Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Microwave Determination of the Volume of a Pressure Vessel



Michael R. Moldover, James W. Schmidt, Keith A. Gillis, James B. Mehl, John D. Wright


Using microwave techniques that are scalable to very large volumes, we measured the interior volume of a 0.3 m3, commercially-manufactured, pressure vessel with an uncertainty of 0.05 %, as confirmed by independent, more-accurate, gas-expansion measurements. This pressure vessel (or a much larger one of a similar design) could be used as either a calibrated volume standard or as a gas source and/or a gas collector for the calibration of gas-flow meters. In addition, we determined the expansion of the vessel with temperature (dV/dT)p/V = (35.3{plus or minus}1.9)×10-6 K-1 and we estimated the pressure expansion (dV/dp)T/V = 0.9×10-3 MPa-1. The volume measurement did not require careful thermostatting; its uncertainty was dominated by imperfect modeling of the volume's shape. (The estimated uncertainties are one standard uncertainty with coverage factor k = 1 corresponding to 68 % confidence level.)
Measurement Science and Technology


volume, pressure vessel, flow metrology, flow calibrations, microwave resonances, gas metrology


Moldover, M. , Schmidt, J. , Gillis, K. , Mehl, J. and Wright, J. (2014), Microwave Determination of the Volume of a Pressure Vessel, Measurement Science and Technology, [online], (Accessed May 21, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created December 9, 2014, Updated November 10, 2018