CE 473/573 Groundwater
Fall 2011
Comments on homework 2
General: List units when you substitute numbers into formulas so you can check your work
and avoid errors.
9. Most groups successfully applied the fit of an exponential function; make sure to
display enough digits in the coefficients that Excel fits so that you can avoid rounding
error in the calculations. The hydraulic conductivity is about 1.4 × 10−3 cm/s, which
Fetter’s table 3.7 suggests is a silty sand or fine sand. Does the grain size distribution
support that conclusion? When you compute the Reynolds number, remember that
the head is the total distance from the water in the tube to the outlet above the
soil sample. Also remember that the specific discharge is through the soil; therefore,
the maximum value of the specific discharge is Kh0 /L. If you were to estimate the
conductivity using only two points, you would compute
LAt
ln
K=
tAc
h0
h
.
You can estimate the uncertainty from this formula. That calculation requires including uncertainty caused by L, At , Ac , t, h0 , and h. Use the uncertainty analysis to
identify the main contributors to the uncertainty and suggest improvements to the
experiment. In your discussion of the results, avoid statements that do not really add
anything.
11. All groups calculated a range of travel times approximately equal to what I found.
The range was very large. Predicting contaminant transport at this site would require
further information to narrow the range to something manageable.
12. Most groups got the main concepts and most of the details of this problem. Provide
enough steps in your work so that I can detect any errors. Also, when I ask for a
plot, be quantitative. A hand-drawn plot is acceptable if it notes the key quantitative
features—in this case, the head at the interface between the two soils.
15. The point of this problem is that three values of head are not enough to specify the
conductivities (or the flow) with any certainty. Darcy’s law can give you the ratio
of conductivities; if you pick one (in the silt range), you can compute the other, and
check to see that it is in the silt range. Notice that a source of uncertainty is that you
do not know where soil 1 ends and soil 2 begins. If the soil is in fact divided into two
sections of unknown length, how many values of head would you need to specify the
conductivities uniquely?