Through a series of tests on pipe flow, h, darcy derived an equation for the friction loss in pipe flow as h l = f l d v 2 2 g in which f is a dimensionless coefficient that depends on (a) the average velocity v of the pipe flow; (b) the pipe diameter d; (c) the fluid density rho; (d) the fluid viscosity μ; and (e) the average pipe wall uneveness e (length). using the buckingham π theorem, find a dimensionless function for the coefficient f.