# Immiscible liquids in equilibrium

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

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:

P _{1} = P _{2}

p _{1} =p _{0} +ρ _{A} .gh _{A}

p _{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:

p _{0} +ρ_{ A} . g .h_{ A } = p _{0} +ρ_{ B} . g.h _{B} _

ρ _{A} .h _{A } = 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} .