Water is pumped from a lake to a storage tank 15 m above at a rate of 70 L/s while consuming 15.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump-motor unit and (b) the pressure difference between the inlet and the exit of the pump.

(a) 66.9%

(b) 147.14 kPa

Explanation:

Given:

Elevation of the water tank z = 15 m

Water volume flow rate V = 70 L/s = 0.07 m³/s

Input electric power consumption by the pump, Welec, in = 15.4 kW

Assuming there are no frictional losses in the pipes and changes in kinetic energy, the efficiency of the pump-motor will be;

η = ΔEmech : Welec,

Where;

η is the overall efficiency

ΔEmech is the workdone to move the water pumped from the lake to a storage tank 15m above

Welec is the Input electric power consumption by the pump

Solving for ΔEmech;

ΔEmech = mgh

mass, m = density * volume

Density of water = 1000 kg/m³

m = 1000 kg/m³ * 0.07 m³/s

m = 70 kg/s

∴ ΔEmech = 70 * 9.8 * 15

= 10.3 kW

Substituting the values of ΔEmech and Welec to calculate the overall efficiency

η = (10.3 kW : 15.4 kW) * 100 %

= 0.6688 * 100 %

= 66.88 %

= 66.9 %

The overall efficiency of the pump-motor unit is = 66.9 %

(b) The pressure difference between the inlet and the exit of the pump is calculated to be;

Pressure = ΔEmech : V

= 10.3 : 0.07

= 147.14 kPa