Measuring Gas Pressure: Barometers and Manometers

Gas pressure is the force that gas particles exert per unit area of a surface, and it is measured with barometers (for atmospheric pressure) and manometers (for the pressure of a gas in a container). In brief: standard atmospheric pressure supports a column of mercury 760 mm high, so 1 atm = 760 mmHg = 760 torr = 101,325 Pa.

Pressure is one of the four variables of every gas law, so converting between units and reading instruments correctly are basic skills. This article explains the units, shows how a barometer and the two types of manometer work, gives a conversion table and works through a manometer calculation.

What is gas pressure?

Pressure is defined as force divided by area: P = F / A. Gas particles collide with the walls of their container, and the sum of all these tiny impacts produces a steady push on the wall. The SI unit is the pascal (Pa), which equals one newton per square meter.

The atmosphere also has weight. The column of air above each square meter of the Earth’s surface at sea level has a mass of roughly 10,000 kg, which is why atmospheric pressure is about 100,000 Pa.

Which units are used for pressure?

• Pascal (Pa) and kilopascal (kPa): the SI unit and its common multiple.
• Atmosphere (atm): originally the average sea-level pressure; now defined as exactly 101,325 Pa.
• Millimeter of mercury (mmHg) and torr: the pressure of a mercury column of that height. The torr is defined as exactly 1/760 of an atmosphere, and the two units are numerically equal for practical purposes.
• Bar: exactly 100,000 Pa, close to atmospheric pressure. Weather maps often use millibars (hPa).
• Pounds per square inch (psi): common in the United States, for example for tire pressure.

Pressure unit conversion table

To convert, multiply by the ratio of the two values. For example, 0.85 atm × (760 mmHg / 1 atm) = 646 mmHg.

How does a mercury barometer work?

A barometer measures atmospheric pressure. A glass tube about 1 m long is filled with mercury, closed at one end and inverted into a dish of mercury. The mercury level in the tube drops until the weight of the column equals the pressure of the atmosphere pushing on the surface of the mercury in the dish. The space above the column is a near-vacuum, so it exerts almost no pressure.

At sea level and 0 °C, the column stands at 760 mm. When a storm approaches and the pressure falls, the column drops; in a high-pressure system it rises. Mercury is used because its density, 13.6 g/cm³, is high enough to keep the column to a manageable height. A water barometer would need a column of about 10.3 m.

How does a manometer work?

A manometer is a U-shaped tube partly filled with a liquid, used to measure the pressure of a gas in a container. There are two types.

Closed-end manometer

One arm is sealed with a vacuum above the liquid. The gas pressure equals the difference in the heights of the liquid levels, so P_gas = h (in mmHg) directly. This design is used for low pressures.

Open-end manometer

One arm is open to the atmosphere. The gas pressure is the atmospheric pressure plus or minus the height difference h:

• If the liquid is higher in the arm open to the air, the gas pressure is greater than atmospheric: P_gas = P_atm + h.
• If the liquid is higher in the arm connected to the gas, the gas pressure is lower than atmospheric: P_gas = P_atm − h.
• If both levels are equal, the gas is at atmospheric pressure.

How do you calculate gas pressure from a manometer?

Worked example: open-end manometer

A flask is connected to an open-end mercury manometer. The mercury in the arm open to the air is 48 mm higher than in the arm connected to the flask. The barometer reads 752 mmHg. What are the pressure of the gas in mmHg, atm and kPa?

1. The level is higher on the open side, so the gas pressure is above atmospheric.
2. P_gas = 752 + 48 = 800 mmHg.
3. In atmospheres: 800 mmHg × (1 atm / 760 mmHg) = 1.053 atm.
4. In kilopascals: 1.053 atm × 101.325 kPa/atm = 106.7 kPa.

How was pressure first measured?

Evangelista Torricelli built the first mercury barometer in 1643. He showed that the column of mercury was held up by the pressure of the air rather than by a fear of a vacuum, which was the earlier explanation. In 1648 Blaise Pascal’s brother-in-law Florin Périer carried a barometer up the Puy de Dôme in France, and the column dropped with altitude, supporting the idea. The pascal was named after Pascal, and the torr after Torricelli.

Where are these instruments used today?

Mercury barometers have been largely replaced by electronic sensors because of the toxicity of mercury, but the same physical principle applies. Aneroid barometers use a flexible sealed metal capsule that bends with pressure. Manometers and pressure gauges are used in laboratories, in gas pipelines, in diving equipment and in medicine, where blood pressure is still reported in mmHg.

Which mistakes are common?

• Forgetting atmospheric pressure: with an open-end manometer, the height difference is only a correction to the barometer reading.
• Adding when you should subtract: always check which arm of the manometer has the higher liquid level.
• Mixing units: convert everything to the same unit before adding heights and pressures.
• Confusing gauge and absolute pressure: a tire gauge reads the pressure above atmospheric, so the absolute pressure is about 101 kPa higher.
• Treating mmHg and torr as very different: they are the same for practical calculations.