Diagnostics of Regular Performance of Water Distribution Networks and its Relation to the Network Reliability - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 177

Alternatively, the value of PBI can be determined by summing the pressure buffer and head
loss in the entire network, which is done in Equations 7.9 and 7.10.

1

m

( )

∑ =

pb = p + p L

2

− ∆ z

2

7.9

n 1 j 2 , j j j

2 ρ g

j 1

Similarly, the area of the triangle defined by the friction loss for the entire network is
calculated as:

1

m

= ∑ =

2 2

7.10

hl h L − ∆ z

n f , j j j

2

j 1

Possible negative values of pressure (in either or both nodes) in Equations 7.5, 7.7 and 7.9,
which can occur both in DD- and PDD mode of hydraulic simulation, mean that the buffer
will be reduced, and can theoretically be negative for the entire network; this is a signal of
serious calamity when calculated in DD-mode. Furthermore, Equation 7.7 can in theory result
in division by zero, if sum of the two pressures equals zero. Alternatively, the PBI can be
calculated as:

hl

7.11

PBI =1 −

n

n

pb

n

Mathematically, Equations 7.7 and 7.11 do not yield the same result but will show the same
trend; index n has been added to the PBI in Equation 7.11 to emphasize this difference. As is
the case with NPI , the higher value of PBI will indicate more reliable system.

7.2.3 Network Residence Time

The parameter that could also serve as potential indicator of network reliability assessed
under regular operational conditions is the network residence time (NRT). The NRT value can
be determined as the ratio of total volume and total demand of the network, which yields the
result expressed in units of hrs. By adding the weighting proportional to the pipe flow rates Q j
under regular conditions, to the individual residence time for m pipes, the network value
becomes:

V Q

m

V

= ∑ =1

j j

NRT =

tot

7.12

Q Q Q j

j tot tot

As such, the residence time combines in a simplified way the network geometry with its
hydraulic performance. It is mostly used as an indicator of water quality in distribution
networks but may have potential link with network reliability, as well. For the same level of
demand, the networks with larger volume will have larger conveying capacity assuming that
the pipe flow rates i.e. the head loss will be reducing after adding bigger- or additional pipes.
Eventually, the higher residence time would mean the more reliable network.