K323 / 2027
Pressure overview

Topic 5 of 6

Measuring atmospheric pressure

A liquid-column barometer measures atmospheric pressure from the vertical height of a supported liquid column.

In a stationary liquid, a vertical height difference gives a pressure difference of ρgh. A pressure reference is needed to turn that difference into an atmospheric-pressure reading.

The supplied barometer diagram shows a closed-top tube connected at its lower end to a reservoir of mercury. The reservoir is open to the atmosphere. The space above the mercury column has such a small pressure that we treat it as a vacuum in this model.

Measure the column above the reservoir surface

Supplied mercury density: 13600 kg/m3; g = 10 N/kg. The pressure above the column is approximately zero.

A mercury barometer with a near-vacuum above the columnAn inverted tube is closed at its top and open beneath the surface of mercury in a reservoir. The mercury is continuous through the submerged open end. The reservoir is open to atmospheric pressure. A near-vacuum above the mercury column provides an approximately zero-pressure upper reference. The height h, 0.750 metres, is measured vertically from the reservoir surface to the top of the mercury column. It is neither the whole tube length nor the height above its lower opening. The liquid pressures at A inside the tube and B at the reservoir surface are equal. With the supplied density and gravitational field strength, atmospheric pressure is 102000 Pa.h =0.750 mNearvacuumClosed topOpen to airABA and B: atmospheric pressure

Atmospheric pressure = 13600 x 10 x 0.750 = 102000 Pa.

The labelled vertical height sets the pressure difference. A trapped gas above the column would change the upper pressure reference.

Atmospheric pressure acts on the open reservoir. The vertical height h runs from the reservoir surface to the top mercury meniscus. The space above the column provides the approximately zero-pressure reference.

Follow the two pressure references

  1. At the open reservoir surface, the pressure is atmospheric pressure.
  2. At that same horizontal level inside the connected mercury, the pressure is equal.
  3. Inside the tube, that pressure is the pressure above the column plus the mercury contribution ρgh.
  4. With the top pressure approximately zero, atmospheric pressure is approximately ρgh.
patmosphere = ptop + ρgh
If ptop is negligible, patmosphere = ρghh is the vertical column height above the reservoir surface. It is not the full tube length or the depth of the tube's lower end.

Worked example

Read a 0.750 m mercury column

Use the supplied mercury density of 13600 kg/m3 and g = 10 N/kg. The vertical height above the reservoir is 0.750 m, and the pressure at the top is negligible.

patmosphere = 13600 x 10 x 0.750 = 102000 Pa

The height supplies the pressure difference between the column top and the reservoir level. The near-vacuum at the top makes that difference approximately equal to the full atmospheric pressure.

Why the liquid's density matters

For the same pressure, a less dense liquid needs a taller column. If water of density 1000 kg/m3 were used to represent the same 102000 Pa, then:

h = p / (ρg) = 102000 / (1000 x 10) = 10.2 mThe required water column is much taller than the 0.750 m mercury column because water is less dense.

For a given liquid with unchanged density, a greater atmospheric pressure supports a greater vertical height. Use the current reservoir level as the lower reference when reading h.

The space above the column is part of the explanation

If appreciable gas is trapped above the column, ptop is not zero. Then atmospheric pressure is ptop + ρgh. Using ρgh alone would underestimate it.

Read the pressure unit mmHg

Millimetres of mercury, mmHg (also written mm Hg), is a conventional pressure unit based on a mercury column under fixed reference conditions. A measurement in mm alone is a length; a reading in mmHg is a pressure.

Unit conversion

Convert a pressure of 760 mmHg

Use the supplied approximation 1 mmHg = 133 Pa.

760 x 133 = 101080 Pa, or approximately 1.01 x 105 Pa.

This conversion uses the conventional pressure unit. It does not use the earlier column model's approximation g = 10 N/kg. When calculating pressure from a measured column height using ρgh, use that problem's stated density, g and vertical height.

Identify the top reference and the vertical height. The atmosphere acts on the reservoir and supports the column. The pressure above the column cannot be ignored unless the stated model makes it negligible.