Question

What vertical height of water will exert pressure of $333200\,Pa$ ? Density of water is $1000\,kg{m^{ - 3}}$ and $g = 9.8\,m{s^{ - 2}}$.

Answer 1

Hint: In order to solve this question we need to understand pressure by a gas due to the liquid column above it. Pressure by a liquid is mathematically expressed as product of density of liquid, acceleration due to gravity and height of liquid column above it.Actually according to Bernoulli’s principle the more the height of liquid column above it the more the pressure would be also from the equation of continuity at the efflux point water is continuous so there is no water lag at efflux point.

Complete step by step answer:
Given, pressure of liquid column is, $P = 333200\,Pa$
Since we know, $1Pa = 1\,N{m^{ - 2}}$
So the pressure would be, $P = 333200\,N{m^{ - 2}}$
Also the density of liquid is given as, $\rho = {10^3}\,kg{m^{ - 3}}$
And acceleration due to gravity is, $g = 9.8\,m{s^{ - 2}}$
Let the height of water column be, $h$
So by using formula of pressure we get, $P = \rho gh$
$h = \dfrac{P}{{\rho g}}$
Putting values we get,
$h = \dfrac{{333200}}{{(1000 \times 9.8)}}\,m$
$\therefore h = 34\,m$

Hence, the height of the liquid column above it is 34 m.

Note: It should be remembered that according to Torricelli’s law the speed of efflux or water coming out from hole only depends on square root of height of water column above it so for two holes at the same height of liquid column above it would have same speed no matter what the liquid is. Also after ejecting it traces a parabolic path because the ejecting fluid is only under one force that is force of gravity so ejecting fluid having only one directional acceleration is downward direction.