A continuous belt passes upward through a chemical bath at velocity v0 and picks up a film of liquid of thickness h, density, ρ, and viscosity μ. Gravity tends to make the liquid drain down, but the movement of the belt keeps the fluid from running off completely. Assume that the flow is a well-developed laminar flow with zero pressure gradient, and that the atmosphere produces no shear at the outer surface of the film.

(a) State clearly the boundary conditions at y = 0 and y = h to be satisfied by the velocity.

(b) Calculate the velocity profile.

(c) Determine the rate at which fluid is being dragged up with the belt in terms of μ; ρ; h; v0.