目录 Preface xiii Acknowledgments xv Nomenclature xvii 1.Introduction 1 1.1. Fluid Mechanics 2 1.2. Units of Measurement 3 1.3. Solids, Liquids, and Gases 4 1.4. Continuum Hypothesis 5 1.5. Molecular Transport Phenomena 7 1.6. Surface Tension 11 1.7. Fluid Statics 13 1.8. Classical Thermodynamics 15 1.9. Perfect Gas 20 1.10. Stability of Stratified Fluid Media 21 1.11. Dimensional Analysis 26 Exercises 35 Literature Cited 48 Supplemental Reading 48 2.Cartesian Tensors 49 2.1. Scalars, Vectors, Tensors, Notation 50 2.2. Rotation of Axes: Formal Definition of a Vector 52 2.3. Multiplication of Matrices 54 2.4. Second-Order Tensors 55 2.5. Contraction and Multiplication 58 2.6. Force on a Surface 59 2.7. Kronecker Delta and Alternating Tensor 62 2.8. Vector Dot and Cross Products 63 2.9. Gradient, Divergence, and Curl 64 2.10. Symmetric and Antisymmetric Tensors 66 2.11. Eigenvalues and Eigenvectors of a Symmetric Tensor 68 2.12. Gauss Theorem 70 2.13. Stokes Theorem 72 Exercises 74 Literature Cited 76 Supplemental Reading 76 3.Kinematics 77 3.1. Introduction and Coordinate Systems 77 3.2. Particle and Field Descriptions of Fluid Motion 81 3.3. Flow Lines, Fluid Acceleration, and Galilean Transformation 84 3.4. Strain and Rotation Rates 88 3.5. Kinematics of Simple Plane Flows 95 3.6. Reynolds Transport Theorem 99 Exercises 103 Literature Cited 108 Supplemental Reading 108 4.Conservation Laws 109 4.1. Introduction 110 4.2. Conservation of Mass 111 4.3. Stream Functions 114 4.4. Conservation of Momentum 116 4.5. Constitutive Equation for a Newtonian Fluid 126 4.6. Navier-Stokes Momentum Equation 130 4.7. Noninertial Frame of Reference 132 4.8. Conservation of Energy 137 4.9. Special Forms of the Equations 141 4.10. Boundary Conditions 155 4.11. Dimensionless Forms of the Equations and Dynamic Similarity 162 Exercises 171 Literature Cited 192 Supplemental Reading 193 5. Vorticity Dynamics 195 5.1. Introduction 195 5.2. Kelvins and Helmholtzs Theorems 201 5.3. Vorticity Equation in an Inertial Frame of Reference 206 5.4. Velocity Induced by a Vortex Filament: Law of Biot and Savart 208 5.5. Vorticity Equation in a Rotating Frame of Reference 212 5.6. Interaction of Vortices 216 5.7. Vortex Sheet 220 Exercises 222 Literature Cited 226 Supplemental Reading 226 6.Computational Fluid Dynamics 227 ORÉTAR TRYGGVASON 6.1. Introduction 228 6.2. The Advection-Diffusion Equation 230 6.3. Incompressible Flows in Rectangular Domains 250 6.4. Flow in Complex Domains 267 6.5. Velocity-Pressure Method for Compressible Flow 275 6.6. More to Explore 282 Exercises 288 Literature Cited 291 Supplemental Reading 291 7.Ideal Flow 293 7.1. Relevance of Irrotational Constant-Density Flow Theory 294 7.2. Two-Dimensional Stream Function and Velocity Potential 296 7.3. Construction of Elementary Flows in Two Dimensions 300 7.4. Complex Potential 313 7.5. Forces on a Two-Dimensional Body 316 7.6. Conformal Mapping 319 7.7. Axisymmetric Ideal Flow 324 7.8. Three-Dimensional Potential Flow and Apparent Mass 330 7.9. Concluding Remarks 334 Exercises 335 Literature Cited 347 Supplemental Reading 347 8.Gravity Waves 349 8.1. Introduction 350 8.2. Linear Liquid-Surface Gravity Waves 353 8.3. Influence of Surface Tension 365 8.4. Standing Waves 368 8.5. Group Velocity, Energy Flux, and Dispersion 370 8.6. Nonlinear Waves in Shallow and Deep Water 378 8.7. Waves on a Density Interface 386 8.8. Internal Waves in a Continuously Stratified Fluid 392 Exercises 403 Literature Cited 407 9.Laminar Flow 409 9.1. Introduction 409 9.2. Exact Solutions for Steady Incompressible Viscous Flow 412 9.3. Elementary Lubrication Theory 419 9.4. Similarity Solutions for Unsteady Incompressible Viscous Flow 427 9.5. Flows with Oscillations 437 9.6. Low Reynolds Number Viscous Flow Past a Sphere 441 9.7. Final Remarks 450 Exercises 450 Literature Cited 466 Supplemental Reading 467 10.Boundary Layers and Related Topics 469 10.1. Introduction 470 10.2. Boundary-Layer Thickness