TV WPN

Application TV WPN 1.9 Beta - Theory of Vulnerability of Water Pipe Networks

Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	1	2	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
2	1	4	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0
3	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	100
4	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.72	133967.4	0.017	2.4	0.24	200
5	2	3	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
6	5	6	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	100
7	3	6	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0

Network details (internal variables)

numberLinks = 7
numberNodes = 6
numberReferenceClusters = 2

netData:

1	1	2	200	10	140	131.8	0.01	6	1.01E-6	0.73295835227374	95647.436465028	0.018479236749704	0.0038390892843358	0.76781785686716	0
2	1	4	100	15	160	150.6	0.01	6	1.01E-6	0.84207627969871	125561.07695309	0.017510919910994	0.0042023077554224	0.42023077554224	0
3	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.5931446426406	60841.371264917	0.020295905632133	0.0035129413633003	0.70258827266007	100
4	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.71895362223196	133967.39772679	0.01721593337315	0.0024099814698633	0.24099814698633	200
5	2	3	200	10	140	131.8	0.01	6	1.01E-6	0.73295835227374	95647.436465028	0.018479236749704	0.0038390892843358	0.76781785686716	0
6	5	6	200	5	110	103.6	0.01	6	1.01E-6	0.5931446426406	60841.371264917	0.020295905632133	0.0035129413633003	0.70258827266007	100
7	3	6	100	15	160	150.6	0.01	6	1.01E-6	0.84207627969871	125561.07695309	0.017510919910994	0.0042023077554224	0.42023077554224	0

referenceClustersData:

R0 (100000)	1
R1 (100001)	3

Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Nodes	Links
8	1	2	1.19	12	3	0	-	1-2-1-4-	1-2-
9	1	4	1.01	12	4	0	-	1-2-2-5-	1-4-
10	1	5	1.54	12	3	0	-	1-2-2-3-	1-5-
11	2	3	1.12	12	3	0	-	1-4-4-5-	2-3-
12	3	4	0.94	12	4	100	*	4-5-2-5-	3-4-
13	3	6	1.41	12	3	100	-	4-5-5-6-	3-6-
14	4	5	1.01	12	4	0	-	2-5-2-3-	4-5-
15	4	6	0.94	12	4	100	-	2-5-5-6-	4-6-
16	5	7	1.19	12	3	0	-	2-3-3-6-	5-7-
17	6	7	1.12	12	3	0	-	5-6-3-6-	6-7-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	1.19	12	3	0	-	1	1-2-1-4-	1-2-
10	1	5	1.54	12	3	0	-	1	1-2-2-3-	1-5-
16	5	7	1.19	12	3	0	-	1	2-3-3-6-	5-7-
17	6	7	1.12	12	3	0	*	1	5-6-3-6-	6-7-
18	1	12	1.71	18	3	0	-	1	1-2-4-5-2-5-	1-3-4-
19	2	12	1.36	18	3	0	-	1	1-4-4-5-2-5-	2-3-4-
20	6	12	1.65	18	4	100	-	1	5-6-4-5-2-5-	6-3-4-
21	5	12	1.71	18	4	0	-	1	2-3-4-5-2-5-	5-3-4-

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Step	Nodes	Links
8	1	2	1.19	12	3	*	2	1-2-1-4-	1-2-
10	1	5	1.54	12	3	-	2	1-2-2-3-	1-5-
18	1	12	1.71	18	3	-	2	1-2-4-5-2-5-	1-3-4-
19	2	12	1.36	18	3	-	2	1-4-4-5-2-5-	2-3-4-
21	5	12	1.71	18	4	-	2	2-3-4-5-2-5-	5-3-4-
22	5	17	1.89	18	3	-	2	2-3-5-6-3-6-	5-6-7-
23	12	17	2.07	24	3	-	2	4-5-2-5-5-6-3-6-	3-4-6-7-

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Step	Nodes	Links
21	5	12	1.71	18	4	*	3	2-3-4-5-2-5-	5-3-4-
22	5	17	1.89	18	3	-	3	2-3-5-6-3-6-	5-6-7-
23	12	17	2.07	24	3	-	3	4-5-2-5-5-6-3-6-	3-4-6-7-
24	5	8	1.96	18	3	-	3	2-3-1-2-1-4-	5-1-2-
25	8	12	2.13	24	2	-	3	1-2-1-4-4-5-2-5-	1-2-3-4-

