Question $3$

a$)$ Derive an expression for the $($velocity profile$)$ for steady, laminar, fully developed, pressure driven flow between parallel plates. Fluid is moving in the positive $x$ direction. See figure below.

b$)$ Derive an expression for the the shear stress.

c$)$ Derive an expression for the flow rate.

d$)$ Derive an expression that$($relates the maximum velocity and the average velocity.

e$)$ Sketch the velocity and shear stress profiles.

Total $[40$ Mark