Question $2(25\%)$

A steady, incompressible, laminar flow moves between two vertical, stationary, infinite plates due to

a pressure gradient $\frac{p}{L}.$ Gravity $g$ should be considered.

a$.$ Find an expression for the velocity profile between the plates and sketch it$.(10$ points, mark the

extreme points on the sketch$).$

b$.$ Express the pressure gradient using the average velocity in the cross$-$section. $(8$ points$)$

c$.$ Express the force per unit width $\frac{F}{b}$ acting on the left plate parametrically. Indicate the direction

of the force on the left plate. $(7$ points$)$

Figure $2$: Vertical flow between two stationary plates.