12
V
Re
a
Flow velocity v
average value of the flow velocities over the cross-sectional pipe area.
Acoustic calibration factor k
a
c
α
------------
sin
α
The acoustic calibration factor k
a
is a parameter of the transducer which results from the sound speed c within the trans-
ducer and the angle of incidence (see Fig. 3.2). According to Snell's law of refraction, the angle of propagation in the ad-
joining medium or pipe material is:
c
α
------------
c
β
------------
c
γ
-----------
k
a
=
sin
α
=
sin
β
=
sin
γ
·
Volumetric Flow Rate V
·
V = v · A
The volume of the medium that passes through the pipe per unit time. The volumetric flow rate is calculated from the prod-
uct of the flow velocity v and the cross-sectional pipe area A.
Fluid mechanics correction factor k
Re
With the fluid mechanics correction factor k
Re
, the measured value of the flow velocity in the area of the sound beam is
converted into the value of the flow velocity across the whole cross-sectional pipe area. In case of a fully developed flow
profile, the fluid mechanics correction factor only depends on the Reynolds number and the roughness of the inner pipe
wall. The fluid mechanics correction factor is recalculated by the transmitter for each new measurement.
Mass flow rate m
·
·
m
·
= V · ρ
The mass of the medium that passes through the pipe per unit time. The mass flow rate is calculated from the product of
the volumetric flow rate
·
and the density ρ.
3.2.2
Measurement of the Flow Velocity
The signals are emitted and received by two transducers alternatively in and against the flow direction. If the medium
moves, the signals propagating in the medium are displaced with the flow. This displacement causes a reduction in dis-
tance for the signal in the flow direction and an increase in distance for the signal against the flow direction in the wedge of
the receiving transducer (see Fig. 3.2 and Fig. 3.3). This causes a change in the transit times. The transit time of the signal
in the flow direction is shorter than the transit time against the flow direction. This transit time difference is proportional to
the average flow velocity.
The flow velocity of the medium is calculated as follows:
∆
t
v = k · k ·
------------
2
⋅
t
fl
with
v
– flow velocity of the medium
k
Re
– fluid mechanics correction factor
k
a
– acoustic calibration factor
∆t
– transit time difference
t
fl
– transit time in the medium
k
a
=
