An oil film drains steadily down the side of a vertical wall, as shown. After an initial development at the top of the wall, the film becomes independent of z and of constant thickness. Assume that w = w(x) only that the atmosphere offers no shear resistance to the film. (a) Solve Navier-Stokes for w(x). (b) Suppose that film thickness and [∂ w/∂ x] at the wall are measured. Find an expression which relates μ to this slope [∂ w/∂ x].

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Oil film Air ρ, μ