Determination of pressure balance distortion coefficient and zero-pressure effective area uncertainties

The behaviour of piston-cylinder operated pressure balances is characterized by the distortion coefficient λ and zero-pressure effective area A0 which model the variation of a pressure balance’s area in terms of the applied pressure. This paper determines the uncertainties in λ and A0 when utilizing the method of cross-floating with another pressure balance standard whose parameters and associated uncertainties are known. A limitation that is frequently encountered in many attempts of the uncertainty analysis for a pressure balance is that no readily accessible uncertainty quantification framework for the distortion coefficient is present. As a result the uncertainty in a pressure balance’s area at elevated applied pressures is typically underestimated in the absence of this uncertainty information. We firstly review the uncertainty formulation for a pressure balance generated pressure involving correlation effects in terms of an implicit multivariate matrix equation approach and then utilizing the resulting solution present the methodology to consistently perform the uncertainty analysis for λ and A0