1-Free Sagemcom - Modification with the authorization of the management concerned
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Page 17
UM User Manual (EN) rev. 3.2
5.
FUNCTIONALITIES
The product supports all the following functionalities.
Metering Functions
The main function of the product is the metering of water volume flowing through it. It measures and
computes all of the values described in this chapter.
All the meters are calibrated and checked in metrology accuracy according to the AWWA. This calibra-
tion and these metrology checks are performed once during the manufacturing process. Thus, there is
no need to re-calibrate the meters during their certified lifetime.
Measurements
Measurements are done using ultrasonic wave and measuring the time for sound to progress in both
flow direction. Those times are processed into the metrologic part to obtain the instantaneous flow.
This flow is integrated over time to obtain the volume flown by the meter.
Assuming the notations: c for sound speed in water, v is the flow speed in the spool piece, L is the ul-
trasonic active measurement path length, Tu and Td are the propagation time for downstream and up-
stream.
𝑇𝑢 =
𝐿
(𝑐 − 𝑣)
𝑎𝑛𝑑 𝑇𝑑 =
𝐿
(𝑐 + 𝑣)
𝑙𝑒𝑠 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖
The propagation time difference is then:
𝑑𝑇𝑂𝐹 = 𝑇𝑢𝑝 − 𝑇𝑑𝑤 =
2 × 𝐿 × 𝑣
𝑐
2
− 𝑣
2
≅
2 × 𝐿 × 𝑣
𝑐
2
↔ 𝑣 =
𝑐
2
× 𝑑𝑇𝑂𝐹
2 × 𝐿
The sound speed in water is dependant of the water temperature, so we calculate it out of the sum of
propagation times.
𝑠𝑇𝑂𝐹 = 𝑇𝑢𝑝 + 𝑇𝑑𝑤 =
2 × 𝐿 × 𝑐
𝑐
2
− 𝑣
2
≅
2 × 𝐿
𝑐
↔ 𝑐 =
2 × 𝐿
𝑠𝑇𝑂𝐹
And thus
𝑣 =
2 × 𝐿 × 𝑑𝑇𝑂𝐹
𝑠𝑇𝑂𝐹
2
Once the flow speed is known, the volume noted V is calculated by integration over time based in the
path section S:
𝑉 = ∫ 𝑣 × 𝑆 × 𝛿𝑡
Temperature
The temperature in °C is obtained from the ultrasonic sound speed, using a reversed approximation of
the known Bilaniuk and Wong (1993,1996) convertion of Del Grosso and Mader's 1972 data.
𝑐 = 1.40238677 𝑥 103 + 5.03798765 𝑇 − 5.80980033 𝑥 10 − 2 𝑇
2
+ 3.34296650 𝑥 10 − 4 𝑇
3
− 1.47936902 𝑥 10 − 6 𝑇
4
+ 3.14893508 𝑥 10 − 9 𝑇
5