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To measure mass flow, various methods can be applied,but below we outline the thermal measuring principle,as it is used by Bronkhorst High-Tech B.V.The user need not necessarily know these details tosuccessfully apply Hi-Tec instruments, but it helps tounderstand things better with regard to time- and control characteristics of the instruments. F
T 2 0 - Flow ∆ TT �.φ v = φ m TEMPERATURE 1 FLOW Outputcircuit IGURE B
POWERSUPPLY Voltageregulator Laminar flow element ∆ T = k.C
p . � . φ
v ∆ T= T
2 -T
1 in Kelvin
Amplifier +linearisation ο rC
p = Specific heat ∆ T = k.C
p . φ
m � = Density
SensorbridgeTo power supply OUTPUTSETPOINTTo controlvalve φ
v = Volume flow
Temperaturecompensation Controller φ
m = Mass flowElectrically, temperatures T
R T1 R T2 1 and T
2 are in fact tempe-rature dependent resistors R
T1 and R
T2 . In figure A it isshown how the signals measured in the sensor areamplified to electric signals. All common output signals are available and one can be selected.In the case of mass flow control, the output signal iscontinuously compared with a setpoint signal from avoltage source. Any deviations between setpoint signaland measured signal are translated into a control valveadjustment until the two signals are identical.
R T1 R H R T2 Sensor Flow Turbulence filter IGURE A

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ALIBRATIONANDACCURACY As shown in figure A a part of the gas flows throughthe Sensor, and is warmed up by heater R Each instrument is calibrated under actual operatingconditions whenever possible. Otherwise the FLUIDATdatabase is used to calculate accurate conversion factors. For applications that require a better accuracythan the standard 1% of full scale, Bronkhorst High-Tech can offer the “Polynomial Calibration”: accuracy +/- 0,5% of measured value plus +/- 0,1% offull scale value.
H . Conse-quently the measured temperatures T
1 and T
2 moveapart, as shown in figure B. The formulas for ∆ Tdemonstrate that the temperature difference is directlyproportional to mass flow. F

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