Fluid Mechanics

Dedication About the Authors Preface Acknowledgments Nomenclature Chapter 1. Introduction 1.1. Fluid Mechanics 1.2. Units of Measurement 1.3. Solids, Liquids, and Gases 1.4. Continuum Hypothesis 1.5. Molecular Transport Phenomena 1.6. Surface Tension 1.7. Fluid Statics 1.8. Classical Thermodynamics 1.9. Perfect Gas 1.10. Stability of Stratified Fluid Media 1.11. Dimensional Analysis Exercises Chapter 2. Cartesian Tensors 2.1. Scalars, Vectors, Tensors, Notation 2.2. Rotation of Axes: Formal Definition of a Vector 2.3. Multiplication of Matrices 2.4. Second-Order Tensors 2.5. Contraction and Multiplication 2.6. Force on a Surface 2.7. Kronecker Delta and Alternating Tensor 2.8. Vector Dot and Cross Products 2.9. Gradient, Divergence, and Curl 2.10. Symmetric and Antisymmetric Tensors 2.11. Eigenvalues and Eigenvectors of a Symmetric Tensor 2.12. Gauss’ Theorem 2.13. Stokes’ Theorem Exercises Chapter 3. Kinematics 3.1. Introduction and Coordinate Systems 3.2. Particle and Field Descriptions of Fluid Motion 3.3. Flow Lines, Fluid Acceleration, and Galilean Transformation 3.4. Strain and Rotation Rates 3.5. Kinematics of Simple Plane Flows 3.6. Reynolds Transport Theorem Exercises Chapter 4. Conservation Laws 4.1. Introduction 4.2. Conservation of Mass 4.3. Stream Functions 4.4. Conservation of Momentum 4.5. Constitutive Equation for a Newtonian Fluid 4.6. Navier-Stokes Momentum Equation 4.7. Noninertial Frame of Reference 4.8. Conservation of Energy 4.9. Special Forms of the Equations 4.10. Boundary Conditions 4.11. Dimensionless Forms of the Equations and Dynamic Similarity Exercises Chapter 5. Vorticity Dynamics 5.1. Introduction 5.2. Kelvin’s and Helmholtz’s Theorems 5.3. Vorticity Equation in an Inertial Frame of Reference 5.4. Velocity Induced by a Vortex Filament: Law of Biot and Savart 5.5. Vorticity Equation in a Rotating Frame of Reference 5.6. Interaction of Vortices 5.7. Vortex Sheet Exercises Chapter 6. Computational Fluid Dynamics 6.1. Introduction 6.2. The Advection-Diffusion Equation 6.3. Incompressible Flows in Rectangular Domains 6.4. Flow in Complex Domains 6.5. Velocity-Pressure Method for Compressible Flow 6.6. More to Explore Exercises Chapter 7. Ideal Flow 7.1. Relevance of Irrotational Constant-Density Flow Theory 7.2. Two-Dimensional Stream Function and Velocity Potential 7.3. Construction of Elementary Flows in Two Dimensions 7.4. Complex Potential 7.5. Forces on a Two-Dimensional Body 7.6. Conformal Mapping 7.7. Axisymmetric Ideal Flow 7.8. Three-Dimensional Potential Flow and Apparent Mass 7.9. Concluding Remarks Exercises Chapter 8. Gravity Waves 8.1. Introduction 8.2. Linear Liquid-Surface Gravity Waves 8.3. Influence of Surface Tension 8.4. Standing Waves 8.5. Group Velocity, Energy Flux, and Dispersion 8.6. Nonlinear Waves in Shallow and Deep Water 8.7. Waves on a Density Interface 8.8. Internal Waves in a Continuously Stratified Fluid Exercises Chapter 9. Laminar Flow 9.1. Introduction 9.2. Exact Solutions for Steady Incompressible Viscous Flow 9.3. Elementary Lubrication Theory 9.4. Similarity Solutions for Unsteady Incompressible Viscous Flow 9.5. Flows with Oscillations 9.6. Low Reynolds Number Viscous Flow Past a Sphere 9.7. Final Remarks Exercises Chapter 10. Boundary Layers and Related Topics 10.1. Introduction 10.2. Boundary-Layer Thickness Definitions 10.3. Boundary