FLUID MECHANICS FOR ENGINEERS IN SI UNITS DAVID A. CHIN University of Miami 330 Hudson Street, NY, NY 10013 Vice President and Editorial Director, ECS: Marcia J. Horton Executive Editor: Holly Stark Field Marketing Manager: Demetrius Hall Senior Product Marketing Manager: Bram van Kempen Marketing Assistant: Jon Bryant Editorial Assistant: Amanda Brands Acquisitions Editor, Global Edition: Sourabh Maheshwari Senior Managing Editor: Scott Disanno Production Project Manager: Greg Dulles Assistant Project Editor, Global Edition: Vikash Tiwari Senior Manufacturing Controller, Global Edition: Kay Holman Program Manager: Erin Ault Media Production Manager, Global Edition: Vikram Kumar Director of Operations: Nick Sklitsis Operations Specialist: Maura Zaldivar-Garcia Cover Designer: Lumina Datamatics Cover Photo: © bankerwin/Shutterstock.com Manager, Rights and Permissions: Rachel Youdelman Senior Project Manager, Rights and Permissions: Timothy Nicholls Composition: GEX Publishing Services Typeface: 10.5pt Times LT Pro Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps.
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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 9 8 7 6 5 4 3 2 1 Typeset by GEX Publishing Services ISBN 10: 1-292-16104-3 Printed and bound in Malaysia ISBN 13: 978-1-292-16104-4 To Stephanie and Andrew. “Wherever there is a human being, there is an opportunity for a kindness.” Seneca Contents Preface 11 Chapter 1 Properties of Fluids 17 1.2 Dimensions and Units 20 1.3 Basic Concepts of Fluid Flow 26 1.1 Equation of State 36 1.2 Mixtures of Ideal Gases 37 1.4 Speed of Sound in an Ideal Gas 44 1.2 Non-Newtonian Fluids 53 1.1 Evaporation, Transpiration, and Relative Humidity 63 1.2 Cavitation and Boiling 64 1.9 Thermodynamic Properties of Liquids 67 1.10 Summary of Properties of Water and Air 69 Key Equations in Properties of Fluids 70 Problems 72 Chapter 2 Fluid Statics 87 2.2 Pressure Distribution in Static Fluids 88 2.1 Characteristics of Pressure 88 2.2 Spatial Variation in Pressure 89 2.4 Forces on Plane Surfaces 110 2.5 Forces on Curved Surfaces 120 Contents 5 2.1 Fully Submerged Bodies 127 2.2 Partially Submerged Bodies 132 2.3 Buoyancy Effects Within Fluids 138 2.7 Rigid-Body Motion of Fluids 139 2.1 Liquid with Constant Acceleration 141 2.2 Liquid in a Rotating Container 145 Key Equations in Fluid Statics 148 Problems 150 Chapter 3 Kinematics and Streamline Dynamics 177 3.1 Tracking the Movement of Fluid Particles 181 3.2 The Material Derivative 188 3.3 Dynamics of Flow along a Streamline 192 3.4 Applications of the Bernoulli Equation 202 3.1 Flow through Orifices 203 3.3 Trajectory of a Liquid Jet 214 3.5 Curved Flows and Vortices 222 3.2 Free Vortices 226 Key Equations in Kinematics and Streamline Dynamics 229 Problems 232 Chapter 4 Finite Control Volume Analysis 256 4.2 Reynolds Transport Theorem 257 4.3 Conservation of Mass 259 4.2 Free Discharges from Reservoirs 265 4.3 Moving Control Volumes 267 4.4 Conservation of Linear Momentum 268 4.1 General Momentum Equations 269 4.2 Forces on Pressure Conduits 273 4.3 Forces on Deflectors and Blades 281 4.4 Forces on Moving Control Volumes 282 4.6 Reaction of a Jet 293 4.7 Jet Engines and Rockets 296 4.5 Angular Momentum Principle 298 4.6 Conservation of Energy 307 4.1 The First Law of Thermodynamics 308 6 Contents 4.2 Steady-State Energy Equation 309 4.3 Unsteady-State Energy Equation 320 Key Equations in Finite Control Volume Analysis 323 Problems 327 Chapter 5 Differential Analysis 357 5.3 Conservation of Mass 