First slide

Fluid dynamics

Question

A large tank filled with water to a height i, is to be emptied through a small hole at the bottom. The ratio of time taken for the level to fall from h to h / 2 and that taken for the level to fall from h / 2 to 0 is

Easy

A

$\sqrt{2}$
B

$1 / \sqrt{2}$
C

$(\sqrt{2} - 1)$
D

$1 / (\sqrt{2} - 1)$

Solution

we know that $\propto [\sqrt{H_{1}} - \sqrt{H_{2}}]$
$∴ t_{1} \propto [\sqrt{h} - \sqrt{(h / 2)}] and t_{2} \propto [\sqrt{(h / 2)} - 0] ∴ \frac{t_{1}}{t_{2}} = \frac{1 - 1 / \sqrt{2}}{1 / \sqrt{2}} = (\sqrt{2} - 1)$

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