An oil pump is drawing 25 kW of electric power while pumping

An oil pump is drawing 25 kW of electric power while pumping oil with a density of 860 kg/m3 at a rate of 0.1 m3 /s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 250 kPa and the motor efficiency is 90%, determine the mechanical efficiency of the pump. Take the kinetic energy correction factor to be 1.05, hL = 0.

Diagram of the question can be found below

https://gyazo.com/4b6cfa79e9988c592802c2ce1fb33bb3

Solution

Vout = 86/(860 x 0.06^2 x pi) = 8.84 m/s

work (out) per unit mass = pressure rise/density + 0.5(Vout^2 - Vin^2) = 306.31 J/kg

Output Power = mass flow rate x work per unit mass = 26342.94 W

efficiency = 26342.94/31500 = 0.84