Oil is being driven upwards along the inclined plane by a belt moving with a con

Question

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 are given as:

P=Patm+%u03C1g(Cos%u0398)h-%u03C1g(Cos%u0398)y          u=(gSin%u0398/v)(y2/2) +[(U/h)-(gSin%u0398/v)(h/2)]y

b. Calculate the mass flow rate of oil.

c. What is the gage pressure Pc (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.

Explanation / Answer

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