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A pump on the ground floor of a building...

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 `m^(3)` in 15 min . If the tank is 40 m above the ground and efficiency of the pump is 30% . How much power is consumed by the pump ? (Density of water `10^(3) kg m^(-3) , g = 9.8 ms^(-2)` ) .

Text Solution

Verified by Experts

Given `V = 30 m^(3) , t = 15 xx 60 = 900 s h = 40 m , eta = 30 % , P_("actual") = ? ` g = `9.8 ms^(-2)`
We know that mass of water drawn = (volume) (density)
i.e. `m = 30 xx 10^(3) = 3 xx 10^(4) kg`
by definition power = `("Work done")/("time ")`
i.e. `P = (mgh)/(t) = (3 xx 10^(4) xx 9.8 xx 40)/(900)`
i.e. P = `1.307 xx 10^(4)` W .
Actual power required = `(1.307 xx 10^(4) xx 100)/(30) = 4.357 xx 10^(4) W = 43.57` kilowatt (KW)
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