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with all 3 questions please

A cylindrical rod of diameter KR moves axially with velocity V.=valong the axis of a cylindrical cavity of radius R as seen in Figure 1. The pressure at both ends of the cavity is the same, so that the fluid moves through the annular region solely because of the rod motion. (a) Find the velocity distribution in the narrow annular region using shell momentum balance (35 points) (b) Find the mass rate of flow through the narrow annular region. (35 points) Prepare a qualitative sketch of the velocity profile that would be obtained if a back- pressure were imposed at the right sufficient that there is zero net volumetric flow in the annulus. (30 points) Fluid at pressure po Cylinder of inside radius R Fluid at pressure PL Rod of radius KR moving with velocity V Figure 1 Annular flow with inner cylinder moving axially