Through a series of tests on pipe flow, H. Darcy derived an equation for the friction loss in pipe flow as
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 ρ;
(d) the fluid viscosity μ; and
(e) the average pipe wall uneveness e (length).
Using the Buckingham p theorem, find a dimensionless function for the coefficient f.