Sensors and Transducers - Introduction to Biomechatronics - page 63

FIGURE 2-60
Common differential
pressure flowmeters.
(a) Ventui. (b) Orifice
plate. (c) Nozzle.

where is the density of the fluid upstream from the plate, d is the diameter of the hole

in the orifice plate, and β = d / D , where D is the upstream diameter of the interior
of the pipe. The empirically determined correction factors are C , which is affected by,
for example, diameter ratio, Reynolds number, and pipe roughness, and ε , which is the
expansibility factor.
The Venturi tube, shown in Figure 2-60a, is the oldest type of differential pressure
flowmeter. Because the change in diameter is more gradual, this better approximates the
theoretical result, C , which in this case is close to 0.95. Its major disadvantages are the
lower differential pressure for a given diameter ratio and the expense of manufacture.
The nozzle method shown in Figure 2-60c combines the best features of the other
two techniques, making it both reasonably cheap to manufacture and accurate. Pneumo-
tachographs, discussed in Chapter 10, use a variation of the nozzle method in which a
restrictive element made from a perforated plate, or a large number of narrow-bore pipes,
is used. These offer very little resistance to the airflow, and hence the pressure drop is small.
It follows from equation (2.63) that the pressure gradient technique requires the use
of either a single differential pressure sensor or a pair of absolute sensors. Additionally,
because the flow rate is proportional to the square root of the pressure difference, if a linear
representation of the flow is required then a square root extraction circuit or algorithm
must be applied.
The primary advantage of this technique is the absence of any moving components
and the ready availability of standard pressure sensors. The main disadvantage is the
requirement that the flow may be affected by the use of a restrictive device.

ρ