Mass Flow Meters

A mass flow meter measures the mass of fluid passing through it per unit of time, in units such as kilograms per hour or grams per minute, rather than its volume. Because mass does not change with temperature or pressure, the reading needs no correction for either. The two mass flow technologies are Coriolis and thermal.

Mass flow meters each work off of their own principles, described below. 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 gases and can also measure liquids in specific applications.

How does a mass flow meter work?

A mass flow meter works by sensing a physical effect that depends on mass rather than volume. A Coriolis meter vibrates a tube and measures how the moving mass twists it; the phase shift between the tube’s inlet and outlet is proportional to mass flow. A thermal meter heats a sensor and measures how much heat the fluid carries away, which depends on the number of molecules passing, not their volume.

That is the working principle in both cases: the meter never measures volume and multiplies by density. It reads mass directly, so a change in gas pressure or liquid temperature that would change the volume reading of a turbine or orifice meter leaves a mass meter’s reading unchanged. A Coriolis meter also reports density, since the natural frequency of the vibrating tube depends on the mass of fluid inside it, and from mass and density it can calculate volumetric flow as well.

Mass flow vs. volumetric flow

Volumetric flow is the volume of fluid passing per unit of time, in liters per minute, gallons per minute or cubic meters per hour. Mass flow is the mass passing per unit of time, in grams per minute, kilograms per hour or pounds per hour. The two are related by density: mass flow equals volumetric flow multiplied by density.

For a liquid at a steady temperature, density barely changes, so a volumetric meter and a mass meter tell the same story. For a gas, density changes with every change in pressure and temperature, so a volumetric reading means nothing without stating the conditions. That is why gas flow is quoted in standard units, such as standard cubic feet per minute (SCFM) or standard liters per minute (SLPM), which are mass flow in disguise: the volume the gas would occupy at a reference pressure and temperature. Mass flow matters most where the process depends on quantity of material rather than space it fills: combustion and fuel blending, chemical reactions that run by mole, custody transfer by weight, and any gas measurement.

Mass flow units of measurement

Unit	Symbol	Typical use
Grams per minute	g/min	Laboratory, small liquid and gas lines
Kilograms per hour	kg/h	Process lines, fuel, steam
Pounds per hour	lb/h	U.S. process and steam measurement
Tonnes per hour	t/h	Pipelines, bulk transfer
Standard cubic feet per minute	SCFM	Gas flow, referenced to standard conditions
Standard liters per minute	SLPM	Gas flow, instrument and laboratory gases

Types of mass flow meters

There are two types of mass flow meter: thermal, used mainly for gases, and Coriolis, used for liquids and gases. Everything sold as a mass flow meter is one or the other. Mass flow controllers combine a thermal or Coriolis meter with a control valve in one body.

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.

Dispersion, capillary tube and temperature differential designs

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.

Constant temperature differential vs. constant current

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 sensors.

A second, and less popular, method is called the 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 meter performance and cost

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 in terms of 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.

The two-tube design

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 1,000 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 meter performance, cost and zero stability

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 and twelve thousand dollars.

In practice, the turndown range of a Coriolis flow meter is limited by its capability to measure the mass flow at its minimum flow and the allowable pressure drop at 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’s limitation in measuring a very small phase shift at zero or low flow. This zero stability determines what minimum flow the Coriolis flow meter can measure with a given inaccuracy.

Coriolis vs. thermal mass flow meters

	Coriolis	Thermal
Measures	Mass flow and density	Mass flow
Fluids	Liquids and gases	Gases; liquids in a few designs
Typical accuracy	0.1% to 0.5% of reading	1% to 2% of reading
Turndown	Up to 100:1, limited by zero stability	About 100:1
Moving parts	None; vibrating tube	None
Pressure drop	Moderate, from the tube bends	Very low
Response to changing flow	Slow; averages over tube vibration cycles	Moderate
Effect of pressure, temperature, viscosity	None	None
Price	$2,000 to $12,000	Hundreds to $1,000 for gas; thousands for liquid
Best for	Custody transfer, batching, blending, density measurement	Gas flow, compressed air, burner and combustion air

Mass flow meters for liquids

Coriolis is the mass flow meter for liquids. It measures mass and density directly, at 0.1% to 0.5% of reading, for any liquid that can be pumped through its tubes, and it is the standard choice for liquid custody transfer and batching by weight. Thermal meters are rarely used on liquids because a liquid carries heat away so efficiently that the signal is small and the sensor must be in direct contact with the fluid.

Where the liquid’s density is known and stable, a volumetric meter gives mass flow by multiplication, at the volumetric meter’s accuracy. This is how most fuel consumption, injector and dispensing measurements are made: a positive displacement meter reads volume at 0.2% of reading, and the fuel’s density at the measured temperature converts it to mass. The positive displacement meter costs a fraction of a Coriolis meter, reads down to 0.005 cc/min where a Coriolis meter’s zero stability swamps the signal, and responds in 1.6 milliseconds to a flow that starts, stops or reverses.

When a mass flow meter is the wrong choice

A Coriolis meter is the wrong choice when the flow changes faster than the tube can settle, as it does in fuel injection, valve cycling and pulsed dispensing, when the flow is so small that zero stability dominates the reading, and when the budget will not stretch to two to twelve thousand dollars per point. A thermal meter is the wrong choice for most liquids and for wet or dirty gas.

For low, intermittent or fast-changing liquid flow, a positive displacement meter with a known density is the usual answer. Max piston, gear and helical meters cover 0.005 cc/min to 500 liters per minute at 0.2% to 0.3% of reading, with no straight pipe and no sensitivity to viscosity or flow profile.

• Piston flow meters: 0.005 cc/min to 35 L/min, 0.2% of reading over 200:1, for fuel consumption, injector and valve testing and laboratory work.
• Gear flow meters: 0.5 cc/min to 240 L/min, 0.3% of reading over 100:1, for hydraulics, lubricants, adhesives and chemicals.
• Helical flow meters: 100 cc/min to 500 L/min, 0.2% of reading, for heavy fuels, coatings and resins.

Not sure whether the application calls for mass or volumetric measurement? Call +1 (707) 433-2662 or request a quote and an application engineer will work through the fluid, flow range and density with you.

Frequently asked questions