The second case study is also a real problem, in the city of Itororó, Brazil.
Figure 2 presents the WDN topology, with 1 reservoir, 20 pipes linking 17 demand nodes, 3 loops, and a hydraulic pump with a water catchment level of 222 m, responsible to pump water to the reservoir. Table 6 presents the nodes and pipes characteristic. Available set of seven distinct commercial diameters are presented in Table 7, with the respective costs. In this case, the costs in R$ were converted from USD (USD 1 = R$ 4). The water velocity must be bounded between 0.2 and 3.5 m/s and the minimum required pressure is 15 m for all demand nodes. The Darcy–Weisbach equation is used and a roughness coefficient equal to

m for all pipes was considered. The water kinematic viscosity at 20 °C is

m
2/s. The pump efficiency is 75% and 7,300 h/year is considered as the operation time. The energy cost is 0.134 $/kWh and the annual interest rate is 10%. The lifetime considered is 25 years and the annual increase in the energy is 6%.
Table 6Nodes elevation and demands and pipe lengths
Node/Pipe
. | Elevation (m)
. | Demand (L/s)
. | Pipe length (m)
. |
---|
1 | 220.5 | 5.05 | 324 |
2 | 215.6 | 1.91 | 124 |
3 | 210.4 | 3.81 | 184 |
4 | 210.5 | 1.40 | 206 |
5 | 209.5 | 4.35 | 103 |
6 | 213.2 | 3.51 | 202 |
7 | 218.5 | 3.44 | 134 |
8 | 230.7 | 2.48 | 227 |
9 | 211.5 | 3.06 | 167 |
10 | 213.5 | 1.85 | 166 |
11 | 205.5 | 2.86 | 152 |
12 | 208.8 | 6.11 | 168 |
13 | 215.5 | 5.09 | 177 |
14 | 212.6 | 4.06 | 225 |
15 | 207.5 | 8.05 | 254 |
16 | 219.4 | 4.26 | 263 |
17 | 220.5 | 1.21 | 133 |
18 | | | 321 |
19 | | | 105 |
20 | | | 169 |
Node/Pipe
. | Elevation (m)
. | Demand (L/s)
. | Pipe length (m)
. |
---|
1 | 220.5 | 5.05 | 324 |
2 | 215.6 | 1.91 | 124 |
3 | 210.4 | 3.81 | 184 |
4 | 210.5 | 1.40 | 206 |
5 | 209.5 | 4.35 | 103 |
6 | 213.2 | 3.51 | 202 |
7 | 218.5 | 3.44 | 134 |
8 | 230.7 | 2.48 | 227 |
9 | 211.5 | 3.06 | 167 |
10 | 213.5 | 1.85 | 166 |
11 | 205.5 | 2.86 | 152 |
12 | 208.8 | 6.11 | 168 |
13 | 215.5 | 5.09 | 177 |
14 | 212.6 | 4.06 | 225 |
15 | 207.5 | 8.05 | 254 |
16 | 219.4 | 4.26 | 263 |
17 | 220.5 | 1.21 | 133 |
18 | | | 321 |
19 | | | 105 |
20 | | | 169 |
Table 7Costs for the commercial available diameters for the Itororó WDN
Diameter (m)
. | Cost ($/m)
. | Diameter (m)
. | Cost ($/m)
. |
---|
0.0534 | 24.16 | 0.2042 | 87.62 |
0.0756 | 32.12 | 0.2520 | 118.59 |
0.1084 | 47.09 | 0.2998 | 152.24 |
0.1564 | 63.80 | | |
Diameter (m)
. | Cost ($/m)
. | Diameter (m)
. | Cost ($/m)
. |
---|
0.0534 | 24.16 | 0.2042 | 87.62 |
0.0756 | 32.12 | 0.2520 | 118.59 |
0.1084 | 47.09 | 0.2998 | 152.24 |
0.1564 | 63.80 | | |