National Physical Laboratory

How do I calculate and apply air buoyancy corrections? (FAQ - Mass & Density)

First ascertain whether you are working with true mass or conventional mass.

An air buoyancy correction has to be made, where the measurement uncertainty required of a weighing warrants it, when the volumes (and hence the amount of displaced air) of two masses being compared are different. When working with true mass the value of the correction is equal to the difference in the volumes multiplied by the density of the displaced air. With conventional mass the correction is equal to the difference in the volumes multiplied by the difference between the density of the displaced air and a value of 1.2 kg/m3. More details follow...

True mass

When comparing true mass values the buoyancy correction is given by:

BC = (V1 - V2) × pair

where:

BC is the buoyancy correction to be applied.
V1 is the volume of artefact one (ie M1 / pM1).
V2 is the volume of artefact two (ie M2 / pM2).
pair is the density of the air at the time of comparison.

To apply the calculated buoyancy correction, using the nomenclature above, it should be added arithmetically to the mass value of artifact two, that is:

Mt1 = Mt2 + BC

where:

Mt1 is the true mass of artefact one.
Mt2 is the true mass of artefact two.

Note that if V2 is larger than V1 the buoyancy correction will be negative.

Conventional mass

When calibrating weights, weighings are normally performed on the basis of conventional mass rather than true mass. Where this is so the buoyancy correction does not depend on the value of the 'absolute' density of air but rather how much its value deviates from the conventional value of 1.2 kg/m3 during the weighing process. Thus, because of the way that conventional mass is defined, a comparison made in air at a density of exactly 1.2 kg/m3 requires no buoyancy correction, even if the volumes of the weights being compared differ greatly. When the air density is not at this value, however, the buoyancy correction to be applied is given by:

BC = (V1 - V2) × (pair - 1.2)

and it is applied using the same convention as with the true mass buoyancy correction, that is:

Mc1 = Mc2 + BC

where:

Mc1 is the conventional mass of artefact one.
Mc2 is the conventional mass of artefact two.

The equation for conventional mass buoyancy correction is more complicated than for true mass and it is therefore easier to make a mistake with the sign of the correction. Depending on whether V1 is larger or smaller than V2 and whether the air density is greater or less than 1.2 kg/m3 the buoyancy correction can be positive or negative.

Last Updated: 25 Mar 2010
Created: 9 Aug 2007

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