The problem involves finding the velocity of water flowing out of a hole in a tank. This can be solved using Torricelli's theorem, which states that the speed \( v \) of efflux of a fluid under gravity through a hole at a depth \( h \) is given by the equation:
\(v = \sqrt{2gh}\)
where:
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\) on the surface of the Earth).
- \(h\) is the depth of the hole below the water surface.
Let's evaluate why the velocity \(v\) is \(\sqrt{2gh}\):
- \(h\rho g\): This expression gives force per unit area (pressure), not velocity.
- \(2gh\): This represents the energy per unit mass, not the velocity directly.
- \(\sqrt{2gh}\): Torricelli's theorem directly equates this to the velocity of the efflux at a depth \(h\).
- \(\sqrt{2h\rho g}\): Incorrect because the inclusion of \(\rho\) (density) is not applicable here.
Therefore, the correct answer is the velocity of water flowing out is \(\sqrt{2gh}\).