2. (6 pts x 5 = 30 pts) A jet of fluid with radius a flows downwards and impinges on a horizontal rigid circular plate of radius R. The fluid disperses on the plate and flows off the edge as shown in the figure. A force Fis applied to the plate to keep it stationary. The density of the fluid is p. The velocity of fluid in the jet is u. The fluid is exposed to atmosphere. The thickness of the fluid film at radius r of the plate is d(r). At the edge of the plate, der = R)= do. The velocity of the fluid film at radius r of the plate is V(r). At the edge of the plate, V(r = R) - Vo. Neglect gravity and viscous effects. Take the body of fluid as the control volume, Ra d. Your answers to following questions may contain w, a, R, and p. (a) Derive an expression of V, by applying energy balance (b) Derive an expression of V, by applying mass balance. (e) Take your answer from (a) and (b), derive an expression of de (thickness of fluid film at the plate edge). (d) Following similar steps from part (a) to (c), derive an expression for the thickness d of the film d as a function of radius r. (e) Derive an expression for force F by applying momentum balance. side view top view tu fluid R 2a (1) V. -plate R U = U = Vo