##### Mass Flow Meters

Mass Flow Meters each work off of their own principles that are described within the specific meter description. The end result is that a known mass of material has traveled across the path of the sensor. Mass flow meters are particularly suited to measuring gasses and can also measure liquids in specific applications.

**Thermal mass flow meters**

Thermal mass flow meters place a heat source into the flow stream and measure the heat dissipation using one or more temperature sensors. The majority of thermal flow meters are used for gas flow applications; although there are several designs offered for liquid measurement applications.

Thermal flow meters fall into three main families dispersion, capillary tube, and temperature differential. All of them measure fluid mass flow rate by measuring the heat loss from a heated surface to the flowing fluid. In the case of the thermal dispersion, or immersible, type of flow meter, the heat is transferred to the boundary layer of the fluid flowing over the heated surface. In the case of the capillary-tube type, the heat is transferred to the fluid flowing through a small heated capillary tube that is parallel to the main fluid flow path. Many mass flow controllers (MFC) which combine a mass flow meter, electronics and a valve are based on the capillary design. The third type contains a heated and an unheated RTD attached to the outside of the tube. The temperature differential between the two RTDs provides the primary flow signal; at high flow rates the differential is lower as flow removes more heat, and at low flow rates the differential is higher, as flow removes less heat.

While all thermal flow meters use heat to make their flow measurements, there are two different electronic schemes for measuring the amount of heat dissipated. One method is called the constant temperature differential. Thermal flow meters using this method have two temperature sensors — a heated sensor and another sensor that measures the temperature of the gas. Mass flow rate is computed based on the amount of electrical power required to maintain a constant difference in temperature between the two temperature sensors. A second, and less popular method, is called a constant current method. Thermal mass flow meters using this method also have a heated sensor and another one that senses the temperature of the flow stream. The power to the heated sensor is kept constant. Mass flow is measured as a function of the difference between the temperature of the heated sensor and the temperature of the flow stream. Both methods are based on the principle that higher velocity flow rates result in a greater cooling effect. Both measure mass flow based on the measured effects of cooling in the flow stream.

Thermal mass flow meters operate independent of density, pressure, and viscosity. Accuracy of thermal mass flow meters is typically 1 to 2% of reading. Thermal mass flow meters benefit from having no moving parts, and a nearly unobstructed flow path.

Sensors for gas measurement applications are available from hundreds of dollars, up to one thousand dollars. Sensors for liquid measurement applications usually cost in the thousands of dollars.

**Coriolis Flow Meters**

Coriolis Flow Meters utilize the inertial force of the flowing fluid to impart changes on the vibration of a tube or set of tubes. The Coriolis Effect can then be measured regarding frequency, amplitude, and phase shift to determine the mass flow rate and density of the fluid in the system.

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 turndown range in a 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 a coriolis flow meter which is an offset of the meter output when there is no flow in the meter. This zero stability is the systematic error of the coriolis flow meter due to the sensor limitation to measure a very small phase shift in zero or low flow. This zero stability will determine what minimum flow the coriolis flow meter can measure with certain inaccuracy.