Analytical solutions of some model cases of piston-cylinder assemblies

Abstract

Pressure balances are an important part of the sets of primary pressure standards in many national metrology institutes. The most critical factor determining their accuracy is the effective area of their piston-cylinder assemblies (PCAs). This can be determined (for PCAs with undistorted pressure) by applying a numerical procedure based on a theory by Dadson while knowing a gapprofile (of an axisymmetric PCA approximation). The pressure balances are also a basis for the primary pressure scale of the Czech Metrology Institute. Hence, we wanted to test our programme by computing the effective area from the geometrical data. Therefore, we solved the analytical formulae of Dadson et al (1982) The Pressure Balance—Theory and Practice (London: Her Majesty’s Stationery Office) for several simple geometries with a constant gap width, which are easy to calculate analytically. It is shown that the analytical results always agreed perfectly with the results of our programme. This success confirmed the correctness of our programme. However, it also pointed out a problem of discretization which can be non-negligible, even in the case of relatively simple geometries. We assume that the analytical formulae obtained can be of practical use for any other pressure metrology laboratory requiring an independent way to confirm their own PCA-modelling software.