## Does atmospheric pressure affect pressure balances? (FAQ - Pressure)

Yes, it can in some circumstances but, where it does, it is fairly easy to ensure that its effect on the measurement uncertainties obtained is negligible.

The problem is caused by atmospheric air rendering external pressure balance components - primarily their weights - slightly buoyant; this in turn reduces the downward force they would otherwise exert on the piston. This may or may not cause a significant error in pressure balance operation depending on whether you are:

- cross-floating two pressure balances to compare their effective areas
- using a single pressure balance to generate reference pressures
- working in gauge-mode or absolute-mode (although admittedly in absolute-mode the remaining air surrounding the floating elements is hardly 'atmospheric')
- using conventional mass values or true mass values for the weights

…but first an introduction to buoyancy:

### Air buoyancy

Buoyancy is the upward force exerted on an object when it is immersed, partially or fully, in a fluid - and strictly where the fluid is subjected to a gravitational force but is not in free fall. Its value is equal to the weight of the fluid displaced by the object and this depends on the fluid's density; for air it is very nominally 1.2 kg/m^{3} but varies with pressure, temperature, humidity and composition up to about ±10 % (that is from about 1.1 kg/m^{3} to about 1.3 kg/m^{3}).

All objects surrounded by air and having gravity-induced weight (eg they are on the Earth's surface) experience buoyancy to some degree and it interferes with the process of weighing, making weights appear to have mass values slightly different from their true mass values; the difference can amount to about 150 parts per million for stainless steel weights. To help take this effect into account most weights are ascribed a *conventional mass* value - one that essentially represents the mass value they would *appear* to have, if they were made of a material of density 8 000 kg/m^{3} - ie close to a typical density of stainless steel - and weighed at 20 °C whilst 'immersed' in air of density 1.2 kg/m^{3} (see link below for the formal definition of *conventional mass*). Small corrections - this time only up to about ±15 parts per million for stainless steel weights - can then be calculated and applied, if necessary, to take account of local variations in air density and hence buoyancy.

Such *conventional mass* values are normally ascribed to pressure balance weights too and when using them on a single-sided pressure balance, being operated in gauge mode, it therefore may be necessary to apply corrections, based on local determination of air density. Assuming again that you are using stainless steel weights, the consequences of ignoring this correction will, as said above, be an error of up to about ±15 part per million (±0.0015 %) in weight values and hence force values - through typical climate-induced air density changes.

More information about buoyancy and related corrections can be seen on the related Mass and Density FAQ web pages, specifically:

- What are the differences between mass, true mass and conventional mass values? leading to
- How do I convert from true mass to conventional mass?
- What is buoyancy and how does it affect weighing? leading to
- How do I calculate and apply buoyancy corrections?

### Air buoyancy: potential effects on pressure balance operation

These are listed in four categories below and apply to both gas- and oil-operated pressure balances - although admittedly we are not aware of any oil-operated pressure balances operating in absolute mode.

