$[20$ points$]$ The $x-$velocity in a fully developed laminar flow between two parallel plates, as shown in the following figure, is given by

$u=\frac{1}{2}(-\frac{dp}{dx})(h^2-y^2)$

where the viscosity $,$ half channel height $h,$ and pressure gradient $-\frac{dp}{dx}$ are known constants. The $y-$velocity is $v=0.$

$($a$)$ Determine the volumetric strain rate, the vorticity, and the rate of angular deformation.

$($b$)$ What is the magnitude of shear stress at the plate surfaces