Problems from Middleman's book:
4. Consider a liquid layer falling down a wall that in inclined and angle q from horizontal.
a. Derive the differential equation for the momentum flux in terms of the forcing of gravity.
b. If the fluid is Newtonian, find the velocity profile.
c. For a Newtonian fluid, find a relation between the film thickness d, and the total flow rate per unit width.
d. Suppose that the fluid is not Newtonian, but a Bingham plastic with a stress law as follows:
use the + sign (of ±) if tyx is positive.
Find the velocity profile for the falling film for the case when tyx < t0 and when tyx > t0.
e. Explain the benefit of having a wall paint be a Bingham plastic as opposed to being a Newtonian Fluid.