3 General principles
FLUXUS G809
3.1 Measurement principle
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UMFLUXUS_G809V2-2EN, 2020-06-25
3
General principles
In the ultrasonic flow measurement, the flow velocity of the fluid in a pipe is determined. Further physical quantities are de
-
rived from the flow velocity and from additional physical quantities, if necessary.
3.1
Measurement principle
The flow velocity of the fluid is measured using the transit time difference correlation principle.
3.1.1
Terms
Flow profile
Distribution of flow velocities over the cross-sectional pipe area. For an optimal measurement, the flow profile has to be
fully developed and axisymmetrical. The shape of the flow profile depends on whether the flow is laminar or turbulent and
is influenced by the conditions at the inlet of the measuring point.
Reynolds number Re
Coefficient describing the turbulence behavior of a fluid in the pipe. The Reynolds number Re is calculated from the flow
velocity, the kinematic viscosity of the fluid and the inner pipe diameter.
If the Reynolds number exceeds a critical value (usually approx. 2300, if the fluid flows in a pipe), a transition from a lami
-
nar flow to a turbulent flow takes place.
Laminar flow
A flow without any turbulence. There is no mixing between the parallel flowing layers of the fluid.
Turbulent flow
A flow with turbulences (swirling of the fluid). In technical applications, the flow in the pipe is mostly turbulent.
Transition range
The flow is partly laminar and partly turbulent.
Sound speed c
Speed of the propagating sound. The sound speed depends on the mechanical properties of the fluid or the pipe material.
In pipe materials and other solid materials, a distinction is made between the longitudinal and transversal sound speed.
For the sound speed of some fluids and materials, see annex C.
Flow velocity v
Average value of all flow velocities of the fluid over the cross-sectional pipe area.
Acoustic calibration factor k
a
k
a
=
The acoustic calibration factor k
a
is a transducer parameter which results from the sound speed c within the transducer
and the angle of incidence. According to Snell's law of refraction, the angle of propagation in the adjoining fluid or pipe ma
-
terial is:
k
a
=
=
=
Fluid mechanics correction factor k
Re
With the fluid mechanics calibration 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 calibration factor only depends on the Reynolds number and the roughness of the inner pipe
wall. The fluid mechanics calibration factor is recalculated by the transmitter for each new measurement.
Operating volumetric flow rate
= v · A
The volume of the fluid that passes through the pipe per unit time. The operating volumetric flow rate is calculated from the
product of the flow velocity v and the cross-sectional pipe area A.
c
sin
------------
c
sin
------------
c
sin
------------
c
sin
-----------
V
·
V
·
