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.

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.