Q. Water flows into a large tank with flat bottom at the rate of $10^{-4} \; m^3 s^{-1}$. Water is also leaking out of a hole of area 1 $cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is:

Solution:

Since height of water column is constant therefore, water inflow rate $(Q_{in})$
= water outflow rate
$Q_{in } = 10^{-4} m^{3}s^{-1} $
$ Q_{out } =Au = 10^{-4} \times\sqrt{2gh} $
$ 10^{-4} = 10^{-4} \sqrt{20 \times h} $
$ h = \frac{1}{20} m $
h = 5cm
$\therefore$ correct answer is (4)

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