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Summative Assessment: Flow in Aquifers (Online Only Class)
As you've already seen in the section of the Module on "Darcy's Law", Henri Darcy conducted a set of famous experiments in the mid-1850's that are widely regarded to mark the beginnings of modern hydrogeology. Darcy recognized the connection between how fast water percolates, or seeps, through an aquifer, and the combination of driving forces and aquifer properties. Today you will analyze the data from Darcy's experiments, and explore these relationships first-hand.
- What is an aquifer?
- What physical characteristics of a rock do you think would make it a good aquifer?
This experiment was designed to investigate the relationships between flow rate, aquifer material, fluid properties, head gradient, and flow area. These relationships are described formally by Darcy's Law. For this assessment, you will use Darcy's original data set to quantify the hydraulic conductivity of Darcy's experimental materials.
Files to download:
Download the assignment worksheet (Microsoft Word 2007 (.docx) 22kB Mar28 17) to use when submitting your assignment.
Darcy's data (Excel 2007 (.xlsx) 19kB Mar28 17) (excel file)
- Use Darcy's data set to plot Q/A vs. Î”h/Î”l (with Q/A on the y-axis; Î”h/Î”l on the x-axis) for all four experiments on one scatter plot. You need to label both axes and provide a legend showing which symbols denote which experiment.
- Show the resulting graph below.
- For each experiment, do your data points follow any relationship or trend (linear, exponential, parabolic, etc.)? What does the trend suggest to you about the relationship between Q/A (water flux) and Î”h/Î”l (hydraulic gradient)?
- Calculate the hydraulic conductivity (K) for each tube. Be sure to include proper units as part of your answers. To do this you will need to use Darcy's Law:
Q = KA Î”h/Î”l
Based on the data from Darcy's experiments, there is only one thing in the equation we don't know, K. You should be able to re-arrange the equation to solve for K and then plug in the values from Darcy's data set to find K. *Hint: Q/A is already given to you, so you do not need to solve for A.
- Write the equation for K below. What are the units of K?
- Now that you have solved for K, calculate the average K value for each experiment and write your answer below. Be sure to include units!
- All experimental data are subject to experimental error (uncertainty). This uncertainty may be due to limitations on our ability to accurately measure variables in the lab, variations in environmental conditions or the physical properties of materials, or other factors beyond our control.
- Based on what you have read about Darcy's experimental setup, list a few (at least 2!) possible sources of error in Darcy's experiments.
- Look at the experimental data that you plotted in excel. How does the variation within a single experiment compare to the variation you see among the different experiments #1-4? Hint: To assess variation within an experiment plot a linear trend line and look at the amount of scatter. To assess variation among experiments look at the relative difference between the slopes of the trend lines.
- The K values that you calculated for each of the 4 experiments (in part 2b) basically equal the slope of the linear trend line for each experiment. Based on that knowledge, and the variation you observed within and among experiments in question 3b, answer the following question: Do you think the average K values that you calculated for each experiment are more or less identical to one another, or are they meaningfully different? Explain and support your answer.
- Thought experiment! In this set of 4 experiments the diameter of the sand grains (or grain size) was constant. Based on what you have learned about the relationship between hydraulic conductivity (K) and grain size in the online course material, answer the following question: In general, how would the value of K change if Darcy performed identical experiments but used a much larger grain size?
Grading and Rubric
Each assignment will earn a maximum of 100 points, as described below.
|Work Shown||Possible Points|
|Pre-experiment questions answered correctly||16 points (8 each)|
a. Accurate labeling of axes, legend, and plotting of data points
b. Recognition of the nature of the relationship between water flux and hydraulic gradient
|2. Calculation of hydraulic conductivity|
a. Correct equation for K, including setting up the problem (10 pts), and correct units (2 pts)
b. Correct calculation of average K for each experiment ( 4pts each)
3. Error and experimental variation
a. Several potential sources of error
b. Experimental variation (between & among experiments)
c. Significance of average K values for each experiment
|4. Relationship between K and grain size.||10 points|