Hydraulic Reliability Diagram and Network Buffer Index as Indicators of Water Distribution Network Resilience - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 109

The condition b = 0 is more dependent on the pressure drop and the resistance of pipes that
are to carry the surplus flow. In reality, the flow/demand reduction starts for the drop of
pressures in lower range, which is in hydraulic simulations compared with the PDD
threshold, p min /ρg . Hence, in the above example, Δp n,f 1 = p min - p n,f 1 , and Q 2,f 1 will equal Q tot
as long Δp n,f 1 < 0 .

Figure 5.7 Moody diagram

In general, the order of value of the resistance R will always be (much) higher than the one of
Δp n,f 1 /ρg , which makes the value of b initially low. Moreover, the smaller is the pipe, the
closer the value of b will be to 0. For instance, a 1000 m pipe of 500 mm diameter with
typical friction factor value of 0.025 makes R calculated from Equation 5.4 equal to 66.10
and with pressure drop of say 5 mwc, b = 0.0756. For shorter and smaller pipe, say, L = 300
m, D = 150 mm with λ = 0.030, R will equal 9792.81 and for the same pressure drop of 5
mwc, b = 0.00051. Hence, it can also be assumed that b ≈ 0 in most of practical cases.

The similar analogy as presented in the case of two pipes in parallel can be assumed while
analysing the results of the GA optimised looped networks, shown in Figure 5.4. It is the high
resistance of small pipes in these networks, which is causing relatively high pressure drop
once they are to take over the flows resulting from the burst of bigger pipes. Due to the
relation between the nodal pressure and demand, the pipe friction loss will eventually be
reduced as a result of the demand reduction, making the pipe resistance R far more dominant
component than the pressure drop Δp n,f /ρg . Hence, the looped networks optimised on the
least-cost pipe diameter are likely to perform hydraulically as branched networks, both in
regular and irregular situations. The smaller is the minimum pipe diameter selected in the GA
optimisation, the closer these hydraulic performances will be.

5.4 HYDRAULICS OF LOOPED NETWORKS UNDER STRESS CONDITIONS

Looped networks with certain degree of buffer capacity will be able to withstand the
consequences of pipe failure to the extent that can be assessed by taking into consideration