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Observations on Darcy's Law

Roseanna M. Neupauer
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This activity was selected for the On the Cutting Edge Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

• Scientific Accuracy
• Alignment of Learning Goals, Activities, and Assessments
• Pedagogic Effectiveness
• Robustness (usability and dependability of all components)
• Completeness of the ActivitySheet web page

Summary

Students measure flow rates through the Darcy columns made of water bottles filled with different types and amount of porous material. They observe how all of the parameters in Darcy's law affect the flow rate.

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Context

Audience

Senior level elective and introductory level graduate course

Skills and concepts that students must have mastered

Understanding of the concept of hydraulic head and how to measure it

How the activity is situated in the course

This is a stand-alone exercise that is conducted midway through a 75-minute lecture on Darcy's law.

Goals

Content/concepts goals for this activity

The concept goals of the activity are (1) to develop a physical understanding of Darcy's law and how each parameter affects the flow rate, and (2) to develop an appreciation for the orders of magnitude variability in permeability.

Higher order thinking skills goals for this activity

A higher order thinking skill goal of this activity is to analyze data that contains measurement uncertainty.

Other skills goals for this activity

Other goals of this activity are learning to work in groups and making measurements.

Description of the activity/assignment

Before class, I prepare several "Darcy columns". These are plastic water bottles with a hole in the bottom that is covered with mesh and a rubber stopper. The bottles are filled with soil and water and are capped. One bottle is the reference bottle, with sand of height hs, and water of height hw, and a standard bottle diameter. Each of the remaining bottles are filled with one of the parameters varied: e.g., gravel instead of sand, silt instead of sand, sand of height 2hs instead of hs, water of height 2hw instead of hw, larger diameter bottle, etc. In class, student split into groups and each group is given a bottle, flexible ruler, funnel, graduated cylinder, and a large cup of water. As a group, they note the material type, measure the flow area, measure the height of porous material, and measure the difference in head across the porous material. Then they measure the flow rate, while maintaining a constant head. They repeat the flow measurement for their column, and then they repeat the process with one or more other columns, depending on the time available. Each group records their results on a table, and the class results are tabulated on the board. As a class, we discuss the whether or not their results follow Darcy's law. We also discuss the measurement errors, repeatability of the results, and the differences in flow rate for sand, gravel, and silt.

Determining whether students have met the goals

There is no formal evaluation of goals.