1. An incompressible, two-dimensional flow has the following stream function: Ψ = A·rn·sin(nθ) where n and A are constants Prove that a velocity potential exists, then find an expression for the velocity potential. Also, determine the units of A and n.
2. A temperature probe is inserted into glycerin at 20°C flowing at 1 cm/s. Approximating the probe as a 5 mm sphere, determine: a. The drag force on the sphere b. The location of the separation point c. The coefficient of drag if the velocity is 2.4 m/s
3. Derive the boundary layer equation for laminar axisymmetric flow along the outside of a cylinder.
4. Consider natural convection from a horizontal heated surface. Use Buckingham Pi Theorem to determine which dimensionless number you would used to investigate this phenomenon.