Mass flow measurement by throttling devices

Measurement of mass flow can be made easier assuming that the motion in the duct is almost one-dimensional (gradual and small variations of area, constant speed in each section, no production of entropy) and incompressible. Between two stations of the tube both the incompressible Bernoulli equation and the conservation of volumetric flow are valid:

UA = U2A2

from which the mass flow in the pipe can be found:

This method of measuring the mass flow rate is used in throttling devices. The advantages of these devices include robustness, reproducibility of the calibration and their insensitivity to the Reynolds number, above certain minimum values, and to the asymmetry and the disturbance caused by duct obstructions and deviations upstream.

Calibration formulas of these devices are always in the form of Equation (2.8) even if the assumptions of validity of that formula are far from being met. Correction factors are introduced:

■ the flow coefficient, C, takes into account that the flow is not truly one-dimensional and isentropic;

■ the expansion factor (coefficient of compressibility), e2, takes into account the variation in density that occurs when the ratio of pressure generated by the throttling device reaches high values.

The formula for throttling devices then becomes: