6. [8pts] Oil, of density p and viscosity , drains steadily down the side of a vertical plate, as shown in the figure. Assume that the flow is fully developed and that the atmosphere offers no shear resistance to the surface of the film. a. Sketch an approximate shape of the velocity profile. (You can sketch on the figure) b. Solve the Navier-Stokes equation for W(X), and state the reasons for all your simplifications. c. Suppose that film thickness & and the slope of the velocity are measured with a laser- profile at the wall 8x/@wall Doppler anemometer. Find an expression for oil viscosity as a function of p, 8, g, 'aw' ox@wall Plate Mass Conservation: () a(pv) a(pw) + + + 0 Ot dy dz Navier-Stokes Equation in the z-direction Ot +u +12 +w - - Oil film + P8 +1 dw + dw dw + dr dz g Air