Fluid Mechanics, Second Edition

This is the most comprehensive introductory graduate or advanced undergraduate text in fluid mechanics available. It builds from the fundamentals, often in a very general way, to widespread applications to technology and geophysics. In most areas, an understanding of this book can be followed up by specialized monographs and the research literature. The material added to this new edition will provide insights gathered over 45 years of studying fluid mechanics. Many of these insights, such as universal dimensionless similarity scaling for the laminar boundary layer equations, are available nowhere else. Likewise for the generalized vector field derivatives. Other material, such as the generalized stream function treatment, shows how stream functions may be used in three-dimensional flows. The CFD chapter enables computations of some simple flows and provides entrée to more advanced literature. *New and generalized treatment of similar laminar boundary layers. *Generalized treatment of streamfunctions for three-dimensional flow . *Generalized treatment of vector field derivatives. *Expanded coverage of gas dynamics. *New introduction to computational fluid dynamics. *New generalized treatment of boundary conditions in fluid mechanics. *Expanded treatment of viscous flow with more examples. Cover 1 Frontmatter 4 Half Title Page 4 Title Page 6 Copyright 7 Dedication 8 Table of Contents 10 Preface 20 Preface to First Edition 22 Authors Notes 0 Chapter 1: Introduction 28 1. Fluid Mechanics 28 2. Units of Measurement 29 3. Solids, Liquids, and Gases 30 4. Continuum Hypothesis 31 5. Transport Phenomena 32 6. Surface Tension 35 7. Fluid Statics 36 8. Classical Thermodynamics 39 9. Perfect Gas 43 10. Static Equilibrium of a Compressible Medium 44 Exercises 49 Literature Cited 50 Supplemental Reading 50 Chapter 2: Cartesian Tensors 51 1. Scalars and Vectors 51 2. Rotation of Axes: Formal Definition of a Vector 52 3. Multiplication of Matrices 55 4. Second-Order Tensor 56 5. Contraction and Multiplication 58 6. Force on a Surface 59 7. Kronecker Delta and Alternating Tensor 62 8. Dot Product 63 9. Cross Product 63 10. Operator: Gradient, Divergence, and Curl 64 11. Symmetric and Antisymmetric Tensors 65 12. Eigenvalues and Eigenvectors of a Symmetric Tensor 67 13. Gauss' Theorem 69 14. Stokes Theorem 0 15. Comma Notation 73 16. Boldface vs Indicial Notation 74 Exercises 74 Literature Cited 76 Supplemental Reading 76 Chapter 3: Kinematics 77 1. lntroduction 77 2. Lagrangian and Eulerian Specifications 78 3. Material Derivative 79 4. Streamline, Path Line, and Streak Line 80 5. Reference Frame and Streamline Pattern 83 6. Linear Strain Rate 83 7. Shear Strain Rate 85 8. Vorticity and Circulation 85 9. Relative Motion Near a Point: Principal Axes 87 10. Kinematic Considerations of Parallel Shear Flows 90 11. Kinematic Considerations of Vortex Flows 92 12. One-, Two-, and Three-Dimensional Flows 95 13. The Streamfunction 96 14. Polar Coordinates 99 Exercises 100 Supplemental Reading 102 Chapter 4: Conservation Laws 103 1. Introduction 103 2. Time Derivatives of Volume Integrals 104 3. Conservation of Mass 106 4. Streamfunctions: Revisited and Generalized 108 5. Origin of Forces in Fluid 109 6. Stress at a Point 111 7. Conservation of Momentum 113 8. Momentum Principle for a Fixed Volume 115 9. Angular Momentum Principle for a Fixed Volume 119 10. Constitutive Equation for Newtonian Fluid 121 11. Navier-Stokes Equation 124 12. Rotating Frame 126 13. Mechanical Energy Equation 131 14. First Law of Thermodynamics: Thermal Energy Equation 135 15. Second Law of Thermodynamics: Entropy Production 136 16. Bernoulli Equation 137 17. Applications of Bernoulli's Equation 141 18. Boussinesq Approximation 144 19. Boundary Conditions 148 Exercises 149 Literature Cited 151 Supplemental Reading 151 Chapter 5: Vorticity Dynamics 152 1. Introduction 152 2. Vortex Lines and Vortex Tubes 153 3. Role of Viscosity in Rotational and Irrotational Vortices 153 4. Kelvin's Circulation Theorem 157 5. Vorticity Equation in a Nonrotating Frame 161 6. Vorticity Equation in a Rotating Frame 163 7. Interaction of Vortices 168 8. Vortex Sheet 171 Exercises 172 Literature Cited 173 Supplemental Reading 174 Chapter 6: Irrotational Flow 175 1. Relevance of Irrotational Flow Theory 175 2. Velocity Potential: Laplace Equation 177 3. Application of Complex Variables 179 4. Flow at a Wall Angle 181 5. Sources and Sinks 183 6. Irrotational Vortex 184 7. Doublet 184 8. Flow Past a Half-Body 186 9. Flow Past a Circular Cylinder without Circulation 187 10. Flow Past a Circular Cylinder