Fundamental mechanics of fluids

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 . Karman-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