MATHEMATICAL MODEL OF PNEUMATIC CHANNEL OF GAS PRESSURE MEASURING TRANSDUCER

The paper is devoted to the study of the impact of operational factors, particularly gas leakage through the damages of pneumatic channels of measuring transducers of gas pressure and pressure drop, on the measuring result of these parameters and, therefore, on the measured value of gas flow rate and volume using pressure differential flowmeters. During the operation of gas metering units, connecting tubes, valve blocks, and averaging chambers of the standard primary device must be hermetic. However, they may become non-tight because of operational factors, and gas leakage may occur. Such leaks distort the measured pressure drop or pressure value, which can lead to a distortion of the measurement result of the gas flow rate by the metering unit. 
The authors developed a mathematical model of a pneumatic channel of gas pressure measuring transducer with existing damage. For this purpose, a mathematical model of the connecting tube, which connects the pressure averaging chamber with the pressure transducer chamber, has been developed for the stationary gas mode. A mathematical model of gas leakage through damage like "through-hole" was also developed. Based on the mathematical model of the connecting tube and the model of the process of gas leakage through the hole, a mathematical model of the pneumatic channel with a gas leakage hole was obtained. 
Modeling and investigating the impact of gas pressure, geometric characteristics of damage, and connecting line on the measuring result of pressure or pressure drop was performed. Particularly, the value of the negative systematic error of the gas pressure measurement, which occurs as a result of gas leakage through the hole in the connecting tube, is calculated for a set of fixed values of the geometric characteristics of the pneumatic channel. 
The paper shows that an increase in the pressure in the measuring tube leads to an increase in the modulus of pressure absolute error caused by the gas leakage through the hole in the connecting tube. The gas flow rate through the hole in the connecting tube and, accordingly, the pressure measurement error depends on the diameter of the through-hole and the location of the leakage. An increase in the hole diameter leads to an increase in the modulus of the absolute error of the pressure measurement. 
As the length of the connecting tube from the connection point with the measuring pipeline to the point of gas outflow increases, the pressure measurement error increases by the modulus.