The viscous, incompressible flow between the parallel plates is caused by both the motion of the bottom plate and pressure gradient $d\frac{P}{d}x.$

$P=(\frac{b^2}{2}U)(d\frac{P}{d}x),$ where $d\frac{P}{d}x>0.$

a$)$ Find the velpcity profile along the flow direction $($axial$)$

b$)$ Make a plot by hand or excel of the dimensionless velocity distribution to demonstrate $(\frac{u}{U}$ vs$.\frac{y}{b})$ for $P=4.$ For this case where does the maximum velocity occur?