Environmental Engineering Reference
In-Depth Information
Or, if
I
a
is constant
I
a
×
f
abs
,
a
M
a
,1
(
T
)
T
×
C
a
,1
(
T
)
=
(11.15)
in which
T
=
exposure time [d]
Milk and Egg Concentrations
Contaminant mass in milk or eggs is calculated from the following differential
equation:
dm
a
,2
dt
=
k
a
×
m
a
,1
(11.16)
in which
m
a,
2
=
total mass of contaminant excreted by the animal (i.e., mass of contami-
nant in milk produced by cows or eggs produced by hens) [mg]
If I
a
is constant with time
, the calculation of the excreted contaminant mass is as
follows:
1
e
−
(
ka
+
λ
a
)
×
t
dm
a
,2
dt
k
a
k
a
+
λ
a
×
e
−
(
ka
+
λ
a
)
×
t
(11.17)
=
f
abs
,
a
×
I
a
×
−
+
k
a
×
m
a
,1
(0)
×
The solution of this equation can be written as follows:
k
a
k
a
e
−
(
ka
+
λ
a
)
×
t
m
a
,2
(
t
)
=
k
a
+
λ
a
×
f
abs
,
a
×
I
a
×
+
×
f
abs
,
a
×
I
a
×
t
+
λ
a
)
2
(
ka
(11.18)
k
a
e
−
(
ka
+
λ
a
)
×
t
−
k
a
+
λ
a
×
m
a
,1
(0)
×
+
Constant
As
m
a
,2
(0)
=
0,
m
a
,2
(
t
), can be rewritten as follows:
(
k
a
+
λ
a
)
m
a
,1
(0) -
(
k
a
+
λ
a
)
f
abs
,
s
×
I
a
k
a
k
a
m
a
,2
(
t
)
=
k
a
+
λ
a
×
f
abs
,
s
×
I
a
×
t
+
(11.19)
×
1
e
−
(
k
a
+
λ
a
)
×
t
−
and
−
−
m
a
,2
(
t
)
m
a
,2
(
t
T
)
=
(11.20)
C
a
,2
(
T
)
−
−
M
a
,2
(
t
)
M
a
,2
(
t
T
)
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