Civil Engineering Reference
In-Depth Information
concentration of pesticides, are time-dependent and time travel analysis offers the tool
to calculate the time variable. The travel time,
T
, is determined from the equation,
T
L
/
v
,
where
L
is pipe length and
v
is velocity of flow.
The age of water provides information on how long water has existed at specific points
in the distribution system. Generally, longer travel times imply greater water quality
problems. Normally, water can reach a point in the distribution system from more than
one path. Therefore, the age of water typically consists of a distribution of ages. Instead
of determining the actual distribution of ages at a particular point, average water age
is often used.
Underlying Principles of Water Quality Models
The actual physical system of pipes, pumps, valves, fittings, and storage facilities is
modeled as a network of links that are connected at nodes in branched or looped
configuration.
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Links represent pipes, pumps, or valves. Nodes serve as junction,
source, consumption, and storage points. A network water-quality model predicts how
the concentration of a dissolved substance varies with time throughout the network
under a known set of hydraulic conditions and source input patterns. Its governing
equations rest on the principles of conservation of mass coupled with reaction kinetics.
The following phenomena occurring in the distribution system are represented in a
typical water-quality model:
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Advective Transport
A dissolved substance travels in a pipe with the same average
velocity as the carrier fluid, while at the same time reacting (either growing or decay-
ing) at some rate. Longitudinal dispersion is usually not an important transport mech-
anism (intermixing of mass between adjacent parcels of water traveling down a pipe).
Advective transport within a pipe can be represented with the following equation:
C
C
i
i
u
r
(
C
)
(22-1)
i
i
t
x
where
C
i
concentration (M / L
3
) in pipe
i
as a function of distance
x
and time
t
,
u
flow velocity (L / T) in pipe
i
, and
r
(
C
i
)
rate of reaction (M / L
3
/ T) as a function
of concentration.
Mixing at Pipe Junctions
At pipe junctions receiving inflow from two or more
pipes, mixing is assumed to be complete and instantaneous. The concentration of a
substance in water leaving the junction is simply the flow-weighted sum of the con-
centrations from the inflowing pipes. For a specific node
k
, the concentration leaving
is calculated as:
QC
in
in
C
(22-2)
k
,out
Q
in
where
Q
in
is the flow into node
k
from various sources (including pipes and other
external sources) and
C
in
the concentration in each source feeding mode
k
.
