How Does a Mercury Barometer Measure Atmospheric Pressure?
Fluid Pressure: How a Mercury Barometer Measures Atmospheric Pressure
The dish is open, so the atmosphere presses down on its surface with pressure p₀. The tube was filled with mercury and inverted, leaving a near-vacuum above the column, so p ≈ 0 at Level 2. Trace the mercury from Level 2 down to Level 1: the only thing adding pressure along that path is the weight of the column itself. Both routes to Level 1 must give the same pressure, so p₀ = ρgh. The column height is not a length here — it is a pressure reading.
Two controls exist to break the two most common misreadings. Tilt the tube and the mercury runs further along the bore, L = h / cos θ, but the violet height never changes: only the vertical height enters ρgh, because only vertical depth builds pressure in a fluid. Widen the bore and the mercury volume grows with d² while h again does not move — area cancels out of p = F/A, so h is independent of how much mercury is in the tube. A barometer reads the same whether the tube is thin or fat, upright or leaning.
At standard atmospheric pressure, 101325 Pa, the column stands at exactly 760 mm. That is by construction: the torr is 1/760 of a standard atmosphere, and the conventional millimeter of mercury is defined using ρ = 13595.1 kg m⁻³ and g = 9.80665 m s⁻². Swap in water and the same pressure needs h = 10.33 m, a barometer taller than a three-storey building — mercury is 13.6× denser, so its column is 13.6× shorter.
How Does a Mercury Barometer Work?
A mercury barometer measures atmospheric pressure by balancing it against the weight of a mercury column. The tube is sealed and evacuated, so the pressure above the column is effectively zero. At the open dish surface, atmospheric pressure p₀ must equal the pressure produced by the column standing above that level, which gives p₀ = ρgh. At one standard atmosphere, 101325 Pa, the column stands at exactly 760 mm.
Drag the pressure slider and the column tracks it. Tilt the tube to 30° and the mercury runs 878 mm along the bore while the vertical height stays fixed at 760 mm — only vertical height enters ρgh. Widen the bore from 4 mm to 24 mm and the mercury volume grows 36×, while h does not move at all
Mercury Barometer Concept
- A mercury barometer measures atmospheric pressure.
- Setup:
- Fill a long glass tube completely with mercury.
- Invert it with the open end submerged in a mercury reservoir.
- A mercury column remains in the tube.
- The small empty space at the top is almost a vacuum, so its pressure is negligible.
- Pressure balance:
- At the reservoir surface, pressure = atmospheric pressure p₀.
- At the top of the mercury column, pressure ≈ 0.
- Using p₂ = p₁ + ρ g (y₁ − y₂), substituting values gives p₀ = ρ g h.
- Meaning of this relation:
- The height h of the mercury column is proportional to atmospheric pressure p₀.
- Tube area does not matter.
- Height depends only on mercury density (slightly changes with temperature) and local g (varies with location).
- Standard values:
- At 0 °C and g = 9.80665 m/s², 1 atm = 760 mm of mercury = 760 mmHg = 760 torr.
- In practice, corrections are applied for temperature, local g, and capillary effects.
