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A 25 m deep well contains water upto ...

A 25 m deep well contains water upto 15 m . An engine evacuates the well in 1.5 hrs . If the diameter of the well is 2 m ,calculate the power of the engine .

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Radius of well , `r = 2/2 = 1m `
Area of cross section of well ,
`A = pir^(2)`
`= 22/7 xx1^(2)`
` = 22/7 m^(2)`
Depth of water , d = 15 m
Volume of water in the well ,
`V = A xxd`
` = 22/7 xx1^(2) xx15 = 47.143 m^(3)`
Mass of water in the well ,
`M = V xx rho = 47.143 xx10^(3)` kg
As the engine begins to empty the well , the height through which the water has to be raised changes from `(25-15)` m in the strat to `(25-0)` m in the end .
` :. ` Average height of water raised , `h = (10+25)/2 = 17.5 m `
Work done , W = mgh
` = 47.143 xx10^(3) xx9.8 xx17.5`
` =8085.025 xx10^(3)J`
Time taken , ` t = 1.5 hrs = 1.5 xx 60 xx60 s`
Power of the engine ` = W/t = (8085.025 xx10^(3))/(1.5xx60xx60)`
` 1497.2 ` W
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