Potential flow of a film down an inclined plate

Summary

The flow of a liquid film along a semi-infinite flat plate due to gravity is considered, the fluid being assumed inviscid and incompressible. When the Froude numberFr, based on the initial film thickness and velocity, is large compared to unity, solutions can be found by the method of matched asymptotic expansions. The fluid speed and deflection, and the pressure gradient are found toO(Fr ⁻²). Hydraulic theory enters as the first term in the outer expansion, which is valid far downstream from the leading edge. When the liquid falls vertically, the motion represents half of a freely falling jet.