Engineering
1. An incompressible, two-dimensional flow has the following stream function:
W = A’rn’sin(n6) where n and A are constants
Prove that a velocity potential exists, then find an expression for the velocity potential. Also,
determine
the units ofA 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 ifthe 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.