A tank with a small circular hole contains oil on top of water. It is immersed in a large tank of the same oil. Water flows through the hole. What is the velocity of flow initially?

0.63 m/s

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3.7 m/s

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6 m/s

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2.52 m/s

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Solution

The correct option is A
0.63 m/s

$P_{0}$ Applying Bernoulli's Equation,
$P_{1} + ρ_{w} g h_{2} + \frac{1}{2} ρ_{w} V_{1}^{2} = P_{2} + \frac{1}{2} V_{2}^{2} ρ_{)} w$
$P_{1} = P_{0} + ρ_{0} + ρ_{0} g h_{1}$
$P_{2} = P_{0} + ρ_{0} g (h_{1} + h_{2})$
$∴ P_{0} + ρ_{0} g h_{1} + P_{w} + ρ_{0} g h_{2} + \frac{1}{2} ρ_{w} V_{1}^{2} = P_{0} + ρ_{0} g (h_{1} + h_{2}) + \frac{1}{2} V_{2}^{2} ρ_{w}$
$\Rightarrow ρ_{w} g h_{2} + ρ_{0} g h_{2} = \frac{1}{2} V_{2}^{2} ρ_{w}$
Note that we can ignore $V_{1}$ as it will be very small as compared to $V_{2}$
After substituting, $V_{2}$ = 0.63 m/s

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