Q$8$: Falling Film problem.

The flow of a fluid along an inclined flat surface is shown in Figure $1.$ Such films have been studied in connection with wetted$-$wall towers, evaporation, and gas absorption experiments. Assuming the viscosity and density of the fluid are constant, determine:

i$.$ The velocity profile of the fluid.

ii$.$ The average velocity of the fluid.

iii. Fluid volumetric flow.

iv$.$ The force exerted by wall on the fluid.

$2$

Figure $1$: Schematic diagram of falling film experiment for a region length of $L$ where the velocity distribution is fully developed.