Page 238 - Water Engineering Hydraulics, Distribution and Treatment

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Chapter 7
Water Distribution Systems: Modeling and Computer Applications
and head gain occurs in the direction opposite to that of the
flow). For the paths in Fig. 7.4,
In the past, water distribution systems were designed and
operated with little consideration of water quality, due in part
to the difficulty and expense of analyzing a dynamic system.
= H
H
(7.3)
+ H
Path from A to C:
L2
L1
L3
The cost of extensive sampling and the complex interaction
(7.4)
= H
Path from A to B:
− H
H
between fluids and constituents make numeric modeling the
L1
L3
L2
ideal method for predicting water quality.
(7.5)
Loop from A to A:
− H
0 = H
+ H
L1
L2
L3
To predict water quality parameters, an assumption is
made that there is complete mixing across finite distances,
Although the equality can become more complicated
such as at a junction node or in a short segment of pipe.
with minor losses and controlling valves, the same basic
Complete mixing is essentially a mass balance given by
principle can be applied to any path between two points. As 7.6 WATER QUALITY MODELING
shown in Fig. 7.4, the combined head loss around a loop must ∑ Q C
i i
equal zero in order to compute the same hydraulic grade for C = ∑ (7.6)
a
Q i
a given point.
where
7.5 NETWORK ANALYSIS C = average (mixed) constituent concentration
a
7.5.1 Steady-State Network Hydraulics Q = inflow rates
i
C = constituent concentrations of the inflows
i
Steady-state analysis is used to determine the operating
behavior of a system at a specific point in time or under
steady-state conditions. This type of analysis can be useful 7.6.1 Age Modeling
in discovering the short-term effect of fire flows or average
demand conditions on the system. Water age provides a general indication of the overall water
For this type of analysis, the network equations are deter- quality at any given point in the system. Age is typically
mined and solved with tanks being treated as fixed-grade measured from the time that the water enters the system
boundaries. The results that are obtained from this type of from a tank or reservoir until it reaches a junction. Along a
analysis are instantaneous values, and they may not be rep- given link, water age is computed as follows:
resentative of the values of the system a few hours—or even x
a few minutes—later in time. A = A j−1 + (7.7)
j
v
where
7.5.2 Extended-Period Simulation
A = age of water at jth mode
j
An extended-period simulation is used to determine the
A = age of water at j − 1 mode
behavior of the system over time. This type of analysis j−1
allows the user to model tanks filling and draining, regu- x = distance from node j − 1 to node j
lating valves opening and closing, and model pressures and v = velocity from node j − 1 to node j
flow rates changing throughout the system in response to
varying demand conditions and automatic control strategies
If there are several paths for water to travel to the jth
formulated by the modeler.
node, the water age is computed as a weighted average using
Whereas a steady-state model may tell the user whether
Eq. (7.8):
the system has the capability to meet a specific demand,
an extended-period simulation indicates whether the system [ ( ) ]
∑ Q AA + x
has the ability to provide acceptable levels of service over i i v i
AA = (7.8)
a period of minutes, hours, or days. Extended-period sim- j ∑ Q i
ulations can also be used for energy consumption and cost
studies, as well as for water quality modeling. where AA is the average age at the node immediately
j
Data requirements for an extended-period simulation go upstream of node j;AA is the average age at the node imme-
i
beyond what is needed for a steady-state analysis. The user diately upstream of node i; x is the distance from the ith
i
must determine water usage patterns, provide more detailed node to the jth node; v is the velocity from the ith node to
i
tank information, and enter operational rules for pumps and the jth node; and Q is the flow rate from the ith node to the
i
valves. jth node.