Flow passes through two infinitely long parallel plates, with the flow in the $x$ direction. The plates are spaced $2h$ apart and the origin of the coordinate system $(x,y)=(0,0)$ is at the mid point between the two plates $($top plate being at $y=h,$ bottom plate being at $y=-h).$

Starting with the complete Navier$-$Stokes equations in vector form, write the dimensions for each term, and describe what each term in the equation represent.

Clearly state all the assumptions $($including neglecting the body force$),$ and solve for the velocity profile in this flow.

Find the expressions for the maximum velocity of this flow $u_{\text{m}\text{a}\text{x}},$ and the wall shear stress ${}_w$