with Circulation 190 11. Forces on a Two-Dimensional Body 193 12. Source Near a Wall: Method of Images 197 13. Conformal Mapping 198 14. Flow Around an Elliptic Cylinder with Circulation 200 15. Uniqueness of Irrotational Flows 202 16. Numerical Solution of Plane Irrotational Flow 203 17. Axisymmetric Irrotational Flow 208 18. Streamfunction and Velocity Potential for Axisymmetric Flow 211 19. Simple Examples of Axisymmetric Flows 212 20. Flow Around a Streamlined Body of Revolution 214 21. Flow Around an Arbitrary Body of Revolution 215 22. Concluding Remarks 216 Exercises 217 Literature Cited 219 Supplemental Reading 219 Chapter 7: Gravity Waves 220 1. Introduction 221 2. The Wave Equation 221 3. Wave Parameters 223 4. Surface Gravity Waves 226 5. Some Features of Surface Gravity Waves 230 6. Approximations for Deep and Shallow Water 236 7. Influence of Surface Tension 240 8. Standing Waves 243 9. Group Velocity and Energy Flux 245 10. Group Velocity and Wave Dispersion 248 11. Nonlinear Steepening in a Nondispersive Medium 252 12. Hydraulic Jump 254 13. Finite Amplitude Waves of Unchanging Form in a Dispersive Medium 257 14. Stokes' Drift 0 15. Waves at a Density Interface between Infinitely Deep Fluids 261 16. Waves in a Finite Layer Overlying an Infinitely Deep Fluid 265 17. Shallow Layer Overlying an Infinitely Deep Fluid 267 18. Equations of Motion for a Continuously Stratified Fluid 269 19. Internal Waves in a Continuously Stratified Fluid 272 20. Dispersion of Internal Waves in a Stratified Fluid 275 21. Energy Considerations of Internal Waves in a Stratified Fluid 277 Exercises 281 Literature Cited 282 Chapter 8: Dynamic Similarity 283 1. Introduction 283 2. Nondimensional Parameters Determined from Differential Equations 284 3. Dimensional Matrix 288 4. Buckingham's Pi Theorem 289 5. Nondimensional Parameters and Dynamic Similarity 291 6. Comments on Model Testing 293 7. Significance of Common Nondimensional Parameters 295 Exercises 297 Literature Cited 297 Supplemental Reading 297 Chapter 9: Laminar Flow 298 1. Introduction 298 2. Analogy between Heat and Vorticity Diffusion 300 3. Pressure Change Due to Dynamic Effects 300 4. Steady Flow between Parallel Plates 301 5. Steady Flow in a Pipe 304 6. Steady Flow between Concentric Cylinders 306 7. Impulsively Started Plate: Similarity Solutions 309 8. Diffusion of a Vortex Sheet 316 9. Decay of a Line Vortex 317 10. Flow Due to an Oscillating Plate 319 11. High and Low Reynolds Number Flows 322 12. Creeping Flow Around a Sphere 324 13. Nonuniformity of Stokes' Solution and Oseen's Improvement 329 14. Hele-Shaw Flow 333 15. Final Remarks 335 Exercises 336 Literature Cited 338 Supplemental Reading 338 Chapter 10: Boundary Layers and Related Topics 339 1. Introduction 339 2. Boundary Layer Approximation 340 3. Different Measures of Boundary Layer Thickness 345 4. Boundary Layer on a Flat Plate with a Sink at the Leading Edge: Closed Form Solution 348 5. Boundary Layer on a Flat Plate: Blasius Solution 350 6. von Karman Momentum Integral 359 7. Effect of Pressure Gradient 362 8. Separation 363 9. Description of Flow Past a Circular Cylinder 366 10. Description of Flow Past a Sphere 373 11. Dynamics of Sports Balls 374 12. Two-Dimensional Jets 377 13. Secondary Flows 385 14. Perturbation Techniques 386 15. An Example of a Regular Perturbation Problem 391 16. An Example of a Singular Perturbation Problem 393 17. Decay of a Laminar Shear Layer 398 Exercises 401 Literature Cited 403 Supplemental Reading 404 Chapter 11: Computational Fluid Dynamics 405 1. Introduction 405 2. Finite Difference Method 407 3. Finite Element Method 412 4. Incompressible Viscous Fluid Flow 420 5. Two Examples 433 6. Concluding Remarks 451 Exercises 454 Literature Cited 455 Chapter 12: Instability 456 1. Introduction 457 2. Method of Normal Modes 458 3. Thermal Instability: The Benard Problem 0 4. Double-Diffusive Instability 471 5. Centrifugal Instability: Taylor Problem 475 6. Kelvin-Helmholtz Instability 480 7. Instability of Continuously Stratified Parallel Flows 488 8. Squire's Theorem and Orr-Sommerfeld Equation 494 9. Inviscid Stability of Parallel Flows 498 10. Some Results of Parallel Viscous Flows 502 11. Experimental Verification of Boundary Layer Instability 507 12. Comments on Nonlinear Effects 509 13. Transition 510 14. Deterministic Chaos 512 Exercises 520 Literature Cited 522 Chapter 13: Turbulence 523 1. Introduction 523 2. Historical Notes 525 3. Averages 526 4. Correlations and Spectra 529 5. Averaged Equations of Motion 533 6. Kinetic Energy Budget of Mean Flow 539 7. Kinetic Energy Budget of Turbulent Flow 