Unformatted text preview: Fluid Mechanics
Fourth Edition Frank M. White
University of Rhode Island Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis
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CONSULTING EDITORS
Jack P. Holman, Southern Methodist University
John Lloyd, Michigan State University
Anderson
Computational Fluid Dynamics: The Basics with Applications
Anderson
Modern Compressible Flow: With Historical Perspective
Arora
Introduction to Optimum Design
Borman and Ragland
Combustion Engineering
Burton
Introduction to Dynamic Systems Analysis
Culp
Principles of Energy Conversion
Dieter
Engineering Design: A Materials & Processing Approach
Doebelin
Engineering Experimentation: Planning, Execution, Reporting
Driels
Linear Control Systems Engineering
Edwards and McKee
Fundamentals of Mechanical Component Design
Gebhart
Heat Conduction and Mass Diffusion
Gibson
Principles of Composite Material Mechanics
Hamrock
Fundamentals of Fluid Film Lubrication
Heywood
Internal Combustion Engine Fundamentals
Hinze
Turbulence Kimbrell
Kinematics Analysis and Synthesis
Kreider and Rabl
Heating and Cooling of Buildings
Martin
Kinematics and Dynamics of Machines
Mattingly
Elements of Gas Turbine Propulsion
Modest
Radiative Heat Transfer
Norton
Design of Machinery
Oosthuizen and Carscallen
Compressible Fluid Flow
Oosthuizen and Naylor
Introduction to Convective Heat Transfer Analysis
Phelan
Fundamentals of Mechanical Design
Reddy
An Introduction to Finite Element Method
Rosenberg and Karnopp
Introduction to Physical Systems Dynamics
Schlichting
BoundaryLayer Theory
Shames
Mechanics of Fluids
Shigley
Kinematic Analysis of Mechanisms
Shigley and Mischke
Mechanical Engineering Design
Shigley and Uicker
Theory of Machines and Mechanisms
Stiffler
Design with Microprocessors for Mechanical Engineers Histand and Alciatore
Introduction to Mechatronics and Measurement Systems Stoecker and Jones
Refrigeration and Air Conditioning Holman
Experimental Methods for Engineers Turns
An Introduction to Combustion: Concepts and Applications Howell and Buckius
Fundamentals of Engineering Thermodynamics Ullman
The Mechanical Design Process Jaluria
Design and Optimization of Thermal Systems Wark
Advanced Thermodynamics for Engineers Juvinall
Engineering Considerations of Stress, Strain, and Strength Wark and Richards
Thermodynamics Kays and Crawford
Convective Heat and Mass Transfer White
Viscous Fluid Flow Kelly
Fundamentals of Mechanical Vibrations Zeid
CAD/CAM Theory and Practice About the Author Frank M. White is Professor of Mechanical and Ocean Engineering at the University
of Rhode Island. He studied at Georgia Tech and M.I.T. In 1966 he helped found, at
URI, the first department of ocean engineering in the country. Known primarily as a
teacher and writer, he has received eight teaching awards and has written four textbooks on fluid mechanics and heat transfer.
During 1979–1990 he was editorinchief of the ASME Journal of Fluids Engineering and then served from 1991 to 1997 as chairman of the ASME Board of Editors and of the Publications Committee. He is a Fellow of ASME and in 1991 received
the ASME Fluids Engineering Award. He lives with his wife, Jeanne, in Narragansett,
Rhode Island. v To Jeanne Contents Preface xi
Chapter 1
Introduction 3
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14 Preliminary Remarks 3
The Concept of a Fluid 4
The Fluid as a Continuum 6
Dimensions and Units 7
Properties of the Velocity Field 14
Thermodynamic Properties of a Fluid 16
Viscosity and Other Secondary Properties 22
Basic FlowAnalysis Techniques 35
Flow Patterns: Streamlines, Streaklines, and
Pathlines 37
The Engineering Equation Solver 41
Uncertainty of Experimental Data 42
The Fundamentals of Engineering (FE) Examination 43
ProblemSolving Techniques 44
History and Scope of Fluid Mechanics 44
Problems 46
Fundamentals of Engineering Exam Problems 53
Comprehensive Problems 54
References 55 Chapter 2
Pressure Distribution in a Fluid 59
2.1
2.2
2.3
2.4
2.5 Pressure and Pressure Gradient 59
Equilibrium of a Fluid Element 61
Hydrostatic Pressure Distributions 63
Application to Manometry 70
Hydrostatic Forces on Plane Surfaces 74 2.6
2.7
2.8
2.9
2.10 Hydrostatic Forces on Curved Surfaces 79
Hydrostatic Forces in Layered Fluids 82
Buoyancy and Stability 84
Pressure Distribution in RigidBody Motion 89
Pressure Measurement 97
Summary 100
Problems 102
Word Problems 125
Fundamentals of Engineering Exam Problems 125
Comprehensive Problems 126
Design Projects 127
References 127 Chapter 3
Integral Relations for a Control Volume 129
3.1
3.2
3.3
3.4
3.5
3.6
3.7 Basic Physical Laws of Fluid Mechanics 129
The Reynolds Transport Theorem 133
Conservation of Mass 141
The Linear Momentum Equation 146
The AngularMomentum Theorem 158
The Energy Equation 163
Frictionless Flow: The Bernoulli Equation 174
Summary 183
