Environmental Engineering Reference
In-Depth Information
Analogously, the solution for the corresponding 3D situation is given by:
"
#
!
2
2
2
y
m
y
s
y
1
1
2
x
m
x
s
x
z m
z
s
z
f ðx; yÞ¼
p
2
þ
þ
exp
3
p
s
x
s
y
s
z
(16.11)
From the given formulae solutions can be derived for various 2D and 3D
situations. Some of these will be presented in the remainder of this chapter
16.2
2D Instantaneous Line Source
The explicit formula for transient transport, including diffusion/dispersion, constant
advection in
x
-direction and decay is given by:
!
!
2
M
1
4
t
ðx vtÞ
y
2
D
y
cðx; y; tÞ¼
pt
p
exp
þ
lt
(16.12)
D
x
4
D
x
D
y
(see also: Fried
1975
;Kinzelbach
1987
).
M
denotes the total mass per unit length in
that situation. Figure
16.4
depicts the surface plot of an example 2D Gaussian puff.
The plot was produced using the M-file
'GaussianPuff.m
' with input data:
30
40
2D Gaussian puff
concentration
25
30
20
20
15
10
10
0.
0
5
0.4
0
0.2
y
0
x
-0.2
-0.2
Fig. 16.4 Transport solution for an instantaneous source in 2D
