Environmental Engineering Reference
In-Depth Information
With a few exceptions, the results of 'pdd3' and 'pdd5' show reasonable compliance. In cases
where the minimum pressures differ for the same available demand, the referring nodes will
be positioned downstream of the closed pipe, making this difference irrelevant, as e.g. in the
case of failure of pipes 19, or 27 to 29. Yet, it shows that the concept of disconnection i.e.
reconfiguration of the network as a result of negative pressures maintained in 'pdd2' and
'pdd4' can create convergence problems. One possible reason is that the pressure build-up
above the upper threshold, resulting from the demand reduction, actually calls for the
restoration of original configuration and demand in the next iteration, resulting eventually in
never-ending loop. This has been observed in couple of cases and would ask for improvement
of the algorithm. Moreover, even in some of the cases where the convergence of 'pdd4' has
been reached, the results appear to be significantly different than in case of 'pdd3' and 'pdd5'.
This is visible in all the cases where 'pdd2' have not converged. Moreover, being in fact a part
of the 'pdd4' concept, makes those results also questionable.
The second sample of the results, shown in Table 3.20, gives the situation of the failure of 12
peripheral pipes: 2, 4, 12, 13, 18, 22, 46, 34, 68, 66, 52, and 55. All of these have been
positioned at higher elevations (the network is located in a valley). Nevertheless, the results
show full compliance, the reason being the low flows carried by those pipes; no failure of any
of these would cause a drop of the demand.
Table 3.21 Combined gravity network, pipes carrying larger flows
Mode
Qtot
P min Node Pmax Node Mode
Qtot
P min Node Pmax Node Mode
Qtot
P min Node Pmax Node
(l/s) (mwc)
(mwc)
(l/s) (mwc)
(mwc)
(l/s) (mwc)
(mwc)
failure 16
from
5
to
13 failure 30
from
55
to
46 failure 7
from
5
to
11
DD 41.57 -965.34 40
60.49 5
DD 41.57 -150.00 54
76.39 55
DD 41.57 22.72 8
78.99 46
PDD1 23.57 -29.24 40
71.02 5
PDD1 37.12
2.74 44
81.69 55
PDD1 41.57 22.72 8
78.99 46
PDD2 17.31 -15.08 35
72.26 5
PDD2 31.64
0.00 54
86.98 55 PDD2 41.57 22.72 8
78.99 46
PDD3 17.14 -39.88 40
70.93 5
PDD3 37.12
2.74 44
81.69 55 PDD3 41.57 22.72 8
78.99 46
PDD4 15.72 -29.21 40
71.26 5
PDD4 37.10
3.29 44
81.71 55 PDD4 41.57 22.72 8
78.99 46
PDD5 17.14 -39.87 40
70.93 5
PDD5 37.12
2.75 44
81.69 55 PDD5 41.57 22.72 8
78.99 46
failure 20
from
15
to
16 failure 59
from
31
to
22 failure 60
from
22
to
23
DD 41.57 24.37 40
79.27 46
DD 41.57 -617.51 28
79.41 46
DD 41.57 -425.4 23
79.41 46
PDD1 41.57 24.37 40
79.27 46
PDD1 39.56
-0.05 28
81.26 46
PDD1 39.84 -0.21 25
81.01 46
PDD2 41.57 24.37 40
79.27 46 PDD2 39.48
0.00 31
81.26 46 PDD2 39.84 -0.21 25
81.01 46
PDD3 41.57 24.37 40
79.27 46 PDD3 39.49
-1.70 28
81.25 46 PDD3 39.78 -0.96 25
81.01 46
PDD4 41.57 24.37 40
79.27 46 PDD4 39.47
1.89 28
81.28 46 PDD4 39.78 -0.96 25
81.01 46
PDD5 41.57 24.51 40
79.41 46 PDD5 39.49
-1.71 28
81.13 46 PDD5 39.78 -0.97 25
80.88 46
failure 38
from
33
to
32 failure 42
from
36
to
37 failure 62
from
47
to
48
DD 41.57
-6.89 40
76.90 46
DD 41.57 -293.66 39
79.41 46
DD 41.57 -431.1 50
79.41 46
PDD1 41.19
0.86 40
77.62 46
PDD1 40.41
0.50 39
80.90 46
PDD1 40.58 -2.32 50
81.09 46
PDD2 41.19
0.86 40
77.62 46 PDD2 40.41
0.50 39
80.90 46 PDD2 40.38
0.00 51
81.08 46
PDD3 41.19
0.86 40
77.62 46 PDD3 40.41
0.50 39
80.90 46 PDD3 40.41 -6.01 50
81.06 46
PDD4 41.19
0.86 40
77.62 46 PDD4 40.39
4.38 39
80.93 46 PDD4 40.39 -6.41 50
81.06 46
PDD5 41.19
0.80 40
77.49 46 PDD5 40.41
0.50 39
80.77 46 PDD5 40.39 -6.42 50
80.93 46
failure 31
from
46
to
54 failure 39
from
33
to
35 failure 50
from
22
to
27
DD 41.57 -1E+07 54
79.41 46
DD 41.57 -4E+06 40
79.41 46
DD 41.57 -6.87 26
79.41 46
PDD1 32.31
0.00 54
91.70 46
PDD1 39.20 -22.58 40
83.49 46
PDD1 41.26
9.99 26
79.69 46
PDD2 32.31
0.00 54
91.70 46 PDD2 38.56
-5.01 35
83.49 46 PDD2 41.26
9.99 26
79.69 46
PDD3 32.31
0.00 54
91.70 46 PDD3 38.37 -35.68 40
83.49 46 PDD3 41.26
9.99 26
79.69 46
PDD4 32.31
0.00 54
91.70 46 PDD4 38.56 -33.27 40
83.49 46 PDD4 41.26
9.99 26
79.69 46
PDD5 32.31
0.00 54
91.62 46 PDD5 38.26 -38.26 40
83.37 46 PDD5 41.26
9.99 26
79.55 46
Finally, the last batch of the results in Table 3.21 shows the consequences of the failure of
pipes that carry comparatively larger flows. Those are: 16, 30, 7, 20, 59, 60, 38, 42, 62, 31,
39 and 50. With few exceptions, the calculations of 'pdd2' to 'pdd5' point similar results in
terms of the available demand, critical nodes and the maximum pressure. Again the
 
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