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
26	17	21	2.83	30	2	0	*	4	5-6-3-6-2-3-4-5-2-5-	6-7-5-3-4-
27	8	21	2.9	30	2	0	-	4	1-2-1-4-2-3-4-5-2-5-	1-2-5-3-4-

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
28	8	26	4.02	42	0	0	*	5	1-2-1-4-5-6-3-6-2-3-4-5-2-5-	1-2-6-7-5-3-4-

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
29	28	100000	0	-	-	-	-	-	--	--

Aglutination process step: 7

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
30	29	100001	0	-	-	-	-	-	--	--

Net hierarchical model (computation)

branch cluster # index # step # original net # left # right # intact # top # hierarchy level #
30 # 0 # 7 # 0 # 29 # 100001 # 0 # -1 # 0 #
29 # 0 # 6 # 0 # 28 # 100000 # 0 # 30 # 1 #
100001 # 1 # -1 # 2 # -1 # -1 # 0 # 30 # 1 #
28 # 0 # 5 # 0 # 8 # 26 # 0 # 29 # 2 #
100000 # 0 # -1 # 2 # -1 # -1 # 0 # 29 # 2 #
8 # 0 # 0 # 0 # 1 # 2 # 0 # 28 # 3 #
26 # 0 # 4 # 0 # 17 # 21 # 0 # 28 # 3 #
1 # 0 # -1 # 1 # -1 # -1 # 0 # 8 # 4 #
2 # 1 # -1 # 1 # -1 # -1 # 0 # 8 # 4 #
17 # 9 # 0 # 0 # 6 # 7 # 0 # 26 # 4 #
21 # 7 # 1 # 0 # 5 # 12 # 0 # 26 # 4 #
6 # 5 # -1 # 1 # -1 # -1 # 0 # 17 # 5 #
7 # 6 # -1 # 1 # -1 # -1 # 0 # 17 # 5 #
5 # 4 # -1 # 1 # -1 # -1 # 0 # 21 # 5 #
12 # 4 # 0 # 0 # 3 # 4 # 0 # 21 # 5 #
3 # 2 # -1 # 1 # -1 # -1 # 0 # 12 # 6 #
4 # 3 # -1 # 1 # -1 # -1 # 0 # 12 # 6 #

Net hierarchical model (show path)

Link: 30
Link: 29 (top: 30)
Link: 28 (top: 29)
Link: 8 (top: 28)
Link: 1 (top: 8)
Link: 2 (top: 8)
Link: 26 (top: 28)
Link: 17 (top: 26)
Link: 6 (top: 17)
Link: 7 (top: 17)
Link: 21 (top: 26)
Link: 5 (top: 21)
Link: 12 (top: 21)
Link: 3 (top: 12)
Link: 4 (top: 12)
Link: 100000 (top: 29)
Link: 100001 (top: 30)

Branch clusters (failure cenarios)

30
29
28
8
26
17
21
12

The graphical represention of the net hierarquical model is limited to 6 levels due to the space available.

2 - branch cluster / failure cenario)

Failure cenario: 28

-> Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	1	2	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
2	1	4	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0
3	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	100
4	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.72	133967.4	0.017	2.4	0.24	200
5	2	3	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
6	5	6	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	100
7	3	6	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Nodes	Links
8	1	2	1.19	12	3	0	-	1-2-1-4-	1-2-
9	1	4	1.01	12	4	0	-	1-2-2-5-	1-4-
10	1	5	1.54	12	3	0	-	1-2-2-3-	1-5-
11	2	3	1.12	12	3	0	-	1-4-4-5-	2-3-
12	3	4	0.94	12	4	100	*	4-5-2-5-	3-4-
13	3	6	1.41	12	3	100	-	4-5-5-6-	3-6-
14	4	5	1.01	12	4	0	-	2-5-2-3-	4-5-
15	4	6	0.94	12	4	100	-	2-5-5-6-	4-6-
16	5	7	1.19	12	3	0	-	2-3-3-6-	5-7-
17	6	7	1.12	12	3	0	-	5-6-3-6-	6-7-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	1.19	12	3	0	-	1	1-2-1-4-	1-2-
10	1	5	1.54	12	3	0	-	1	1-2-2-3-	1-5-
16	5	7	1.19	12	3	0	-	1	2-3-3-6-	5-7-
17	6	7	1.12	12	3	0	*	1	5-6-3-6-	6-7-
18	1	12	1.71	18	3	0	-	1	1-2-4-5-2-5-	1-3-4-
19	2	12	1.36	18	3	0	-	1	1-4-4-5-2-5-	2-3-4-
20	6	12	1.65	18	4	100	-	1	5-6-4-5-2-5-	6-3-4-
21	5	12	1.71	18	4	0	-	1	2-3-4-5-2-5-	5-3-4-

