Definitions. Fluids, material regions, control volumes.
Continuum Mechanics. The continuum approximation and
its limitations. Free path length. Density and velocity.
Kinematics Lagrangian and Eulerian derivatives. Particle
paths, streamlines, steady flows. Lagrangian and Eulerian time
derivatives. Decomposition of particle evolution in strain and
rotation. Vorticity. Linear shear flow. Circulation.
Basic Laws. Integral conservation of mass, momentum, and
energy and the second law in integral and differential forms.
Reynolds transport/Leibnitz theorem. Divergence theorem.
Relationships to computational fluid dynamics. Stress
tensor. Inviscid flow. Expansion coefficient. Integral
conservation laws for arbitrary regions.
Example Incompressible Flows. Duct flow, Bernoulli law,
effects of viscosity, entrance length, friction factor, critical
Reynold number, head loss. Stokes' second problem, similarity.
Vorticity Dynamics Vorticity and circulation. Kelvin's
theorem. Boundary layers and wakes. Starting vortices.
2D Ideal Flows Velocity potential and streamfunction.
Boundary conditions. Bernoulli law for unsteady potential flows.
Boundary Layers. The limit of small viscosity: boundary
layer equations. Boundary layer along a flat plate and similarity.
Boundary layer thickness, wall shear, displacement thickness.
