each other, but the volume
remains relatively constant because of the strong cohesive forces
between the molecules. As a result, a liquid takes the shape of the
container it is in, and it forms a free surface in a larger
container in a gravitational field. A gas, on the other hand,
expands until it encounters the walls of the container and fills
the entire available space. This is because the gas mole- cules are
widely spaced, and the cohesive forces between them are very small.
Unlike liquids, gases cannot form a free surface (Fig. 14).
Although solids and fluids are easily distinguished in most cases,
this dis- tinction is not so clear in some borderline cases. For
example, asphalt appears and behaves as a solid since it resists
shear stress for short periods of time. But it deforms slowly and
behaves like a fluid when these forces are exerted for extended
periods of time. Some plastics, lead, and slurry mixtures exhibit
similar behavior. Such borderline cases are beyond the scope of
this text. The fluids we will deal with in this text will be
clearly recognizable as fluids. Intermolecular bonds are strongest
in solids and weakest in gases. One reason is that molecules in
solids are closely packed together, whereas in gases they are
separated by relatively large distances (Fig. 15). The molecules in
a solid are arranged in a pattern that is repeated through- out.
Because of the small distances between molecules in a solid, the
attrac- tive forces of molecules on each other are large and keep
the molecules at 3 CHAPTER 1 Fn Ft F Normal to surface Tangent to
surface Force acting on area dA dA FIGURE 13 The normal stress and
shear stress at the surface of a fluid element. For fluids at rest,
the shear stress is zero and pressure is the only normal stress.
Free surface Liquid Gas FIGURE 14 Unlike a liquid, a gas does not
form a free surface, and it expands to fill the entire available
space. (a) (b) (c) FIGURE 15 The arrangement of atoms in different
phases: (a) molecules are at relatively fixed positions in a solid,
(b) groups of molecules move about each other in the liquid phase,
and (c) molecules move about at random in the gas phase. Shear
stress: t Ft dA Normal stress: s Fn dA cen72367_ch01.qxd 10/29/04
2:31 PM Page 3
29. fixed positions. The molecular spacing in the liquid phase
is not much differ- ent from that of the solid phase, except the
molecules are no longer at fixed positions relative to each other
and they can rotate and translate freely. In a liquid, the
intermolecular forces are weaker relative to solids, but still
strong compared with gases. The distances between molecules
generally increase slightly as a solid turns liquid, with water
being a notable exception. In the gas phase, the molecules are far
apart from each other, and a mole- cular order is nonexistent. Gas
molecules move about at random, continu- ally colliding with each
other and the walls of the container in which they are contained.
Particularly at low densities, the intermolecular forces are very
small, and collisions are the only mode of interaction between the
mol- ecules. Molecules in the gas phase are at a considerably
higher energy level than they are in the liquid or solid phase.
Therefore, the gas must release a large amount of its energy before
it can condense or freeze. Gas and vapor are often used as
synonymous words. The vapor phase of a substance is customarily
called a gas when it is above the critical tempera- ture. Vapor
usually implies a gas that is not far from a state of condensation.
Any practical fluid system consists of a large number of molecules,
and the properties of the system naturally depend on the behavior
of these mole- cules. For example, the pressure of a gas in a
container is the result of momentum transfer between the molecules
and the walls of the container. However, one does not need to know
the behavior of the gas molecules to determine the pressure in the
container. It would be sufficient to attach a pressure gage to the
container (Fig. 16). This macroscopic or classical approach does
not require a knowledge of the behavior of individual mole- cules
and provides a direct and easy way to the solution of engineering
problems. The more elaborate microscopic or statistical approach,
based on the average behavior of large groups of individual
molecules, is rather involved and is used in this text only in the
supporting role. Application Areas of Fluid Mechanics Fluid
mechanics is widely used both in everyday activities and in the
design of modern engineering systems from vacuum cleaners to
supersonic aircraft. Therefore, it is important to develop a good
understanding of the basic prin- ciples of fluid mechanics. To
begin with, fluid mechanics plays a vital role in the human body.
