Fluid Mechanics Fluid Mechanics Eighth Edition Frank M. White University of Rhode Island FLUID MECHANICS, EIGHTH EDITION Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2016 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2011, 2008, and 2003. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some 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 DOC/DOC 1 0 9 8 7 6 5 ISBN 978-9-38-596549-4 MHID 9-38-596549-2 Senior Vice President, Products & Markets: Kurt L. Strand V ice President, General Manager, Products & Markets: Marty Lange Vice President, Content Design & Delivery: K imberly Meriwether David Managing Director: T homas Timp Brand Manager: T homas Scaife Director, Product Development: Rose Koos Product Developer: Lorraine Bucze k Marketing Manager: N ick McFadden Director, Content Design & Delivery: Linda Avenarius Program Manager: L ora Neyens Content Project Manager: L isa Brufl odt Content Project Manager: T ammy Juran Buyer: S usan K. Culbertson Content Licensing Specialists: Deanna Dausener Cover Image: Doug Sherman/Geofi le Compositor: Aptara®, Inc. P rinter: R. R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data White, Frank M. Fluid mechanics/Frank M. White, University of Rhode Island.—Eighth edition. pages cm Includes index. ISBN 978-9-38-596549-4 (alk. paper)—ISBN 9-38-596549-2 (alk. paper) 1. Fluid mechanics. I. Title. TA357.W48 2016 620.1’06—dc23 2014034259 The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites. www.mhhe.com About the Author Frank M. White is Professor Emeritus 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 fi rst 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 fl uid mechanics and heat transfer. From 1979 to 1990, he was editor-in-chief of the A SME 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 x i 2.9 Pressure Distribution in Rigid-Body Motion 91 2.10 Pressure Measurement 99 Chapter 1 Summary 103 Introduction 3 Problems 103 Word Problems 126 1.1 Preliminary Remarks 3 Fundamentals of Engineering Exam Problems 126 1.2 The Concept of a Fluid 4 Comprehensive Problems 127 1.3 The Fluid as a Continuum 6 Design Projects 129 1.4 Dimensions and Units 7 References 130 1.5 Properties of the Velocity Field 15 1.6 Thermodynamic Properties of a Fluid 15 Chapter 3 1.7 Viscosity and Other Secondary Properties 23 Integral Relations for a Control Volume 133 1.8 Basic Flow Analysis Techniques 39 1.9 Flow Patterns: Streamlines, Streaklines, and Pathlines 39 3.1 Basic Physical Laws of Fluid Mechanics 133 1.10 The Fundamentals of Engineering (FE) Examination 43 3.2 The Reynolds Transport Theorem 137 1.11 The History of Fluid Mechanics 43 3.3 Conservation of Mass 144 Summary 44 3.4 The Linear Momentum Equation 149 Problems 45 3.5 Frictionless Flow: The Bernoulli Equation 163 Fundamentals of Engineering Exam Problems 52 3.6 The Angular Momentum Theorem 172 Comprehensive Problems 53 3.7 The Energy Equation 178 References 56 Summary 189 Problems 189 Chapter 2 Word Problems 216 Pressure Distribution in a Fluid 59 Fundamentals of Engineering Exam Problems 217 Comprehensive Problems 218 2.1 Pressure and Pressure Gradient 59 Design Project 219 2.2 Equilibrium of a Fluid Element 61 References 219 2.3 Hydrostatic Pressure Distributions 62 2.4 Application to Manometry 69 Chapter 4 2.5 Hydrostatic Forces on Plane Surfaces 72 Differential Relations for Fluid Flow 221 2.6 Hydrostatic Forces on Curved Surfaces 80 2.7 Hydrostatic Forces in Layered Fluids 83 4.1 The Acceleration Field of a Fluid 222 2.8 Buoyancy and Stability 85 4.2 The Differential Equation of Mass Conservation 224 vii viii Contents 4.3 The Differential Equation of Linear Momentum 230 6.10 Multiple-Pipe Systems 389 4.4 The Differential Equation of Angular Momentum 237 6.11 Experimental Duct Flows: Diffuser Performance 395 4.5 The Differential Equation of Energy 238 6.12 Fluid Meters 