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 π (length). Using the Buckingham p theorem, find a dimensionless function for the coefficient f.
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