9 Course Outline

The course will likely cover:

• 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.
• Newtonian Fluids. Newtonian and inviscid stress tensors, Stokes' hypothesis. Fourier's law. Navier-Stokes equations.
• 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.
• Turbulent Flows. Reynolds decomposition, Reynolds stresses, mixing length and dimensional analysis models.