Discussion
If a huge tank has a small side hole at a depth of 2 m from the surface of water, then the velocity of water flowing through the hole is \((g = 10ms^{-2})\)
Answer: B
The velocity is \(2\sqrt{10}\) m s-1.
By Torricelli's theorem, water leaves a small hole at depth \(h\) below the free surface with speed \(v = \sqrt{2gh}\), the speed of a body falling freely through \(h\). In a huge tank the surface barely moves, so its speed can be ignored.
\[ \begin{aligned} v &= \sqrt{2 \times 10 \times 2} = \sqrt{40} \\ &= 2\sqrt{10} \text{ m s}^{-1} \end{aligned} \]
\(2\sqrt{5} = \sqrt{20}\) is \(\sqrt{gh}\), which drops the factor 2, and \(\sqrt{10}\) is smaller still.
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