Published: June 2015
The classic textbook on fluid mechanics is revised and updated by Dr. David Dowling to better illustrate this important subject for modern students.
With topics and concepts presented in a clear and accessible way, Fluid Mechanics guides students from the fundamentals to the analysis and application of fluid mechanics, including compressible flow and such diverse applications as aerodynamics and geophysical fluid mechanics. Its broad and deep coverage is ideal for both a first or second course in fluid dynamics at the graduate or advanced undergraduate level, and is well-suited to the needs of modern scientists, engineers, mathematicians, and others seeking fluid mechanics knowledge.
Table of Contents- 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
