It is known that it takes five minutes to empty a rectangular vessel when filled one-third of its volume with kerosene through an orifice in its bottom. Now, find the time taken in minutes for emptying vessel when it is completely filled with kerosene: (Take `sqrt(3) = 1.73`)

Answer

`08.65`

Explanation

Using equation of continuity,
`A_(1)V_(1) = A_(2)V_(2)`
`-A(dh)/(dt) = A_(0) sqrt(2gh)`
Where, `A_0` is area of orifice, A is area of crosssection of vessel and h is height to which tank is filled.
`therefore int_(0)^(1)dt = -A/(A_(0) sqrt(2g)) int_(h)^(0) h^(-1//2) dh`
`therefore t = A/A_(0) sqrt((2h)/g) rArr t prop sqrt(h)`
`therefore t_(1)/t_(2) = sqrt((h//3)/h) = 1/sqrt(3)`
`therefore t_(2) = 5 xx sqrt(3) = 5 xx 1.73 = 8.65` min