365 5.2 The Stream Function 372 5.4 Conservation of Momentum 375 5.2 Navier–Stokes Equation 379 5.3 Nondimensional Navier–Stokes Equation 381 5.5 Solutions of the Navier–Stokes Equation 385 5.1 Steady Laminar Flow Between Stationary Parallel Plates 385 5.2 Steady Laminar Flow Between Moving Parallel Plates 388 5.3 Steady Laminar Flow Adjacent to Moving Vertical Plate 391 5.4 Steady Laminar Flow Through a Circular Tube 394 5.5 Steady Laminar Flow Through an Annulus 396 5.6 Steady Laminar Flow Between Rotating Cylinders 399 5.1 Bernoulli Equation for Steady Inviscid Flow 404 5.2 Bernoulli Equation for Steady Irrotational Inviscid Flow 407 5.4 Two-Dimensional Potential Flows 411 5.7 Fundamental and Composite Potential Flows 415 5.1 Principle of Superposition 415 5.3 Line Source/Sink Flow 418 5.4 Line Vortex Flow 421 5.5 Spiral Flow Toward a Sink 424 5.7 Flow Around a Half-Body 428 5.9 Flow Around a Circular Cylinder 437 5.1 Occurrence of Turbulence 443 5.2 Turbulent Shear Stress 443 5.3 Mean Steady Turbulent Flow 445 5.9 Conservation of Energy 446 Key Equations in Differential Analysis of Fluid Flows 449 Problems 455 Contents 7 Chapter 6 Dimensional Analysis and Similitude 477 6.2 Dimensions in Equations 477 6.1 Conventional Method of Repeating Variables 483 6.2 Alternative Method of Repeating Variables 486 6.3 Method of Inspection 487 6.4 Dimensionless Groups as Force Ratios 488 6.5 Dimensionless Groups in Other Applications 493 6.6 Modeling and Similitude 494 Key Equations for Dimensional Analysis and Similitude 506 Problems 507 Chapter 7 Flow in Closed Conduits 525 7.2 Steady Incompressible Flow 526 7.3 Friction Effects in Laminar Flow 532 7.4 Friction Effects in Turbulent Flow 536 7.1 Estimation of Pressure Changes 544 7.2 Estimation of Flow Rate for a Given Head Loss 546 7.3 Estimation of Diameter for a Given Flow Rate and Head Loss 547 7.4 Head Losses in Noncircular Conduits 548 7.5 Empirical Friction Loss Formulas 549 7.6 Local Head Losses 552 7.7 Pipelines with Pumps or Turbines 559 7.8 Building Water Supply Systems 573 7.1 Specification of Design Flows 574 7.2 Specification of Minimum Pressures 574 7.3 Determination of Pipe Diameters 576 Key Equations for Flow in Closed Conduits 583 Problems 587 Chapter 8 Turbomachines 608 8.2 Mechanics of Turbomachines 609 8.3 Hydraulic Pumps and Pumped Systems 614 8.1 Flow Through Centrifugal Pumps 616 8.6 System Characteristics 632 8 Contents 8.7 Limits on Pump Location 635 8.8 Multiple Pump Systems 640 8.9 Variable-Speed Pumps 642 8.1 Performance Characteristics of Fans 644 8.2 Affinity Laws of Fans 645 8.5 Hydraulic Turbines and Hydropower 648 8.3 Practical Considerations 658 Key Equations for Turbomachines 664 Problems 668 Chapter 9 Flow in Open Channels 693 9.1 Steady-State Continuity Equation 694 9.2 Steady-State Momentum Equation 694 9.3 Steady-State Energy Equation 711 9.3 Water Surface Profiles 724 9.2 Classification of Water Surface Profiles 725 9.4 Computation of Water Surface Profiles 737 Key Equations in Open-Channel Flow 746 Problems 749 Chapter 10 Drag and Lift 759 10.1 Friction and Pressure Drag 762 10.2 Drag and Lift Coefficients 762 10.3 Flow over Flat Surfaces 765 10.4 Flow over Curved Surfaces 767 10.3 Estimation of Drag Coefficients 770 10.1 Drag on Flat Surfaces 770 10.2 Drag on Spheres and Cylinders 774 10.3 Drag on Vehicles 781 10.4 Drag on Ships 784 10.5 Drag on Two-Dimensional Bodies 785 10.6 Drag on Three-Dimensional Bodies 786 10.7 Drag on Composite Bodies 786 10.8 Drag on Miscellaneous Bodies 789 10.4 Estimation of