Geoscience Reference
In-Depth Information
pollutants in the lagoon are flushed, it must be remembered that they are still present
elsewhere in the marine coastal zone.
6.3.3.1.1 Integral Flushing Time
The minimum value of the integral flushing time (i.e., the quickest flushing of the
lagoon) required for a complete reduction of pollution in a lagoon can be estimated
using the concept of well-mixed reactors, provided the lagoon is well mixed. If we
consider the flushing time to be the characteristic time required for an e -fold renewal
of water ( e is a Eulerian number approximately equal to 2.71828) or reduction of a
pollutant concentration in the lagoon to 37% of its initial value when it is flushed
by nonpolluted water, this concentration as a function of time is given by
Ct
( )
=⋅
C
exp(
t
/
τ flush
)
(6.31)
0
τ flush
=
Vq
/
(6.32)
avg
flush
where t is time, is the initial concentration of pollutant in the lagoon, is the
flushing time (or ventilation, or hydraulic replacement according to Kjerfve 3 ),
is the average lagoon volume, and is the discharge rate of the ventilation stream.
The flushing time is the time it takes for the initial concentration to be diluted to a
concentration
C 0
τ flush
V avg
q flush
C
e
2.71828). A total of 93.4 and 95% dilution are
attained in times equivalent to and , respectively.
When a lagoon has several input sources of water (including inlets) with dis-
charge
C
=
(where e
=
0
τ
=⋅
e
τ
τ
=⋅
flush
3
τ
90%
flush
95
%
q i
and concentration
, the evolution of the concentration in the lagoon given
c i
by a well-mixed solution is
(
)
τ
Ct
( )
=⋅
C
exp(
t
/
τ
)
+
flush
qc
exp(
t
/
τ
)
(6.33)
0
flush
i
i
flush
V
avg
V
avg
τ flush
=
(6.34)
q i
τ
flush
V
Q
1
1
i
i
flush
avg
=
=
,
where
τ
=
(6.35)
flush
flush
i
τ
τ
flush
τ
i
i
It is important to note that the flushing time depends only on the hydrographic
characteristics of a lagoon and not on the absolute values of the initial and input
pollutant concentrations. Equation (6.31) and Equation (6.32) describe the system
adaptation to a new level of pollution load, and (as well as and ) is
the characteristic time scale for the system to adapt to a new equilibrium concentration.
τ flush
τ 90%
τ 95%
 
 
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