Question

A centrifugal pump is used to deliver 60 kg of water per second. The inlet and outlet pressures are 1 bar and 4.3 bar respectively. The suction is 2.3 m below the centre of the pump and delivery is 8.5 m above the centre of the pump. The suction and delivery pipe diameters are 200 mm and 100 mm respectively. Determine the capacity of the electric motor to run the pump in kW and per kg of water.

Answer 1

Solution.

$m=60kg;$

$p_1=1bar=10^5Pa;$

$p_2=4.3bar=4.3\sdot10^5Pa;$

$h_1=2.3m;$

$h_2=8.5m;$

$d_1=200mm=0.2m;$

$d_2=100mm=0.1m;$

$W-?$

$W= m [(p_1V_1- p_2V_2) + (Z_1 - Z_2) g- (v_1²/2 - v_2²/2) ]$

$Z_1=0m; Z_2=h_1+h_2; Z_2=10.8m;$

$V_1=V_2=1/\rho$ ;

$m=\rho Sv \implies v=m/(\rho S);$

$S=\pi d^2/4;$

$S_1=(3.14\sdot0.04m^2)/4=0.0314m^2;$

$S_2=(3.14\sdot0.01m^2)/4=0.00785m^2;$

$v_1=60kg/(1000kgm^{-3}\sdot 0.0314m^2)=1.9ms^{-1};$

$v_2=60kg/(1000kgm^{-3}\sdot0.00785m^2)=7.6ms^{-1};$

$W=60\sdot[(10^5/1000-4.3\sdot10^5/1000)+(0-10.8)\sdot9.8-(1.805-28.88)]=-24526J/s=24.526kW;$

$W/m=24.526kW/60kg=408.765kW/kg;$

Answer: $W=24.526kW;$

$W/m=408.765kW/kg.$