Question

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s, determine (a) mechanical power that is converted to thermal energy (in kW) during this process due to frictional effects and (b) the pump efficiency (%). Take the density of water to be 1000 kg/m3 and g-9.81 m/s2 0.03 m /s 45 m 20 kw Pump O (a) 0.4 kW, (b) 22% o (a) 6.8 kW, (b) 66% 0 (a) 20.4 kW, (b) 18% o (a) 9.8 kW, (b) 27%

Answer 1

Applying Bernoulli's equation from pump discharge to higher reservoir. P1/rho*g + V1²/2g +Z1 = P2/rho*g +V2²/g +Z2

Since pipe diameter is same velocity will ve same and z2-z1= 45 m

Thus delta P = 45*rho*g = 45×1000×9.8 = 441000 Pa

Pump needs to deliver this power for pressure drop

We know that power = flow rate× delta P = 0.03*441000 = 13230 W = 13.23 kW

Total power given to system = 20 kW

Thus power converted into thermal energy = 20-13.23 =6.8 kW

Efficiency of pump = power delivered/ input power *100

= 13.23/20×100 = 66%

Thus 2nd option is correct