Consider flow between infinite, parallel plates. The upper plate moves to the right ( \(+x\) direction) at \(v_{x}=3 \mathrm{~mm} / \mathrm{s}\). There is no pressure variation in the \(x\)-direction, but there is a constant body force in that direction due to the action of an imposed electric field, \(F_{\text {body }}=800 \mathrm{~N} / \mathrm{m}^{3}\). The gap between the plates is \(h=0.1 \mathrm{~mm}\). The liquid viscosity is \(0.02 \mathrm{Ns} / \mathrm{m}^{2}\).

a. Derive the differential equation governing the liquid flow.

b. What are the boundary conditions if the lower plate at \(y=0\) is stationary?

c. Where is the location of maximum velocity located?

d. What is the volumetric flow rate between the plates for a plate width of \(0.1 \mathrm{~m}\) ?