Viscous Flow Syllabus
 1. Derivation of mass, momentum, and total energy equation of a viscous fluid starting from the mass conservation principle, Newton's law, and the first law of thermo. Assignment #1. 2. Stokes hypothesis and Navier's stress-strain relationship. Navier-Stokes equations. Assignment #2. 3. Derivation of momentum equation from the Navier-Stokes for a constant-density and constant-viscosity fluid. 4. Couette flow. Viscous flow in journal bearing. Viscous flow in clutch. Momentum equations in cylindrical coordinates. Assignment #3. 5. External viscous flow over flat plates. Derivation of skin friction coefficient from momentum equations using boundary layer assumptions. Laminar and turbulent boundary layer over flat plates. Assignment #4. 6. Internal viscous flow in pipes and ducts. Derivation of friction factor from momentum equations. Fully-developed laminar and turbulent flow. Assignment #5. 7. Midterm break. Midterm exam. 8. Internal viscous flow using energy method. Derivation of energy equation for pipe systems from first law of thermodynamics. Pump power, valve loss coefficient. Assignment #6. 9. Short overview of the Finite Volume method and how it can be applied to 1D fully-developed flow in a channel. Exact solution to fully developed laminar flow in a channel. Assignment #7. 10. Introduction to turbulence modeling. Reynolds ensemble averaging. Reynolds-averaged mass and momentum equations. 11. Boussinesq approximation. Prandtl algebraic turbulence model. Assignment #8. 12. Derivation of the turbulence kinetic energy transport equation for advanced turbulence models. One-equation versus two-equation turbulence models. Outline of $k\epsilon$ and $k\omega$ turbulence models. Assignment #9. 13. Design optimization of the code for 1D fully-developed flow in a channel: possible implementation of variable grid spacing, higher-order interpolation polynomials, optimal relaxation parameters, etc. Design Project. 14. Example problems in preparation for the final exam. 15. Final exam.
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