5.3 Pressure relationships with leakage, minimum night flow, and burst frequency
5.3.2 Pressure – minimum night flow relationship
distribution system. In this regard, although the results were obtained in one season of the year, they still represent the actual values of N1 in the DMAs since the soil condition would not have notable effects on the leakage.
y = 2.042e0.0074x R2 = 0.2712
0.000 1.000 2.000 3.000 4.000 5.000 6.000
0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 100.000
Average Zone Night Pressure (m) Measured minimum night flow (MNF) m3/h
Fig. 5.3 Determination of a relationship between pressure and leakage using excel charts – BCA DMA data from 01 to 15 April 2008
The N1 values found could make it possible for a utility to make quick predictions of pressure management opportunities as recommended by Fantozzi et al. (2006) and Tooms and Morrison (2005), and the likely effect on leak flow rates using equation 4.4 or 4.5. For instance, if Chinyonga DMA pressure is reduced by 20%, leakage would be reduced by 30%.
Similarly, if BCA DMA pressure is reduced by 20%, leakage would be reduced by 20%.
Therefore, the calculated results of N1 values could be used for prediction of any leakage reductions resulting from any pressure reductions in the specific study sites. Furthermore, the results found could also be applied in other areas with similar characteristics within the entire water supply area to make predictions for the likely pressure management opportunities. This rapid type of analysis which gives an indication of likely benefits of pressure reductions would be a motivation for most utilities to manage their real losses efficiently.
Table 5.8 Measured pressure and MNF figures for Chinyonga and BCA DMAs: 2 to 15 April 2008
CHINYONGA TOWNSHIP DATA BCA TOWNSHIP DATA
Date
Average zone night pressure,
AZNP m
MNF M3/h
Average zone night pressure,
AZNP M
MNF m3/h
02/04/08 74.953 8.010 83.598 4.150 02/04/08 75.038 7.560 83.700 2.760
03/04/08 No flow 84.452 4.780
03/04/08 No flow 84.451 4.080
04/04/08 51.771 5.860 85.003 5.180
04/04/08 53.284 5.400 84.779 5.100
05/04/08 72.247 8.215 71.620 3.570
05/04/08 72.420 7.800 69.350 3.429
06/04/08 77.215 8.303 83.655 4.775
06/04/08 77.274 7.800 83.732 4.680
08/04/08 70.217 7.195 38.101 2.085
08/04/08 70.320 7.000 35.299 1.920
09/04/08 72.038 6.975 64.915 4.050
09/04/08 71.279 6.888 64.458 3.900
11/04/08 76.156 8.685 26.067 4.016
11/04/08 71.630 8.520 23.931 3.240
13/04/08 76.462 9.610 78.018 2.921
13/04/08 76.496 9.540 77.003 2.808
15/04/08 78.523 8.885 78.418 3.470
15/04/08 78.572 8.406 78.156 3.420
AZNP is average zone night pressure measured within the same period of minimum night flow measurement.
Theoretical analysis
The investigation of the relationship between pressure and MNF was done by using equation 4.6, and the values of leakage exponents N1 as already calculated. For Chinyonga DMA, mean N1 value was found as 1.6 and expected night use (ENU) was found to be 1.875 m3/hour as determined in Appendix B3. Therefore, the theoretical relationship between MNF and pressure for Chinyonga DMA can be written as:
6 .
875 1
.
1 KP
MNF = + ………..…………..(5.1)
The measured pressure and MNF were used to estimate the value of K. The average K value found for all the combinations using equation 5.1 was 0.00771, which was then substituted in equation 5.1. Equation 5.1 was then used for calculating MNF theoretically for comparison
with the actual measured values. Results of the computed MNF compared with the measured MNF values are shown in Table 5.9.
Table 5.9 Comparison of measured MNF and calculated MNF for Chinyonga data collected from 2 to 15 April 2008.
Date of MNF Measurement
Average pressure, P during MNF measurement
(m)
Measured MNF (m3/hour)
Calculated MNF (m3/hour)
Deviation (m3/hour)
%age deviation
02/04/08 74.953 8.010 8.170 -0.160 -2%
02/04/08 75.038 7.560 8.181 -0.621 -8%
04/04/08 51.771 5.860 5.418 0.442 8%
04/04/08 53.284 5.400 5.580 -0.180 -3%
05/04/08 72.247 8.215 7.821 0.394 5%
05/04/08 72.420 7.800 7.843 -0.043 -1%
06/04/08 77.215 8.303 8.468 -0.165 -2%
06/04/08 77.274 7.800 8.475 -0.675 -9%
08/04/08 70.217 7.195 7.563 -0.368 -5%
08/04/08 70.320 7.000 7.576 -0.576 -8%
09/04/08 72.038 6.975 7.794 -0.819 -12%
09/04/08 71.279 6.888 7.697 -0.809 -12%
11/04/08 76.156 8.685 8.328 0.357 4%
11/04/08 71.630 8.520 7.742 0.778 9%
13/04/08 76.462 9.610 8.368 1.242 13%
13/04/08 76.496 9.540 8.372 1.168 12%
15/04/08 78.523 8.885 8.642 0.243 3%
15/04/08 78.572 8.406 8.648 -0.242 -3%
Average Deviation -1%
Calculated MNF = 1.875 + 0.0077*(P)1.6
From Table 5.9, it can be seen that the average deviation of the computed MNF values to the actual measured MNF values is about 1%. This shows that there is a slight difference between measured and calculated MNF values. From the results of the data from Chinyonga DMA, it can be concluded that there is a relationship between pressure and minimum night flow.
