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A fixed container of height H with large...

A fixed container of height `H` with large cross-sectional area `A` is completely filled with water. Two small orifice of cross-sectional area `a` are made, one at the bottom and the other on the vertical side of the container at a distance H/2 from the top of the container find the time taken by the water level to reach a height of H/2 from the bottom of the container.

Text Solution

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`V_(1)=sqrtT(2g(h-H//2)),V_(2)=sqrt(2gh)therefore` By continuity equation
`A(-(dh)/(dt))=a(V_(1)+V_(2))impliesA(-(dh)/(dt))=a{sqrt(2g(h-H//2))+sqrt(2gh)}`
or `-(A)/(asqrt(2g))underset(H)overset(H//2)int(dh)/(sqrt(h)+sqrt(h-H//2))=underset(0)overset(t)intdtimpliest=(2A)/(3a)(sqrt(2)-1)sqrt((H)/(g))`
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