Environmental Engineering Reference
In-Depth Information
7.2
HYDRAULIC PROPERTIES AS INDICATORS OF NETWORK RELIABILITY
7.2.1 Network Power Balance
As mentioned in Chapter 6, the power balance in any water distribution network consists of
the power input
P
i
made at location of supply points (sources and service tanks discharging
their volume) and pumping stations:
l
k
∑
∑
P
=
Q
H
+
Q
h
7.1
i
s
s
p
p
s
=
1
p
=
1
the power loss
P
l
inflicted by the friction- and minor losses:
m
t
∑
∑
P
=
Q
h
+
Q
h
7.2
l
j
f
,
j
v
m
.
v
j
=
1
v
=
1
and residual power
P
r
at discharge points:
n
∑
=
7.3
P
=
Q
H
r
i
i
i
1
The parameters in Equations 7.1 to 7.3 have the following meaning:
H
x
(
x
=
s, i
) indicate the
piezometric heads at
l
sources, and
n
nodes, which includes all the junctions with discharge
and tanks that are supplied from the network, respectively. The values of
h
x
(
x
=
p, f, m
)
include the heads of
k
pumps, the pipe friction losses of
m
pipes and the minor losses of
t
major valves, respectively. Finally,
Q
x
(
x = s, p, i, j, v
) stands for corresponding flow
supplying the network (
s
), being conveyed through it (
p, j
and
v
), or withdrawn from it (
i
),
respectively. Hence,
P
i
=
P
r
+
P
l
. The network potential to supply the nodal demands
Q
i
and
heads
H
i
as per design can be assessed against the ratio of the power loss and power input.
The
network power index
(NPI) would therefore be:
P
NPI
=1
−
l
P
7.4
i
The hypothesis tested in this research is that there is a correlation between
NPI
and network
reliability. For theoretical range of values between 0 and 1, the higher value of
NPI
will
indicate the more reliable system. This index is simplified version of the resilience indices of
Todini (2000) and Prasad and Park (2004), which does not take the pressure threshold i.e. the
surplus head/power but the total input head/power into consideration. In this case, the impact
of the pressure threshold is observed while running the pressure demand driven (PDD)
simulations that is not the situation with the two resilience indices from the literature.
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