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Step	Nodes	Links
8	1	2	1.19	12	3	*	2	1-2-1-4-	1-2-
10	1	5	1.54	12	3	-	2	1-2-2-3-	1-5-
18	1	12	1.71	18	3	-	2	1-2-4-5-2-5-	1-3-4-
19	2	12	1.36	18	3	-	2	1-4-4-5-2-5-	2-3-4-
21	5	12	1.71	18	4	-	2	2-3-4-5-2-5-	5-3-4-
22	5	17	1.89	18	3	-	2	2-3-5-6-3-6-	5-6-7-
23	12	17	2.07	24	3	-	2	4-5-2-5-5-6-3-6-	3-4-6-7-

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Step	Nodes	Links
21	5	12	1.71	18	4	*	3	2-3-4-5-2-5-	5-3-4-
22	5	17	1.89	18	3	-	3	2-3-5-6-3-6-	5-6-7-
23	12	17	2.07	24	3	-	3	4-5-2-5-5-6-3-6-	3-4-6-7-
24	5	8	1.96	18	3	-	3	2-3-1-2-1-4-	5-1-2-
25	8	12	2.13	24	2	-	3	1-2-1-4-4-5-2-5-	1-2-3-4-

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
26	17	21	2.83	30	2	0	*	4	5-6-3-6-2-3-4-5-2-5-	6-7-5-3-4-
27	8	21	2.9	30	2	0	-	4	1-2-1-4-2-3-4-5-2-5-	1-2-5-3-4-

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
28	8	26	4.02	42	0	0	*	5	1-2-1-4-5-6-3-6-2-3-4-5-2-5-	1-2-6-7-5-3-4-

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
29	28	100000	0	-	-	-	-	-	--	--

Aglutination process step: 7

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
30	29	100001	0	-	-	-	-	-	--	--

-> Net hierarchical model (computation)

-> Net hierarchical model (show path)

-> Branch clusters (failure cenarios)

30
29
28
8
26
17
21
12

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E_R=0.57142857142857
γ_r^-=1
φ=1.75
Blow sequence: 5->7->1->2

3 - branch cluster / failure cenario)

Failure cenario: 8

-> Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	1	2	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
2	1	4	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	1.19	12	0	0	*	0	1-2-1-4-	1-2-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
9	8	100000	0	-	-	-	-	-	--	--

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
10	9	100001	0	-	-	-	-	-	--	--

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
11	10	100002	0	-	-	-	-	-	--	--

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
12	11	100003	0	-	-	-	-	-	--	--

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
13	12	100004	0	-	-	-	-	-	--	--

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
14	13	100005	0	-	-	-	-	-	--	--

-> Net hierarchical model (computation)

branch cluster # index # step # original net # left # right # intact # top # hierarchy level #
14 # 0 # 6 # 0 # 13 # 100005 # 0 # -1 # 0 #
13 # 0 # 5 # 0 # 12 # 100004 # 0 # 14 # 1 #
100005 # 5 # -1 # 2 # -1 # -1 # 0 # 14 # 1 #
12 # 0 # 4 # 0 # 11 # 100003 # 0 # 13 # 2 #
100004 # 4 # -1 # 2 # -1 # -1 # 0 # 13 # 2 #
11 # 0 # 3 # 0 # 10 # 100002 # 0 # 12 # 3 #
100003 # 3 # -1 # 2 # -1 # -1 # 0 # 12 # 3 #
10 # 0 # 2 # 0 # 9 # 100001 # 0 # 11 # 4 #
100002 # 2 # -1 # 2 # -1 # -1 # 0 # 11 # 4 #
9 # 0 # 1 # 0 # 8 # 100000 # 0 # 10 # 5 #
100001 # 1 # -1 # 2 # -1 # -1 # 0 # 10 # 5 #
8 # 0 # 0 # 0 # 1 # 2 # 0 # 9 # 6 #
100000 # 0 # -1 # 2 # -1 # -1 # 0 # 9 # 6 #
1 # 0 # -1 # 1 # -1 # -1 # 0 # 8 # 7 #
2 # 1 # -1 # 1 # -1 # -1 # 0 # 8 # 7 #