The heart is constantly pumping blood to all parts of the human
body through the arteries and veins, and the lungs are the sites of
airflow in alternating directions. Needless to say, all artificial
hearts, breathing machines, and dialysis systems are designed using
fluid dynamics. An ordinary house is, in some respects, an
exhibition hall filled with appli- cations of fluid mechanics. The
piping systems for cold water, natural gas, and sewage for an
individual house and the entire city are designed primarily on the
basis of fluid mechanics. The same is also true for the piping and
duct- ing network of heating and air-conditioning systems. A
refrigerator involves tubes through which the refrigerant flows, a
compressor that pressurizes the refrigerant, and two heat
exchangers where the refrigerant absorbs and rejects heat. Fluid
mechanics plays a major role in the design of all these compo-
nents. Even the operation of ordinary faucets is based on fluid
mechanics. We can also see numerous applications of fluid mechanics
in an automo- bile. All components associated with the
transportation of the fuel from the 4 FLUID MECHANICS Pressure gage
FIGURE 16 On a microscopic scale, pressure is determined by the
interaction of individual gas molecules. However, we can measure
the pressure on a macroscopic scale with a pressure gage.
cen72367_ch01.qxd 10/29/04 2:31 PM Page 4
30. fuel tank to the cylindersthe fuel line, fuel pump, fuel
injectors, or carbu- retorsas well as the mixing of the fuel and
the air in the cylinders and the purging of combustion gases in
exhaust pipes are analyzed using fluid mechanics. Fluid mechanics
is also used in the design of the heating and air-conditioning
system, the hydraulic brakes, the power steering, automatic
transmission, and lubrication systems, the cooling system of the
engine block including the radiator and the water pump, and even
the tires. The sleek streamlined shape of recent model cars is the
result of efforts to mini- mize drag by using extensive analysis of
flow over surfaces. On a broader scale, fluid mechanics plays a
major part in the design and analysis of aircraft, boats,
submarines, rockets, jet engines, wind turbines, biomedical
devices, the cooling of electronic components, and the trans-
portation of water, crude oil, and natural gas. It is also
considered in the design of buildings, bridges, and even billboards
to make sure that the struc- tures can withstand wind loading.
Numerous natural phenomena such as the rain cycle, weather
patterns, the rise of ground water to the top of trees, winds,
ocean waves, and currents in large water bodies are also governed
by the principles of fluid mechanics (Fig. 17). 5 CHAPTER 1 Piping
and plumbing systems Photo by John M. Cimbala. Cars Photo by John
M. Cimbala. Power plants Vol. 57/Photo Disc. Aircraft and
spacecraft Vol. 1/Photo Disc. Human body Vol. 110/Photo Disc. Wind
turbines Vol. 17/Photo Disc. Natural flows and weather Vol.
16/Photo Disc. Industrial applications Courtesy UMDE Engineering,
Contracting, and Trading. Used by permission. FIGURE 17 Some
application areas of fluid mechanics. Boats Vol. 5/Photo Disc.
cen72367_ch01.qxd 10/29/04 2:31 PM Page 5
31. 12 I THE NO-SLIP CONDITION Fluid flow is often confined by
solid surfaces, and it is important to under- stand how the
presence of solid surfaces affects fluid flow. We know that water
in a river cannot flow through large rocks, and goes around them.
