CE 473/573 Groundwater
Fall 2009
Comments on homework 1
1. Some groups did not reproduce the results in Table 2.2 of the PMWIN manual. You
will get another chance to explain the effect of the parameters on the volume out. For
example, why does the total volume out not double when either the head difference
or the horizontal hydraulic conductivity doubles? How can the effect of the recharge
rate be explained?
2. No major problems. A couple groups worked the problem for spheres of given size.
More efficient is to work it for a general diameter D.
3. No problems.
4. The representative elemental area needs to be large enough so that the porosity is
stable but small enough that large scale variations in the aquifer are not included.
For point P, as the number of squares increases, the porosity approaches 0.5. One
could choose the REA such that the porosity is within 1% (or some other number) of
0.5
0.57
0.56
0.55
Porosity
0.54
0.53
0.52
0.51
0.5
0.49
0.48
5
10
15
20
Number of squares on a side
25
30
5. In dimensional analysis, one writes K = f (d, g, ρ, µ). With 5 variables and 3 dimensions (mass, length, and time), one gets two dimensionless groups. To proceed further,
argue that (1) since the weight drives the flow, the density and gravity should be considered together as ρg and (2) since K does not have dimensions of mass, the mass
units must cancel. Therefore, write K = f (ρg/µ, d) and conclude that there is only
one group, which must be constant. Then K ∝ ρgd2 /µ.
6. When the density increases, the weight—a force that drives flow through a porous
medium—also increases. Therefore, K should increase.