Problems 184
Word Problems 210
Fundamentals of Engineering Exam Problems 210
Comprehensive Problems 211
Design Project 212
References 213 vii viii Contents Chapter 4
Differential Relations for a Fluid Particle 215
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11 The Acceleration Field of a Fluid 215
The Differential Equation of Mass Conservation 217
The Differential Equation of Linear Momentum 223
The Differential Equation of Angular Momentum 230
The Differential Equation of Energy 231
Boundary Conditions for the Basic Equations 234
The Stream Function 238
Vorticity and Irrotationality 245
Frictionless Irrotational Flows 247
Some Illustrative Plane Potential Flows 252
Some Illustrative Incompressible Viscous Flows 258
Summary 263
Problems 264
Word Problems 273
Fundamentals of Engineering Exam Problems 273
Comprehensive Applied Problem 274
References 275 Chapter 5
Dimensional Analysis and Similarity 277
5.1
5.2
5.3
5.4
5.5 Introduction 277
The Principle of Dimensional Homogeneity 280
The Pi Theorem 286
Nondimensionalization of the Basic Equations 292
Modeling and Its Pitfalls 301
Summary 311
Problems 311
Word Problems 318
Fundamentals of Engineering Exam Problems 319
Comprehensive Problems 319
Design Projects 320
References 321 Chapter 6
Viscous Flow in Ducts 325
6.1
6.2
6.3
6.4 ReynoldsNumber Regimes 325
Internal versus External Viscous Flows 330
Semiempirical Turbulent Shear Correlations 333
Flow in a Circular Pipe 338 6.5
6.6
6.7
6.8
6.9
6.10 Three Types of PipeFlow Problems 351
Flow in Noncircular Ducts 357
Minor Losses in Pipe Systems 367
MultiplePipe Systems 375
Experimental Duct Flows: Diffuser Performance 381
Fluid Meters 385
Summary 404
Problems 405
Word Problems 420
Fundamentals of Engineering Exam Problems 420
Comprehensive Problems 421
Design Projects 422
References 423 Chapter 7
Flow Past Immersed Bodies 427
7.1
7.2
7.3
7.4
7.5
7.6 ReynoldsNumber and Geometry Effects 427
MomentumIntegral Estimates 431
The BoundaryLayer Equations 434
The FlatPlate Boundary Layer 436
Boundary Layers with Pressure Gradient 445
Experimental External Flows 451
Summary 476
Problems 476
Word Problems 489
Fundamentals of Engineering Exam Problems 489
Comprehensive Problems 490
Design Project 491
References 491 Chapter 8
Potential Flow and Computational Fluid Dynamics 495
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9 Introduction and Review 495
Elementary PlaneFlow Solutions 498
Superposition of PlaneFlow Solutions 500
Plane Flow Past ClosedBody Shapes 507
Other Plane Potential Flows 516
Images 521
Airfoil Theory 523
Axisymmetric Potential Flow 534
Numerical Analysis 540
Summary 555 Contents
Problems 695
Word Problems 706
Fundamentals of Engineering Exam Problems 707
Comprehensive Problems 707
Design Projects 707
References 708 Problems 555
Word Problems 566
Comprehensive Problems 566
Design Projects 567
References 567 Chapter 9
Compressible Flow 571
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10 Introduction 571
The Speed of Sound 575
Adiabatic and Isentropic Steady Flow 578
Isentropic Flow with Area Changes 583
The NormalShock Wave 590
Operation of Converging and Diverging Nozzles 598
Compressible Duct Flow with Friction 603
Frictionless Duct Flow with Heat Transfer 613
TwoDimensional Supersonic Flow 618
PrandtlMeyer Expansion Waves 628
Summary 640
Problems 641
Word Problems 653
Fundamentals of Engineering Exam Problems 653
Comprehensive Problems 654
Design Projects 654
References 655 Chapter 10
OpenChannel Flow 659
10.1
10.2
10.3
10.4
10.5
10.6
10.7 Introduction 659
Uniform Flow; the Chézy Formula 664
Efficient UniformFlow Channels 669
Specific Energy; Critical Depth 671
The Hydraulic Jump 678
Gradually Varied Flow 682
Flow Measurement and Control by Weirs 687
Summary 695 Chapter 11
Turbomachinery 711
11.1
11.2
11.3
11.4
11.5
11.6 Introduction and Classification 711
The Centrifugal Pump 714
Pump Performance Curves and Similarity Rules 720
Mixed and AxialFlow Pumps:
The Specific Speed 729
Matching Pumps to System Characteristics 735
Turbines 742
Summary 755
Problems 755
Word Problems 765
Comprehensive Problems 766
Design Project 767
References 767 Appendix A Physical Properties of Fluids 769 Appendix B CompressibleFlow Tables 774 Appendix C Conversion Factors 791 Appendix D Equations of Motion in Cylindrical
Coordinates 793 Appendix E Introduction to EES 795 Answers to Selected Problems 806
Index 813 ix Preface General Approach The fourth edition of this textbook sees some additions and deletions but no philosophical change. The basic outline of eleven chapters and five appendices remains the
same. The triad of integral, differential, and experimental approaches is retained and
is approached in that order of presentation. The book is intended for an undergraduate
course in fluid mechanics, and there is plenty of material for a full year of instruction.
