Volume Using Multiple Integration

This is a PAST exam question. Please help me understand how to go about questions a and b. I think I need some kind of double integral or something?

Velocity field bewteen two plates, 1 fixed, 1 moving with u=Asin(omega*t)

Two infinite parallel plates are separated by a distance h. The space between them is filled with a Newtonian fluid, density (rho), viscosity (mu). The lower plate is fixed, but the upper plate executes a sinusoidal motion. (U=A*sin(omego*t) Calculate the velocity field between the plates, and plot some representative profiles. coordinates x-dir along plate y-dir normal to plate

Calculating rates of strain, vorticity, and rate of dilatation for 3 flows.

Calculate the rates of strain, vorticity, and rates of dilatation for 3 flows. a) u=cx, v=cy, w=-2cz b) u=c, v=w=0 c) u=2cy, v=w=0

Determining which cases represent 2-D flow with constant density.

Which of the following sets of equations represent possible cases of two-dimensional flow with constant density? a) u=x+y; v=x-y b) u=x+2y; v=x^2-y^2 c) u=4x+y; v=x-(y^2) d) u=x*t+2y; v=x^2-y*(t^2) e) u=x*t^2 ; v=x*y*t+y^2

Derive expressions for the velocity in outer and inner regions of flow in long tube.

Problem statement in attachment.