The computations were also done using data from BCA DMA to confirm if the relationship determined using Chinyonga DMA data is correct. The expected night use for BCA was found as 0.1937 m3/hour from Appendix B3, while mean N1 value was found as 1.0. A similar approach was followed to compute K, and an average value of 0.0594 was found. Equation 4.6 was then used to compute MNF values for comparison with the measured values. The results of the comparison of the measured MNF and calculated MNF values are presented in Table 5.10.
From the comparison, it can be seen that an average deviation of 8% was found. The average deviation is relatively small considering the fact that a difference is always expected between
theoretical and measured values due to accuracy of field measurements. In this regard, the comparison also confirms that there is a relationship between pressure and MNF.
Table 5.10 Comparison of measured MNF and calculated MNF for BCA data collected from 2 to 15 April 2008.
Date of MNF Measurement
Average pressure during MNF measurement
(m)
Measured MNF (m3/hour)
Calculated MNF (m3/hour)
Deviation (m3/hour)
%age Deviation
02/04/08 83.598 4.150 4.931 -0.781 -19%
02/04/08 83.700 2.760 4.937 -2.177 -79%
03/04/08 84.452 4.780 4.979 -0.199 -4%
03/04/08 84.451 4.080 4.979 -0.899 -22%
04/04/08 85.003 5.180 5.010 0.170 3%
04/04/08 84.779 5.100 4.997 0.103 2%
05/04/08 71.620 3.570 4.259 -0.689 -19%
05/04/08 69.350 3.429 4.132 -0.703 -21%
06/04/08 83.655 4.775 4.934 -0.159 -3%
06/04/08 83.732 4.680 4.939 -0.259 -6%
08/04/08 38.101 2.085 2.371 -0.286 -14%
08/04/08 35.299 1.920 2.213 -0.293 -15%
09/04/08 64.915 4.050 3.882 0.168 4%
09/04/08 64.458 3.900 3.857 0.043 1%
11/04/08 26.067 4.016 1.689 2.327 58%
11/04/08 23.931 3.240 1.568 1.672 52%
13/04/08 78.018 2.921 4.618 -1.697 -58%
13/04/08 77.003 2.808 4.561 -1.753 -62%
15/04/08 78.418 3.470 4.641 -1.171 -34%
15/04/08 78.156 3.420 4.626 -1.206 -35%
Average Deviation -8%
Calculated MNF = 0.1937 + 0.0594*(P)1.0
Excel analysis
The analysis was also done using excel spreadsheets by plotting measured MNF values against corresponding measured pressure values as given in Table 5.8. The results of the graphs that were obtained are presented as Fig. 5.4 and 5.5 for Chinyonga and BCA DMAs respectively.
The graphical approach did not produce reliable results. Regardless of that, the exponential curve provides a better correlation coefficient (R2) than the other forms of curves. It can be seen that the theoretical relationship as presented by equation 4.6 is still being emulated and as such it is still being confirmed.
y = 2.2261e0.0173x R2 = 0.7419
0.000 2.000 4.000 6.000 8.000 10.000 12.000
0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 100.000
Average Zone Night Pressure (m) Measured minimum night flow (MNF) m3/h
Fig. 5.4 Graph of MNF against pressure to confirm their relationship using Chinyonga data measured from 2 to 15 April 2008
y = 2.2342e0.0069x R2 = 0.2703
0.000 1.000 2.000 3.000 4.000 5.000 6.000
0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000 100.000
Average Zone Night Pressure (m) Measured minimum night flow (MNF) m3/h
Fig. 5.5 Graph of MNF against pressure to confirm their relationship using BCA data measured from 2 to 15 April 2008
The analysis using both approaches confirms that there is a relationship between pressure and minimum night flow (MNF). The relationship follows an exponential function and is as provided by equation 4.6. It should be mentioned that Marunga et al. (2006) and Nkhoma et al. (2005) in studies conducted in Zimbabwe and Malawi respectively observed that as pressure decreased, the MNF also decreased, which is a confirmation of the results found in this study. In this regard, once a value of pressure is known during night hours, an expected MNF can be estimated using the general relationship as assumed. Therefore, regardless the fact that in UK from 1994 as reported by McKenzie et al. (2002b), it was indicated that there is no relationship between MNF and pressure; the findings of this study have found that there is a relationship.