Mechanics

# Immiscible liquids in equilibrium

Non-miscible liquids of different densities are in equilibrium at different levels

Simon Stevin was an engineer and mathematician who demonstrated that the pressure inside a liquid depends only on the depth and not on the shape of the container.

In the figure above we have a U-shaped tube that contains two different liquids, liquid A and liquid B, which do not mix, that is, they are miscible. Let us consider the pressures p 1 and p 2 at points 1 and 2, located at the same horizontal level passing through the separation surface between liquids A and B.

Being points of the same liquid (A) at rest, from the first consequence of Stevin’s law, we can say that both pressures are equal, that is:

1 = P 2

1 =p 0 +ρ A .gh A

2 =p 0 +ρ B .gh B

Where, in the equations above, p 0 is the atmospheric pressure and h A and h B are the heights of the free surfaces of liquids A and B in relation to points 1 and 2, that is, in relation to the horizontal line passing through the separation surface between the two liquids.

If we equate the two equations p 1 and p 2 , we get:

0 +ρ A . g .h A  = p 0 +ρ B . g.h B _

ρ A .h  = ρ B .h B

According to the equation above, and also based on the figure above, we can say that ρ A .<h B eh A >ρ B .

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