-> Net hierarchical model (show path)

Link: 14
Link: 13 (top: 14)
Link: 12 (top: 13)
Link: 11 (top: 12)
Link: 10 (top: 11)
Link: 9 (top: 10)
Link: 8 (top: 9)
Link: 1 (top: 8)
Link: 2 (top: 8)
Link: 100000 (top: 9)
Link: 100001 (top: 10)
Link: 100002 (top: 11)
Link: 100003 (top: 12)
Link: 100004 (top: 13)
Link: 100005 (top: 14)

-> Branch clusters (failure cenarios)

14
13
12
11
10
9
8

E_R=0.28571428571429
γ_r^-=0.2953675547236
φ=1.0337864415326
Blow sequence: 1->2

4 - branch cluster / failure cenario)

Failure cenario: 26

-> Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	0
2	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.72	133967.4	0.017	2.4	0.24	0
3	2	3	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77	0
4	5	6	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	100
5	3	6	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Nodes	Links
8	1	2	0.94	12	2	-	4-5-2-5-	1-2-
9	1	4	1.41	12	2	-	4-5-5-6-	1-4-
10	2	3	1.01	12	3	-	2-5-2-3-	2-3-
11	2	4	0.94	12	3	*	2-5-5-6-	2-4-
12	3	5	1.19	12	2	-	2-3-3-6-	3-5-
13	4	5	1.12	12	3	-	5-6-3-6-	4-5-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	New branch cluster	Step	Nodes	Links
12	3	5	1.19	12	2	*	1	2-3-3-6-	3-5-
14	1	11	1.65	18	2	-	1	4-5-2-5-5-6-	1-2-4-
15	3	11	1.71	18	2	-	1	2-3-2-5-5-6-	3-2-4-
16	5	11	1.36	18	2	-	1	3-6-2-5-5-6-	5-2-4-

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
14	1	11	1.65	18	2	0	*	2	4-5-2-5-5-6-	1-2-4-
17	11	12	2.13	24	1	0	-	2	2-5-5-6-2-3-3-6-	2-4-3-5-

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
18	12	14	2.83	30	0	0	*	3	2-3-3-6-4-5-2-5-5-6-	3-5-1-2-4-

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
19	18	100000	0	-	-	-	-	-	--	--

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
20	19	100001	0	-	-	-	-	-	--	--

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
21	20	100002	0	-	-	-	-	-	--	--

Aglutination process step: 7

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
22	21	100003	0	-	-	-	-	-	--	--

-> Net hierarchical model (computation)

branch cluster # index # step # original net # left # right # intact # top # hierarchy level #
22 # 0 # 7 # 0 # 21 # 100003 # 0 # -1 # 0 #
21 # 0 # 6 # 0 # 20 # 100002 # 0 # 22 # 1 #
100003 # 3 # -1 # 2 # -1 # -1 # 0 # 22 # 1 #
20 # 0 # 5 # 0 # 19 # 100001 # 0 # 21 # 2 #
100002 # 2 # -1 # 2 # -1 # -1 # 0 # 21 # 2 #
19 # 0 # 4 # 0 # 18 # 100000 # 0 # 20 # 3 #
100001 # 1 # -1 # 2 # -1 # -1 # 0 # 20 # 3 #
18 # 0 # 3 # 0 # 12 # 14 # 0 # 19 # 4 #
100000 # 0 # -1 # 2 # -1 # -1 # 0 # 19 # 4 #
12 # 4 # 0 # 0 # 3 # 5 # 0 # 18 # 5 #
14 # 1 # 1 # 0 # 1 # 11 # 0 # 18 # 5 #
3 # 2 # -1 # 1 # -1 # -1 # 0 # 12 # 6 #
5 # 4 # -1 # 1 # -1 # -1 # 0 # 12 # 6 #
1 # 0 # -1 # 1 # -1 # -1 # 0 # 14 # 6 #
11 # 3 # 0 # 0 # 2 # 4 # 0 # 14 # 6 #
2 # 1 # -1 # 1 # -1 # -1 # 0 # 11 # 7 #
4 # 3 # -1 # 1 # -1 # -1 # 0 # 11 # 7 #

