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Teaching Flownet Concepts to Engineering Undergraduates Using Electrical Analogy of Groundwater Flow

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2011 ASEE Annual Conference & Exposition


Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011



Conference Session

Pedagogical Innovations in Laboratory Education

Tagged Division

Division Experimentation & Lab-Oriented Studies

Page Count


Page Numbers

22.1392.1 - 22.1392.17



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Paper Authors


Murthy Kasi North Dakota State University

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Murthy Kasi is currently an Environmental Engineering doctoral candidate in the Department of Civil Engineering and an Instructor in the Fluid Mechanics laboratory for undergraduates at North Dakota State University, Fargo, North Dakota, USA. He obtained his Bachelors degree in Civil Engineering from Andhra University, India, and Masters in Environmental Engineering from South Dakota State University, Brookings, SD, USA. Areas of concentration of his doctoral research are groundwater bioremediation, wastewater treatment, and water quality modeling. He has been active in the NDSU student Chapter of Water Environment Federation /American Water Works Association.

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Yaping Chi North Dakota State University

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Yaping Chi is currently a Ph.D. student in Water Resources Engineering in the Department of Civil Engineering and a Teaching Assistant in the Fluid Mechanics laboratory for undergraduates at North Dakota State University, Fargo, North Dakota, USA. She obtained her Bachelor’s degree in Resources and Environment Engineering from Anhui University of Science and Technology, China; and Master’s in Water Resources Engineering from China University of Geosciences, China. Areas of concentration of her doctoral research are quantification of microtopography, combined experimental and modeling study on overland flow generation.

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G. Padmanabhan North Dakota State University

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G. Padmanabhan, Ph. D., P.E., M. ASEE, F. ASCE is a professor of civil engineering at North Dakota State University, Fargo, North Dakota. He is a long standing member of ASEE and ASCE. Currently, he is also the Director of North Dakota Water Resources Research Institute. He has been active in STEM education outreach activities to minorities at the college and high and middle school levels for the last ten years.

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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. 10.18260/1-2--18679

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