$($a$)$ Use a shell momentum balance to determine the steady$-$state velocity profile, $vz(x),$ where

the $z-$axis is parallel to the moving surface and the $x-$axis is normal to the surface, measured

from the air$-$liquid interface, as shown. State ALL assumptions.

$($b$)$ Derive an expression for the z$-$component of the force exerted by the fluid on the surface.

$($c$)$ Derive an expression for the volumetric flow rate, $Q,$ as a function of the speed of the moving

surface $V.$

$($d$)$ What value of $V$ is required to make $Q=0?$