Oil is being driven upwards along the inclined plane by a

Question

Show all assumptions, derivations, integrals and calculations-

Oil is being driven upwards along the inclined plane by a belt moving with a constant velocity of U= 1 m/s. The width of the belt is b=1 m and its length is L = 20 m. The flow of oil between points A and B is assumed to be laminar and fully developed.

a. Using Navier Stokes equations show that the pressure field and velocity profile is given as:

P = P_atm + ρg(Cosθ)h - ρg(Cosθ)y

U = (gSinθ/v)(y²/2) + [(U/h) - (gSinθ/v)(h/2)]y

DO IT STEP BY STEP SHOWING EVERY ASSUMPTION AND SIMPLIFICATION

b. Calculate the mass flow rate of oil.

c. What is the gage pressure P_C(N/m²) at point C?

d. What is the power(Watts) used by the belt to draw up the oil along the inclined plane between points A and B?

e. Where will be the deviations from fully developed assumption? Overall, how good is the fully developed assumption in this flow? Explain in a few sentences.