III. (20%) A layer of oil is in a steady motion along a moving belt, as shown in the figure below. The

belt slides upward, at an inclination 0 and speed V. Outside the layer of oil is air at atmospheric pressure.

a) Let y = 0 be the surface of the belt and set y = h at the air-oil interface. Determine the velocity profile

in the oil, u(y).

b) Determine the shear stress along the belt.

c) Plot the velocity profile in the fluid using the computer (choose reasonable values for quantities that

may be needed; use either air or water)

h

Oil

10

Belt

+00

x