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Project Summary

Difficulty	6  –  7
Time required	Average (about one week)
Prerequisites	None
Material Availability	Readily available
Cost	Low ($20 - $50)
Safety	No issues

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Abstract

Objective

The goal of this project is to model the flow of groundwater, and to calculate the flow rate using Darcy's formula.

Introduction

Fresh water exists not only in lakes and streams on the surface of the earth, but also underground. These subsurface sources of freshwater are called underground aquifers, and the water in them is called groundwater.

Like water on the surface, groundwater can also flow. And like water on the surface, groundwater also flows downhill. Groundwater can also move in response to differences in pressure from the overlying rock, soil, and water. The rate of groundwater flow will also depend on the material through which the water is flowing. Materials that are more solid will reduce the flow rate, while materials that are more porous will increase the flow rate.

Darcy's Law is a relationship that explains fluid flow in porous media, such as often seen in geological formations. The basic formula to calculate the flow rate, Q, is:

• K is a permeability coefficient (describes the porosity of the underground formation),
• A is the cross sectional area,
• h₁ is the height of the inlet head,
• h₂ is the height of the outlet head, and
• L is the path length of the flow.

Understanding how groundwater moves is important for predicting how quickly underground aquifers will be replenished when water is drawn up from wells drilled down from the surface. Sometimes groundwater can become tainted with salt water or even toxic compounds seeping from a contaminated source. In these cases it is especially important to understand groundwater movement, in order to contain the spread and prevent contamination of aquifers used for drinking water or irrigation.

In this project, you will use plastic soda bottles to make models of water flowing through underground formations. You will fill the bottles with different materials (e.g., sand, gravel, silty clay, etc.) and then measure water flow to see the effects of different types of formations. You can investigate the effects of pressure by making outlets at different heights on the bottle. The height of the water above the outlet creates the pressure, so the lower the outlet is, the more pressure there will be. By measuring the flow rate at the outlet, you can see how well Darcy's Law predicts your results.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• groundwater,
• aquifer,
• porosity,
• Darcy's Law,
• artesian well,
• drawdown.

Bibliography

These websites will help you get started with your background research on groundwater and Darcy's Law:

• Mullen, K., 2006. "Darcy's Law," National Groundwater Association [accessed November 30, 2006] http://www.ngwa.org/educator/lessonplans/darcy.cfm.
• SDSU, date unknown. "Applying Darcy's Law to a Confined Aquifer," San Diego State University, Department of Geological Sciences [accessed November 30, 2006] http://www.geology.sdsu.edu/classes/geol351/darcys.htm.
• Wikipedia contributors, 2006. "Darcy's Law," Wikipedia, The Free Encyclopedia [accessed November 30, 2006] http://en.wikipedia.org/w/index.php?title=Darcy%27s_law&oldid=87395188.
• water table draw-down animation:
  GROW, 2004. "Water Table Drawdown," Geotechnical, Rock and Water Resources Library [accessed November 30, 2006] http://www.grow.arizona.edu/Grow--GrowResources.php?ResourceId=168.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• 4 (or more) 2 L plastic bottles,
• plastic tubing (e.g., aquarium tubing, drinking straw),
• sharp knife,
• modeling clay,
• large measuring cup or graduated beaker for measuring outflow,
• timer or stopwatch,
• material to simulate subsurface, e.g.:
  • pea gravel,
  • aquarium gravel,
  • sand,
  • clay soil,
  • mixtures of clay and sand.

Experimental Procedure

1. Do your background research and make sure that you are knowledgeable about the terms, concepts, and questions, above.
2. Prepare at least four 2 L bottles for measuring flow rates, as described in Figure 1, below:

   Figure 1. Each soda bottle should have a single outlet hole. Make four bottles, each with an outlet hole at a different height. To collect the outflow, connect a short length of drinking straw or aquarium tubing to the outlet hole, and seal the edges with modeling clay. Use a large measuring cup or other graduated container to catch the outflow. (Thanks to John LeVasseur for the soda bottle drawing from which this diagram was adapted.)

3. To investigate the effect of pressure on underground water flow, compare the flow rate from the different outlet holes. Fill each bottle with the same medium (e.g., sand).
   • Keep the water level in the bottle constant by pouring water in at the top.
   • Measure the outflow by collecting the water in a graduated container and measuring how much water you collect in a given time period (e.g., 10, 20, or 30 seconds).
   • Convert your flow rate to liters per minute for comparing the different conditions.
   • Calculate the pressure head for each condition by measuring the difference between the heights of the inlet (h₁) and outlet (h₂). The arrows in Figure 2 show the pressure head (h₁ − h₂) for each of the outlet holes.
   • Graph your results by plotting flow rate (y-axis) vs. delta h (the inlet height minus the outlet height, as shown in Figure 1). How well does Darcy's Law predict your results?
4. To investigate the effect of different materials on underground water flow, use different materials to fill the bottles. Compare the measured flow rates for the different materials (using outlets at the same height). Can you use Darcy's Law to calculate the K value (permeability coefficient) for each material?

Variations

• What do you think will happen to flow rate if you change the diameter of the bottle? Can you relate this change to groundwater movement?
• What do you think will happen to the flow rate if you change the diameter of the outlet tubing?

• For more science project ideas in this area of science, see Geology Project Ideas.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on:

• Gevorkian, G., 2004. "Darcy's Law and Underground Water Flow," California State Science Fair Abstract [accessed November 30, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J0606.pdf.

Last edit date: 2006-12-08 11:00:00

Career Focus

If you like this project, you might enjoy exploring careers in Geology.

	Geoscientist Just as a doctor uses tools and techniques, like x-rays and stethoscopes, to look inside the human body, geoscientists explore deep inside a much bigger patient—planet Earth. Geoscientists seek to better understand our planet, and to discover natural resources, like water, minerals, and petroleum oil, which are used in everything from shoes, fabrics, roads, roofs, and lotions to fertilizers, food packaging, ink, roads, and CD’s. The work of geoscientists affects everyone and everything.			Geographer When you hear the word geography, you might think of maps and names of state capitals, but the work of geographers is much more than creating maps and identifying places. Geographers look at how people, places, and Earth are connected. They study the economy, social conditions, climate, and topography of a region to help answer questions in urban and regional planning, business, agriculture, and medicine.

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