A manometer is a device for measuring pressure. It is simply a U tube filled with a liquid of known density (r). If the pressure on the two open limbs of the U tube are equal (atmospheric pressure PA) the levels will be the same.
However if the pressure on one side rises the liquid on that level will be forced down while that in the other limb will rise. The difference between the two liquid levels give the pressure difference between the two ends of the tube.
If two liquids of different
density that do not mix are poured into a beaker the two limbs of a U tube the one with the
greater density will "fall" to the bottom with the one of lower density floating on top. (Vinegar
and oil are a good example. Vinegar is more dense than oil and so will float on top of
it).
If these two liquids are poured into the two limbs of a U tube they will take up the
positions shown in the diagram with the denser liquid at the bottom. Since the pressure at a
given depth in a liquid is the same at all points the heights of the two liquid columns above X
must exert equal pressures.
Therefore:
An interesting problem is that with vinegar and oil in the same bottle. The oil will float on the vinegar, and the problem is to be able to pour any required proportional mixture of the two liquids (say 20% oil and 80% vinegar) from the bottle. You must not use anything except the bottle and your hands!