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.
• Thermodynamics Simple systems, extensive and intensive properties. Second law. Ideal gasses.
• 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. Complex variable theory, complex conjugate, polar form. Uniform flow, point source, point vortex, doublet, corner, Rankine body, Finite bodies. Cylinder. Unsteady boundary layer separation. Circulation, lift, and drag: Kutta-Joukowski and D'Alembert results. Conformal transformations. Flat plate and Joukowski airfoils. Contour integrals. Blasius' formulas.
• 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.