The efficiency of a pump is assumed to be a function of discharge flow rate Q, pressure increase ∆p, pipe diameter D, and fluid properties density ρ and viscosity μ. Use dimensional analysis to find an expression for pump efficiency.

A thin sheet of liquid flows down a roof. The liquid sheet velocity is a function of density ρ, slope angle θ, viscosity μ, surface tension σ, roof length l, and gravity g. Develop an expression for the velocity using the F, M, L, T system with g_c.