Abstract
Laplace equation is the basic differential equation that governs the steady flow of a fluid through an isotropic and homogeneous porous medium and also the steady flow of current in a conducting medium. Therefore, a steady-state groundwater flow problem can be formulated as an analogous electrical current flow problem. A flow net, set of grids formed by orthogonally intersecting equipotential lines and flow lines, is a graphical solution to the equations of steady groundwater flow. By definition, flownet for the original groundwater problem and the corresponding analogous electrical problem should be similar. This feature allows the possibility of introducing the concepts of flownets to students using the easily demonstrable electrical counterpart of the problem in a laboratory setting. This paper discusses the efforts of the authors to widen the scope of an experiment already included in the Fluid Mechanics laboratory course of a Civil Engineering curriculum and to better teach flownet principles using the electrical analogy of groundwater flow problems. Students used a simple experimental setup to obtain flownets for selected groundwater flow situations with different boundary conditions using the electrical analogy concept. Students also used a groundwater flow computer model to obtain flownets for the same flow situations and compared the results. The laboratory lesson plan consisted of five steps: (i) study and understand the selected physical groundwater problems, (ii) conceptualize the corresponding analogous electrical problems (iii) use the electrical analogy experimental setup to obtain flownets, (iv) study and understand the mathematical formulation of the problems, and (v) compare the analogous results with those obtained from a groundwater flow computer model. Sample results obtained by students are presented. The student feedback indicated that this approach resulted in an effective learning of the concepts involved.
Highlights
Flownets are convenient graphical representations of steady patterns of groundwater flow consisting of equipotential lines and stream or flow lines
We present our experience with an instructional unit as part of our civil engineering undergraduate Fluid Mechanics laboratory for exploring flownet concepts in groundwater flow through an electrical circuit analogy and through the use of a computer model, Visual MODFLOW
The results for the three selected scenarios (2, 4-2, and 5-1) for electrical analogy are presented in Fig. 4 (a), (c) and (e), and their corresponding results concerning Visual MODFLOW are presented in Fig. 4 (b), (d) and (f)
Summary
Flownets are convenient graphical representations of steady patterns of groundwater flow consisting of equipotential lines and stream or flow lines. Groundwater flow, flow of heat in a heat-conducting medium, flow of magnetic flux, and flow of current in an electrical conducting medium, are all governed by the Laplace equation and flownet concepts are applicable to all these situations. The basic common feature (analogy) of all these phenomena enables one to transfer the solution of a problem in one discipline to a similar problem in another discipline In this experiment we will obtain the flownet pattern for a groundwater flow situation using the electrical counterpart of the problem. We present our experience with an instructional unit as part of our civil engineering undergraduate Fluid Mechanics laboratory for exploring flownet concepts in groundwater flow through an electrical circuit analogy and through the use of a computer model, Visual MODFLOW. Basic concepts of groundwater flow, electrical analogy, flownets, and the Visual MODFLOW software features were taught. Student feedback was obtained to understand the effectiveness of the approach with regard to improving student learning
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