handbook of modern sensors

11.3 Thermal Transport Sensors 363
To determine the mass flow rate per unit time, for a incompressible medium, Eq.
(11.10) is simplified to
q = ξA 2
√
p, (11.11)
where ξ is a coefficient which is determined through calibration. The calibration must
be done with a specified liquid or gas over an entire operating temperature range; thus,
the value of ξ may be different at different temperatures. It follows from the above that
the pressure gradient technique essentially requires the use of either one differential
pressure sensor or two absolute sensors. If a linear representation of the output signal is
required, a square root extraction must be used. The root extraction can be performed
in a microprocessor by using one of the conventional computation techniques. An
advantage of the pressure gradient method is in the absence of moving components
and use of standard pressure sensors which are readily available. A disadvantage is
in the restriction of flow by resistive devices.
11.3 Thermal Transport Sensors
A good method for measuring flow would be by somehow marking the flowing
medium and detecting the movement of the mark. For example, a mark can be a
floating object that can move with the medium while being stationary with respect
to the medium. The time which it would take the object to move with the flow from
one position to another could be used for the calculation of the flow rate. Such an
object may be a float, radioactive element, or dye which changes optical properties
(e.g., color) of flowing medium. Also, the mark can be a different gas or liquid whose
concentration and rate of dilution can be detectable by appropriate sensors.
In medicine, a dye dilution method of flow measurement is used for studies in
hemodynamics. In most instances, however, placing any foreign material into the
flowing medium is either impractical or forbidden for some other reasons. An alternative
would be to change some physical properties of the moving medium and to
detect the rate of displacement of a changed portion or rate of its dilution. Usually,
the best physical property that can be easily modified without causing undesirable
effects is temperature.
Figure 11.4A shows a sensor which is called a thermoanemometer. It is composed
of three small tubes immersed into a moving medium. Two tubes contain temperature
detectors R 0 and R s . The detectors are thermally coupled to the medium and are thermally
isolated from the structural elements and the pipe where the flow is measured.
In between the two detectors, a heating element is positioned. Both detectors are connected
to electrical wires through tiny conductors to minimize thermal loss through
conduction (Fig. 11.4B). The sensor operates as follows. The first temperature detector
R 0 measures the temperature of the flowing medium. The heater warms up the
medium and the elevated temperature is measured by the second temperature detector
R s . In a still medium, heat would be dissipated from the heater through media to both
detectors. In a medium with a zero flow, heat moves out from the heater mainly by
thermal conduction and gravitational convection. Because the heater is positioned