Communicating Vessels - Interactive Simulation

Interactive simulation of communicating vessels principle with pressure balance and liquid levels

Left Level: 0.00 m
Right Level: 0.00 m
Level Difference: 0.00 m
Bottom Pressure: 0.00 Pa

Liquid Comparison

Left Liquid
Right Liquid

Parameters

Display Options

Presets

Physics Formulas

Pressure: P = ρgh
Same Liquid: h₁ = h₂ (levels equal)
Different Liquids: ρ₁gh₁ = ρ₂gh₂ (pressure balance)
Level Ratio: h₁/h₂ = ρ₂/ρ₁

What are Communicating Vessels?

Communicating vessels are containers connected at the bottom that allow liquid to flow between them. The fundamental principle states that in communicating vessels containing the same liquid at rest, the liquid levels are equal regardless of the shape or size of the vessels. This is because pressure at the bottom depends only on liquid density (ρ), gravitational acceleration (g), and liquid height (h), following the formula P = ρgh.

Principle of Communicating Vessels

When the same liquid fills connected vessels, the pressure at any given horizontal level must be equal for equilibrium. At the bottom of the vessels, pressure P₁ = ρgh₁ on the left must equal pressure P₂ = ρgh₂ on the right. This requires h₁ = h₂, meaning the liquid levels equalize. The width or shape of the vessels doesn't affect the equilibrium height - only the liquid density and gravitational field matter.

Different Liquids

When different liquids with densities ρ₁ and ρ₂ occupy the two sides, the liquid levels are not equal. Instead, the pressures balance: ρ₁gh₁ = ρ₂gh₂. This gives the relationship h₁/h₂ = ρ₂/ρ₁ - the heavier liquid has a lower level. For example, if mercury (ρ = 13600 kg/m³) is on the left and water (ρ = 1000 kg/m³) is on the right, the mercury level will be about 13.6 times lower than the water level.

Real-World Applications

Communicating vessels principles are everywhere: water pots and kettles have spouts that indicate water level, water gauges in boilers show steam drum level, ship locks use connected chambers to raise/lower boats, and civil engineers use water levels for construction. Understanding this principle helps design fountains, plumbing systems, and hydraulic machinery throughout history and modern engineering.

Effect of Tilting

When communicating vessels are tilted, the liquid surface remains horizontal (perpendicular to gravity). The liquid levels measured vertically from a common reference remain equal for the same liquid. However, the liquid depth along the tilted vessel walls varies - the liquid appears deeper on the lower side. This demonstrates that it's the vertical height, not the path length, that determines pressure.