That is, the water velocity normal to the rock surface must be
zero, and water approaching the surface normally comes to a
complete stop at the sur- face. What is not so obvious is that
water approaching the rock at any angle also comes to a complete
stop at the rock surface, and thus the tangential velocity of water
at the surface is also zero. Consider the flow of a fluid in a
stationary pipe or over a solid surface that is nonporous (i.e.,
impermeable to the fluid). All experimental observa- tions indicate
that a fluid in motion comes to a complete stop at the surface and
assumes a zero velocity relative to the surface. That is, a fluid
in direct contact with a solid sticks to the surface due to viscous
effects, and there is no slip. This is known as the no-slip
condition. The photo in Fig. 18 obtained from a video clip clearly
shows the evolu- tion of a velocity gradient as a result of the
fluid sticking to the surface of a blunt nose. The layer that
sticks to the surface slows the adjacent fluid layer because of
viscous forces between the fluid layers, which slows the next
layer, and so on. Therefore, the no-slip condition is responsible
for the development of the velocity profile. The flow region
adjacent to the wall in which the viscous effects (and thus the
velocity gradients) are significant is called the boundary layer.
The fluid property responsible for the no-slip condition and the
development of the boundary layer is viscosity and is dis- cussed
in Chap. 2. A fluid layer adjacent to a moving surface has the same
velocity as the surface. A consequence of the no-slip condition is
that all velocity profiles must have zero values with respect to
the surface at the points of contact between a fluid and a solid
surface (Fig. 19). Another consequence of the no-slip condition is
the surface drag, which is the force a fluid exerts on a surface in
the flow direction. When a fluid is forced to flow over a curved
surface, such as the back side of a cylinder at sufficiently high
velocity, the boundary layer can no longer remain attached to the
surface, and at some point it separates from the surfacea process
called flow separation (Fig. 110). We emphasize that the no-slip
condition applies everywhere along the surface, even down- stream
of the separation point. Flow separation is discussed in greater
detail in Chap. 10. 6 FLUID MECHANICS FIGURE 18 The development of
a velocity profile due to the no-slip condition as a fluid flows
over a blunt nose. Hunter Rouse: Laminar and Turbulent Flow Film.
Copyright IIHR-Hydroscience & Engineering, The University of
Iowa. Used by permission. Relative velocities of fluid layers
Uniform approach velocity, V Zero velocity at the surface Plate
FIGURE 19 A fluid flowing over a stationary surface comes to a
complete stop at the surface because of the no-slip condition.
Separation point FIGURE 110 Flow separation during flow over a
curved surface. From G. M. Homsy et al, Multi-Media Fluid
Mechanics, Cambridge Univ. Press (2001). ISBN 0-521-78748-3.
Reprinted by permission. cen72367_ch01.qxd 10/29/04 2:32 PM Page
6
32. A similar phenomenon occurs for temperature. When two
bodies at differ- ent temperatures are brought into contact, heat
transfer occurs until both bodies assume the same temperature at
the points of contact. Therefore, a fluid and a solid surface have
the same temperature at the points of contact. This is known as
no-temperature-jump condition. 13 I A BRIEF HISTORY OF FLUID
MECHANICS1 One of the first engineering problems humankind faced as
cities were devel- oped was the supply of water for domestic use
and irrigation of crops. Our urban lifestyles can be retained only
with abundant water, and it is clear from archeology that every
successful civilization of prehistory invested in the construction
and maintenance of water systems. The Roman aqueducts, some of
which are still in use, are the best known examples. However, per-
haps the most impressive engineering from a technical viewpoint was
done at the Hellenistic city of Pergamon in present-day Turkey.
There, from 283 to 133 BC, they built a series of pressurized lead
and clay pipelines (Fig. 111), up to 45 km long that operated at
pressures exceeding 1.7 MPa (180 m of head). Unfortunately, the
names of almost all these early builders are lost to history. The
earliest recognized contribution to fluid mechanics the- ory was
made by the Greek mathematician Archimedes (285212 BC). He
formulated and applied the buoyancy principle in historys first
nondestruc- tive test to determine the gold content of the crown of
King Hiero I. The Romans built great aqueducts and educated many
conquered people on the benefits of clean water, but overall had a
poor understanding of fluids the- ory. (Perhaps they shouldnt have
killed Archimedes when they sacked Syracuse.) During the Middle
Ages the application of fluid machinery slowly but steadily
expanded. Elegant piston pumps were developed for dewatering mines,
and the watermill and windmill were perfected to grind grain, forge
metal, and for other tasks. For the first time in recorded human
history sig- nificant work was being done without the power of a
muscle supplied by a person or animal, and these inventions are
generally credited with enabling the later industrial revolution.
