Question

A beaker is filled with a liquid up to a height h. If A and B are two points, one on the free surface and one at the base as shown, such that the minimum distance between the two is l, what will be the pressure at point B?

I got this question during an internship interview.

My query is from Pressure Distribution in a Fluid in chapter Pressure and Its Measurement of Fluid Mechanics

Answer 1

To determine the pressure at point $B$, let's analyze the situation step by step:

Given Information:

1. The liquid is filled to a height $h$ in the beaker.
2. $A$: A point on the free surface where the pressure is atmospheric (PatmP_{\text{atm}}Patm​).
3. $B$: A point at the base of the beaker at a depth $h$ from the free surface.
4. $l$: The minimum distance between $A$ and $B$.

The pressure at $B$ due to the liquid column can be calculated using the hydrostatic pressure formula:

PB=Patm+ρghP_B = P_{\text{atm}} + \rho g hPB​=Patm​+ρgh

Explanation of Parameters:

• $\rho$: Density of the liquid.
• $g$: Acceleration due to gravity.
• $h$: Vertical height of the liquid column above point $B$.

Key Notes:

• The minimum distance $l$ between points $A$ and $B$ does not influence the pressure at $B$ because hydrostatic pressure depends only on the vertical height $h$, not on the path or actual distance $l$ between the points.
• PatmP_{\text{atm}}Patm​ accounts for the atmospheric pressure acting on the free surface of the liquid.

Final Expression:

The pressure at point $B$ is:

PB=Patm+ρghP_B = P_{\text{atm}} + \rho g hPB​=Patm​+ρgh

Would you like help visualizing this or clarifying any related concepts?