PART 12 Aquifer pumping tests - Dr. M. Zreda - University of Arizona
PART 12 Aquifer pumping tests - Dr. M. Zreda - University of Arizona
PART 12 Aquifer pumping tests - Dr. M. Zreda - University of Arizona
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Aquifer</strong> <strong>pumping</strong> <strong>tests</strong> 89<br />
Boundary conditions:<br />
BC1: Prescribed head at the lake:<br />
h = H at r = R<br />
BC2: Prescribed flux at the well (= <strong>pumping</strong> rate Q):<br />
Q = K(2πrb)(∂h/∂r) at r = r w (well radius)<br />
or, after rearranging and putting T = Kb:<br />
---------<br />
Q<br />
r<br />
2πT<br />
h ∂<br />
= -----<br />
∂r<br />
Solution:<br />
Integrate once:<br />
Use BC2: C 1 = Q/(2πT)<br />
Rearrange by grouping r terms together<br />
Integrate<br />
Use BC1:<br />
r h ∂<br />
----- = C1 ∂r<br />
∂r<br />
∂h = C1---- r<br />
Q<br />
h = C1lnr + C2 = --------- lnr + C2 2πT<br />
C 2<br />
Q<br />
= H – --------- lnR<br />
2πT<br />
Final solution for h becomes<br />
h – H<br />
---------<br />
Q r<br />
=<br />
⎛ln- ⎞<br />
2πT ⎝ R⎠<br />
Thiem equation<br />
Hydrogeology, 431/531 - <strong>University</strong> <strong>of</strong> <strong>Arizona</strong> - Fall 2007 <strong>Dr</strong>. Marek <strong>Zreda</strong>
Change language