Question

Storage tank 18 m Pump Water is pumped from a lake to a storage tank 18 m above at a rate of 64 L/s while consuming 21.2 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. b) AP- a) 1 kPa

Answer 1

(a)

Mass flow rate of water,

m = $\rho$ * volume flow rate

m = 1000 * 64*10^-3 = 64 kg/s

Change in mechanical energy of fluid,

$\Delta$E = m [(P2 - P1 / $\rho$ ) + (V2² - V1² / 2) + g(h2 - h1)]

$\Delta$E = 64 [0 + 0 + 9.8*(18 - 0)]

$\Delta$E = 11289.6 W =  11.28 kW

Efficiency of pump motor unit,

$\eta$ = $\Delta$ E / W = 11.28 / 21.2

$\eta$ = 0.5325

$\eta$ = 53.25 %

(b)

Pressure b/w inlet and the exit of the pump,

$\Delta$P =  $\Delta$E / volume flow rate

$\Delta$P = 11.28 / 64*10^-3

$\Delta$P =  176.4 kPa