High-precision in situ measurement of speed of sound in hydraulic systems

An existing ISO standard frequency-domain method for measurement of speed of sound in a hydraulic pipeline is enhanced and extended in this article to include in situ measurement of pressure transducer calibration factors. Transducer mounting stresses are shown to cause variations in the calibration factors, and the proposed method can be used to eliminate these uncertainties, consequently improving the accuracy of the speed of sound. 95% confidence ranges in the speed of sound of less than ±0.1% have been achieved, and such high precision cannot be achieved by other practical methods. The method can also been extended to estimate viscosity and mean flow velocity, but accuracy is less good. Novel time-domain versions of the method are introduced. These may be valuable for real-time monitoring, and changes in speed of sound or calibration factor can be tracked with minimal delay. Some examples showing the effect of sudden aeration are presented; a sudden drop in speed of sound is apparent.