Layer on a Flat Plate: Blasius Solution 10.4. Falkner-Skan Similarity Solutions of the Laminar Boundary-Layer Equations 10.5. von Karman Momentum Integral Equation 10.6. Thwaites’ Method 10.7. Transition, Pressure Gradients, and Boundary-Layer Separation 10.8. Flow Past a Circular Cylinder 10.9. Flow Past a Sphere and the Dynamics of Sports Balls 10.10. Two-Dimensional Jets 10.11. Secondary Flows Exercises Chapter 11. Instability 11.1. Introduction 11.2. Method of Normal Modes 11.3. Kelvin-Helmholtz Instability 11.4. Thermal Instability: The Bénard Problem 11.5. Double-Diffusive Instability 11.6. Centrifugal Instability: Taylor Problem 11.7. Instability of Continuously Stratified Parallel Flows 11.8. Squire’s Theorem and the Orr-Sommerfeld Equation 11.9. Inviscid Stability of Parallel Flows 11.10. Results for Parallel and Nearly Parallel Viscous Flows 11.11. Experimental Verification of Boundary-Layer Instability 11.12. Comments on Nonlinear Effects 11.13. Transition 11.14. Deterministic Chaos Exercises Chapter 12. Turbulence 12.1. Introduction 12.2. Historical Notes 12.3. Nomenclature and Statistics for Turbulent Flow 12.4. Correlations and Spectra 12.5. Averaged Equations of Motion 12.6. Homogeneous Isotropic Turbulence 12.7. Turbulent Energy Cascade and Spectrum 12.8. Free Turbulent Shear Flows 12.9. Wall-Bounded Turbulent Shear Flows 12.10. Turbulence Modeling 12.11. Turbulence in a Stratified Medium 12.12. Taylor’s Theory of Turbulent Dispersion Exercises Chapter 13. Geophysical Fluid Dynamics 13.1. Introduction 13.2. Vertical Variation of Density in the Atmosphere and Ocean 13.3. Equations of Motion for Geophysical Flows 13.4. Geostrophic Flow 13.5. Ekman Layers 13.6. Shallow-Water Equations 13.7. Normal Modes in a Continuously Stratified Layer 13.8. High- and Low-Frequency Regimes in Shallow-Water Equations 13.9. Gravity Waves with Rotation 13.10. Kelvin Wave 13.11. Potential Vorticity Conservation in Shallow-Water Theory 13.12. Internal Waves 13.13. Rossby Wave 13.14. Barotropic Instability 13.15. Baroclinic Instability 13.16. Geostrophic Turbulence Exercises Chapter 14. Aerodynamics 14.1. Introduction 14.2. Aircraft Terminology 14.3. Characteristics of Airfoil Sections 14.4. Conformal Transformation for Generating Airfoil Shapes 14.5. Lift of a Zhukhovsky Airfoil 14.6. Elementary Lifting Line Theory for Wings of Finite Span 14.7. Lift and Drag Characteristics of Airfoils 14.8. Propulsive Mechanisms of Fish and Birds 14.9. Sailing against the Wind Exercises Chapter 15. Compressible Flow 15.1. Introduction 15.2. Acoustics 15.3. One-Dimensional Steady Isentropic Compressible Flow in Variable-Area Ducts 15.4. Normal Shock Waves 15.5. Operation of Nozzles at Different Back Pressures 15.6. Effects of Friction and Heating in Constant-Area Ducts 15.7. One-Dimensional Unsteady Compressible Flow in Constant-Area Ducts 15.8. Two-Dimensional Steady Compressible Flow 15.9. Thin-Airfoil Theory in Supersonic Flow Exercises Chapter 16. Introduction to Biofluid Mechanics 16.1. Introduction 16.2. The Circulatory System in the Human Body 16.3. Modeling of Flow in Blood Vessels 16.4. Introduction to the Fluid Mechanics of Plants Exercises Appendix A. Conversion Factors, Constants, and Fluid Properties Appendix B. Mathematical Tools and Resources Appendix C. Founders of Modern Fluid Dynamics Appendix D. Visual Resources Index