Fundamental Mechanics of Fluids, Third Edition

GOVERNING EQUATIONS

Basic Conservation Laws
. Statistical and Continuum Methods
. Eulerian and Lagrangian Coordinates
. Material Derivative
. Control Volumes
. Reynolds' Transport Theorem
. Conservation of Mass
. Conservation of Momentum
. Conservation of Energy
. Discussion of Conservation Equations
. Rotation and Rate of Shear
. Constitutive Equations
. Viscosity Coefficients
. Navier-Stokes Equations
. Energy Equation
. Governing Equations for Newtonian Fluids
. Boundary Conditions
Flow Kinematics
. Flow Lines
. Circulation and Vorticity
. Stream Tubes and Vortex Tubes
. Kinematics of Vortex Lines
Special Forms of the Governing Equations
. Kelvin's Theorem
. Bernoulli Equation
. Crocco's Equation
. Vorticity Equation

IDEAL-FLUID FLOW

Two-Dimensional Potential Flows
. Stream Function
. Complex Potential and Complex Velocity
. Uniform Flows
. Source, Sink, and Vortex Flows
. Flow in a Sector
. Flow Around a Sharp Edge
. Flow Due to a Doublet
. Circular Cylinder Without Circulation
. Circular Cylinder With Circulation
. Blasius' Integral Law
. Force and Moment on a Circular Cylinder
. Conformal Transformations
. Joukowski Transformation
. Flow Around Ellipses
. Kutta Condition and the Flat-Plate Airfoil
. Symmetrical Joukowski Airfoil
. Circular-Arc Airfoil
. Joukowski Airfoil
. Schwarz-Christoffel Transformation
. Source in a Channel
. Flow Through an Aperture
. Flow Past a Vertical Flat Plate
Three-Dimensional Potential Flows
. Velocity Potential
. Stokes' Stream Function
. Solution of the Potential Equation
. Uniform Flow
. Source and Sink
. Flow Due to a Doublet
. Flow Near a Blunt Nose
. Flow Around a Sphere
. Line-Distributed Source
. Sphere in the Flow Field of a Source
. Rankine Solids
. D'Alembert's Paradox
. Forces Induced by Singularities
. Kinetic Energy of a Moving Fluid
. Apparent Mass
Surface Waves
. The General Surface-Wave Problem
. Small-Amplitude Plane Waves
. Propagation of Surface Waves
. Effect of Surface Tension
. Shallow-Liquid Waves of Arbitrary Form
. Complex Potential for Traveling Waves
. Particle Paths for Traveling Waves
. Standing Waves
. Particle Paths for Standing Waves
. Waves in Rectangular Vessels
. Waves in Cylindrical Vessels
. Propagation of Waves at an Interface

VISCOUS FLOWS OF INCOMPRESSIBLE FLUIDS

Exact Solutions
. Couette Flow
. Poiseuille Flow
. Flow Between Rotating Cylinders
. Stokes' First Problem
. Stokes' Second Problem
. Pulsating Flow Between Parallel Surfaces
. Stagnation-Point Flow
. Flow in Convergent and Divergent Channels
. Flow Over a Porous Wall
Low-Reynolds-Number Solutions
. The Stokes Approximation
. Uniform Flow
. Doublet
. Rotlet
. Stokeslet
. Rotating Sphere in a Fluid
. Uniform Flow Past a Sphere
. Uniform Flow Past a Circular Cylinder
. The Oseen Approximation
Boundary Layers
. Boundary-Layer Thickness
. The Boundary-Layer Equations
. Blasius Solution
. Falkner-Skan Solutions
. Flow Over a Wedge
. Stagnation-Point Flow
. Flow in a Convergent Channel
. Approximate Solution for a Flat Surface
. General Momentum Integral
. Kármán-Pohlhausen Approximation
. Boundary-Layer Separation
. Stability of Boundary Layers
Buoyancy-Driven Flows
. The Boussinesq Approximation
. Thermal Convection
. Boundary-Layer Approximations
. Vertical Isothermal Surface
. Line Source of Heat
. Point Source of Heat
. Stability of Horizontal Layers

COMPRESSIBLE FLOW OF INVISCID FLUIDS

Shock Waves
. Propagation of Infinitesimal Disturbances
. Propagation of Finite Disturbances
. Rankine-Hugoniot Equations
. Conditions for Normal Shock Waves
. Normal Shock-Wave Equations
. Oblique Shock Waves
One-Dimensional Flows
. Weak Waves
. Weak Shock Tubes
. Wall Reflection of Waves
. Reflection and Refraction at an Interface
. Piston Problem
. Finite-Strength Shock Tubes
. Nonadiabatic Flows
. Isentropic-Flow Relations
. Flow Through Nozzles
Multi-Dimensional Flows
. Irrotational Motion
. Janzen-Rayleigh Expansion
. Small-Perturbation Theory
. Pressure Coefficient
. Flow Over a Wave-Shaped Wall
. Pandtl-Glauert Rule for Subsonic Flow
. Ackert's Theory for Supersonic Flows
. Prandtl-Meyer Flow

Appendix A. Vector Analysis
Appendix B. Tensors
Appendix C. Governing Equations
Appendix D. Complex Variables
Appendix E. Thermodynamics
Index