Problems in Middleman's book:

4.30 (for this problem look how to find the solution and a way to get a more physically relevant solution at http://www.nd.edu/~mjm/rotatingsphere.nb)

Solve problem 4.20, but allow for the possibility that the flow is not perpendicular to gravity and that there can be an average pressure gradient. Also allow the fluids to have different densities.

a. Find the solution in the limit that flow is due only to an imposed pressure gradient. (assume horizontal) Plot profiles while the most important variable changes.

b. Find the solution in the limit that flow is due only to the moving wall. (assume horizontal) Plot profiles while the most important variable changes.

c. Find the solution in the limit that flow is due only to gravity (not horizontal). Plot profiles while the most important variable changes.

d. What dimensionless groups govern the flow character for this problem?