June 26, 2011
June 26, 2011
June 29, 2011
Division Experimentation & Lab-Oriented Studies
22.1392.1 - 22.1392.17
A Simple Experiment to Illustrate Groundwater Flownet Concepts toEngineering Undergraduates via Physical, Analogous, Mathematical, andComputer ModelingThe basic differential equation governing phenomena such as steady flow of a fluid through anisotropic and homogeneous soil, flow of heat in a conducting medium, flow of magnetic flux,flow of current in a conducting medium, laminar flow of fluids, and so on is Laplace's equation.This allows a problem in one discipline to be viewed as an analogous problem in anotherdiscipline with the same type of governing equations. Flownet is a good example to illustratethis idea. Construction of a flow net is an indirect way of obtaining the solution to Laplace'sequation with appropriate boundary conditions. Students conducted a simple experiment using aplexiglass tray, mildly-ionized water, electrodes, voltmeter, and a voltage probe to obtainflownets for selected groundwater flow situations with diffrent boundary conditions using theelectrical analogy concept. Students were asked to study and understand the selected physicalgroundwater problem first. Next, they were asked to conceive the corresponding electricallyanalogous problem for solving which they could use the experimental set up. Then, students hadto study and understand the mathematical formulation in the differential and difference forms ofthe problem. Finally the students were also asked to compare their results using a popularcomputer model used in the groundwater profession. The idea of using an electricallyconducting medium to illustrate electrical analogy is not new. However, the emphasis in thispaper is to give the students an idea of physical, analogous, mathematical, and computermodeling. Students learned that flow net is a pictorial or graphical representation of flowpatterns. The net consists of equipotential lines and flow lines. Equipotential lines are linesalong which a constant potential exists. Flow lines are lines along which the velocity vectors aretangent. By definition, flow lines and equipotential lines are orthogonal to one another.Conventionally, these two families of curves are drawn so that they form a pattern of curvilinearsquares. Stream lines always intersect equipotential lines orthogonally. Students learned theequations involved in the groundwater problem and understood that problems with geometricallyregular boundaries can be solved mathematically with relative ease, but not so with irregularboundaries. However, the electrical analogy experiment provided a method for the students tosolve groundwater flow problems, particularly the ones with geometrically irregular boundaries.Student work and the results of a survey on the effectiveness of the approach are also presented.
Kasi, M., & Chi, Y., & Padmanabhan, G. (2011, June), Teaching Flownet Concepts to Engineering Undergraduates Using Electrical Analogy of Groundwater Flow Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. https://peer.asee.org/18679
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