Introduction to Fluid Mechanics Edward J. Schaffer OXFORD UNIVERSITY PRESS INTRODUCTION TO FLUID MECHANICS INTRODUCTION TO FLUID MECHANICS Edward J. Duke University Ira M. Katz Lafayette College James P.
Schaffer Lafayette College New York Oxford OXFOR D U N IVE RSITY PR ESS 2005 This book is dedicated to Nana and Pops, who inspired me, Meg, who loved me, and Mike, Erin, and Kerry, who cheered me on. —EJS Oxford University Press Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto Copyright © 2005 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.com Oxford is a registered trademark of Oxford University Press All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Shaughnessy, Edward J. Introduction to fluid mechanics/Edward J.1'06—dc22 2004044802 Printing number: 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper CONTENTS PREFACE xiii 1 F U N D A M E N TA L S CHAPTER 1 Fundamental Concepts 1.2 Gases, Liquids, and Solids 14 1.3 Methods of Description 22 1.2 Continuum and Noncontinuum Descriptions 24 1.6 Choice of Description 28 1.4 Dimensions and Unit Systems 29 1.4 Preferred Unit Systems 32 1.6 Summary 35 Problems 36 CHAPTER 2 Fluid Properties 2.1 Introduction 43 v vi CONTENTS 2.2 Mass, Weight, and Density 43 2.1 Pressure Variation in a Stationary Fluid 54 2.3 Buoyancy and Archimedes’ Principle 58 2.4 Pressure Variation in a Moving Fluid 60 2.4 Temperature and Other Thermal Properties 64 2.2 Coefficient of Thermal Expansion 67 2.5 The Perfect Gas Law 70 2.1 Internal Energy, Enthalpy, and Specific Heats of a Perfect Gas 70 2.2 Limits of Applicability 71 2.6 Bulk Compressibility Modulus 73 2.1 Speed of Sound 76 2.1 Pressure Jump Across a Curved Interface 87 2.2 Contact Angle and Wetting 90 2.10 Summary 97 Problems 99 CHAPTER 3 Case Studies in Fluid Mechanics 3.2 Common Dimensionless Groups in Fluid Mechanics 105 3.1 Flow in a Round Pipe 115 3.2 Flow Through Area Change 120 3.3 Pump and Fan Laws 124 3.4 Flat Plate Boundary Layer 128 3.5 Drag on Cylinders and Spheres 132 3.6 Lift and Drag on Airfoils 137 CONTENTS vii 3.4 Summary 140 Problems 141 CHAPTER 4 Fluid Forces 4.2 Classification of Fluid Forces 148 4.3 The Origins of Body and Surface Forces 149 4.1 Flow Over a Flat Plate 171 4.2 Flow Through a Round Pipe 173 4.3 Lift and Drag 175 4.6 Stress in a Fluid 178 4.7 Force Balance in a Fluid 187 4.8 Summary 190 Problems 191 CHAPTER 5 Fluid Statics 5.1 Integral Hydrostatic Equation 202 5.2 Differential Hydrostatic Equation 205 5.4 Hydrostatic Pressure Distribution 210 5.1 Constant Density Fluid in a Gravity Field 211 5.2 Variable Density Fluid in a Gravity Field 218 5.3 Constant Density Fluid in Rigid Rotation 222 5.4 Constant Density Fluid in Rectilinear Acceleration 229 5.1 Planar Aligned Surface 234 5.2 Planar Nonaligned Surface 238 5.1 Planar Aligned Surface 256 5.2 Planar Nonaligned Surface 260 5.7 Resultant Force and Point of Application 267 5.8 Buoyancy and Archimedes’ Principle 269 5.9 Equilibrium and Stability of Immersed Bodies 275 5.10 Summary 278 Problems 280 viii CONTENTS CHAPTER 6 The Velocity Field and Fluid Transport 6.2 The Fluid Velocity Field 300 6.4 The Substantial Derivative 319 6.5 Classification of Flows 320 6.1 One-, Two-, and Three-Dimensional Flow 321 6.2 Uniform, Axisymmetric, and Spatially Periodic Flow 327 6.3 Fully Developed Flow 331 6.4 Steady Flow, Steady Process, and Temporally Periodic Flow 332 6.6 No-Slip, No-Penetration Boundary Conditions 336 6.8 Average Velocity and Flowrate 358 6.9 Summary 363 Problems 365 CHAPTER 7 Control Volume Analysis 7.2 Basic Concepts: System and Control Volume 376 7.3 System and Control Volume Analysis 377 7.4 Reynolds Transport Theorem for a System 381 7.5 Reynolds Transport Theorem for a Control Volume 382 7.6 Control Volume Analysis 385 7.4 Angular Momentum Balance 439 7.7 Summary 450 Problems 452 CHAPTER 8 Flow of an