Again the creators of most of the progress are unknown, but the
devices themselves were well documented by several technical
writers such as Georgius Agricola (Fig. 112). The Renaissance
brought continued development of fluid systems and machines, but
more importantly, the scientific method was perfected and adopted
throughout Europe. Simon Stevin (15481617), Galileo Galilei
(15641642), Edme Mariotte (16201684), and Evangelista Torricelli
(16081647) were among the first to apply the method to fluids as
they investigated hydrostatic pressure distributions and vacuums.
That work was integrated and refined by the brilliant
mathematician, Blaise Pascal (1623 1662). The Italian monk,
Benedetto Castelli (15771644) was the first per- son to publish a
statement of the continuity principle for fluids. Besides for-
mulating his equations of motion for solids, Sir Isaac Newton
(16431727) applied his laws to fluids and explored fluid inertia
and resistance, free jets, and viscosity. That effort was built
upon by the Swiss Daniel Bernoulli 7 CHAPTER 1 1 This section is
contributed by Professor Glenn Brown of Oklahoma State University.
FIGURE 111 Segment of Pergamon pipeline. Each clay pipe section was
13 to 18 cm in diameter. Courtesy Gunther Garbrecht. Used by
permission. FIGURE 112 A mine hoist powered by a reversible water
wheel. G. Agricola, De Re Metalica, Basel, 1556. cen72367_ch01.qxd
10/29/04 2:32 PM Page 7
33. (17001782) and his associate Leonard Euler (17071783).
Together, their work defined the energy and momentum equations.
Bernoullis 1738 classic treatise Hydrodynamica may be considered
the first fluid mechanics text. Finally, Jean dAlembert (17171789)
developed the idea of velocity and acceleration components, a
differential expression of continuity, and his paradox of zero
resistance to steady uniform motion. The development of fluid
mechanics theory up through the end of the eighteenth century had
little impact on engineering since fluid properties and parameters
were poorly quantified, and most theories were abstractions that
could not be quantified for design purposes. That was to change
with the development of the French school of engineering led by
Riche de Prony (17551839). Prony (still known for his brake to
measure power) and his associates in Paris at the Ecole Polytechnic
and the Ecole Ponts et Chaussees were the first to integrate
calculus and scientific theory into the engineering curriculum,
which became the model for the rest of the world. (So now you know
whom to blame for your painful freshman year.) Antonie Chezy
(17181798), Louis Navier (17851836), Gaspard Coriolis (17921843),
Henry Darcy (18031858), and many other contributors to fluid
engineering and theory were students and/or instructors at the
schools. By the mid nineteenth century fundamental advances were
coming on several fronts. The physician Jean Poiseuille (17991869)
had accurately measured flow in capillary tubes for multiple
fluids, while in Germany Gotthilf Hagen (17971884) had
differentiated between laminar and turbu- lent flow in pipes. In
England, Lord Osborn Reynolds (18421912) contin- ued that work and
developed the dimensionless number that bears his name. Similarly,
in parallel to the early work of Navier, George Stokes (1819 1903)
completed the general equations of fluid motion with friction that
take their names. William Froude (18101879) almost single-handedly
developed the procedures and proved the value of physical model
testing. American expertise had become equal to the Europeans as
demonstrated by James Franciss (18151892) and Lester Peltons
(18291908) pioneering work in turbines and Clemens Herschels
(18421930) invention of the Ven- turi meter. The late nineteenth
century was notable for the expansion of fluid theory by Irish and
English scientists and engineers, including in addition to Reynolds
and Stokes, William Thomson, Lord Kelvin (18241907), William
Strutt, Lord Rayleigh (18421919), and Sir Horace Lamb (18491934).
