Question

A cylinder of height $20m$ is completely filled with water. The velocity of efflux of water (in $m{s}^{-1}$) through a small hole on the side wall of the cylinder near its bottom is:

• A. $10m{s}^{-1}$
• B. $20m{s}^{-1}$
• C. $25.5m{s}^{-1}$
• D. $5m{s}^{-1}$

Answer 1

Answer: (B)

$20m{s}^{-1}$

Given that

Pressure at the top surface $=P_1=p_{atm}$

Pressure at the hole, $P_2=p_{atm}$

Here height of the cylinder , $h=20m$

From Bernoulli's Theorem we have:

Sum of all mechanical energies remains constant at a point over all points.

$⟹P+\rho gh+\frac{1}{2}\rho v^2=constant$

where $\rho$ is the density of the fluid and $v$ is the velocity at that point .

So, applying Bernoulli Theorem at top and bottom of the cylinder we get :

$P_{atm}+\rho gh=P_{atm}+\frac{1}{2}\rho v^2$

$v=\sqrt{2gh}=\sqrt{2\times 20\times 10}=20m{s}^{-1}$