Part IV. Analyzing the Data Now that you have a set of voltage measurements at the intersection points on your grid we can draw contours to illustrate the electrical potential field, and flow lines to indicate the electrical flow. Your graph should have a number of individual points that you need to use to draw contour lines. See Figure 3a for an example. As elevation contour lines represent points of equal elevation, voltage contour lines represent points of equal voltage. Choosing a contour interval (the difference between subsequent lines of equal voltage) depends on the range of voltages you measured. For example, if you measured from 200 to 400 millivolts, you could choose a contour interval of 20 millivolts. The contour lines would be drawn at 200, 220, 240, 260, etc. millivolts, all the way up to 400 millivolts. Three rules for drawing contours: Contours must be continuous. Like a topographic map describes a continuous land surface, the electrical field should also be considered a continuous surface. The contours do end however at the boundaries of the system (the basin edges). "No" sharp angles. Again, most land surface elevations change smoothly from one point to the next. Exceptions are man-made structures like buildings. Contours cannot cross each other. Voltages progressively change from one level to the next; in areas where the voltage changes quickly the contours may get very close to each other, but should not touch. Questions 1. On Graph 2, draw several flow lines at various pathways to show how electrical flow is occurring in the landfill. Do the flow lines converge on the hole that you made? If all went well, the graph should show that the flowlines all point towards the hole (see my results in Figure 3b). The key to the method is that the analyst can use the contours and converging flowlines to locate the various leaks. Naturally the field application requires larger voltages which makes the technique more sensitive: the contour intervals can be set at relatively finer scales which allows for much more exact locations of the holes. 2. Think about the similarities we have shown between and electrical and groundwater systems. What happens to water flow in groundwater systems at impermeable boundaries and impermeable objects? Another common technique for determining leaks from landfills is to drill wells around the perimeter of the landfill, and analyze the water to see if any telltale signatures are present (for example, high levels of mercury). 3. What advantages does the electrical method have over water well testing for locating landfill leaks? 4. Think about the conditions you created in order to perform this lab. If you were to adapt this technique at a real landfill, what other factors would you need to think about in order to interpret the data? Hint: do you think you would get the same results from a filled versus an empty (water only) landfill basin? 5. Would you be able to use this technique if the land outside the landfill were completely dry? Why or why not? 6. Would the composition of the ground material (outside of the landfill) have any effect on the technique? Why or why not? 7. Can you think of situations where contour lines might not be continuous in land surfaces? In electrical fields? Clean up The salt solution will corrode everything. Be sure to wipe off all the meter parts, electrodes, battery, and bare wires. As you can imagine, a lot of salt will remain in the sand. In future experiments, you will need much less (or none at all) salt in the solution to saturate the sand.
Some Lab Options You can also use Part II to introduce the concept of drawing contour lines from individual points. Rather than keeping the meter probe at a fixed voltage, you can measure a number of points within the basin, then try to draw the even-value (e.g., 1, 2, 3, 4, and 5 volt) contours. For both the circuit demonstration (Part II) and landfill lab (Part III), you can make things more interesting by adding conducting and/or nonconducting items in the landfill (as would be the case in an actual landfill). This will complicate the equipotential lines and flowpaths. For example, putting a non-conducting object in the basin will violate the "no sharp angles" rule, as the contour lines will intersect with the object and stop. You can also experiment with creating more than one hole in the landfill, as is typically the case during the real applications of this technique. See how these affect the equipotential lines and flowpaths. One method used in the field is to change water levels in the landfill to constrain the search for leaks to particular areas (levels) of the liner.