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Fluid Mechanics McGraw-Hill Series in Mechanical Engineering 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 Histand and Alciatore Introduction to Mechatronics and Measurement Systems Holman Experimental Methods for Engineers Howell and Buckius Fundamentals of Engineering Thermodynamics Jaluria Design and Optimization of Thermal Systems Juvinall Engineering Considerations of Stress, Strain, and Strength Kays and Crawford Convective Heat and Mass Transfer Kelly Fundamentals of Mechanical Vibrations 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 Boundary-Layer 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 Stoecker and Jones Refrigeration and Air Conditioning Turn s An Introduction to Combustion: Concepts and Applications Ullman The Mechanical Design Process Wark Advanced Thermodynamics for Engineers Wark and Richards Thermodynamics White Viscous Fluid Flow Zeid CAD/CAM Theory and Practice 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 Bangkok Bogotá Caracas Lisbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto 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 text- books on fluid mechanics and heat transfer. During 1979–1990 he was editor-in-chief of the ASME Journal of Fluids Engi- neering and then served from 1991 to 1997 as chairman of the ASME Board of Edi- tors 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 General Approach xi Preface The fourth edition of this textbook sees some additions and deletions but no philo- sophical 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 se- mester. The more specialized and applied topics from Chapters 7 to 11 are then cov- ered at our university in a second semester. The informal, student-oriented style is re- tained and, if it succeeds, has the flavor of an interactive lecture by the author. 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 practi- cal and realistic fluids engineering experiences. Problems are grouped according to topic, and some are labeled either with an asterisk (especially challenging) or a com- puter-disk icon (where computer solution is recommended). A number of new pho- tographs 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 chap- ters. These comprehensive problems grow and recur throughout the book as new con- cepts arise. Six more open-ended design projects have been added, making 15 projects in all. The projects allow the student to set sizes and parameters and achieve good de- sign with more than one approach. An entirely new addition is a set of 95 multiple-choice problems suitable for prepar- ing 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. Learning Tools Content Changes New to this book, and to any fluid mechanics textbook, is a special appendix, Ap- pendix 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 ex- tremely attractive tool for applied engineering problems. Not only does it solve arbi- trarily complex systems of equations, written in any order or form, but also it has built- in property evaluations (density, viscosity, enthalpy, entropy, etc.), linear and nonlinear regression, and easily formatted parameter studies and publication-quality plotting. The author is indebted to Professors Sanford Klein and William Beckman, of the Univer- sity 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 Prob- lems. 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 nu- merical goal and sometimes directly applying yourself and hoping for the best result. 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 ex- ample, the discussion of the fluid acceleration vector has been moved entirely to Chap- ter 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 problem- solving 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 rigid-body motions. An improved section on pressure measurement discusses modern microsensors, such as the fused-quartz bourdon tube, micromachined silicon capacitive and piezoelectric sensors, and tiny (2 mm long) silicon resonant-frequency devices. Chapter 3 tightens up the energy equation discussion and retains the plan that Bernoulli’s equation comes last, after control-volume mass, linear momentum, angu- lar 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 ba- sic partial differential equations of fluid mechanics. More extensive discussion con- tinues 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 con- tain 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 pipe-flow 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. xii Preface Supplements EES Software Chapter 8 picks up from the sample plane potential flows of Section 4.10 and plunges right into inviscid-flow analysis, especially aerodynamics. The discussion of numeri- cal 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 X- 33 and VentureStar vehicles. In the discussion of open-channel flow, Chapter 10, we have further attempted to make the material more attractive to civil engineers by adding real-world comprehen- sive problems and design projects from the author’s experience with hydropower proj- ects. More emphasis is placed on the use of friction factors rather than on the Man- ning 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. 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, for- merly App. C, is now omitted and relegated to the Instructor’s Resource CD. The Solutions Manual provides complete and detailed solutions, including prob- lem statements and artwork, to the end-of-chapter problems. It may be photocopied for posting or preparing transparencies for the classroom. The Engineering Equation Solver (EES) was developed by Sandy Klein and Bill Beck- man, both of the University of Wisconsin—Madison. A combination of equation-solving 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 publication-quality plotting capability. Sim- ple 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 ta- bles are built-in, as are psychometric functions and Joint Army Navy Air Force (JANAF) table data for many common gases. Transport properties are also provided for all sub- stances. EES allows the user to enter property data or functional relationships written in Pascal, C, Cϩϩ, or Fortran. The EES engine is available free to qualified adopters via a password-protected 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 on-line 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. Preface xiii 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, Uni- versity of Rhode Island; William Palm, University of Rhode Island; Deborah Pence, University of Rhode Island; Stuart Tison, National Institute of Standards and Technol- ogy; Paul