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25 January, 15:23

Water is pumped from a lake to a storage tank 20 m above at a rate of 95 L/s while consuming 22.3 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. 25 January, 15:41
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    (a) η = 0.835 = 83.5%

    (b) ΔP = 196000 Pa = 196 KPa

    Explanation:

    (a)

    The useful output of the pump-motor system will the power required to pump the water to the storage tank. That power is given as:

    P = ρghQ

    where,

    P = Power to pump = ?

    ρ = density of water = 1000 kg/m³

    g = 9.8 m/s²

    h = height = 20 m

    Q = Volume Flow Rate = (95 L/s) (0.001 m³/1 L) = 0.095 m³/s

    Therefore,

    P = (1000 kg/m³) (9.8 m/s²) (20 m) (0.095 m³/s)

    P = 18620 W = 18.62 KW

    So, now the efficiency is given as:

    η = Desired Output/Required Input

    where,

    η = overall efficiency = ?

    Desired Output = Power to Pump = 18.62 KW

    Required Input = Electric Power = 22.3 KW

    Therefore,

    η = 18.62 KW/22.3 KW

    η = 0.835 = 83.5%

    (b) The pressure difference between inlet and the outlet is given by the formula:

    ΔP = ρgh

    where,

    ΔP = Pressure Difference = ?

    ρ = density of water = 1000 kg/m³

    g = 9.8 m/s²

    h = height = 20 m

    Therefore,

    ΔP = (1000 kg/m³) (9.8 m/s²) (20 m)

    ΔP = 196000 Pa = 196 KPa
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