The author covers the first six chapters and part of Chapter 7 in the introductory semester. The more specialized and applied topics from Chapters 7 to 11 are then covered at our university in a second semester. The informal, studentoriented style is retained and, if it succeeds, has the flavor of an interactive lecture by the author. Learning Tools Approximately 30 percent of the problem exercises, and some fully worked examples,
have been changed or are new. The total number of problem exercises has increased
to more than 1500 in this fourth edition. The focus of the new problems is on practical and realistic fluids engineering experiences. Problems are grouped according to
topic, and some are labeled either with an asterisk (especially challenging) or a computerdisk icon (where computer solution is recommended). A number of new photographs and figures have been added, especially to illustrate new design applications
and new instruments.
Professor John Cimbala, of Pennsylvania State University, contributed many of the
new problems. He had the great idea of setting comprehensive problems at the end of
each chapter, covering a broad range of concepts, often from several different chapters. These comprehensive problems grow and recur throughout the book as new concepts arise. Six more openended design projects have been added, making 15 projects
in all. The projects allow the student to set sizes and parameters and achieve good design with more than one approach.
An entirely new addition is a set of 95 multiplechoice problems suitable for preparing for the Fundamentals of Engineering (FE) Examination. These FE problems come
at the end of Chapters 1 to 10. Meant as a realistic practice for the actual FE Exam,
they are engineering problems with five suggested answers, all of them plausible, but
only one of them correct.
xi xii Preface New to this book, and to any fluid mechanics textbook, is a special appendix, Appendix E, Introduction to the Engineering Equation Solver (EES), which is keyed to
many examples and problems throughout the book. The author finds EES to be an extremely attractive tool for applied engineering problems. Not only does it solve arbitrarily complex systems of equations, written in any order or form, but also it has builtin property evaluations (density, viscosity, enthalpy, entropy, etc.), linear and nonlinear
regression, and easily formatted parameter studies and publicationquality plotting. The
author is indebted to Professors Sanford Klein and William Beckman, of the University of Wisconsin, for invaluable and continuous help in preparing this EES material.
The book is now available with or without an EES problems disk. The EES engine is
available to adopters of the text with the problems disk.
Another welcome addition, especially for students, is Answers to Selected Problems. Over 600 answers are provided, or about 43 percent of all the regular problem
assignments. Thus a compromise is struck between sometimes having a specific numerical goal and sometimes directly applying yourself and hoping for the best result. Content Changes There are revisions in every chapter. Chapter 1—which is purely introductory and
could be assigned as reading—has been toned down from earlier editions. For example, the discussion of the fluid acceleration vector has been moved entirely to Chapter 4. Four brief new sections have been added: (1) the uncertainty of engineering
data, (2) the use of EES, (3) the FE Examination, and (4) recommended problemsolving techniques.
Chapter 2 has an improved discussion of the stability of floating bodies, with a fully
derived formula for computing the metacentric height. Coverage is confined to static
fluids and rigidbody motions. An improved section on pressure measurement discusses
modern microsensors, such as the fusedquartz bourdon tube, micromachined silicon
capacitive and piezoelectric sensors, and tiny (2 mm long) silicon resonantfrequency
devices.
Chapter 3 tightens up the energy equation discussion and retains the plan that
Bernoulli’s equation comes last, after controlvolume mass, linear momentum, angular momentum, and energy studies. Although some texts begin with an entire chapter
on the Bernoulli equation, this author tries to stress that it is a dangerously restricted
relation which is often misused by both students and graduate engineers.
In Chapter 4 a few inviscid and viscous flow examples have been added to the basic partial differential equations of fluid mechanics. More extensive discussion continues in Chapter 8.
