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A cylindrical vessel of area of cross se...

A cylindrical vessel of area of cross section `A` is filled with a liquid up to a height `H`. A very small hole of area of cross section a is made at the bottom of the vellel. Find the time taken by the vessel to become empty.

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The liquid escapes with a velocity `(=sqrt(2gh))` which varies with the level of liquid. Hence, we have of the use integral. Let y be the height of the liquid at an insant. This height changes by `dy` in time `dt`.
Volume of water leaving out per second `=A dv dt`

At the hole volume escapiong per second
is` av=asqrt(2gy)`
`:. asqrt(2gh)=-A(dy)/(dt)impliesint_(H)^(0)(-dy)/(sqrt(y))=(asqrt(2g))/Aint_0^tdt`
`t=A/(asqrt(2g))2sqrt(H)` (assuming `agt gtA`)
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