# A King, a Bridge and Mass Flow Measurement

Following on our previous blog, ‘Top 5 reasons to use Mass Flow Meters (MFM) and controllers (MFC) with thermal inline CTA measurement’, we now focus on the measurement principle of these mass flow meters using inline CTA measurement (Constant Temperature Anemometry).

King’s Law and CTA meters

The working principle of these CTA flow meters and 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)

Wheatstone bridge and CTA 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.

Video explaining the operating principle of a Mass Flow Meter based on CTA measurement