For the flow between two parallel plates as shown in the figure below

a$)$ Derive an expression for the velocity profile of the form $u(y)=\frac{1}{2}\frac{dp}{dx}y(y-h)+\frac{Uy}{h}$

b$)$ Plot the velocity profile against height of the channel if $dp=0dx$

c$)$ Plot the velocity profile against height of the channel if $v=0$