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Front Cover
Founders of Modern Fluid Dynamics
Fluid Mechanics
Copyright
Dedication
In Memory of Pijush Kundu
In Memory of Ira Cohen
About the Third Author
Contents
About the DVD
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
Literature Cited
Supplemental Reading
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
2.14. Comma Notation
Exercises
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
Chapter 5 - Vorticity Dynamics
5.1. Introduction
5.2. Kelvin’s Circulation Theorem
5.3. Helmholtz’s Vortex Theorems
5.4. Vorticity Equation in a Nonrotating Frame
5.5. Velocity Induced by a Vortex Filament: Law of Biot and Savart
5.6. Vorticity Equation in a Rotating Frame
5.7. Interaction of Vortices
5.8. Vortex Sheet
Exercises
Literature Cited
Supplemental Reading
Chapter 6 - Ideal Flow
6.1. Relevance of Irrotational Constant-Density Flow Theory
6.2. Two-Dimensional Stream Function and Velocity Potential
6.3. Construction of Elementary Flows in Two Dimensions
6.4. Complex Potential
6.5. Forces on a Two-Dimensional Body
6.6. Conformal Mapping
6.7. Numerical Solution Techniques in Two Dimensions
6.8. Axisymmetric Ideal Flow
6.9. Three-Dimensional Potential Flow and Apparent Mass
6.10. Concluding Remarks
Exercises
Literature Cited
Supplemental Reading
Chapter 7 - Gravity Waves
7.1. Introduction
7.2. Linear Liquid-Surface Gravity Waves
7.3. Influence of Surface Tension
7.4. Standing Waves
7.5. Group Velocity, Energy Flux, and Dispersion
7.6. Nonlinear Waves in Shallow and Deep Water
7.7. Waves on a Density Interface
7.8. Internal Waves in a Continuously Stratified Fluid
Exercises
Literature Cited
Chapter 8 - Laminar Flow
8.1. Introduction
8.2. Exact Solutions for Steady Incompressible Viscous Flow
8.3. Elementary Lubrication Theory
8.4. Similarity Solutions for Unsteady Incompressible Viscous Flow
8.5. Flow Due to an Oscillating Plate
8.6. Low Reynolds Number Viscous Flow Past a Sphere
8.7. Final Remarks
Exercises
Literature Cited
Supplemental Reading
Chapter 9 - Boundary Layers and Related Topics
9.1. Introduction
9.2. Boundary-Layer Thickness Definitions
9.3. Boundary Layer on a Flat Plate: Blasius Solution
9.4. Falkner-Skan Similarity Solutions of the Laminar Boundary-Layer Equations
9.5. Von Karman Momentum Integral Equation
9.6. Thwaites’ Method
9.7. Transition, Pressure Gradients, and Boundary-Layer Separation
9.8. Flow Past a Circular Cylinder
9.9. Flow Past a Sphere and the Dynamics of Sports Balls
9.10. Two-Dimensional Jets
9.11. Secondary Flows
Exercises
Literature Cited
Supplemental Reading
Chapter 10 - Computational Fluid Dynamics
10.1. Introduction
10.2. Finite-Difference Method
10.3. Finite-Element Method
10.4. Incompressible Viscous Fluid Flow
10.5. Three Examples
10.6. Concluding Remarks
Exercises
Literature Cited
Supplemental Reading
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
Literature Cited
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
12.13. Concluding Remarks
Exercises
Literature Cited
Supplemental Reading
Chapter 13 - Geophysical Fluid Dynamics
13.1. Introduction
13.2. Vertical Variation of Density in the Atmosphere and Ocean
13.3. Equations of Motion
13.4. Approximate Equations for a Thin Layer on a Rotating Sphere
13.5. Geostrophic Flow
13.6. Ekman Layer at a Free Surface
13.7. Ekman Layer on a Rigid Surface
13.8. Shallow-Water Equations
13.9. Normal Modes in a Continuously Stratified Layer
13.10. High- and Low-Frequency Regimes in Shallow-Water Equations
13.11. Gravity Waves with Rotation
13.12. Kelvin Wave
13.13. Potential Vorticity Conservation in Shallow-Water Theory
13.14. Internal Waves
13.15. Rossby Wave
13.16. Barotropic Instability
13.17. Baroclinic Instability
13.18. Geostrophic Turbulence
Exercises
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
Chapter 15 - Compressible Flow
15.1. Introduction
15.2. Acoustics
15.3. Basic Equations for One-Dimensional Flow
15.4. Reference Properties in Compressible Flow
15.5. Area-Velocity Relationship in One-Dimensional Isentropic Flow
15.6. Normal Shock Waves
15.7. Operation of Nozzles at Different Back Pressures
15.8. Effects of Friction and Heating in Constant-Area Ducts
15.9. Pressure Waves in Planar Compressible Flow
15.10. Thin Airfoil Theory in Supersonic Flow
Exercises
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
Appendix A - Conversion Factors, Constants, and Fluid Properties
A.1. Conversion Factors
A.2. Physical Constants
A.3. Properties of Pure Water at Atmospheric Pressure
A.4. Properties of Dry Air at Atmospheric Pressure
A.5. The Standard Atmosphere
Appendix B - Mathematical Tools and Resources
B.1. Partial and Total Differentiation
B.2. Changing Independent Variables
B.3. Basic Vector Calculus
B.4. The Dirac Delta function
B.5. Common Three-Dimensional Coordinate Systems
B.6. Equations in Curvilinear Coordinate Systems
Appendix C - Founders of Modern Fluid Dynamics
Ludwig Prandtl (1875–1953)
Geoffrey Ingram Taylor (1886–1975)
Supplemental Reading
Appendix D - Visual Resources
Index
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