Water is pumped from a lake to a storage tank 23 m above at

Water is pumped from a lake to a storage tank 23 m above at a rate of 73 L/s while consuming 20.7 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) eta = % b) Delta P = kPa

Solution

Convert the flow rate to m³/s:
(73 L/s) (1 m³ / 1000 L) = 0.073 m³/s

Water\'s density is:
= 1000 kg/m³.

Find the mass flow rate:
(0.073 m³/s) (1000 kg/m³) = 73 kg/s

Work to move 1 kg of water 23 m up:
W = U = m g h
W / m = (9.81 m/s²) (23 m) = 225.63 J per kg

Energy required:
(225.63 J per kg) (73 kg/s) = 16470 J/s = 16470 W = 16.470 kW

Pump efficiency:
= energy required / energy consumed = (16.470 kW) / (20.7 kW) = 0.6732 = 79.56 %

Pressure difference:
P = g h = (1000 kg/m³) (9.81 m/s²) (23 m) = 2256300 Pa = 225.63 kPa