Hydraulic Reliability Diagram and Network Buffer Index as Indicators of Water Distribution Network Resilience - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 112

Figure 5.8 and 5.9 show the above balances of flows and pressures/friction losses in the
example of network 10. The results obtained for PDD threshold pressure of 20 mwc are
further processed in Tables 5.1 and 5.2 for pipes and nodes, respectively.

Table 5.1 Net10, results for pipes

Geometry No-failure Failure J7-J3 Change

ID j L j D j λ j R j Q j h f,j λ j,f R j,f Q j,f h f,j,f ΔQ j,f Δh f,j,f →

(s 2 /m 5 ) (s 2 /m 5 ) (-) (m) (mm) (-) (l/s) (mwc) (-) (l/s) (mwc) (l/s) (mwc) (Y)

R1-J2 3000 200 0.026 20140 30.05 18.19 0.026 20140 20.32 8.32 -9.73 -9.87

R1-J6 1300 200 0.026 8727 39.95 13.93 0.026 8727 40.05 14.00 0.10 0.07

J2-J7 1500 200 0.026 10070 20.05 4.05 0.027 10457 10.32 1.11 -9.73 -2.94

J6-J7 3500 50 0.043 39793094 0.46 8.42 0.045 41643936 -0.32 -4.26 -0.78 -12.68 Y

J7-J3 1000 100 0.031 256143 10.51 28.29 0 0 0 0 -10.51 -28.29

J6-J4 1700 150 0.028 51793 29.49 45.04 0.028 51793 30.37 47.77 0.88 2.73

J3-J4 2500 50 0.043 28423639 0.51 7.39 0.041 27101609 -1.04 -29.31 -1.55 -36.70 Y

Table 5.2 Net10, results for nodes (PDD threshold, p min / ρg = 20 mwc)

Topography No-failure Failure J7-J3 Change

ID i z i k i p i /ρg Q i p i,f /ρg Q i,f Δp i,f /ρg ΔQ i,f ↓

(-) (msl) (l/s/mwc 0.5 ) (mwc) (l/s) (mwc) (l/s)

(mwc) (l/s) (Y)

R1 90 - 0 -70 0 -60.37 0 9.63 Y

J2 50 2.236 21.91 10 31.60 10 9.69 0

J3 0 2.236 39.25 10 0.22 1.04 -39.03 -8.96 Y

J4 10 6.708 21.84 30 19.12 29.33 -2.72 -0.67 Y

J6 25 2.236 51.26 10 51.20 10 -0.06 0

J7 40 2.236 27.82 10 40.47 10 12.65 0

Resulting from the failure of the pipe connecting nodes J7 and J3 , the pressure will drop
below the threshold in nodes J3 and J4 causing the reduction of demand of 8.96 and 0.67 l/s
respectively. The drop of pressure in node J6 has no impact on the demand because the
pressure in that node after the pipe failure is still well above the threshold. Finally, the
pressure in nodes J2 and J7 will grow as a result of overall demand i.e. head loss reduction.
Also, the failure has caused the change of flow direction in pipes connecting nodes J6 and J7 ,
and J3 and J4 .

Two categories of junctions give possibility to correlate the flow in the failed pipe under
regular supply with the loss of demand resulting from the calamity. In junctions that represent
sources, the negative demand increase indicates the total demand loss. Hence, after
combining Equation 5.8 and 5.9:

l l k

( )

∑ ∑∑

Q 1 − ADF = ∆ Q = ∆ Q 5.14

tot f s , f s , j , f

s = 1 s = 1 j = 1

Thus, each pipe j connected to the source s , carries after the failure of pipe f a flow
increment/decrement that can be correlated to the total loss. In the above network, ΔQ R1,f =
9.63 l/s, which balances the flow decrement of pipe connecting the source in R1 with J2 (of -
9.73 l/s) and the flow increment of the pipe connection with J6 (of 0.10 l/s).

In the second category are the two junctions that connect the failed pipe f . The continuity
equation in this case will look as: