Groundwater Drawdown by Pumping - Environmental Modeling - page 236

2 prhv r ¼ Q

Instead of the total height of the groundwater layer, the height of the water
table h above the base has to be considered. Using Darcy's Law, as stated
above, yields:

rh @ h

Q

@ r ¼

2 pK

or

r @ h 2

Q
pK

@ r ¼

with the general solution:

Q
pK

h 2 ¼ log ðrÞþC

As above, the knowledge of a pair ( r 0 , h 0 ) helps to determine the integra-
tion constant C and the formula ( 12.3 ) results.

h changes with the radius r , as already explained above. We compute the
changing values in a short command sequence. In the MATLAB command

®

window specify the new input parameter first:

K = 1.e-4;

The following line initiates the computation of the vector of piezometric heads:

h = sqrt(h0*h0 + (Q/(pi*K))*log(r/r0));

sqrt denotes the squareroot. With the next command the results are shown as
a green broken ine:

plot (r,h,'--g');

Exercise. Change the value for K and compare drawdowns of piezometric head in
a single figure! Use the command

hold on;

to keep the graphic, and the command

legend (‚K=1.e-4');