541 8. Turbulence Production and Cascade 544 9. Spectrum of Turbulence in Inertial Subrange 547 10. Wall-Free Shear Flow 549 11. Wall-Bounded Shear Flow 555 12. Eddy Viscosity and Mixing Length 563 13. Coherent Structures in a Wall Layer 566 14. Turbulence in a Stratified Medium 567 15. Taylor's Theory of Turbulent Dispersion 573 Exercises 579 Literature Cited 580 Supplemental Reading 581 Chapter 14: Geophysical Fluid Dynamics 582 1. Introduction 582 2. Vertical Variation of Density in Atmosphere and Ocean 584 3. Equations of Motion 586 4. Approximate Equations for a Thin Layer on a Rotating Sphere 589 5. Geostrophic Flow 591 6. Ekman Layer at a Free Surface 596 7. Ekman Layer on a Rigid Surface 601 8. Shallow-Water Equations 604 9. Normal Modes in a Continuously Stratified Layer 606 10. High- and Low-Frequency Regimes in Shallow-Water Equations 613 11. Gravity Waves with Rotation 615 12. Kelvin Wave 618 13. Potential Vorticity Conservation in Shallow-Water Theory 622 14. Internal Waves 625 15. Rossby Wave 635 16. Barotropic Instability 640 17. Baroclinic Instability 642 18. Geostrophic Turbulence 650 Exercises 653 Literature Cited 654 Chapter 15: Aerodynamics 656 1. Introduction 656 2. The Aircraft and Its Controls 657 3. Airfoil Geometry 660 4. Forces on an Airfoil 660 5. Kutta Condition 662 6. Generation of Circulation 663 7. Conformal Transformation for Generating Airfoil Shape 665 8. Lift of Zhukhovsky Airfoil 669 9. Wing of Finite Span 672 10. Lifting Line Theory of Prandtl and Lanchester 673 11. Results for Elliptic Circulation Distribution 678 12. Lift and Drag Characteristics of Airfoils 680 13. Propulsive Mechanisms of Fish and Birds 682 14. Sailing Against the Wind 683 Exercises 685 Literature Cited 687 Supplemental Reading 687 Chapter 16: Compressible Flow 688 1. Introduction 688 2. Speed of Sound 692 3. Basic Equations for One-Dimensional Flow 694 4. Stagnation and Sonic Properties 698 5. Area-Velocity Relations in One-Dimensional Isentropic Flow 703 6. Normal Shock Wave 707 7. Operation of Nozzles at Different Back Pressures 712 8. Effects of Friction and Heating in Constant-Area Ducts 717 9. Mach Cone 721 10. Oblique Shock Wave 723 11. Expansion and Compression in Supersonic Flow 727 12. Thin Airfoil Theory in Supersonic Flow 729 Exercises 731 Literature Cited 732 Supplemental Reading 733 Backmatter 734 Appendix A: Some Properties of Common Fluids 734 Appendix B: Curvilinear Coordinates 737 Appendix C: Founders of Modern Fluid Dynamics 742 Index 745 Back Cover 766 Referex This is the most comprehensive introductory graduate or advanced undergraduate text in fluid mechanics available. It builds from the fundamentals, often in a very general way, to widespread applications to technology and geophysics. In most areas, an understanding of this book can be followed up by specialized monographs and the research literature.

The material added to this new edition will provide insights gathered over 45 years of studying fluid mechanics. Many of these insights, such as universal dimensionless similarity scaling for the laminar boundary layer equations, are available nowhere else. Likewise for the generalized vector field derivatives. Other material, such as the generalized stream function treatment, shows how stream functions may be used in three-dimensional flows. The CFD chapter enables computations of some simple flows and provides entrée to more advanced literature.

*New and generalized treatment of similar laminar boundary layers.
*Generalized treatment of streamfunctions for
three-dimensional flow .
*Generalized treatment of vector field derivatives.
*Expanded coverage of gas dynamics.
*New introduction to computational fluid dynamics.
*New generalized treatment of boundary conditions in fluid mechanics.
*Expanded treatment of viscous flow with more examples. This book is a basic introduction to the subject of fluid mechanics and is intended for undergraduate and beginning graduate students of science and engineering. There is enough material in the book for at least two courses. No previous knowledge of the subject is assumed, and much of the text is suitable in a first course on the subject. On the other hand, a selection of the advanced topics could be used in a second course. I have not tried to indicate which sections should be considered advanced; the choice often depends on the teacher, the university, and the field of study. Particular effort has been made to make the presentation clear and accurate and at the same time easy enough for students. Mathematically rigorous approaches have been avoided in favor of the physically revealing ones.