1. Derive the Navier-Stokes equations of fluid mechanics from fundamental conservation principles.
2. Derive and explain the quasi one-dimensional compressible flow equations from fundamental principles with appropriate simplifications and approximations.
3. Apply the one-dimensional flow equations to isentropic flow processes with area change, and to flows with fluid friction, heat transfer, mass addition, and other driving potentials.
4. Derive and apply the Rankine-Hugoniot equations for a normal shock.
5. Analyze flow through oblique shocks, using normal shock equations, graphs or tables.
6. Analyze supersonic flows and explain the starting problem for supersonic inlets.
7. Apply the equations for Prandtl-Meyer expansion waves and analyze flows involving discrete-approximation expansion waves.
8. Explain modes of combustion waves, and describe the major features of the detonation and deflagration modes of premixed combustion.
9. Derive the equations of inviscid, adiabatic, steady multi-dimensional flow and apply them to simple flows.
10. Derive the equations of unsteady one-dimensional homoentropic flow.
11. Explain and apply the method of characteristics to simple unsteady one-dimensional homoentropic flow, shock tube flow, and steady two-dimensional flow.
12. Derive linearized equations of transonic flow and apply them to transonic nozzle analysis.