handbook of modern sensors

362 11 Flow Sensors
(A)
(B)
Fig. 11.3. Two types of flow resistor: a narrow channel (A) and a porous plug (B).
plug which somewhat restricts the medium flow. A differential pressure sensor is
positioned across the resistor. When moving mass enters the higher-resistance area,
its velocity increases in proportion to the resistance increase:
The Bernoulli equation defines differential pressure as 1
v 1a = v 2a R. (11.8)
p = p 1 − p 2 = ρ 2 (v2 2a − v2 1a ) = k ρ 2 v2 2a (1 − R2 ), (11.9)
where k is the correction coefficient which is required because the actual pressure
p 2 is slightly lower than the theoretically calculated pressure. From Eq. (11.9), the
average velocity can be calculated as
√
1 2
v 2a = √ p. (11.10)
k(1 − R 2 ) ρ 1 It is assumed that both pressure measurements are made at the same height (y = 0), which
is usually the case.