Inviscid Fluid: the Bernoulli Equation 8.2 Frictionless Flow Along a Streamline 475 CONTENTS ix 8.1 Bernoulli Equation for an Incompressible Fluid 479 8.3 Bernoulli Equation for a Compressible Fluid 487 8.4 Static, Dynamic, Stagnation, and Total Pressure 490 8.5 Applications of the Bernoulli Equation 496 8.4 Flow through Area Change 511 8.5 Draining of a Tank 518 8.6 Relationship to the Energy Equation 521 8.7 Summary 524 Problems 526 CHAPTER 9 Dimensional Analysis and Similitude 9.2 Buckingham Pi Theorem 536 9.3 Repeating Variable Method 540 9.4 Similitude and Model Development 549 9.5 Correlation of Experimental Data 554 9.6 Application to Case Studies 557 9.1 DA of Flow in a Round Pipe 557 9.2 DA of Flow through Area Change 558 9.3 DA of Pump and Fan Laws 559 9.4 DA of Flat Plate Boundary Layer 561 9.5 DA of Drag on Cylinders and Spheres 562 9.6 DA of Lift and Drag on Airfoils 562 9.7 Summary 563 Problems 564 2 D I F F E R E NTI A L A N A LYS I S O F F L O W CHAPTER 10 Elements of Flow Visualization and Flow Structure 10.1 Particle Path, Velocity, Acceleration 578 10.2 Lagrangian Fluid Properties 589 x CONTENTS 10.3 The Eulerian–Lagrangian Connection 590 10.4 Material Lines, Surfaces, and Volumes 592 10.5 Pathlines and Streaklines 597 10.6 Streamlines and Streamtubes 603 10.7 Motion and Deformation 607 10.9 Rate of Rotation 619 10.3 Irrotational Flow and Velocity Potential 632 10.10 Rate of Expansion 635 10.2 Incompressible Fluid and Incompressible Flow 638 10.11 Rate of Shear Deformation 650 10.12 Summary 653 Problems 654 CHAPTER 11 Governing Equations of Fluid Dynamics 11.4 Constitutive Model for a Newtonian Fluid 671 11.5 Navier–Stokes Equations 678 11.2 Derivation of the Bernoulli Equation 692 11.7 The Energy Equation 699 11.1 Initial and Boundary Conditions 702 11.3 Computational Fluid Dynamics (CFD) 706 11.9 Summary 708 Problems 709 CHAPTER 12 Analysis of Incompressible Flow 12.2 Steady Viscous Flow 718 12.1 Plane Couette Flow 720 CONTENTS xi 12.2 Circular Couette Flow 723 12.3 Poiseuille Flow Between Parallel Plates 732 12.4 Poiseuille Flow in a Pipe 737 12.5 Flow over a Cylinder (CFD) 741 12.3 Unsteady Viscous Flow 744 12.1 Startup of Plane Couette Flow 749 12.2 Unsteady Flow over a Cylinder (CFD) 752 12.2 Steady Turbulent Flow Between Parallel Plates (CFD) 757 12.5 Inviscid Irrotational Flow 760 12.1 Plane Potential Flow 761 12.2 Elementary Plane Potential Flows 769 12.3 Superposition of Elementary Plane Potential Flows 772 12.4 Flow over a Cylinder with Circulation 777 12.6 Summary 780 Problems 782 3 A P P L I C ATI O N S CHAPTER 13 Flow in Pipes and Ducts 13.2 Steady, Fully Developed Flow in a Pipe or Duct 793 13.1 Major Head Loss 799 13.3 Friction Factors in Laminar Flow 805 13.4 Friction Factors in Turbulent Flow 812 13.3 Analysis of Flow in Single Path Pipe and Duct Systems 817 13.1 Minor Head Loss 824 13.2 Pump and Turbine Head 835 13.4 Analysis of Flow in Multiple Path Pipe and Duct Systems 846 13.5 Elements of Pipe and Duct System Design 851 13.1 Pump and Fan Selection 853 13.6 Summary 864 Problems 867 CHAPTER 14 External Flow 14.1 Introduction 882 xii CONTENTS 14.2 Boundary Layers: Basic Concepts 884 14.1 Laminar Boundary Layer on a Flat Plate 887 14.2 Turbulent Boundary Layer on a Flat Plate 894 14.3 Boundary Layer on an Airfoil or Other Body 898 14.3 Drag: Basic Concepts 902 14.1 Low Reynolds Number Flow 905 14.5 Lift and Drag of Airfoils 926 14.6 Summary 933 Problems 935 CHAPTER 15 Open Channel Flow 15.2 Basic Concepts in Open Channel Flow 945 15.3 The Importance of the Froude Number 952 15.1 Flow over a Bump or Depression 953 15.2 Flow in a Horizontal Channel of Varying Width 961 15.3 Propagation of Surface Waves 965 15.4 Energy Conservation in Open Channel Flow 978 15.2 Specific Energy Diagrams 986 15.5 Flow in a Channel of Uniform Depth 989 15.1 Uniform Flow Examples 994 15.2 Optimum Channel Cross Section 999 15.6 Flow in a Channel with Gradually Varying Depth 1003 15.7 Flow Under a Sluice Gate 1003 15.8 Flow Over a Weir 1009 15.9 Summary 1012 Problems 1014 Appendixes Appendix A Fluid Property Data for Various Fluids A-1 Appendix B Properties of the U. Standard Atmosphere B-1 Appendix C Unit Conversion Factors C-1 CREDITS D-1 I NDEX I-1 PREFACE This book is intended primarily for use in a one-quarter or one-semester introductory fluid mechanics course.
