handbook of modern sensors

370 11 Flow Sensors
cies are mixed in a nonlinear circuit (a mixer). The output low-frequency differential
harmonics are selected by a bandpass filter. That differential is defined as
f = f s − f r ≈± 2f sv
c , (11.20)
where f s and f r are the frequencies in the transmitting and receiving crystals, respectively,
and the plus/minus signs indicate different directions of flow. An important
conclusion from the above equation is that the differential frequency is directly proportional
to the flow velocity. Obviously, the crystals must have much smaller sizes
than the clearance of the tube of flow. Hence, the measured velocity is not the average
but rather a localized velocity of flow. In practical systems, it is desirable to
calibrate ultrasonic sensors with actual fluids over the useful temperature range, so
that contribution of a fluid viscosity is taken into account.
An ultrasonic piezoelectric sensors/transducer can be fabricated of small ceramic
disks encapsulated into a flowmeter body. The surface of the crystal can be protected
by a suitable material, (e.g., silicone rubber). An obvious advantage of an ultrasonic
sensor is in its ability to measure flow without a direct contact with the fluid.
11.5 Electromagnetic Sensors
The electromagnetic flow sensors are useful for measuring the movement of conductive
liquids. The operating principle is based on the discovery of Faraday and Henry
(see Section 3.4 of Chapter 3) of the electromagnetic induction. When a conductive
media (wire, for instance) or for this particular purpose, flowing conductive liquid
crosses the magnetic flux lines, the electromotive force (e.m.f.) is generated in the
conductor. The value of the e.m.f. is proportional to velocity of moving conductor
[Eq. (3.37) of Chapter 3]. Figure 11.10 illustrates a tube of flow positioned into magnetic
field B. There are two electrodes incorporated into a tube to pick up the e.m.f.
(A)
(B)
Fig. 11.10. Principle of an electromagnetic flowmeter: (A) position of electrodes is perpendicular
to the magnetic field; (B) relationships between flow and electrical and magnetic vectors.