Communicating Vessels

vessels that are interconnected at the bottom (see Figure 1). When communicating vessels with diameters large enough to negate the capillary effect are filled with the same fluid, the fluid levels are of the same height regardless of the shape of the vessels. This is the working principle of fluid manometers and water-gauges for steam boilers. If the communicating vessels are filled with different fluids, the heights of the fluid columns (measured from the surface where the fluids

Figure 1

are in contact with each other) are inversely proportional to the densities; that is, ρ₁h₁ = ρ₂h₂, where ρ_1, ρ₂, h₁, and h₂ are, respectively, the densities and heights of the fluid columns. This relation is used to determine the density of a fluid. If, however, one of the legs of the communicating vessels is sealed, then the level difference will depend on the pressure in the sealed leg; this is the working principle of sealed manometers.