# A King, a Bridge and Inline Mass Flow Measurement

December 15 , 2020 Nicolaus Dirscherl

As Managing Director of M+W Instruments GmbH, I often explain and give training about the inline measurement principle used for our MASS-STREAM flow meter series. M+W Instruments is a wholly owned subsidiary of Bronkhorst. At our production site in Leonhardsbuch, Germany, we manufacture instruments of Bronkhorst's MASS-STREAM™ product line.

This product series of mass flow meters measures flow inline following the CTA principle (CTA = Constant Temperature Anemometry). In this blog I try to share a little bit of my knowledge about this measurement principle.

## King's Law and CTA meters

The working principle of these inline flow meters and flow controllers is based on King’s Law. King’s Law can be attributed to L.V. King, who in 1914 published his famous King’s Law, mathematically describing heat transfer in flows. He used a heated wire immersed in a fluid to measure the mass velocity at a point in the flow.

This can be described by the following formula:

P = P0 + C · Φmn
P: Heater power
P0: Heater power offset at zero flow
C: Constant (device-dependent)
Φm: Mass flow

n: dimensionless figure (type 0.5)

Video explaining the principle of operation of the MASS-STREAM thermal mass flow controller

Wheatstone bridge

## Wheatstone bridge and CTA flow meters

According to King’s Law, the greater the velocity of the gas across the probes, the greater the cooling effect. The electronics are realized with a Wheatstone bridge, which is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer.

The two probes of the CTA sensor act as the legs of the Wheatstone bridge and as the heater probe is cooled by the fluid, the resistance of the probe is decreased and more energy is required to maintain the temperature difference.

The CTA sensor is aiming to keep this temperature difference (delta-T) between the two probes at a constant level. The flow rate and the heater energy required to maintain this constant delta-T are proportional and thus indicate the mass flow of the gas. The actual mass flow rate is calculated by measuring the variable power required to maintain this constant temperature difference as the gas flows across the sensor.

Wheatstone bridge

## What are applications of inline mass flow meters?

As I’ve mentioned before, the CTA sensor is measuring the flow rate inline. This means that no by-pass is required which makes these mass flow meters less sensitive to humidity and contamination. Besides, the pressure loss is negligible. This makes the instruments the ideal solutions for the following applications:

## Would you like to know more?

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