-> Net hierarchical model (show path)

Link: 22
Link: 21 (top: 22)
Link: 20 (top: 21)
Link: 19 (top: 20)
Link: 18 (top: 19)
Link: 12 (top: 18)
Link: 3 (top: 12)
Link: 5 (top: 12)
Link: 14 (top: 18)
Link: 1 (top: 14)
Link: 11 (top: 14)
Link: 2 (top: 11)
Link: 4 (top: 11)
Link: 100000 (top: 19)
Link: 100001 (top: 20)
Link: 100002 (top: 21)
Link: 100003 (top: 22)

-> Branch clusters (failure cenarios)

22
21
20
19
18
12
14
11

5 - branch cluster / failure cenario)

Failure cenario: 17

-> Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	5	6	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	0
2	3	6	100	15	160	150.6	0.01	6	1.01E-6	0.84	125561.1	0.018	4.2	0.42	0

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	1.12	12	0	0	*	0	5-6-3-6-	1-2-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
9	8	100000	0	-	-	-	-	-	--	--

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
10	9	100001	0	-	-	-	-	-	--	--

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
11	10	100002	0	-	-	-	-	-	--	--

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
12	11	100003	0	-	-	-	-	-	--	--

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
13	12	100004	0	-	-	-	-	-	--	--

-> Net hierarchical model (computation)

branch cluster # index # step # original net # left # right # intact # top # hierarchy level #
13 # 0 # 5 # 0 # 12 # 100004 # 0 # -1 # 0 #
12 # 0 # 4 # 0 # 11 # 100003 # 0 # 13 # 1 #
100004 # 4 # -1 # 2 # -1 # -1 # 0 # 13 # 1 #
11 # 0 # 3 # 0 # 10 # 100002 # 0 # 12 # 2 #
100003 # 3 # -1 # 2 # -1 # -1 # 0 # 12 # 2 #
10 # 0 # 2 # 0 # 9 # 100001 # 0 # 11 # 3 #
100002 # 2 # -1 # 2 # -1 # -1 # 0 # 11 # 3 #
9 # 0 # 1 # 0 # 8 # 100000 # 0 # 10 # 4 #
100001 # 1 # -1 # 2 # -1 # -1 # 0 # 10 # 4 #
8 # 0 # 0 # 0 # 1 # 2 # 0 # 9 # 5 #
100000 # 0 # -1 # 2 # -1 # -1 # 0 # 9 # 5 #
1 # 0 # -1 # 1 # -1 # -1 # 0 # 8 # 6 #
2 # 1 # -1 # 1 # -1 # -1 # 0 # 8 # 6 #

-> Net hierarchical model (show path)

Link: 13
Link: 12 (top: 13)
Link: 11 (top: 12)
Link: 10 (top: 11)
Link: 9 (top: 10)
Link: 8 (top: 9)
Link: 1 (top: 8)
Link: 2 (top: 8)
Link: 100000 (top: 9)
Link: 100001 (top: 10)
Link: 100002 (top: 11)
Link: 100003 (top: 12)
Link: 100004 (top: 13)

-> Branch clusters (failure cenarios)

13
12
11
10
9
8

E_R=0.28571428571429
γ_r^-=0.27915045530755
φ=0.97702659357642
Blow sequence: 6->7

6 - branch cluster / failure cenario)

Failure cenario: 21

-> Net definition

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss
1	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7
2	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.72	133967.4	0.017	2.4	0.24
3	2	3	200	10	140	131.8	0.01	6	1.01E-6	0.73	95647.4	0.018	3.8	0.77

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	0.94	12	1	0	*	0	4-5-2-5-	1-2-
9	2	3	1.01	12	1	0	-	0	2-5-2-3-	2-3-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
10	3	8	1.71	18	0	0	*	1	2-3-4-5-2-5-	3-1-2-

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
11	10	100000	0	-	-	-	-	-	--	--

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
12	11	100001	0	-	-	-	-	-	--	--

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
13	12	100002	0	-	-	-	-	-	--	--

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
14	13	100003	0	-	-	-	-	-	--	--

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
15	14	100004	0	-	-	-	-	-	--	--

Aglutination process step: 7

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
16	15	100005	0	-	-	-	-	-	--	--

