Earth 111 Module 6.1 Summative Assessment
Groundwater and aquifers: Darcy Tube Activity
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 was the first to recognize the connection between the forces driving subsurface flow, the rates of flow, and aquifer hydraulic properties. Today you will recreate these experiments, and explore these relationships first-hand.
Grading and Rubric
PART 1: Pre-experiment Questions
1.1 What is an aquifer?
1.2 What physical characteristics of a rock or sediment do you think would make it a good aquifer? Please explain in 3-4 sentences.
PART II: Data Analysis. Use the excel spreadsheet with Darcy’s Data to answer the following questions.
2.1. Use Darcy's data set to calculate Δh/ΔL (green cells in excel spreadsheet).
(Nothing to answer here; I will refer to the excel spreadsheet for your calculations)
2.2. Now in excel plot the Darcy flux, Q/A, vs. the hydraulic gradient, Δh/ΔL. The plot must follow these guidelines:
· Q/A on the y-axis, Δh/ΔL on the x-axis
· All four experiments need to be plotted on ONE scatter plot (but as different series)
· Axes need to be labeled (including units!)
· Graph needs a legend showing which symbols denote which experiment
Show the resulting graph below. A screen cap of your plot is fine.
2.3. 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 Darcy flux, Q/A, and hydraulic gradient, Δh/ΔL? Please explain.
2.4. Here we will calculate the hydraulic conductivity, K, for each experiment. Be sure to include proper units in your answer. To do this you will need to use Darcy’s Law:
Q/A = K(Δh/ΔL)
Based on the data from Darcy's experiments, there is only one thing in the equation we don’t know, and that is K. Re-arrange the equation to solve for K and then in excel plug in the values from Darcy’s data set to solve for K.
a. Write the general equation for K below. Be careful solving it. What are the units of K?
K =
b. Now that you have solved for K, calculate the average K value for each experiment (orange cells in excel spreadsheet) and write your answer below. Be sure to include units!
average K (experiment 1) =
average K (experiment 2) =
average K (experiment 3) =
average K (experiment 4) =
PART III: Interpretation. Use the excel spreadsheet and your online readings to answer the following questions.
3.1 Go back to your plot in excel and add trend lines for each of the experiments. If you need help using the trend line feature in excel, see the following link.
a. Include a screen cap of your plot below, and for each trend line show the equation of the line and the coefficient of determination (R2).
b. How do the slopes of your trend lines compare to the average values of K you determined in question 2.4 for each experiment?
3.2 We are now going to use the plots to explore variation in the experiments that Darcy ran using his setup.
a. To assess variation within an experiment, or in other words the amount of scatter in the data, we are going to look at the R2 value. For each experiment, are the trend lines a good approximation of the data (i.e. is the value of R2 close to 1)? Or is there a lot of scatter in the data (i.e., is the value of R2 is closer to 0?) Please explain.
b. To assess variation among experiments look at the relative difference between the slopes of the trend lines. Are all of the slopes different? Do some of the trend lines overlap (i.e., the slopes are identical?).
c. All of these experiments were conducted using the same material (sand), so we would expect the hydraulic conductivity, K, to remain the same for all experiments. Is this the case? Explain.
3.3 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 and explain a few (at least 2!) possible sources of error in Darcy's experiments.
3.4 Thought experiment! In Darcy’s 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. Look back in your online reading for help. In general, how would the value of K change if Darcy performed identical experiments but used a much larger grain size? Please explain your answer.
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