Show that the pressure produced due to a fluid column depends on the height of the fluid column and the density of the fluid.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
Consider a fluid at rest in a container. The density of the fluid is $\rho$ and the height of the fluid column is $h$,as shown in the figure.
The weight of the fluid in the cylinder is $W = mg \ldots(1)$
Since the mass of the fluid $m = \text{volume} \times \text{density} = Ah\rho$,
$\therefore W = (Ah\rho g) \ldots(2)$
The pressure produced at the bottom of the container due to this weight is
$P = \frac{\text{Weight } W}{\text{Area } A}$
$\therefore P = \frac{Ah\rho g}{A}$
$\therefore P = h\rho g \ldots(3)$
This equation shows that the pressure produced due to a fluid column depends on the height of the fluid column $h$ and the density of the fluid $\rho$.

Explore More

Similar Questions

If the atmospheric pressure is $P_a$,then the pressure $P$ at depth $h$ below the surface of a liquid of density $\rho$ open to the atmosphere is:

The pressure at a point $10 \ m$ below the surface of water is (take atmospheric pressure $P_0 = 1.01 \times 10^5 \ Nm^{-2}$ and $g = 10 \ ms^{-2}$):

An inverted tube barometer is kept on a lift moving downward with a deceleration $\alpha$. The density of mercury is $\rho$ and the acceleration due to gravity is $g$. If the atmospheric pressure is $P_0$,then:

What is the pressure in $atm$ on a swimmer $10\; m$ below the surface of a lake?

Water stands up to height $h$ behind a dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. The density of water is $\rho$ and the acceleration due to gravity is $g$. If the atmospheric pressure force is also considered,the point of application of the total force acting on the dam due to water above $O$ is:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo