A continuous belt, passing upward through a chemical bath at speed \(U_{0}\), picks up a liquid film of thickness \(h\), density \(ho\), and viscosity \(\mu\). Gravity tends to make the liquid drain down, but the movement of the belt keeps the liquid from running off completely. Assume that the flow is fully developed and laminar with zero pressure gradient, and that the atmosphere produces no shear stress at the outer surface of the film. State clearly the boundary conditions to be satisfied by the velocity at \(y=0\) and \(y=h\). Obtain an expression for the velocity profile.

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Uo -h Too g 41 dx |dy| p = Patm Belt P8.31 Bath