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A wide cylindrical tank with a small opening in the bottom has a water column of height $h_{1}$ and density d. Above the water column, there is a layer of kerosene oil of thickness $h_{2}$ and density 0.8d. The velocity of efflux through the opening is

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$\sqrt{2 {gh}_{1}}$

$\sqrt{2 g (0.8 h_{2} + h_{1})}$

$\sqrt{2 g (h_{1} + h_{2})}$

Data is not sufficient

answer is B.

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Detailed Solution

According to Bernoulli's theorem total energy of the liquid at the bottom of the vessel is equal to total energy of the flow just outside the vessel.

$P_{1} = P_{2} + \frac{1}{2} d v^{2}$

$P_{0} + 0.8 d g h_{2} + d g h_{1} = P_{0} + \frac{1}{2} d v^{2}$

$v^{2} = 1.6 g h_{2} + 2 g h_{1}$

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