If total head available at the inlet of pipe and f1 is the loss of head due to friction in the pipe, the maximum efficiency of transmission of power (ηmax) is

Efficiency (η) of power transmission through pipe is the ratio of power available at outlet of the pipe to the power supplied at the inlet of the pipe.

ηmax = P(actual)/P(ideal) = P(outlet)/P(inlet)

P(outlet) = pgQ × (H – hf)

P(inlet) = pgQ × H

where H = total head

hf = Friction head loss

ρ = Density of liquid

Q = flow rate of liquid

g = Acceleration due to gravity

ηmax = pgQ × (H – hf)/ pgQ × H

Now, numerator and denominator pgQ canceled each other.

ηmax = (H – hf)/H