The Barometer
Simple Explanation
A barometer measures atmospheric pressure using a column of mercury: a tube filled with mercury is inverted into a mercury reservoir, and atmospheric pressure pushes mercury up the tube until the height of the column balances that pressure. At sea level, this height is about 760 mm.
Why Do We Need It?
The barometer was historically the primary instrument for measuring atmospheric pressure, and its design directly demonstrates the relationship between pressure, liquid column height, and density.
Formula
Barometric (Column) Pressure
P = hρg
The pressure exerted by a column of liquid depends on the height of the column, the density of the liquid, and gravity — a barometer uses this to measure atmospheric pressure from the height of a mercury column it supports.
- P
- — Pressure at the base of the column, in Pa
- h
- — Height of the liquid column, in metres
- ρ
- — Density of the liquid (e.g. mercury, 13,600 kg/m³), in kg/m³
- g
- — Acceleration due to gravity, 9.8 m/s²
When to use it: Use to find atmospheric pressure from the height of mercury a barometer supports, or the pressure exerted by any column of liquid of known height.
Worked Example
Finding atmospheric pressure from a barometer's mercury height
A mercury barometer shows a column height of 0.76 m. Find atmospheric pressure (mercury density = 13,600 kg/m³, g = 9.8 m/s²).
Why Does This Work?
The mercury column rises until the pressure it exerts at its base (hρg) exactly balances the atmospheric pressure pushing on the mercury reservoir below — mercury is used specifically because its high density keeps the column height manageable (about 76 cm, versus over 10 m if water were used instead).
Real-Life Example
Predicting weather with barometric pressure
Weather forecasters track changes in barometric (atmospheric) pressure to predict incoming weather.
A falling barometer reading (dropping mercury column height) typically signals an approaching low-pressure system, often bringing storms — this practical application relies directly on the barometer accurately measuring changes in atmospheric pressure.
Practice
A mercury barometer at high altitude shows a column height of only 0.60 m. Find the atmospheric pressure there (ρ = 13,600 kg/m³, g = 9.8 m/s²).
MediumCommon mistake
Assuming a wider barometer tube would give a different (higher) reading — the column HEIGHT depends only on the pressure and the liquid's density, not on the tube's width; a wider tube simply holds more mercury at the same height.
Quick Review
- A barometer measures atmospheric pressure from a supported mercury column height (~760 mm at sea level).
- P = hρg: the column rises until it balances atmospheric pressure.
- Mercury is used for its high density, keeping the column a manageable height.