Density of a liquid above a column of water

[takando12]

Homework Statement

A column of water 40 cm high supports a 30 cm column of an unknown liquid.What is the density of the liquid?

Homework Equations

The Attempt at a Solution

As per the instruction of the teacher I equated their pressures.
h₁ρ₁g=h₂ρ₂g. And hence arrived at the answer. But I don't understand why we are doing this.Why should the pressures of both the columns be equal? I am trying to think of what would happen if they weren't equal but I can't get it. The unknown liquid column will be acted on by atmospheric pressure at the top. What will the pressure at the interface of the 2 liquids be?

 

[haruspex]

Why should the pressures of both the columns be equal?

Where the two meet, right?
If the pressure in one is P and the cross sectional area where they meet is A then what force does it exert on the other fluid? What will happen if they push on the interface area with unequal forces?

 

[theodoros.mihos]

Any total pressure difference that not satisfy Bernoulli's equation make fluid acceleration. For unmoved liquid, pressure on the same label must be the same.

 

[takando12]

ok. So for the columns to remain in equilibrium, the pressures(or forces) they exert on each other should be equal.
the first column exerts pressure on the second at the interface, but i thought the second only exerts pressure on the bottom of the container? but it actually does on the first.

 

[haruspex]

ok. So for the columns to remain in equilibrium, the pressures(or forces) they exert on each other should be equal.
the first column exerts pressure on the second at the interface, but i thought the second only exerts pressure on the bottom of the container? but it actually does on the first.

They must exert pressure on each other at the interface. Action and reaction.