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# Modeling Darcy's Law

• What is Darcy’s Law?
• Why is the behavior of subterranean water important? How can Darcy’s Law be used in hazardous material spills?

You may have already seen water seeping out from the side of a cliff made by a road cut or from a cliff at the beach. This ground water flows through porous levels of the earth.You often see it in beach cliffs because at least some part of these cliffs is made from porous sandstone. Understanding the behavior of this ground water and how it flow through the earth is very important when determining the damage caused by chemical spills.It is also helpful in knowing where to to drill a well.

Darcy’s law describes the rate of flow of water as a function of the porousity of the rock, the relative height of the inlet and outlet of the water, and how far the water travels between the inlet and the outlet.

Q = KA (h1-h2)/L

in which Q is the flow rate, A is the cross-section of the rock, h1 is the height of the inlet head in which the water flows into the rock, h2 is the height of the outlet head from which the water leaves the rock and L is the path of the flow.

• Sharp knife (an Exacto knife is excellent, but a steak knife will also work)
• Stop watch (the stop watch found on iPhones works well)
• Between 4 and 16 2-liter soda bottles. At a minimum you will need four – but the more you have, the less time consuming your work will be.
• Plastic tubing. (aquarium tubing is excellent, although even a drinking straw will work in a pinch)
• Modeling clay or putty
• At least three of the following:sand, soil, clay soil, mixture of clay soil and regular soil, aquarium gravel.
1. Using the knife, make a small hole in a 2-liter soda bottle two inches from the bottom of the bottle. Insert 6-inch length of plastic tubing into the hole so that approximately 2 inches remains inside the bottle. This tubing is so that you can collect all the water that drains out of the bottle. Since your measurements would not be accurate if water escaped from the hole, press some putty or modeling clay around the hole in the bottle so that water will go through the tubing and not leak out.
2. Repeat step #2, only this time placing a single hole 4 inches from the bottom of the bottle. Repeat again with a two new bottles, placing the hole 6 and 8 inches from the bottom.
3. Fill each of the four bottles with one type of soil or sand. Each bottle should contain the same material. The only difference should be the height of the hole in the bottle. The top two inches of the bottle should be empty so that water can be added.
4. Add 250 ml of water to the bottle and start your stop watch. Measure how much water you collect in a fixed period of time. This period of time may vary depending upon the type of material you put in the bottle, but should be anywhere between 10 and 30 seconds. Repeat this step with all four bottles. For example, you might collect 100 ml in 30 seconds.
5. Convert your results into liters per minute. For example, 300 ml in 30 seconds would convert to 0.3 liters per 0.5 minutes.
6. Repeat the experiment using a set of four bottles for every type of soil, gravel or other material.
7. Graph your results. The x-axis represents the flow rate and the y-axis represents the difference between the top of the bottle and the outlet where you put the tubing.
8. Use Darcy’s law and calculate the permeability coefficient.

Terms/Concepts: Darcy’s Law; Ground water; Aquifer; Porosity; Drawdown

References:

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