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Point H was selected in this Pareto set with the method of Young (1993), and is shown by a triangle in Figure 8. Capital cost and FRI values for this solution are $7,244,479 and 0.17, respectively. Solution H is able to supply 80% of the reliability of solution G while its cost is only 0.7 of that. By a similar comparison between points H and F it is concluded that although the cost of solution H is 1.2 times higher than solution F, its reliability is 13 times higher. Furthermore, Table 3 shows the diameters of solution H, while the FRI index data for this solution is reported in Table 4. It is seen in Table 4 that Node 2 appears to have a high head. The model chooses pipes' diameters such that the pressure of the nodes immediately downstream the reservoir is relatively high in order to cope with the head losses throughout the gravity network.

Table 3

Pipe diameters for solution H in the Hanoi network

PipeD (cm)PipeD (cm)
101.60 18 60.96 
101.60 19 101.60 
101.60 20 50.80 
101.60 21 50.80 
101.60 22 101.60 
101.60 23 101.60 
101.60 24 101.60 
101.60 25 50.80 
76.20 26 50.80 
10 101.60 27 60.96 
11 101.60 28 50.80 
12 60.96 29 50.80 
13 40.64 30 30.48 
14 30.48 31 40.64 
15 30.48 32 40.64 
16 60.96 33 101.60 
17 60.96 34 101.60 
PipeD (cm)PipeD (cm)
101.60 18 60.96 
101.60 19 101.60 
101.60 20 50.80 
101.60 21 50.80 
101.60 22 101.60 
101.60 23 101.60 
101.60 24 101.60 
101.60 25 50.80 
76.20 26 50.80 
10 101.60 27 60.96 
11 101.60 28 50.80 
12 60.96 29 50.80 
13 40.64 30 30.48 
14 30.48 31 40.64 
15 30.48 32 40.64 
16 60.96 33 101.60 
17 60.96 34 101.60 
Table 4

Nodal pressure heads and FRI indices for solution H in the Hanoi network

NodeHead (m)MemFFRINodeHead (m)MemFFRI
97.21 0.0092 0.0087 18 52.23 0.5227 0.4874 
62.55 0.0099 0.0089 19 61.01 0.0100 0.0090 
58.56 0.1051 0.1045 20 52.19 0.5252 0.4097 
53.63 0.4305 0.4149 21 43.06 0.8718 0.8311 
48.51 0.7681 0.7294 22 42.64 0.8928 0.7050 
47.35 0.8449 0.7877 23 46.62 0.8928 0.7050 
46.04 0.9312 0.9055 24 45.47 0.9690 0.9292 
45.04 0.9976 0.8499 25 44.77 0.9845 0.8134 
10 42.16 0.8126 0.5670 26 42.16 0.8127 0.7760 
11 41.78 0.7878 0.7680 27 42.15 0.8121 0.7306 
12 41.51 0.7694 0.5982 28 44.18 0.9461 0.9323 
13 37.39 0.4980 0.4745 29 42.99 0.8672 0.6813 
14 39.50 0.6371 0.5403 30 42.80 0.8548 0.7344 
15 39.57 0.6416 0.6326 31 42.97 0.8659 0.8613 
16 42.26 0.8189 0.6718 32 44.61 0.9745 0.6546 
17 45.41 0.9730 0.9308 – – – – 
NodeHead (m)MemFFRINodeHead (m)MemFFRI
97.21 0.0092 0.0087 18 52.23 0.5227 0.4874 
62.55 0.0099 0.0089 19 61.01 0.0100 0.0090 
58.56 0.1051 0.1045 20 52.19 0.5252 0.4097 
53.63 0.4305 0.4149 21 43.06 0.8718 0.8311 
48.51 0.7681 0.7294 22 42.64 0.8928 0.7050 
47.35 0.8449 0.7877 23 46.62 0.8928 0.7050 
46.04 0.9312 0.9055 24 45.47 0.9690 0.9292 
45.04 0.9976 0.8499 25 44.77 0.9845 0.8134 
10 42.16 0.8126 0.5670 26 42.16 0.8127 0.7760 
11 41.78 0.7878 0.7680 27 42.15 0.8121 0.7306 
12 41.51 0.7694 0.5982 28 44.18 0.9461 0.9323 
13 37.39 0.4980 0.4745 29 42.99 0.8672 0.6813 
14 39.50 0.6371 0.5403 30 42.80 0.8548 0.7344 
15 39.57 0.6416 0.6326 31 42.97 0.8659 0.8613 
16 42.26 0.8189 0.6718 32 44.61 0.9745 0.6546 
17 45.41 0.9730 0.9308 – – – – 

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