QUESTION2[70pts] A room humidifier uses a rotating impeller (angular velocity ) to intake water from a tank. The fluid has a kinematic viscosity and the fluids intake flow rate is . The water spreads out on the impeller surface and the thin water film eventually breaks up into drops in the air. We want to determine the thickness of the film layer . Assume that the flow is steady, incompressible, and axisymmetric. Furthermore, you may assume that the radial velocity varies linearly with r, such that vr(r,z)=r.F(z) and that the pressure in the film is everywhere atmospheric. (a) Simplify the NS equations in the radial direction with the assumption that the fluid has a solid body rotation in the angular direction, and that in the inertial term (LHS of the NS equation), the only significant term is 2 . (b) Solve the equation from part (a) to determine the expression of the radial velocity vr(r,z). (c) Use the result in (b) to obtain an expression relating the flow rate to the film thickness , , , and . (d) Droplets will form when the film thickness is below a critical value . Determine the expression of the minimum angular velocity of the impeller that will ensure that droplets are formed.