Water is pumped from a lake to a storage tank 18 m above at

Water is pumped from a lake to a storage tank 18 m above at a rate of 70 L/s while consuming 20.4 kW of electric power. The storage tank is open to the atmosphere. The heat loss in the piping system is 3.2 m. The diameter of the pipe is 5 cm on the intake side and 7 cm on the discharge side. The kinetic energy correction factor (alpha) is 1.1 everywhere. Assume the elevation difference between the pump inlet and the outlet to be negligible. Determine the overall efficiency of the pump-motor. Determine the pressure difference the inlet and exit of the pump.

Solution

Convert the flow rate to m³/s:
(70 L/s) (1 m³ / 1000 L) = 0.07 m³/s

Water\'s density is:
= 1000 kg/m³.

Find the mass flow rate:
(0.07 m³/s) (1000 kg/m³) = 70 kg/s

Work to move 1 kg of water 18 m up:
W = U = m g h
W / m = (9.81 m/s²) (18 m) = 176.58 J per kg

Energy required:
(176.58 J per kg) (70 kg/s) = 12360.6 J/s = 12360.6 W = 12.3606 kW

Pump efficiency:
= energy required / energy consumed = (12.3606 kW) / (20.4 kW) = 0.6059 = 60.59%

Pressure difference:
P = g h = (1000 kg/m³) (9.81 m/s²) (18 m) = 176580 Pa = 176.580 kPa