An engine can pump 30,000 L of water to a vertical height of 45 m in 10 min. Calculate the work done by the machine and the power. (Density of water = `10^3 kg//m^3, 1000 L - 1 m^3 , g = 9.8 ms^(-2)`)

Explanation

Given volume of water, V = `30, 000 L = ( 30, 000)/(1000) = 30 m ^(3)`
mass of water = volume `xx` density `= 30 xx 1000 kg = 30, 000 kg`
Work done by the machine = `mgh = 30, 000 xx 9.8 xx 45 = 1.323 xx 10 ^(7) J.`
Power `= ("Work Done")/("Time")`
` = ( 1. 323 xx 10 ^(7))/( 600) (therefore` Time = 10 min `= 10 xx 60 s = 600 s`)
`= 22. 06 xx 10 ^(3) Js ^(-1) = 22. 0 5 kW ( therefore 1 kW = 1000 Js ^(-1))`