Our goal is to provide both a balanced introduction to all the tools used for solving fluid mechanics problems today and a foundation for further study of this important and exciting field. By learning about analytical, em- pirical (existing experimental data and accepted engineering practice), experimental (new experimental data, which will need to be obtained), and computational tools, students learn that an engineering problem can be approached in many different ways and on several different levels. This distinction of approach is especially important in fluid mechanics, where all these tools are used extensively. Although the traditional methodology of engineering fluid mechanics is thoroughly covered, this text also includes elements of differential analysis presented at a level appropriate for the target student audience.
We also make use of outputs from commer- cially available computational fluid dynamics codes to help illustrate the phenomena of interest. It is not ex- pected that students will perform any computational fluid mechanics simulations. However, with computa- tional solutions becoming routine, economical, and accessible to engineers with bachelor’s degrees, it is important that students be familiar with the use of this type of information. Therefore, computa- tionally produced figures are used in the text for expository purposes.
Throughout the text, CFD icons indicate when the subject matter directly, or indirectly, relates to computational methods. There are also a large number of figures, photographs, and solved problems to give students an understanding of the many exciting problems in fluid mechanics and the tools used to solve them. The visual approach to understanding fluid mechanics is highlighted with the use of visual CD/Kinematics/Compressibility/Compressible and Incompressible Fluids icons that point students to resources such as websites, books, and especially, the excellent CD Multi-Media Fluid Mechanics.* A third icon, called FE, is used to note material that is covered in the Fundamentals of Engineering exam. We have organized the text in three parts to give to each instructor the flexibility needed to meet the needs of his or her students and course(s).
Part 1, Fundamentals, contains the first nine chapters and covers the traditional body of introductory ma- terial. Our emphasis here is on developing an understanding of fundamental ideas. The judicious use of soft- ware packages to perform routine mathematical and graphical operations is intended to allow the student to concentrate on ideas rather than mathematics. Here, and elsewhere in the text, we employ a visual presenta- tion of results to enhance student learning and to encourage students to do the same in their own problem solv- ing.
An important feature of Part 1 is the introduction to empirical methods in Chapter 3, rather than covering this much later, as is the case in other texts. Chapter 3 includes simple but effective case studies on pipe flow, *© 2000, 2004 by Stanford University and its licensors, published by Cambridge University Press. xiii xiv PREFACE drag on spheres and cylinders, lift and drag on airfoils, and other topics. The student is thus empowered to solve important and interesting fluid mechanics problems in these areas without being forced to wait until the end of the course for the “good stuff.