Page 276 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch07_230-264.qxd 8/2/10 8:44 PM Page 236

236 Chapter 7 Water Distribution Systems: Modeling and Computer Applications
Whereas a steady-state model may tell the user whether the system has the capability
to meet a specific demand, an extended-period simulation indicates whether the system has
the ability to provide acceptable levels of service over a period of minutes, hours, or days.
Extended-period simulations can also be used for energy consumption and cost studies, as
well as for water quality modeling.
Data requirements for an extended-period simulation go beyond what is needed for a
steady-state analysis. The user must determine water usage patterns, provide more detailed
tank information, and enter operational rules for pumps and valves.

7.6 WATER QUALITY MODELING
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.
The cost of extensive sampling and the complex interaction between fluids and con-
stituents makes numeric modeling the ideal method for predicting water quality.
To predict water quality parameters, an assumption is made that there is complete
mixing across finite distances, such as at a junction node or in a short segment of pipe.
Complete mixing is essentially a mass balance given by
a Q C
i i
C = (7.6)
a
a Q t
where
C a average (mixed) constituent concentration
Q i inflow rates
C i constituent concentrations of the inflows.

7.6.1 Age Modeling

Water age provides a general indication of the overall water quality at any given point in the
system. Age is typically measured from the time that the water enters the system from a tank
or reservoir until it reaches a junction. Along a given link, water age is computed as follows:
x
A = A j-1 + (7.7)
j
v
where
A j age of water at jth node
A j 1 age of water at j l node
x distance from node j l to node j
v velocity from node j 1 to node j.
If there are several paths for water to travel to the jth node, the water age is computed
as a weighted average using the Eq. 7.8:
x
a Q cAA + a b d
i
i
v
AA = i (7.8)
j
a Q i
where AA is the average age at the node immediately upstream of node j; AA is the
j
i
average age at the node immediately upstream of node i; x is the distance from the ith node
i
to the jth node; v is the velocity from the ith node to the jth node; and Q is the flow rate
i
i
from the ith node to the jth node .