The actual sound velocity measurements were carried out as follows: For each measurement an artificial leak was created by opening a hydrant outside the measuring section; the escaping water was discharged in a systematic manner. Only accelerometers were used. Hydrophones were not applied because of the anticipated influence of the network pressure. All measurements were taken on uniform pipe sections of a known material. Sections with varying materials and/or diameters were not tested. The measurements were filtered during analysis to produce a clear correlation result. The filters were set so that only clearly coherent signals were processed. Interference noise, as can be seen in Figure 7 to the right and left of the selected region, was not used for the correlation, as it dramatically increases the ambiguity of the correlation peak.
The results were divided into different sound velocity classes. The width of each class was 50 m/s. The results can be seen inFigures 8and9.
The sound velocities for PE80 d110 are between 207 m/s and 582 m/s. The very low and the very high sound velocities between them represent only about 3% of all measurements, suggesting a measuring error. With an 81% probability the measured sound velocity was between 401 m/s and 500 m/s.
Similar results were found for PVCu DN100. Once again the sound velocities were between 401 m/s and 500 m/s with an 81% probability.
Comparing the measured sound velocities with the table values from all manufacturers included in the analysis and with the calculated theoretical sound velocities shows that there does not appear to be a universally applicable sound velocity for each material and diameter, and that neither the theoretical calculation nor the table values accurately represent the actual conditions in the pipe network. In addition, the assumption that PE pipes propagate noise more slowly than PVC pipes could not be proved.
The length of the pipeline is often thought to be a possible influencing factor on the sound velocity. Therefore the measuring results were also plotted against the length of the measuring section (Figures 10and11).
Figures 10and11show that in PE80 pipelines the scattering of the results was higher on very short measuring sections (< 10 m) than on longer measuring sections. In PVCu pipes this effect was apparent up to a section length of approximately 35 m. However, there was no direct correlation between length of measuring section and noise propagation velocity. Therefore the sound velocity can vary with the same probability on short or long sections.
Another assumption is that the measured sound velocity is directly dependent on the frequency of the leak noise. Since all the correlation results were filtered to reduce the ambiguity of the peak, the average, filtered frequency was calculated for each measurement.Figures 12and13show the sound velocities plotted against the average filter frequencies.
Figure 12shows that – in line with expectations – the majority of the noise in the low frequency range was coherent and therefore particularly suitable for correlation. At the same time, much of the noise showed a clear coherence in the range between 500 Hz and around 700 Hz. However, the range at which the filter was set had no discernible influence on the sound velocity measurement. The measured values were in the same sound velocity range for both low and high filter frequencies.
In the case of measurements on PVCu pipelines, the clear majority of the noise was in the frequency range below 300 Hz. The few higher-frequency measurements also produced sound velocities in the same range (Figure 13).
Therefore no direct correlation between sound velocity and leak frequency could be proved.
To summarise, we can conclude that the sound velocity in a pipe does not have a fixed value which can be taken from a table or calculated. Instead, the actual sound velocity appears in practice to depend on many factors which the user cannot be aware of. No dependence on pipeline length or the chosen filters could be proved.
So what is the significance of these findings for the practical use of correlators in the pipe network?
In order to answer this question, we have to consider the potential sources of error.
It is clear from equation (1) that an error in determining the length is halved in the result. That is not the case with the sound velocity. A possible inaccuracy always shows up in the result as the product ofv ∙ Δt. What that means in practice can be seen from the following example calculation:
Let us assume that a correlator on a PVCu DN100 pipeline of length 100 m has calculated a time delay of 160 ms. The sound velocity in this pipeline is very probably between 350 m/s and 500 m/s (seeFigure 9). Using the critical velocities in equation (1) gives us the following:
