CE 473/573 Groundwater
Fall 2012
Comments on homework 3
12. Be careful and explicit with units in the uncertainty calculations. Some groups confused the absolute and relative uncertainties and produced enormous uncertainties
that should have sounded the alarm. Unless your dependent variable depends only
weakly on an independent variable, the relative uncertainty in the dependent variable
should be no less than the relative uncertainty in the independent variable.
13. Make sure to define head correctly; it is the distance from the outlet to the water
level in the tube. Therefore, the maximum Reynolds number should be computed as
Kh0 Ac /L. The hydraulic conductivity can be computed from two measurements of
the head, but which two? What if one was misread? Better is to fit an exponential
curve to the data and use the exponent of the fit to find K, as we did in class. In
the uncertainty analysis, include uncertainty from all measured parameters; several
groups omitted h0 , h, or both. I would expect the tube area to contribute more
uncertainty to K than the cylinder area because the uncertainty in the diameter is
the same for both and the diameter of the cylinder is greater than the diameter of the
tube.
14. As in problem 4, you will need to estimate the hydraulic conductivity of sandy loam to
estimate the flow. Then once you choose a flow meter, you can get its accuracy, which
is usually reported as a certain percentage of the full-scale reading. The flow meter
I chose would have a 10% uncertainty at the flow I estimated (see attached sheet).
That uncertainty dominates the rest, so to improve my experiment, I would have to
get a better flow meter. The volume/time method has less uncertainty because I plan
to collect enough water to reduce the relative uncertainty in the volume and time. In
other words, with fixed uncertainty in the volume, the relative uncertainty decreases
has the volume increases.