A belt moves upward at velocity V, dragging a film of viscous liquid of thickness h as shown in the figure. Gravity is aligned with negative y direction. Near the belt, the fluid moves upward due to no-slip. At its outer edge, the film has a free surface (i.e. no shear stress) Assuming that the only non-zero velocity is v(x), with zero shear stress at the outer film edge. The fluid has viscosity u and density p. Assuming steady flow, no pressure gradient, fully developed flow. Please answer the following: What assumptions can be made about this flow scenario? Write out the N.S. equation governing this flow along the flow direction, and A). C). reduce this equation to a second order ordinary differential equation. D). Find the solution of v(x) to this ODE using appropriate Boundary Conditions.

A belt moves upward at velocity V, dragging a film of viscous liquid of thickness h as shown in the figure. Gravity is aligned with negative y direction. Near the belt, the fluid moves upward due to no-slip. At its outer edge, the film has a free surface (i.e. no shear stress) Assuming that the only non-zero velocity is v(x), with zero shear stress at the outer film edge. The fluid has viscosity u and density p. Assuming steady flow, no pressure gradient, fully developed flow. Please answer the following: What assumptions can be made about this flow scenario? Write out the N.S. equation governing this flow along the flow direction, and A). C). reduce this equation to a second order ordinary differential equation. D). Find the solution of v(x) to this ODE using appropriate Boundary Conditions.