These individuals investigated a large number of problems including
dimen- sional analysis, irrotational flow, vortex motion,
cavitation, and waves. In a broader sense their work also explored
the links between fluid mechanics, thermodynamics, and heat
transfer. The dawn of the twentieth century brought two monumental
develop- ments. First in 1903, the self-taught Wright brothers
(Wilbur, 18671912; Orville, 18711948) through application of theory
and determined experi- mentation perfected the airplane. Their
primitive invention was complete and contained all the major
aspects of modern craft (Fig. 113). The NavierStokes equations were
of little use up to this time because they were too difficult to
solve. In a pioneering paper in 1904, the German Ludwig Prandtl
(18751953) showed that fluid flows can be divided into a layer near
the walls, the boundary layer, where the friction effects are
significant and an outer layer where such effects are negligible
and the simplified Euler 8 FLUID MECHANICS FIGURE 113 The Wright
brothers take flight at Kitty Hawk. National Air and Space Museum/
Smithsonian Institution. cen72367_ch01.qxd 10/29/04 2:32 PM Page
8
34. and Bernoulli equations are applicable. His students,
Theodore von Krmn (18811963), Paul Blasius (18831970), Johann
Nikuradse (18941979), and others, built on that theory in both
hydraulic and aerodynamic applica- tions. (During World War II,
both sides benefited from the theory as Prandtl remained in Germany
while his best student, the Hungarian born Theodore von Krmn,
worked in America.) The mid twentieth century could be considered a
golden age of fluid mechanics applications. Existing theories were
adequate for the tasks at hand, and fluid properties and parameters
were well defined. These sup- ported a huge expansion of the
aeronautical, chemical, industrial, and water resources sectors;
each of which pushed fluid mechanics in new directions. Fluid
mechanics research and work in the late twentieth century were
domi- nated by the development of the digital computer in America.
The ability to solve large complex problems, such as global climate
modeling or to opti- mize the design of a turbine blade, has
provided a benefit to our society that the eighteenth-century
developers of fluid mechanics could never have imagined (Fig. 114).
The principles presented in the following pages have been applied
to flows ranging from a moment at the microscopic scale to 50 years
of simulation for an entire river basin. It is truly mind-boggling.
Where will fluid mechanics go in the twenty-first century? Frankly,
even a limited extrapolation beyond the present would be sheer
folly. However, if history tells us anything, it is that engineers
will be applying what they know to benefit society, researching
what they dont know, and having a great time in the process. 14 I
CLASSIFICATION OF FLUID FLOWS Earlier we defined fluid mechanics as
the science that deals with the behav- ior of fluids at rest or in
motion, and the interaction of fluids with solids or other fluids
at the boundaries. There is a wide variety of fluid flow problems
encountered in practice, and it is usually convenient to classify
them on the basis of some common characteristics to make it
feasible to study them in groups. There are many ways to classify
fluid flow problems, and here we present some general categories.
Viscous versus Inviscid Regions of Flow When two fluid layers move
relative to each other, a friction force develops between them and
the slower layer tries to slow down the faster layer. This internal
resistance to flow is quantified by the fluid property viscosity,
which is a measure of internal stickiness of the fluid. Viscosity
is caused by cohesive forces between the molecules in liquids and
by molecular colli- sions in gases. There is no fluid with zero
viscosity, and thus all fluid flows involve viscous effects to some
degree. Flows in which the frictional effects are significant are
called viscous flows. However, in many flows of practical interest,
there are regions (typically regions not close to solid surfaces)
where viscous forces are negligibly small compared to inertial or
pressure forces. Neglecting the viscous terms in such inviscid flow
regions greatly simplifies the analysis without much loss in
accuracy. The development of viscous and inviscid regions of flow
as a result of inserting a flat plate parallel into a fluid stream
of uniform velocity is shown in Fig. 115. The fluid sticks to the
plate on both sides because of 9 CHAPTER 1 FIGURE 114 The Oklahoma
Wind Power Center near Woodward consists of 68 turbines, 1.5 MW
each. Courtesy Steve Stadler, Oklahoma Wind Power Initiative. Used
by permission. Inviscid flow region Viscous flow region Inviscid
flow region FIGURE 115 The flow of an originally uniform fluid
stream over a flat plate, and the regions of viscous flow (next to
the plate on both sides) and inviscid flow (away from the plate).
