An open tank filled with water (density) $\rho$ has a narrow hole at a depth of $h$ below the water surface. The velocity of water flowing out is

• A

  $h \rho g$
• B

  $2 g h$
• Correct answer
  C

  $\sqrt{2 g h}$
• D

  gh

Solution

From Bernoulli's theorem $\begin{aligned} p+0+\rho g H & =p+\frac{1}{2} \rho v^2+\rho g(H-h) \\ \frac{1}{2} \rho v^2 & =\rho g h \\ \Rightarrow \quad v & =\sqrt{2 g h}\end{aligned}$

Hence, the correct answer is option: 'C'.