(Solved): A liquid film of constant thickness \( L \) flows down an inclined wall that makes an angle \( \the ...

A liquid film of constant thickness \( L \) flows down an inclined wall that makes an angle \( \theta \) with the horizontal. The liquid has density \( \rho \) and viscosity \( \mu \). Derive the velocity profile in terms of the fluid density and viscosity, acceleration of gravity, \( g \), angle \( \theta \), and film thickness. Use a shell momentum balance and show all steps in the derivation. Hint: Use a coordinate system aligned with the inclined wall as shown in the diagram below.