Problems from Middleman's book:

1. 3.2

2. 3.15

3. 3.27

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 t_yx is positive.

Find the velocity profile for the falling film for the case when t_yx < t₀ and when t_yx > t₀.

e. Explain the benefit of having a wall paint be a Bingham plastic as opposed to being a Newtonian Fluid.