Lupke, Druck Inc.; Ray Worden, Russka, Inc.; Amy Flanagan, Russka, Inc.; Søren Thalund, Greenland Tourism a/s; Eric Bjerregaard, Greenland Tourism a/s; Mar- tin Girard, DH Instruments, Inc.; Michael Norton, Nielsen-Kellerman Co.; Lisa Colomb, Johnson-Yokogawa Corp.; K. Eisele, Sulzer Innotec, Inc.; Z. Zhang, Sultzer Innotec, Inc.; Helen Reed, Arizona State University; F. Abdel Azim El-Sayed, Zagazig University; Georges Aigret, Chimay, Belgium; X. He, Drexel University; Robert Lo- erke, 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; Sheldon Green, University of British Columbia; Robert Martinuzzi, University of Western Ontario; Joel Ferziger, Stanford University; Kishan Shah, Stanford University; Jack Hoyt, San Diego State University; Charles Merkle, Pennsylvania State University; Ram Balachandar, Univer- sity of Saskatchewan; Vincent Chu, McGill University; and David Bogard, University of Texas at Austin. The editorial and production staff at WCB McGraw-Hill have been most helpful throughout this project. Special thanks go to Debra Riegert, Holly Stark, Margaret Rathke, Michael Warrell, Heather Burbridge, Sharon Miller, Judy Feldman, and Jen- nifer Frazier. Finally, I continue to enjoy the support of my wife and family in these writing efforts. xiv Preface Preface xi Chapter 1 Introduction 3 1.1 Preliminary Remarks 3 1.2 The Concept of a Fluid 4 1.3 The Fluid as a Continuum 6 1.4 Dimensions and Units 7 1.5 Properties of the Velocity Field 14 1.6 Thermodynamic Properties of a Fluid 16 1.7 Viscosity and Other Secondary Properties 22 1.8 Basic Flow-Analysis Techniques 35 1.9 Flow Patterns: Streamlines, Streaklines, and Pathlines 37 1.10 The Engineering Equation Solver 41 1.11 Uncertainty of Experimental Data 42 1.12 The Fundamentals of Engineering (FE) Examination 43 1.13 Problem-Solving Techniques 44 1.14 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 Pressure and Pressure Gradient 59 2.2 Equilibrium of a Fluid Element 61 2.3 Hydrostatic Pressure Distributions 63 2.4 Application to Manometry 70 2.5 Hydrostatic Forces on Plane Surfaces 74 vii Contents 2.6 Hydrostatic Forces on Curved Surfaces 79 2.7 Hydrostatic Forces in Layered Fluids 82 2.8 Buoyancy and Stability 84 2.9 Pressure Distribution in Rigid-Body Motion 89 2.10 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 Basic Physical Laws of Fluid Mechanics 129 3.2 The Reynolds Transport Theorem 133 3.3 Conservation of Mass 141 3.4 The Linear Momentum Equation 146 3.5 The Angular-Momentum Theorem 158 3.6 The Energy Equation 163 3.7 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 [...]... Inc.) 2 Chapter 1 Introduction 1.1 Preliminary Remarks Fluid mechanics is the study of fluids either in motion (fluid dynamics) or at rest (fluid statics) and the subsequent effects of the fluid upon the boundaries, which may be either solid surfaces or interfaces with other fluids Both gases and liquids are classified as fluids, and the number of fluids engineering applications is enormous: breathing,... provides a natural and easy complement to the theory You should keep in mind that theory and experiment should go hand in hand in all studies of fluid mechanics 1.2 The Concept of a Fluid From the point of view of fluid mechanics, all matter consists of only two states, fluid and solid The difference between the two is perfectly obvious to the layperson, and it is an interesting exercise to ask a layperson... the properties of the fluid as a function of position and time is considered to be the solution to the problem In almost all cases, the emphasis is on the space-time distribution of the fluid properties One rarely keeps track of the actual fate of the specific fluid particles.6 This treatment of properties as continuum-field functions distinguishes fluid mechanics from solid mechanics, where we are... applied shear or tangential stress A solid can resist a shear stress by a static deformation; a fluid cannot Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid The fluid moves and deforms continuously as long as the shear stress is applied As a corollary, we can say that a fluid at rest must be in a state of zero shear stress, a state often called the hydrostatic... theory of rarefied-gas flow [8] In principle, all fluid- mechanics problems can be attacked from the molecular viewpoint, but no such attempt will be made here Note that the use of continuum calculus does not preclude the possibility of discontinuous jumps in fluid properties across a free surface or fluid interface or across a shock wave in a compressible fluid (Chap 9) Our calculus in Chap 4 must be flexible... engines, filters, jets, and sprinklers, to name a few When you think about it, almost everything on this planet either is a fluid or moves within or near a fluid The essence of the subject of fluid flow is a judicious compromise between theory and experiment Since fluid flow is a branch of mechanics, it satisfies a set of welldocumented basic laws, and thus a great deal of theoretical treatment is available... nonequilibrium effects such as chemical and nuclear reactions in flowing fluids which are not treated in this text Pressure Pressure is the (compression) stress at a point in a static fluid (Fig 1.1) Next to velocity, the pressure p is the most dynamic variable in fluid mechanics Differences or gradients in pressure often drive a fluid flow, especially in ducts In low-speed flows, the actual magnitude... secondary variables which characterize specific fluid- mechanical behavior The most important of these is viscosity, which relates the local stresses in a moving fluid to the strain rate of the fluid element Viscosity When a fluid is sheared, it begins to move at a strain rate inversely proportional to a property called its coefficient of viscosity Consider a fluid element sheared in one 1.7 Viscosity... is to illustrate the type of vector operations used in fluid mechanics and to make clear the dominance of the velocity field in determining other flow properties Note: The fluid acceleration, item 2 above, is not as simple as it looks and actually involves four different terms due to the use of the chain rule in calculus (see Sec 4.1) EXAMPLE 1.5 Fluid flows through a contracting section of a duct, as... units Primary Dimensions In fluid mechanics there are only four primary dimensions from which all other dimensions can be derived: mass, length, time, and temperature.4 These dimensions and their units in both systems are given in Table 1.1 Note that the kelvin unit uses no degree symbol The braces around a symbol like {M} mean “the dimension” of mass All other variables in fluid mechanics can be expressed