First slide

Fluid dynamics

Question

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

Easy

A

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

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

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

Data is not sufficient

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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