Fluid Dynamics 2

Introduction Review of inviscid fluids Continuum hypothesis Time derivatives Mass conservation Kinematic boundary condition Momentum conservation Dynamic boundary condition Steady flow past a circular cylinder The governing equations Viscosity Rate of strain tensor The stress tensor The constitutive equation Boundary conditions The energy equation Scaling estimates Compressibility Viscosity Low Reynolds number flows Properties of the Stokes equations Instantaneity Linearity Reversibility Uniqueness Minimum dissipation Solving the Stokes equations Stokes flow due to a translating sphere Dimensional analysis Brute force Comments Reciprocal Theorem Movement of rigid particles in viscous fluids Special cases Stokes flow in a corner Flow in a thin layer Lubrication theory Thrust bearing Flow in a Hele-Shaw cell Saffman-Taylor instability Gravitational spreading Vorticity generation and confinement Vorticity equation Planar flows Vorticity generation Vorticity confinement on a flat plate Stagnation point flow The bathtub vortex Boundary layers Introduction Steady boundary layers Blasius boundary layer Similarity solutions High Reynolds number flow past a wedge Outer problem The boundary layer Numerical solution Separation of the boundary layer Converging and diverging flow in a wedge Aerodynamics Complex potential Conformal mappings Flow past an ellipse with circulation Forces, drag and lift The Kutta-Joukowski condition Physical mechanism Kelvin-Helmholtz instability Rising bubbles Dimensional analysis Low Reynolds number, low capillary number High Reynolds number, low capillary number The oblate spheroidal bubble Spherical cap bubble The skirted bubble Stress tensor: EJH approach