Fundamentals of Boundary Layers, National Committee from Fluid
Mechanics Films, Education Development Center. cen72367_ch01.qxd
11/16/04 11:33 AM Page 9
35. the no-slip condition, and the thin boundary layer in which
the viscous effects are significant near the plate surface is the
viscous flow region. The region of flow on both sides away from the
plate and unaffected by the presence of the plate is the inviscid
flow region. Internal versus External Flow A fluid flow is
classified as being internal or external, depending on whether the
fluid is forced to flow in a confined channel or over a surface.
The flow of an unbounded fluid over a surface such as a plate, a
wire, or a pipe is external flow. The flow in a pipe or duct is
internal flow if the fluid is completely bounded by solid surfaces.
Water flow in a pipe, for example, is internal flow, and airflow
over a ball or over an exposed pipe during a windy day is external
flow (Fig. 116). The flow of liquids in a duct is called
open-channel flow if the duct is only partially filled with the
liquid and there is a free surface. The flows of water in rivers
and irrigation ditches are examples of such flows. Internal flows
are dominated by the influence of viscosity throughout the flow
field. In external flows the viscous effects are limited to
boundary lay- ers near solid surfaces and to wake regions
downstream of bodies. Compressible versus Incompressible Flow A
flow is classified as being compressible or incompressible,
depending on the level of variation of density during flow.
Incompressibility is an approx- imation, and a flow is said to be
incompressible if the density remains nearly constant throughout.
Therefore, the volume of every portion of fluid remains unchanged
over the course of its motion when the flow (or the fluid) is
incompressible. The densities of liquids are essentially constant,
and thus the flow of liq- uids is typically incompressible.
Therefore, liquids are usually referred to as incompressible
substances. A pressure of 210 atm, for example, causes the density
of liquid water at 1 atm to change by just 1 percent. Gases, on the
other hand, are highly compressible. A pressure change of just 0.01
atm, for example, causes a change of 1 percent in the density of
atmospheric air. When analyzing rockets, spacecraft, and other
systems that involve high- speed gas flows, the flow speed is often
expressed in terms of the dimen- sionless Mach number defined as
where c is the speed of sound whose value is 346 m/s in air at room
tem- perature at sea level. A flow is called sonic when Ma 1,
subsonic when Ma 1, supersonic when Ma 1, and hypersonic when Ma 1.
