$($Optional$)$ A thin layer of glycerin flows down an inclined, wide plate with the velocity distribution shown in the figure. For $h=0\mathrm{.}8cm$ and $a=20,$ determine the surface velocity, $U.$ Note that for equilibrium, the component of weight acting parallel to the plate surface must be balanced by the shearing force developed along the plate surface. In your analysis assume a unit plate width.