Diagnostics of Regular Performance of Water Distribution Networks and its Relation to the Network Reliability - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 199

First of all, the correlations between the pipe volumes and flows have been tested on the set
of 16 simple networks used in the analyses discussed in Chapters 5 and 6. Here, the networks
have been more stringently optimised, on continuous range of diameters and without
specified limits. This has been done to check to which extent the results would comply with
those in Table 5. The GA optimisation done by EO-optimiser shows the layouts and
hydraulic performance of the nets as displayed in Figures 7.18 and 7.19.

Obviously, the figures show more refined selection of pipe diameters done to fit the
minimum pressure of 20 mwc more accurately, which eventually has been achieved, whilst
the loped layout has been brought even more close to a branched configuration. Table 7.15
shows the results of correlation between the pipe volumes and flows with the loss of demand
and mutually (left side), which is eventually compared to the values of the six indices used as
reliability measures (right side).

Table 7.15 Correlation between pipe flows and volumes and its relation to loss of demand

No.Name V j Q j V j Q j NPI PBI NRT ADF avg NBI I n

1 CO20Net01 0.45 1.00 0.45 0.53 -0.41 0.80 0.67 0.00 0.02

2 CO20Net02 1.00 1.00 1.00 0.61 0.37 1.37 0.54 0.00 0.17

3 CO20Net03 0.83 1.00 0.83 0.65 0.83 2.15 0.29 0.00 0.26

4 CO20Net04 0.91 1.00 0.91 0.71 0.92 1.37 0.50 0.00 0.42

5 CO20Net05 0.98 1.00 0.98 0.64 0.54 0.65 0.64 0.00 0.12

6 CO20Net06 0.96 1.00 0.96 0.63 0.49 0.52 0.72 0.00 0.17

7 CO20Net07 0.92 1.00 0.92 0.48 0.32 0.77 0.73 0.00 0.01

8 CO20Net08 0.96 1.00 0.96 0.68 0.71 0.65 0.83 0.01 0.11

9 CO20Net09 0.98 1.00 0.98 0.67 0.79 1.03 0.76 0.00 0.10

10 CO20Net10 0.68 1.00 0.68 0.49 0.63 0.80 0.73 0.00 0.05

11 CO20Net11 0.95 1.00 0.95 0.54 0.60 0.84 0.74 0.00 0.08

12 CO20Net12 0.85 1.00 0.87 0.66 0.76 0.96 0.81 0.08 0.20

13 CO20Net13 0.96 1.00 0.97 0.53 0.65 0.76 0.77 0.01 0.07

14 CO20Net14 0.97 1.00 0.97 0.78 0.72 1.18 0.84 0.02 0.09

15 CO20Net15 0.98 1.00 0.97 0.75 0.82 0.94 0.78 0.00 0.15

16 CO20Net16 0.97 1.00 0.97 0.78 0.91 0.89 0.88 0.02 0.21

Expectedly, the results for volumes and flows show stronger correlation than those in Table
5. Still, this correlation is much weaker in case of CO20Net 01 , 03 , 10 and 12 than for the rest
of the networks. The relation between the pipe volume and flow can be easily described using
the Darcy-Weisbach equation:

λ L

3

L

7.13

V = Q = Q

2 gDh v

f

Hence, the correlation between the pipe volumes and flows will be perfect in theory in case
the ratio of the pipe length and velocity is equal for all network pipes. It is then easy to find
out why the correlation will be weak. For example, network CO20Net01 (Figure 7.18, upper
left) could have been optimised manually so that the entire available pipe head loss is utilised,
leading to the minimum pressure of exactly 20 mwc, in all three discharge nodes. Table 7.16
shows the results obtained by EO-optimiser, by manual calculation of pipe diameters at
maximum available pipe head loss, and the calculation of pipe lengths and diameters that
correlate the pipe volumes and flows based on the optimised volume of P01.