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Mass Standards

Air Buoyancy Compensation    Gravimetric Calibrations

Air Buoyancy

When an object is weighed while immersed in a fluid environment, that object is subject to a buoyancy effect from the surrounding fluid.

Archimede's Principle states A body experiences a loss in weight equal to the weight of the medium it displaces. This principle explains why ships float and balloons rise. It also explains why the weight of an object is affected by the environment in which it is weighed.

During most weighings the environment surrounding the weighing apparatus is air. The actual density of air may be calculated, but can be taken to be approximately 1.20 kg/m3 (depends on temperature and pressure). This can be looked at as a buoyancy force of 1.20 kg/m3 acting on the sample being weighed.

If we were to place a 100 g standard (8000 kg/m3) in a vessel on one side of an equal arm balance in air at standard pressure (101.3 kPa) and temperature (20° C), and an identical vessel, filled with water (1000 kg/m3) to balance the standard on the other side, the balance would indicate equilibrium as the weight on one side of the balance would exactly counterbalance the weight on the other side.

If we then enclosed the balance in a bell jar and generate a vacuum in it, we would have effectively eliminated the liquid environment (air) surrounding the balance. The balance would then tilt to the side with the vessel filled with water. This can be explained simply due to the fact that the vessel filled with water displaced more air, due to the lower density of the water as compared to the standard. This means that this side was experiency a greater buoyancy effect from the surrounding air. Removing the air removed this buoyancy and the balanced moved to reflect the greater mass on the side with the water.

The calculations are:

Air Buoyancy
  Calibrated Weight Water
Air Density 0.0012 g/cm3 0.0012 g/cm3
Weight in Air 100.000 g 100.000 g
Density 8.0 g/cm3 1.0 g/cm3
Volume 12.5 cm3 100 cm3
Buoyancy 12.5 cm3 * 1.2 mg/cm3 = 15 mg 100 cm3 * 1.2 mg/cm3 = 120 mg
Weight in Vacuum 100.015 g 100.120 g

What dos this mean to you? In most industrial countries of the world, balances and scales are calibrated using weights calibrated with an apparent density of 8000 kg/m3. If you then use this balance to weigh objects with a different density, an air buoyancy error will be introduced.

Obviously, this error is relatively small, and for most weighings can be ignored. However, for weighings of a very high accuracy, this error must be accounted for. The error will also be introduced in weighings at different times when the air density conditions change.

To correct for the effects of air buoyancy, use the following formulas.

Air Density Determination

Air Buoyancy Correction

Using an example of:
Balance Reading = 200.0000 grams
Atmospheric Pressure = 1018 hPa (101.8 kPa)
Relative Humidity = 70%
Temperature = 20° Celsius
Density of Standard = 8000 kg/m3
Density of sample = 2600 kg/m3

We get the following results:

Air Density

Buoyancy Correction

Canada's Metrology System

In order to remain in accordance with OIML recommendations (OIML R111), Canada recently switched from using a standard density of 8.4 g/cm3 @ 0° Celsius to that of 8.0 g/cm3 @ 20° C. This change reflects the move away from Brass Standards and to Stainless Steel Standards.

This change introduced a variation in all of the nations test standards. Although the change was very small (for a given weight, the mass value will be higher by about 7 parts per million), it was enough to place several standards outside of the acceptable tolerance range. A 1 kilogram weight would change by about 7 mg. To this day, many Brass Standards continue to be used for calibrating industrial working (trade) standards.

The certificate issued for the standards is issued for Apparent Mass in Air vs. Stainless Steel Standards @ 8000 kg/m3

Last modified: 12 July 2009 15:09:36