Lift Coefficients 791 10.1 Lift on Airfoils 791 10.2 Lift on Airplanes 794 10.3 Lift on Hydrofoils 799 Contents 9 10.4 Lift on a Spinning Sphere in Uniform Flow 800 Key Equations for Drag and Lift 803 Problems 806 Chapter 11 Boundary-Layer Flow 827 11.2 Laminar Boundary Layers 829 11.1 Blasius Solution for Plane Surfaces 829 11.2 Blasius Equations for Curved Surfaces 834 11.3 Turbulent Boundary Layers 836 11.2 Turbulent Boundary Layer on a Flat Surface 837 11.3 Boundary-Layer Thickness and Shear Stress 844 11.3 Momentum Integral Equation 850 11.4 General Formulations for Self-Similar Velocity Profiles 854 11.5 Mixing-Length Theory of Turbulent Boundary Layers 856 11.3 Velocity-Defect Law 858 11.4 One-Seventh Power Law Distribution 859 11.6 Boundary Layers in Closed Conduits 859 11.1 Smooth Flow in Pipes 860 11.2 Rough Flow in Pipes 861 11.3 Notable Contributors to Understanding Flow in Pipes 862 Key Equations for Boundary-Layer Flow 863 Problems 867 Chapter 12 Compressible Flow 884 12.2 Principles of Thermodynamics 885 12.3 The Speed of Sound 891 12.4 Thermodynamic Reference Conditions 898 12.1 Isentropic Stagnation Condition 898 12.2 Isentropic Critical Condition 903 12.5 Basic Equations of One-Dimensional Compressible Flow 905 12.6 Steady One-Dimensional Isentropic Flow 907 12.1 Effect of Area Variation 907 12.3 Flow in Nozzles and Diffusers 910 12.8 Steady One-Dimensional Non-Isentropic Flow 935 12.1 Adiabatic Flow with Friction 936 12.2 Isothermal Flow with Friction 949 12.3 Diabatic Frictionless Flow 951 12.4 Application of Fanno and Rayleigh Relations to Normal Shocks 957 10 Contents 12.9 Oblique Shocks, Bow Shocks, and Expansion Waves 962 12.2 Bow Shocks and Detached Shocks 970 12.3 Isentropic Expansion Waves 972 Key Equations in Compressible Flow 977 Problems 984 Appendix A Units and Conversion Factors 999 A.2 Conversion Factors 1000 Appendix B Fluid Properties 1003 B.3 The Standard Atmosphere 1005 B.6 Nitrogen 1008 Appendix C Properties of Areas and Volumes 1009 C.2 Properties of Circles and Spheres 1011 C.3 Volumes 1012 Appendix D Pipe Specifications 1013 D.2 Ductile Iron Pipe 1014 D.4 Physical Properties of Common Pipe Materials 1014 Bibliography 1015 Index 1026 Preface Beginning with my formative years as a graduate student at Caltech and Georgia Tech, I have applied fluid mechanics in the context of many engineering disciplines. Also, having taken all of the graduate-level fluid mechanics courses in mechanical engineering, aerospace engineer- ing, civil engineering, and geophysics, and having taught fluid mechanics for more than 30 years, I felt well qualified and motivated to author a fluid mechanics textbook for engineering students.
The unique features of this textbook are that it: (1) focuses on the basic principles of fluid mechanics that engineering students are likely to apply in their subsequent required undergraduate coursework, (2) presents the material in a rigorous fashion, and (3) provides many quantitative examples and illustrations of fluid mechanics applications. Students in all engineering disciplines where fluid mechanics is a core course should find this textbook stimulating and useful. In some chapters, the nature of the material necessitates a bias to- wards practical applications in certain engineering disciplines, and the disciplinary area of the author also contributes to the selection and presentation of practical examples throughout the text. In this latter respect, practical examples related to civil engineering applications are particularly prevalent.