Chapter 5 is more successful when one selects scaling variables before using the pi
theorem. Nevertheless, students still complain that the problems are too ambiguous and
lead to too many different parameter groups. Several problem assignments now contain a few hints about selecting the repeating variables to arrive at traditional pi groups.
In Chapter 6, the “alternate forms of the Moody chart” have been resurrected as
problem assignments. Meanwhile, the three basic pipeflow problems—pressure drop,
flow rate, and pipe sizing—can easily be handled by the EES software, and examples
are given. Some newer flowmeter descriptions have been added for further enrichment.
Chapter 7 has added some new data on drag and resistance of various bodies, notably
biological systems which adapt to the flow of wind and water. Preface xiii Chapter 8 picks up from the sample plane potential flows of Section 4.10 and plunges
right into inviscidflow analysis, especially aerodynamics. The discussion of numerical methods, or computational fluid dynamics (CFD), both inviscid and viscous, steady
and unsteady, has been greatly expanded. Chapter 9, with its myriad complex algebraic
equations, illustrates the type of examples and problem assignments which can be
solved more easily using EES. A new section has been added about the suborbital X33 and VentureStar vehicles.
In the discussion of openchannel flow, Chapter 10, we have further attempted to
make the material more attractive to civil engineers by adding realworld comprehensive problems and design projects from the author’s experience with hydropower projects. More emphasis is placed on the use of friction factors rather than on the Manning roughness parameter. Chapter 11, on turbomachinery, has added new material on
compressors and the delivery of gases. Some additional fluid properties and formulas
have been included in the appendices, which are otherwise much the same. Supplements The all new Instructor’s Resource CD contains a PowerPoint presentation of key text
figures as well as additional helpful teaching tools. The list of films and videos, formerly App. C, is now omitted and relegated to the Instructor’s Resource CD.
The Solutions Manual provides complete and detailed solutions, including problem statements and artwork, to the endofchapter problems. It may be photocopied for
posting or preparing transparencies for the classroom. EES Software The Engineering Equation Solver (EES) was developed by Sandy Klein and Bill Beckman, both of the University of Wisconsin—Madison. A combination of equationsolving
capability and engineering property data makes EES an extremely powerful tool for your
students. EES (pronounced “ease”) enables students to solve problems, especially design
problems, and to ask “what if” questions. EES can do optimization, parametric analysis,
linear and nonlinear regression, and provide publicationquality plotting capability. Simple to master, this software allows you to enter equations in any form and in any order. It
automatically rearranges the equations to solve them in the most efficient manner.
EES is particularly useful for fluid mechanics problems since much of the property
data needed for solving problems in these areas are provided in the program. Air tables are builtin, as are psychometric functions and Joint Army Navy Air Force (JANAF)
table data for many common gases. Transport properties are also provided for all substances. EES allows the user to enter property data or functional relationships written
in Pascal, C, C!!, or Fortran. The EES engine is available free to qualified adopters
via a passwordprotected website, to those who adopt the text with the problems disk.
The program is updated every semester.
The EES software problems disk provides examples of typical problems in this text.
Problems solved are denoted in the text with a disk symbol. Each fully documented
solution is actually an EES program that is run using the EES engine. Each program
provides detailed comments and online help. These programs illustrate the use of EES
and help the student master the important concepts without the calculational burden
that has been previously required. xiv Preface Acknowledgments So many people have helped me, in addition to Professors John Cimbala, Sanford Klein,
and William Beckman, that I cannot remember or list them all. I would like to express
my appreciation to many reviewers and correspondents who gave detailed suggestions
and materials: Osama Ibrahim, University of Rhode Island; Richard Lessmann, University of Rhode Island; William Palm, University of Rhode Island; Deborah Pence,
University of Rhode Island; Stuart Tison, National Institute of Standards and Technology; Paul Lupke, Druck Inc.; Ray Worden, Russka, Inc.; Amy Flanagan, Russka, Inc.;
Søren Thalund, Greenland Tourism a/s; Eric Bjerregaard, Greenland Tourism a/s; Martin Girard, DH Instruments, Inc.; Michael Norton, NielsenKellerman Co.; Lisa
Colomb, JohnsonYokogawa Corp.; K. Eisele, Sulzer Innotec, Inc.; Z. Zhang, Sultzer
Innotec, Inc.; Helen Reed, Arizona State University; F. Abdel Azim ElSayed, Zagazig
University; Georges Aigret, Chimay, Belgium; X. He, Drexel University; Robert Loerke, Colorado State University; Tim Wei, Rutgers University; Tom Conlisk, Ohio State
University; David Nelson, Michigan Technological University; Robert Granger, U.S.
Naval Academy; Larry Pochop, University of Wyoming; Robert Kirchhoff, University
of Massachusetts; Steven Vogel, Duke University; Capt. Jason Durfee, U.S. Military
Academy; Capt. Mark Wilson, U.S. Military Academy; Shel...
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