Problem $2$ SAE$-30$W Oil $(T=60C)$ flows between two parallel plates separated by a thin $(2mm)$

oil$-$filled gap. The flow is laminar and can be assumed to have a linear velocity distribution. The top plate is

moving towards the right at $4c\frac{m}{s},$ and the bottom plate is moving towards the left at $2c\frac{m}{s}.$

$2\mathrm{.}1$ Sketch the velocity distribution $u(y)$ between the plates.

$2\mathrm{.}2$ What is the shape of the shear stress distribution between the plates?

$2\mathrm{.}3$ What is the flowrate $($magnitude and direction$)$ of the oil per unit width? $(\frac{m^3}{s}\frac{?}{m})$

$2\mathrm{.}4$ What is the magnitude of the force required to pull the top plate at constant speed if its underside area is

$0\mathrm{.}3m^2?$ Include a free body diagram for the top plate.