Environmental Engineering Reference
In-Depth Information
in which
C
a
,2
(
average contaminant concentration in the excreted tissue (milk or
eggs) by the animal for
T
)
=
T
[mg/kg]
M
a
,2
(
t
)
=
mass of tissue excreted by animal
a
from
t
=
0to
t
[kg]
T
is equal to one day and
M
j
If
a
,2
(daily weight of tissue produced by the animal)
is constant,
m
a
,1
(0)
(
k
a
+
λ
a
)
f
abs
,
s
×
I
a
M
j
a
,2
f
abs
,
s
×
I
a
k
a
k
a
C
a
,2
(
t
)
=
k
a
+
λ
a
×
+
(
k
a
+
λ
a
)
×
−
e
−
(
k
a
+
λ
a
)
×
(
t
−
1)
e
−
(
k
a
+
λ
a
)
×
t
(11.21)
−
×
M
j
a
,2
If I
a
varies with time
,
m
a
,2
has to be integrated over short time intervals where
I
a
and
m
a
,1
may be regarded as constant:
I
a
×
1
e
−
(
k
a
+
λ
a
)
×
T
k
a
m
a
,2
(
t
)
=
m
a
,2
(
t
−
T
)
+
T
×
a
)
×
f
abs
,
s
×
−
(
k
a
+
λ
e
−
(
k
a
+
λ
a
)
×
T
+
T
×
k
a
×
−
×
m
a
,1
(
t
T
)
(11.22)
If
T
is equal to one day,
m
a
,2
(
t
)
−
m
a
,2
(
t
−
T
)
C
a
,2
(
t
)
=
(11.23)
M
j
a
,2
and
I
a
×
1
e
−
(
k
a
+
λ
a
)
+
k
a
e
−
(
k
a
+
λ
a
)
a
×
f
abs
,
s
×
−
k
a
×
m
a
,1
(
t
−
1)
×
k
a
+
λ
C
a
,2
(
t
)
=
M
j
a
,2
(11.24)
Time Required to Reach Steady-State Concentrations and Definition of
B
Ta
According to equation (
11.11
), when growth of animals is negligible and
I
a
is
constant,
C
a,
1
is close to the steady-state if:
f
abs
,
s
×
I
a
C
a
,1
(
t
)
≈
(11.25)
(
k
a
+
λ
a
)
×
M
a
,1
or
e
−
(
k
a
+
λ
a
)
t
≈
0
(11.26)
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