An irrigation pump is used to draw water from a reservoir and deliver it to an i

Question

An irrigation pump is used to draw water from a reservoir and deliver it to an irrigation ditch, at a mass flow rate of 15 kg/s. The inflow from the reservoir and the outflow to the ditch are through pipes of diameters 10 cm and 7.5 respectively. If the water temperature is at 15 deg Celsius at both inflow and outflow, the outflow is 50 m higher than the inflow, and one third of the input power to the pump is lost as heat transfer to the surroundings,

a) Find the power that must be supplied to the pump
b) By how much would the calculated input power change if the kinetic energy of the water were neglected?

Explanation / Answer

I will indicate input by subscript i and output by subscript o.
Vi = flow rate/ area = 1.909 m/s
Vo = 3.4 m/s

change in kinetic energy = 3.936

also potential energy = g*50

Total head = 493.936

so total power = 493.936*15 = 7.409 kW

also this is actually two third of total energy,

total Power to pump = 3*7.409 kW / 2 = 11.11 kW

b) If we neglect kinetc energy , then total power = 7.35 kW

power input to pump = 11.025 kW

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