A vertical belt is moving upward continuously through a liquid bath at a velocity $V$. A film of the liquid adheres to the belt, which tends to drain downward due to gravity. The equilibrium thickness of the film is determined by the steady-state condition at which the downward drainage velocity of the surface of the film is exactly equal to the upward velocity of the belt. Derive an equation for the film thickness if the fluid is

(a) Newtonian

(b) A Bingham plastic