Consider a liquid film falling down a vertical plate under the action of gravity as shown in the figure. The system is open to atmosphere and under steady state.

a$)(5$p$)$ Draw the volume element

b$)(20$p$)$ Derive the differential equation expressing the system

c$)(5$p$)$ Write the boundary conditions

d$)(10$p$)$ Solve the equation and find integral constants at steady state.