Definitions 475 10.3. Boundary Layer on a Flat Plate: Blasius Solution 478 10.4. Falkner-Skan Similarity Solutions of the Laminar Boundary-Layer Equations 484 10.5. von Karman Momentum Integral Equation 486 10.6. Thwaites Method 488 10.7. Transition, Pressure Gradients, and Boundary-Layer Separation 494 10.8. Flow Past a Circular Cylinder 501 10.9. Flow Past a Sphere and the Dynamics of Sports Balls 509 10.10. Two-Dimensional Jets 513 10.11. Secondary Flows 520 Exercises 521 Literature Cited 531 Supplemental Reading 532 11. Instability 533 11.1. Introduction 534 11.2. Method of Normal Modes 536 11.3. Kelvin-Helmholtz Instability 537 11.4. Thermal Instability: The Bénard Problem 544 11.5. Double-Diffusive Instability 553 11.6. Centrifugal Instability: Taylor Problem 557 11.7. Instability of Continuously Stratified Parallel Flows 563 11.8. Squires Theorem and the Orr-Sommerfeld Equation 570 11.9. Inviscid Stability of Parallel Flows 573 11.10. Results for Parallel and Nearly Parallel Viscous Flows 576 11.11. Experimental Verification of Boundary-Layer Instability 582 11.12. Comments on Nonlinear Effects 584 11.13. Transition 584 11.14. Deterministic Chaos 586 Exercises 594 Literature Cited 601 12.Turbulence 603 12.1. Introduction 604 12.2. Historical Notes 606 12.3. Nomenclature and Statistics for Turbulent Flow 608 12.4. Correlations and Spectra 613 12.5. Averaged Equations of Motion 618 12.6. Homogeneous Isotropic Turbulence 626 12.7. Turbulent Energy Cascade and Spectrum 630 12.8. Free Turbulent Shear Flows 638 12.9. Wall-Bounded Turbulent Shear Flows 648 12.10. Turbulence Modeling 665 12.11. Turbulence in a Stratified Medium 671 12.12. Taylors Theory of Turbulent Dispersion 677 Exercises 682 Literature Cited 695 Supplemental Reading 697 13.Geophysical Fluid Dynamics 699 13.1. Introduction 700 13.2. Vertical Variation of Density in the Atmosphere and Ocean 702 13.3. Equations of Motion for Geophysical Flows 704 13.4. Geostrophic Flow 709 13.5. Ekman Layers 714 13.6. Shallow-Water Equations 721 13.7. Normal Modes in a Continuously Stratified Layer 723 13.8. High- and Low-Frequency Regimes in Shallow-Water Equations 729 13.9. Gravity Waves with Rotation 731 13.10. Kelvin Wave 734 13.11. Potential Vorticity Conservation in Shallow-Water Theory 738 13.12. Internal Waves 742 13.13. Rossby Wave 751 13.14. Barotropic Instability 756 13.15. Baroclinic Instability 758 13.16. Geostrophic Turbulence 765 Exercises 768 Literature Cited 770 Supplemental Reading 771 14.Aerodynamics 773 14.1. Introduction 774 14.2. Aircraft Terminology 775 14.3. Characteristics of Airfoil Sections 779 14.4. Conformal Transformation for Generating Airfoil Shapes 786 14.5. Lift of a Zhukhovsky Airfoil 791 14.6. Elementary Lifting Line Theory for Wings of Finite Span 794 14.7. Lift and Drag Characteristics of Airfoils 803 14.8. Propulsive Mechanisms of Fish and Birds 807 Literature Cited 878 14.9. Sailing Against the Wind 809 Exercises 811 Literature Cited 817 Supplemental Reading 817
15. Compressible Flow 819 15.1. Introduction 820 15.2. Acoustics 823 15.3. One-Dimensional Steady Isentropic Compressible Flow in Variable-Area Ducts 828 15.4. Normal Shock Waves 841 15.5. Operation of Nozzles at Different Back Pressures 849 15.6. Effects of Friction and Heating in Constant-Area Ducts 853 15.7. One-Dimensional Unsteady Compressible Flow in Constant-Area Ducts 858 15.8. Two-Dimensional Steady Compressible Flow 863 15.9. Thin-Airfoil Theory in Supersonic Flow 872 Exercises 875 Supplemental Reading 879
Appendix A 881 Appendix B 885 Appendix C 899 Appendix D 903 Index 905 16. Introduction to Biofluid Mechanics (Online Chapter) e1 PORTONOVO S. AYYASWAMY 16.1. Introduction e2 16.2. The Circulatory System in the Human Body e2 16.3. Modeling of Flow in Blood Vessels e18 16.4. Introduction to the Fluid Mechanics of Plants e65 Exercises e71 Acknowledgments e72 Literature Cited e72 Supplemental Reading e73
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