Problem $1.$ A Newtonian fluid of constant viscosity $,$ and constant density $,$ is contained in the space between a stationary inclined plane and a plate $($see image below$).$ The plate is pulled in the negative z$-$direction at a constant velocity $V.$ Using equations of motion in rectangular coordinates, calculate:

$($a$)$ Velocity profile of the fluid.

$($b$)$ The velocity $V$ for which the volumetric flow rate $(Q)$ is equal to zero. Consider the width of the plate: $w$

$($c$)$ The total force in the plate. Consider the length of the plate: $L,$ and width: $w$

Hint:

Set up your assumptions, and then apply the appropriate equation of motion for Newtonian fluids.

For part $($b$)$ set up the equation of volumetric flow rate $Q,$ and make it equal to zero. Then solve for $V.$