Consider the laminar flow fluid layer with density $$ and viscosity $$ falling down a

plane inclined at an angle $$ with respect to the horizontal. If $$ is the thickness of

the layer in the fully developed stage. The air offers no shear stress to the free

surface. The pressure gradient along the flow direction is zero.

a$)$ Find the velocity distribution $(),$ where x$-$axis points in the direction of flow

along the free surface, and the y$-$axis points toward the plane.

b$)$ Find the frictional stress on the wall