An incompressible viscous flow is contained between two parallel plates separated from each other by distance b$.$ The flow is caused by the movement of the bottom plate which has a velocity U$,$ while the upper plate is fixed. The flow has zero pressure gradient in the x$-$direction. The velocity of the moving plate is U $=6\mathrm{.}5$ m$/$s and b$=1$ m$.$ a$)$ Determine the flow rate passing between the two plates per unit width $($the width is perpendicular to the drawing plane$).$ b$)$ Calculate the magnitude of the rotation. c$)$ Calculate the volumetric dilatation rate.