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15 June, 23:11

Water is pumped from a lake to a storage tank 15 m above at a rate of 70 L/s while consuming 15.4 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.

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  1. 15 June, 23:27
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    (a) 66.9%

    (b) 147.14 kPa

    Explanation:

    Given:

    Elevation of the water tank z = 15 m

    Water volume flow rate V = 70 L/s = 0.07 m³/s

    Input electric power consumption by the pump, Welec, in = 15.4 kW

    Assuming there are no frictional losses in the pipes and changes in kinetic energy, the efficiency of the pump-motor will be;

    η = ΔEmech : Welec,

    Where;

    η is the overall efficiency

    ΔEmech is the workdone to move the water pumped from the lake to a storage tank 15m above

    Welec is the Input electric power consumption by the pump

    Solving for ΔEmech;

    ΔEmech = mgh

    mass, m = density * volume

    Density of water = 1000 kg/m³

    m = 1000 kg/m³ * 0.07 m³/s

    m = 70 kg/s

    ∴ ΔEmech = 70 * 9.8 * 15

    = 10.3 kW

    Substituting the values of ΔEmech and Welec to calculate the overall efficiency

    η = (10.3 kW : 15.4 kW) * 100 %

    = 0.6688 * 100 %

    = 66.88 %

    = 66.9 %

    The overall efficiency of the pump-motor unit is = 66.9 %

    (b) The pressure difference between the inlet and the exit of the pump is calculated to be;

    Pressure = ΔEmech : V

    = 10.3 : 0.07

    = 147.14 kPa
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