Aquifer Baseflow and 2D Meshing - Environmental Modeling - page 247

whether an aquifer is confined or unconfined. However, the transition from poten-
tial to piezometric head h depends on the conditions of the aquifer.

The transformation formulae are derived from the equivalent defining equation:

'

ð qdx

'ðxÞ¼ (13.10)

and further:

8
<
:

KH ð @ h

@x dx

for the confined aquifer

'ðxÞ¼ (13.11)

K ð h @ h

ð @ h 2
@x dx

K
2 @x dx ¼

for the unconfined aquifer

Thus follows finally:

(

ThðxÞh 0 ð Þ

for the confined aquifer

'ðxÞ¼ for the unconfined aquifer (13.12)

2 h 2

ðxÞh 0

Note that the relation T ¼ KH was applied. The potential is not unique. The
addition of a constant does not change the potential property.

13.2 1D Implementation

For modelling with MATLAB set input parameters first:

®

h0 = 10;
Qx0 = 5.e-5;
K = 0.0001;

Then define the vector x with distances at which h is to be calculated:

x = [1:1:100];

In the following line the vector with piezometric heads for the confined aquifer is
calculated utilizing formula ( 13.6 ):

x = [1:1:100];

The calculation of the unconfined situation, according to formula ( 13.9 ), is
similar:

hu = sqrt (h0*h0 + (2*Qx0/K)*x);