A liquid with density $800$ m$3$ and viscosity mu $=0\mathrm{.}3$ kg$/$m$$s is trapped between two vertical, parallel, and infinite walls separated by a distance h $=20$ mm$.$ The right wall is moving with constant velocity V $=8$ m$/$s upward as shown. Assuming the flow is steady, plane, and has a negligible pressure gradient, find:

a$.$ the velocity profile of the liquid using the Navier$-$Stokes equations,

b$.$ the volume flow rate per meter into the page.

c$.$ the average velocity of the flow