400 4.6 Boundary Conditions for the Basic Equations 241 Summary 421 4.7 The Stream Function 246 Problems 422 4.8 Vorticity and Irrotationality 253 Word Problems 440 4.9 Frictionless Irrotational Flows 255 Fundamentals of Engineering Exam Problems 441 4.10 Some Illustrative Incompressible Viscous Flows 261 Comprehensive Problems 442 Summary 269 Design Projects 444 Problems 269 References 444 Word Problems 280 Fundamentals of Engineering Exam Problems 281 Chapter 7 Comprehensive Problems 281 Flow Past Immersed Bodies 449 References 282 7.1 Reynolds Number and Geometry Effects 449 7.2 Momentum Integral Estimates 453 Chapter 5 7.3 The Boundary Layer Equations 456 Dimensional Analysis and Similarity 285 7.4 The Flat-Plate Boundary Layer 459 5.1 Introduction 285 7.5 Boundary Layers with Pressure Gradient 468 5.2 The Principle of Dimensional Homogeneity 288 7.6 Experimental External Flows 474 5.3 The Pi Theorem 294 Summary 501 5.4 Nondimensionalization of the Basic Equations 304 Problems 502 5.5 Modeling and Similarity 313 Word Problems 515 Summary 325 Fundamentals of Engineering Exam Problems 515 Problems 325 Comprehensive Problems 516 Word Problems 333 Design Project 517 Fundamentals of Engineering Exam Problems 334 References 517 Comprehensive Problems 334 Design Projects 335 Chapter 8 References 336 Potential Flow and Computational Fluid Dynamics 521 8.1 Introduction and Review 521 Chapter 6 8.2 Elementary Plane Flow Solutions 524 Viscous Flow in Ducts 339 8.3 Superposition of Plane Flow Solutions 531 6.1 Reynolds Number Regimes 339 8.4 Plane Flow Past Closed-Body Shapes 537 6.2 Internal versus External Viscous Flows 344 8.5 Other Plane Potential Flows 547 6.3 Head Loss—The Friction Factor 347 8.6 Images 551 6.4 Laminar Fully Developed Pipe Flow 349 8.7 Airfoil Theory 554 6.5 Turbulence Modeling 351 8.8 Axisymmetric Potential Flow 562 6.6 Turbulent Pipe Flow 358 8.9 Numerical Analysis 568 6.7 Four Types of Pipe Flow Problems 366 Summary 577 6.8 Flow in Noncircular Ducts 371 Problems 577 6.9 Minor or Local Losses in Pipe Systems 380 Word Problems 588 Contents ix Comprehensive Problems 588 Problems 724 Design Projects 589 Word Problems 736 References 590 Fundamentals of Engineering Exam Problems 736 Comprehensive Problems 736 Design Projects 738 Chapter 9 References 738 Compressible Flow 593 9.1 Introduction: Review of Thermodynamics 593 Chapter 11 9.2 The Speed of Sound 598 Turbomachinery 741 9.3 Adiabatic and Isentropic Steady Flow 600 9.4 Isentropic Flow with Area Changes 606 11.1 Introduction and Classifi cation 741 9.5 The Normal Shock Wave 613 11.2 The Centrifugal Pump 744 9.6 Operation of Converging and Diverging Nozzles 621 11.3 Pump Performance Curves and Similarity Rules 750 9.7 Compressible Duct Flow with Friction 626 11.4 Mixed- and Axial-Flow Pumps: The Specifi c Speed 760 9.8 Frictionless Duct Flow with Heat Transfer 637 11.5 Matching Pumps to System Characteristics 767 9.9 Mach Waves and Oblique Shock Waves 642 11.6 Turbines 775 9.10 Prandtl-Meyer Expansion Waves 652 Summary 789 Summary 664 Problems 791 Problems 665 Word Problems 804 Word Problems 678 Comprehensive Problems 804 Fundamentals of Engineering Exam Problems 678 Design Project 806 Comprehensive Problems 679 References 806 Design Projects 680 References 681 Appendix A Physical Properties of Fluids 808 Appendix B Compressible Flow Tables 813 Chapter 10 Open-Channel Flow 683 Appendix C Conversion Factors 820 10.1 Introduction 683 Appendix D Equations of Motion in Cylindrical Coordinates 822 10.2 Uniform Flow; The Chézy Formula 689 10.3 Effi cient Uniform-Flow Channels 695 Appendix E Estimating Uncertainty in Experimental Data 824 10.4 Specifi c Energy; Critical Depth 697 10.5 The Hydraulic Jump 704 Answers to Selected Problems 826 10.6 Gradually Varied Flow 708 10.7 Flow Measurement and Control by Weirs 716 Index 833 Summary 723