equotions.

$[10]$ Fluid flow in a part of a mechanical system may be modeled as flow between two parallel plates, separated by $3$ mm $.$ As shown below, the top plate moves at $2m\frac{m}{s}$ to the right $($in $x$ direction$),$ and the bottom plate moves at $1m\frac{m}{s}$ to the left. The viscosity and density of the fluid is $0\mathrm{.}38N-s\frac{ec}{m^2},$ and $912k\frac{g}{m^3},$ respectfully. It may be assumed that there is not pressure gradient in the $x-$direction, which is horizontal. $($a$)$ Provide the governing equations for determining the force $($ N $)$ with which the upper plate needs to be pulled, if the upper and lower plates each have an area of $1m^2.($b$)$ Provide the force with which the upper plate needs to be pulled.