A Newtonian liquid with viscosity $$ and density $$ is flowing out a slit and onto a slide

as shown in the figure below. The slit gap thickness and the film thickness on the slide are

$H$ and $,$ respectively. The angle between the slit wall and the direction of gravity is $.$

It is assumed that the shell balance approach is applicable in both sections I and II$.$

$($a$)$ Derive the average velocity in section I when its pressure gradient is $\frac{p_0-p_L}{L}.$

$($b$)$ Derive the average velocity in section II$.$

$($c$)$ Determine the pressure gradient in section I when $H=.$