Differential analysis of fluid flow. Conservation of mass - the continuity equation. The stream function. The stream function in Cartesian coordinates. The stream function in cylindrical coordinates. The differential linear momentum equation - Cauchy’s equation. The Navier- Stoke’s equation. Derivation of Navier-Stoke’s equation for incompressible, isothermal flow. Differential analysis of fluid flow problems.
The boundary layer equations. Displacement thickness. Momentum thickness. Turbulent flat plate boundary layer. Boundary layers with pressure gradients. Drag and lift. Friction and pressure drag. Drag coefficients of common geometries. Parallel flow over flat plates. Flow over cylinders and spheres. Lift.
Compressible Flow. Stagnation properties. One dimensional isentropic flow. Isentropic flow through nozzles. Shock waves and expansion waves. Duct flow with heat transfer and negligible friction (Rayleigh flow). Adiabatic duct flow with friction.