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Figure shows a stream of fluid emerging ...

Figure shows a stream of fluid emerging from a tube in the base of an open tank. Obtain an expression for `'y'` in terms of `theta` and `'h'`. Can exceed `'h'`?

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We apply Bernoullis equation between points `2` and `3`.
`P_(2)+1/2rhov_(2)^(2)+rhogy_(2)=P_(3)+1/2rhov_(3)^(2)+rhogh_3`
`P_(atm)+1/2rhov_(2)^(2)+0=P_(atm)+1/2rhov_(3)^2+rhogy`………i
As both the points are open the atmosphere `P_(2)=P_(3)=P_(atm)`
Taking ground level as reference level potential energy at point `2` is zero.

Since there is no horizontal acceleration `v_(3)=v_(2) costheta`.
From eqn i we obtain
`y=1/2((v_(2)^(2)-v_(2)^(2)cos^(2)theta))/g=1/2(v_(2)^(2)sin^(2)theta)/g`....ii
From Torricelli's theroem `v_(2)^(2)=2gh`
That, `y=sin^(2)theta`
`y=h` when `sin theta=1`, i.e. `theta=90^@` therefore `y` can never exceed `h`.
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