Environmental Engineering Reference
In-Depth Information
650
given
modelled
600
550
500
450
sedimentation velocity [cm / a]: 0.16402
400
norm of residuals: 6014.9175
350
0
1000
2000
3000
4000
depth [cm]
Fig. 10.7 Exponential fit for
l
and
c
0
10.6 General Procedure
The described zero search procedure for the computation of the optimal fit can also
be applied to parameters of differential equations, i.e. if the solution is not given by
an explicit formula like in the examples treated above. The value for diffusivity is
determined in a new demonstration example, (1) by using analytical formulae, and
(2) by using differential equations.
Example: Diffusivity Estimation
An environmental system is considered with two processes governing the distribu-
tion of a (bio) chemical species. To keep it simple, we examine a one-dimensional
set-up. There are two reservoirs separated by a barrier. The barrier does not allow
fluid flow, but chemical species may penetrate by means of diffusion. The driving
force for diffusion is the fact that the two reservoirs have a different level of
concentration
c
. Additionally, there is a constant source or sink for the examined
species: it is produced or consumed passing through the barrier at a constant rate
Q
.
The differential equation for the steady state of such a system is:
þ Q ¼
@
@x
D
@
c
@x
0
(10.25)
