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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 Bangkok Bogotá Caracas Lisbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto 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 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 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 editor-in-chief 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 Flow-Analysis 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 Problem-Solving 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 Rigid-Body 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 Angular-Momentum 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 Reynolds-Number 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 Pipe-Flow Problems 351 Flow in Noncircular Ducts 357 Minor Losses in Pipe Systems 367 Multiple-Pipe 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 Reynolds-Number and Geometry Effects 427 Momentum-Integral Estimates 431 The Boundary-Layer Equations 434 The Flat-Plate 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 Plane-Flow Solutions 498 Superposition of Plane-Flow Solutions 500 Plane Flow Past Closed-Body 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 Normal-Shock Wave 590 Operation of Converging and Diverging Nozzles 598 Compressible Duct Flow with Friction 603 Frictionless Duct Flow with Heat Transfer 613 Two-Dimensional Supersonic Flow 618 Prandtl-Meyer 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 Open-Channel 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 Uniform-Flow 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 Axial-Flow 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 Compressible-Flow 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, student-oriented 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 computer-disk 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 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 design with more than one approach. An entirely new addition is a set of 95 multiple-choice 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 publication-quality 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 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, 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 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. Preface xiii 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 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 open-channel flow, Chapter 10, we have further attempted to make the material more attractive to civil engineers by adding real-world 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 end-of-chapter 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 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. 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 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 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 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. 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, 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 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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