Q. A water tank, open to the atmosphere, has a leak in it, in the form of a circular hole, located at a height $h$ below the open surface of water. The velocity of the water coming out of the hole is
A) $\sqrt{gh/2}$
B) $\sqrt{gh}$
C) $\sqrt{2gh}$
D) $2\sqrt{gh}$
Explanation
(c) Let $p$ be the atmospheric pressure, $\rho$ the density of the liquid and $v$ the velocity of the efflux of the liquid coming out from the orifice.
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From Bernoulli’s theorem,
$p + 0 + \rho gH = p + \frac{1}{2}\rho v^{2} + \rho g(H - h)$
$\Longrightarrow \ \ \frac{1}{2}\rho v = \rho gh$
$\Longrightarrow \ v =$ $\sqrt{2gh}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.