French scientist Gaspard-Gustave Coriolis published a paper in 1835, containing the mathematical expression for the Coriolis force. A practical application of the Coriolis force is the mass flow meter, for measurement of the mass flow and density of a fluid flowing through a tube or pipe. The operating principle involves inducing a vibration into a tube through which fluid passes. The plane of the vibrating tube provides a reference frame allowing the Coriolis Effect to be measured. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in the frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed allow the mass flow rate and density of the fluid to be calculated.
In a two tube, U-shaped design, fluid flows through parallel tubes. An actuator induces a vibration of the tubes. The two parallel tubes are counter-vibrating, to make the measuring device less sensitive to any external vibrations. The frequency of the vibration depends on the size of the mass flow meter, and ranges from 80 to 1000 vibrations per second. The amplitude of the vibration is too small to be seen, but it can be felt by touch. When no fluid is flowing, the vibration of the two tubes is symmetrical. When there is mass flow, there is some twisting of the tubes. The arm through which fluid flows away from the axis of rotation exerts a force on the fluid increasing its angular momentum, so it lags behind the overall vibration. The arm through which fluid is pushed back towards the axis of rotation exerts a force on the fluid decreasing the fluid's angular momentum again; and that arm leads the overall vibration.
The inlet arm and the outlet arm vibrate with the same frequency as the overall vibration, but when there is mass flow the two vibrations are out of sync, the inlet arm is behind, and the outlet arm is ahead. The two vibrations are shifted in phase with respect to each other, and the degree of phase-shift is related to the amount of mass that is flowing through the tubes.
Coriolis mass measurement is not sensitive to changes in pressure, temperature, viscosity or density. They offer a flow path without any obstructions. Coriolis flow meters are very accurate; most have accuracy specifications from +/-0.1% to 0.5% of reading (plus the zero drift effect) with a turndown rate up to 100:1. Coriolis flow meters are the most costly industrial flow meters made, in terms of average selling price, with the majority priced between two to twelve thousand dollars.
In practice, the rangeability/turndown ratio in the coriolis flow meter is limited by its capability to measure the mass flow in its minimum flow and the allowable pressure drop in its maximum flow. There is a zero stability term in the coriolis flow meter which is an offset of the meter output when there is no flow in the coriolis flow meter. This zero stability is the systematic error of the coriolis flow meter due to the sensor limitation to difference a very small phase shift in zero or low flow. This zero stability will determine how much the minimum flow that the coriolis flow meter can measure with certain inaccuracy.