On the theory of the frequency response of gas and liquid pressure measurement systems with connecting tubes

Pressure sensors often have to be placed at a certain distance from the measured object, which means that the fluid in any connecting tube and the volume of the sensor represent a constituent part of the pressure measurement system. This paper deals with improvements to the modelling of the frequency characteristics of such systems using gases or liquids as the pressure transmission fluids. The Bergh–Tijdeman mathematical model, which represents the state of the art for studying the dynamics of pressure measurement systems with a connecting tube, was supplemented with contributions from thermodynamic effects in the sensor volume and the compliance effects of the connecting tube. The results show that the thermodynamic effects can have a significant influence on the predicted frequency response of gas-filled systems, typically leading to a considerable increase of the damping ratio. The compliance is usually important to consider when modelling liquid-filled systems. In addition, this paper aims to study the validity of approximate, second-order and first-order models of the pressure measurement system. We derived analytical approximations for the corresponding lumped-parameters, i.e. the natural frequency, the damping ratio and the time constant, and identified some discrepancies in the analytical expressions that are often used in the literature. (paper)