In a given arrangement. Find out velocity of water coming out of 'C'.

\sqrt{\frac{2 g h_{3}}{1 - \frac{a^{2}}{A^{2}}}}

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\sqrt{\frac{3 g h_{3}}{1 - \frac{a^{2}}{A^{2}}}}

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\sqrt{\frac{2 g h_{3}}{1 - \frac{a^{3}}{A^{2}}}}

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\sqrt{\frac{3 g h_{3}}{1 - \frac{a^{3}}{A^{2}}}}

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Solution

The correct option is A $\sqrt{\frac{2 g h_{3}}{1 - \frac{a^{2}}{A^{2}}}}$
Applying Bernoulli's equation between liquid surface and point 'C'.

$P_{a} + \frac{1}{2} p v_{1}^{2} = P_{a} - p g h_{3} + \frac{1}{2} p v_{2}^{2}$

Through continuity equation

$A v_{1} = A v_{2}, v_{1} = \frac{a v_{2}}{A}$

$\Rightarrow$ $\frac{1}{2} p \frac{a^{2}}{A^{2}} v_{2}^{2} = - p g h_{3} + \frac{1}{2} p v_{2}^{2}$

$v_{2}^{2} = \frac{2 g h_{3}}{1 - \frac{a^{2}}{A^{2}}}$ ,
$v_{2} =$ $\sqrt{\frac{2 g h_{3}}{1 - \frac{a^{2}}{A^{2}}}}$

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