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A well `20m` deep and `3m` is diameter contains water to a dept of `14m`. How long will a `5 hp` engine take to empty it ?

Answer» Here, depth of well `=20m, `radius `r=(3)/(2)m`
depth of water `=14m,t=?`
`P=5hp=5xx746W`
Area of cross section of well,
`A=pir^(2)=(220/(7))(3//2)^(2)=(99)/(14)m^(2)`
Volume of water in well,
`V=Axxd=(99)/(14)xx14=99m^(3)`
Mass of water in well, `m=Vxxrho=99xx10^(3)kg`
When the well is emptied, depth of water changes from `(20-14)m` in the beginning to `920-14)m` at the end.
`:.` Average height raised, `h=(6+20)/(2)=13m`
Work done, `W=mgh==99xx10^(3)xx9.8xx13`
As `P=(W)/(t)`,
`t=(W)/(P)=(99xx10^(3)xx9.8xx13)/(5xx746)`
`3381.6se cond`


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