**Note:** All the values quoted relate to stainless steel weights and are not valid for other metals.

**Pressure balances operated singly and in gauge mode**- used in this fashion, the values of the pressures generated will be influenced by changes in atmospheric air density
- assuming your weights have been ascribed conventional mass values, the maximum error likely to be caused in a pressure value by not correcting for variations in air density will be about ±15 parts per million (±0.0015 %)
- in the unlikely event that you are working with true mass values the maximum error likely to be caused by not correcting the weights for air buoyancy will be about 150 parts per million ±15 parts per million (0.015 % ±0.002 %).
**Pressure balances operated singly and in absolute mode**- used this way the pressure values generated by the instrument cannot be influenced by changes in atmospheric density BUT
- unless the mass values for the weights being used are true mass values (unlikely) a correction will almost certainly have to be applied (depending on the density of the weights' material) to correct for up to 150 parts per million (0.015 %) of additional downward force being applied to the piston.
**Cross-floating two pressure balances - gauge mode**In this procedure - typically used to calibrate one pressure balance against another - variations in air buoyancy will be insignificant PROVIDED that the weights used on one pressure balance are of the same density as those on the other pressure balance.*Case 1: The weights have the same density value:*In these circumstances - when both weight sets are made from material of essentially the same density (such as stainless steel) - air buoyancy effects are mostly self-cancelling. This is because any variation in air buoyancy will affect both sets of weights in proportion to their mass values and hence the*ratio*of the downward forces being produced by the weights will remain constant. If you then use such ratios, together with*pressure*data, to calculate the*pressures dependent term*in the effective area equation defining a pressure balance's characteristics, buoyancy effects may cause the pressure term to be in error by up to about ±15 parts per million (±0.0015 %) but in this context, and in comparison to other relevant uncertanties, this contribution to the measurement uncertainty will be insignificant.*Case 2: The weights do not have the same density value:*In these circumstances the air buoyancy effects will not completely cancel out and, depending how different the density values are, it may be necessary to apply a correction. If the error so produced is significant in your particular application however, you really ought to be using good quality stainless steel weights on both pressure balances anyway!**Cross-floating two pressure balances - absolute mode**- in these circumstances, with the air pressure surrounding the pressure balances' weights virtually zero, the downward forces acting on each piston will be about 150 parts per million (0.015 % higher) than for gauge-mode use because there is no longer any air buoyancy (assuming the components have a density of around 8 000 kg/m
^{3}). - as in category 3) above, the
*ratio*of the masses in the cross-floated pressure systems will remain the same so no correction is needed provided that the weights on both pressure balances are made from material of the same density. Assuming the use of conventional mass values, the calculated pressure values will again be in error but the knock-on effect on the determination of any pressure dependent term will remain insignificant despite the error being roughly ten times greater than caused by normal atmospheric changes.

### Calculation of buoyancy correction

The most practical way of determining air density is to use the *parametric* method. This calculates air density from measurements of air pressure, temperature and humidity using an equation recommended by the Comité International des Poids et Mesures (CIPM) derived by Giacomo^{[1]} and modified by Davis^{[2]}. This equation also takes carbon dioxide concentration into account but its effect is insignificant in the context of the pressures generated by a pressure balance.

### Ensuring that the uncertainty in estimating air buoyancy has a negligible effect on a pressure balance

For the uncertainties in the measurement of air temperature, pressure and humidity to have a negligible effect on the buoyancy of pressure balance weights - and assuming that state-of-the-art uncertainties are required of the pressure balance - their combined effect should correspond to, say, an uncertainty of no more than about 1 part per million (k = 2) of the mass, and hence force, values. If this uncertainty is given by:

where:

*U*is the combined uncertainty and equals 1 part per million (of*mass value*) and*Up*,*Ut*and*Urh*are all proportionally equal (that is equal in their*mass proportional effects*, not their numerical values)

then the uncertainty in *mass values* (and hence the vertical forces and pressures generated) caused by each of the three parameters needs to be no greater than about 0.6 parts per million [ie √(3×0.62) is approximately equal to 1]. The approximate uncertainties in the measurement of air temperature, pressure and relative humidity required to ensure that none contributes more than this amount are shown in the table below:

Measurement uncertainties combining to produce a±1 ppm (k = 2) uncertainty in mass buoyancy (*) | |

Parameter | Uncertainty in parameter |

temperature | ±1 ºC |

pressure | ±4 hPa |

humidity | ±45 %RH |

(*) Assuming weights of density approximately 8 000 kg/m^{3} and nominal ambient conditions of 20 ºC, 1000 hPa and 50 %RH

From the table it can be seen that it is not too difficult to calculate air buoyancy with adequate accuracy. Temperature is probably the most difficult parameter to measure in some environments but humidity effects are not worth bothering about.

### Summary

Assuming that the figures mentioned at the top of this document (ie 15 ppm and 150 ppm) are significant in terms of the pressure measurement uncertainty required:

- make sure you are using the appropriate mass value convention - unless you have a very specific reason to the contrary you ought to be using conventional mass values rather than true mass values
- when using a pressure balance as a pressure generator (as opposed to cross-floating it) calculate and apply air density buoyancy corrections from knowledge of air temperature and pressure.

### References

- Equation for the determination of the density of moist air (1981) Giacomo, P.
*Metrologia*1982,**15**, 33-40 - Equation for the determination of the density of moist air (1981/91) Davis, R.S.P.
*Metrologia*, 1992,**29**, 67-70.

**Last Updated: 25 Mar 2010**

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