FLOWSIC100 Operating Instructions
Gas Velocity Monitor
Product Description
18 © SICK MAIHAK GmbH · Germany · All rights reserved 8012513/03-2008
Calculating the gas velocity
The measuring path L is equal to the active measuring distance, that is, the area through
which the gas flows. Given the measuring path L, sound velocity c, and the angle of
inclination a between the sound and flow direction, the sound transit time when the signal
is transmitted in the direction of the gas flow (forward direction) can be expressed as:
(2.1)
Against the gas flow (backward direction):
(2.2)
After the resolution to v:
(2.3)
Apart from the two measured transit times, this relationship only contains the active
measuring distance and the angle of inclination as constants.
Speed of Sound
The speed of sound c can be calculated by rearranging formulas 2.1 and 2.2.
(2.4)
Based on the dependencies in formulas 2.5 and 2.7, the speed of sound can be used to
determine the gas temperature, and for diagnosis purposes.
(2.5)
Calculating the gas temperature
Since the speed of sound is dependent on the temperature, the gas temperature can also
be calculated from the transit times (by rearranging formulas 2.4 and 2.5 to derive J).
(2.6)
Formula 2.6 shows that, in addition to the measured transit times, the square of the values
of L and the standard velocity are included in the calculation.
Note: This means that a precise temperature measurement is only possible if the measurement
path L is measured extremely accurately, the gas composition is constant, and a calibration
has been carried out (see Section 4.3.2).
Determining the volumetric flow
The volumetric flow under actual conditions is calculated using the geometric constants of
the duct. The process parameters "pressure", "temperature", and "humidity content" are
required to calculate the volumetric flow under standard conditions. A more detailed
description is provided in Section 2.4..
t
v
L
cv αcos⋅+
-----------------------------
=
t
r
L
cv– αcos⋅
-----------------------------
=
v
L
2 αcos⋅
---------------------
1
t
v
----
1
t
r
--- -
–
⎝⎠
⎛⎞
⋅=
c
L
2
---
t
v
t
r
+
t
v
t
r
⋅
-------------- -
⎝⎠
⎜⎟
⎛⎞
⋅=
cc
0
1
ϑ
273°C
---------------- -
+⋅=
ϑ 273°C
L
2
4 c
0
2
⋅
-----------------
t
v
t
r
+
t
v
t
r
⋅
-------------- -
⎝⎠
⎜⎟
⎛⎞
2
1–⋅
⎝⎠
⎜⎟
⎛⎞
⋅=
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