Liquid flows are incompressible to a high level of accuracy, but
the level of variation in density in gas flows and the consequent
level of approxima- tion made when modeling gas flows as
incompressible depends on the Mach number. Gas flows can often be
approximated as incompressible if the density changes are under
about 5 percent, which is usually the case when Ma 0.3. Therefore,
the compressibility effects of air can be neglected at speeds under
about 100 m/s. Note that the flow of a gas is not necessarily a
compressible flow. Ma V c Speed of flow Speed of sound 10 FLUID
MECHANICS FIGURE 116 External flow over a tennis ball, and the
turbulent wake region behind. Courtesy NASA and Cislunar Aerospace,
Inc. cen72367_ch01.qxd 10/29/04 2:32 PM Page 10
36. Small density changes of liquids corresponding to large
pressure changes can still have important consequences. The
irritating water hammer in a water pipe, for example, is caused by
the vibrations of the pipe generated by the reflection of pressure
waves following the sudden closing of the valves. Laminar versus
Turbulent Flow Some flows are smooth and orderly while others are
rather chaotic. The highly ordered fluid motion characterized by
smooth layers of fluid is called laminar. The word laminar comes
from the movement of adjacent fluid particles together in
laminates. The flow of high-viscosity fluids such as oils at low
velocities is typically laminar. The highly disordered fluid motion
that typically occurs at high velocities and is characterized by
veloc- ity fluctuations is called turbulent (Fig. 117). The flow of
low-viscosity fluids such as air at high velocities is typically
turbulent. The flow regime greatly influences the required power
for pumping. A flow that alternates between being laminar and
turbulent is called transitional. The experiments conducted by
Osborn Reynolds in the 1880s resulted in the establishment of the
dimensionless Reynolds number, Re, as the key parameter for the
determination of the flow regime in pipes (Chap. 8). Natural (or
Unforced) versus Forced Flow A fluid flow is said to be natural or
forced, depending on how the fluid motion is initiated. In forced
flow, a fluid is forced to flow over a surface or in a pipe by
external means such as a pump or a fan. In natural flows, any fluid
motion is due to natural means such as the buoyancy effect, which
manifests itself as the rise of the warmer (and thus lighter) fluid
and the fall of cooler (and thus denser) fluid (Fig. 118). In solar
hot-water systems, for example, the thermosiphoning effect is
commonly used to replace pumps by placing the water tank
sufficiently above the solar collectors. Steady versus Unsteady
Flow The terms steady and uniform are used frequently in
engineering, and thus it is important to have a clear understanding
of their meanings. The term steady implies no change at a point
with time. The opposite of steady is unsteady. The term uniform
implies no change with location over a speci- fied region. These
meanings are consistent with their everyday use (steady girlfriend,
uniform distribution, etc.). The terms unsteady and transient are
often used interchangeably, but these terms are not synonyms. In
fluid mechanics, unsteady is the most gen- eral term that applies
to any flow that is not steady, but transient is typi- cally used
for developing flows. When a rocket engine is fired up, for exam-
ple, there are transient effects (the pressure builds up inside the
rocket engine, the flow accelerates, etc.) until the engine settles
down and operates steadily. The term periodic refers to the kind of
unsteady flow in which the flow oscillates about a steady mean.
Many devices such as turbines, compressors, boilers, condensers,
and heat exchangers operate for long periods of time under the same
conditions, and they are classified as steady-flow devices. (Note
that the flow field near the rotating blades of a turbomachine is
of course unsteady, but we consider the overall flow field rather
than the details at some localities when we classify 11 CHAPTER 1
Laminar Transitional Turbulent FIGURE 117 Laminar, transitional,
and turbulent flows. Courtesy ONERA, photograph by Werl. FIGURE 118
In this schlieren image of a girl in a swimming suit, the rise of
lighter, warmer air adjacent to her body indicates that humans and
warm- blooded animals are surrounded by thermal plumes of rising
warm air. G. S. Settles, Gas Dynamics Lab, Penn State University.
Used by permission. cen72367_ch01.qxd 10/29/04 2:32 PM Page 11
37. devices.) During steady flow, the fluid properties can
change from point to point within a device, but at any fixed point
they remain constant. There- fore, the volume, the mass, and the
total energy content of a steady-flow device or flow section remain
constant in steady operation. Steady-flow conditions can be closely
approximated by devices that are intended for continuous operation
such as turbines, pumps, boilers, con- densers, and heat exchangers
of power plants or refrigeration systems. Some cyclic devices, such
as reciprocating engines or compressors, do not satisfy the
steady-flow conditions since the flow at the inlets and the exits
is pulsat- ing and not steady. However, the fluid properties vary
with time in a peri- odic manner, and the flow through these
devices can still be analyzed as a steady-flow process by using
time-averaged values for the properties. Some fascinating
visuali