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# Physikalisch-Technische Bundesanstalt

Pressure
Working Group 3.33

## Pressure balances

 Pressure balances as standard instruments directly realise the defining equation of pressure. The pressure acts on the bottom surface of a deadweight-loaded piston, which is freely loating in a vertical cylinder. The pressure medium (gas or oil), escapes through a very narrow gap between piston and cylinder (gap width: < 1 µm), thus preventing direct contact between the two components during operation. The force acting on the piston can be determined by weighing, with a relative uncertainty 1 · 10-6 or better. Piston-cylinder assemblies for measuring pressures of up to 350 MPa (left) and 400 MPa (right) Determinations of diameters, combined with measurements of roundness and straightness of the surfaces of piston and cylinder bore, carried out by PTB Working Group 5.31 "Geometrical Standards" the effective cross-sectional area of the piston in the cylinder to be determined according to the theory of Dadson, Greig and Homer with relative uncertainties < 5 · 10-6 for piston diameters between 15 and 50 mm or more. Piston-cylinder assemblies calibrated in this way are available for the measuring ranges up to 2 MPa (pressure medium: Nitrogen) and up to 10 MPa (pressure medium: Oil). Pressure balances with measuring systems as shown on the left-hand side of the above figure are also used as standard devices for measuring the absolute pressure. They are then an alternative to mercury manometers. The smaller cross-sectional areas of the pistons for the measurement of higher pressures are determined in pressure comparison measurements with standard devices already known (step-up procedure). In measuring assemblies of this type, the elastic distortion of piston and cylinder appears as a linear pressure dependence of the cross-sectional area. The pressure coefficient is determined by an iteration process, in which first the pressure variation in the deformed gap is calculated and then, using the finite element method (FEM), the distortion caused by the pressure distribution in the gap. The diagram presents results obtained for the 400 MPa piston-cylinder assembly shown on the night-hand side of the above figure. Corresponding calculations combined with experimental tests were extended to cover measuring range up to 1 GPa for which a twin pressure balance with two weight sets, of 500 kg each, is available. This pressure balance can be operated with piston-cylinder assemblies designed for measuring pressures of up to 10 MPa (4,9 cm²), up to 1 GPa (0,05 cm²), and with assemblies designed for intermediate ranges, such as those for the range up to 400 MPa as described above.
 Elastic deformation of the 400 MPa system

## References

1. Jäger J. et al., Piston-cylinder assemblies of 5 cm2 cross-sectional area used in an oil-operated primary pressure balance standard for the 10 MPa range, Metrologia, 1999,36,541-544.
2. Molinar G. et al., Comparison of methods for calculating distortion in pressure balances up to 400 MPa - EUROMET Project #256, Metrologia, 1998,38,739-759.
3. Molinar G.F. et al., CCM key comparison in the pressure range 0,05 MPa to 1 MPa (gas medium, gauge mode) / Phase A1: Dimensional measurements and calculation of effective area, Metrologia,1999,36,657-662.
4. Legras J.C. et al., CCM key comparison in the pressure range 50 kPa to 1000 kPa (gas medium, gauge mode). Phase A2: Pressure measurements, Metrologia, 1999,36, 663-668.
5. Legras J.C. et al, EUROMET Intercomparison in the pressure range 100 MPa to 700(1000) MPa, Metrologia, 1993/94,30,721-725.

## Contact

Phone: +49 (0)531-592 3230

Jutta König
Phone: +49 (0)531-592 3301
Fax: +49 (0)531-592 3305
E-Mail: Jutta König

Physikalisch-Technische Bundesanstalt
Working Group 3.33 (Pressure)
Bundesallee 100
D-38116 Braunschweig

© Physikalisch-Technische Bundesanstalt, last update: 2010-11-17, Sven Ehlers