-> Net hierarchical model (computation)

branch cluster # index # step # original net # left # right # intact # top # hierarchy level #
16 # 0 # 7 # 0 # 15 # 100005 # 0 # -1 # 0 #
15 # 0 # 6 # 0 # 14 # 100004 # 0 # 16 # 1 #
100005 # 5 # -1 # 2 # -1 # -1 # 0 # 16 # 1 #
14 # 0 # 5 # 0 # 13 # 100003 # 0 # 15 # 2 #
100004 # 4 # -1 # 2 # -1 # -1 # 0 # 15 # 2 #
13 # 0 # 4 # 0 # 12 # 100002 # 0 # 14 # 3 #
100003 # 3 # -1 # 2 # -1 # -1 # 0 # 14 # 3 #
12 # 0 # 3 # 0 # 11 # 100001 # 0 # 13 # 4 #
100002 # 2 # -1 # 2 # -1 # -1 # 0 # 13 # 4 #
11 # 0 # 2 # 0 # 10 # 100000 # 0 # 12 # 5 #
100001 # 1 # -1 # 2 # -1 # -1 # 0 # 12 # 5 #
10 # 0 # 1 # 0 # 3 # 8 # 0 # 11 # 6 #
100000 # 0 # -1 # 2 # -1 # -1 # 0 # 11 # 6 #
3 # 2 # -1 # 1 # -1 # -1 # 0 # 10 # 7 #
8 # 0 # 0 # 0 # 1 # 2 # 0 # 10 # 7 #
1 # 0 # -1 # 1 # -1 # -1 # 0 # 8 # 8 #
2 # 1 # -1 # 1 # -1 # -1 # 0 # 8 # 8 #

-> Net hierarchical model (show path)

Link: 16
Link: 15 (top: 16)
Link: 14 (top: 15)
Link: 13 (top: 14)
Link: 12 (top: 13)
Link: 11 (top: 12)
Link: 10 (top: 11)
Link: 3 (top: 10)
Link: 8 (top: 10)
Link: 1 (top: 8)
Link: 2 (top: 8)
Link: 100000 (top: 11)
Link: 100001 (top: 12)
Link: 100002 (top: 13)
Link: 100003 (top: 14)
Link: 100004 (top: 15)
Link: 100005 (top: 16)

Leaf cluster	Begin node	End node	Lenght (m)	Flow (l/s)	Commercial diameter (mm)	Internal diameter (mm)	Roughness	Operating pressure (Kgf/cm2)	Kinematik viscosity of water (m2/s)	Velocity (m/s)	Reynolds number	Friction factor	Head losses (m/km)	Head loss	Distance (m)
1	4	5	200	5	110	103.6	0.01	6	1.01E-6	0.59	60841.4	0.02	3.5	0.7	0
2	2	5	100	20	200	188.2	0.01	6	1.01E-6	0.72	133967.4	0.017	2.4	0.24	0

-> Aglutination process

Aglutination process step: 0

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
8	1	2	0.94	12	0	0	*	0	4-5-2-5-	1-2-

Aglutination process step: 1

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
9	8	100000	0	-	-	-	-	-	--	--

Aglutination process step: 2

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
10	9	100001	0	-	-	-	-	-	--	--

Aglutination process step: 3

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
11	10	100002	0	-	-	-	-	-	--	--

Aglutination process step: 4

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
12	11	100003	0	-	-	-	-	-	--	--

Aglutination process step: 5

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
13	12	100004	0	-	-	-	-	-	--	--

Aglutination process step: 6

Candidate ID	Leaf cluster candidate (1)	Leaf cluster candidate (2)	Head loss (m)	Damage Demand (Kg/cm2)	Nodal connectivity	Distance from storage tank (m)	New branch cluster	Step	Nodes	Links
14	13	100005	0	-	-	-	-	-	--	--

Failure cenarios:

No.	Cenario	φ	E_R	γ_r^-	Comments
1	5->7->1->2	1.75	0.57	1	Total colapse cenario. Maximum vulnerability.
2	1->2	1.03	0.29	0.3	-
3	3->5->7->4	1.23	0.57	0.7	-
4	6->7	0.98	0.29	0.28	-
5	5->3->4	0.99	0.43	0.43	-
6	3->4	0.82	0.29	0.23	-

Elapsed time: Less than 1 second