Brooks Instrument 5861i - Manual (Page 17)

3-1
Installation and Operation Manual
X-TMF-5861i-MFC-eng
Part Number: 541B111AAG
November, 2008
Brooks ® Model 5861 i
Section 3 Operation
3-1 Theory of Operation
The thermal mass flow sensing technique used in the 5861 i works as
follows:
A precision power supply provides a constant power heat input (P) at the
heater which is located at the midpoint of the sensor tube. (Refer to Figure
3-1) At zero or no flow conditions, the heat reaching each temperature
sensor (one upstream and one downstream of the heater) is equal.
Therefore, the temperatures T1 and T2 are equal. When gas flows through
the tube, the upstream sensor is cooled and the downstream sensor is
heated, producing a temperature difference. The temperature difference
T2-T1 is directly proportional to the gas mass flow.
The equation is: Δ T = A * P * C
p
* m
Where,
Δ T = temperature difference T2 - T1 (°K)
C
p
= specific heat of the gas at constant pressure
(kJ/kg-°K)
P = heater power (kJ/s)
m = mass flow (kg/s)
A = constant of proportionality (S 2 -°K 2 /kJ 2 )
A bridge circuit interprets the temperature difference and a differential
amplifier generates a linear 0-5 Vdc signal directly proportional to the gas
mass flow rate.
The flow restrictor shown in Figure 3-1 performs a ranging function similar
to a shunt resistor in an electrical ammeter. The restrictor provides a
pressure drop that is linear with flow rate. The sensor tube has the same
linear pressure drop/flow relationship. The ratio of the restrictor flow to the
sensor tube flow remains constant over the range of the meter. Different
restrictors have different pressure drops and produce meters with different
full scale flow rates. The span adjustment in the electronics affects the fine
adjustment of the controller's full scale flow.
.