A continuous belt passes upward through a chemical bath at velocity Vo and picks up a film of liquid of thickness h, density p, and viscosity μ. Gravity tends to make the liquid drain down, butthe 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. Use the shell-balance approach to (1) derive the governing differential equations. (2) State the boundary conditions for the systems. (3) Determine the velocity profile. Clearly list any assumptions needed. [DO NOT sketch the velocity profile.]

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