Problem 1 Rising Wall: Consider a thin fluid film of width W, that is attached to an infinitely long vertical wall. The fluid falls down due to gravity. At x = 0 there is a no-slip wall that is moving upwards at a speed V. At x = W, there is a free-slip surface. Assume that there is no velocity in the x direction, there are no pressure gradients, and that the flow is steady. No Slip Wall W x Free Slip Surface g a. Derive the velocity profile v as a function of x. (Hand derivation) b. Calculate the volumetric flux Q of the fluid film. (Hand derivation) C. Calculate the wall velocity V that would result in no net volume flux. d. (Hand derivation) = If we let gravity be g 10, the viscosity be v = 0.1, and the film thickness be W = 0.1. Determine the wall velocity needed to have zero net volume flux and plot the velocity profile. (Matlab script and plot)