AC 2011-84: TEACHING FLOWNET CONCEPTS TO ENGINEERING UN-DERGRADUATES USING ELECTRICAL ANALOGY OF GROUNDWA-TER FLOW

Murthy Kasi, North Dakota State University

Murthy Kasi is currently an Environmental Engineering doctoral candidate in the Department of CivilEngineering and an Instructor in the Fluid Mechanics laboratory for undergraduates at North DakotaState University, Fargo, North Dakota, USA. He obtained his Bachelors degree in Civil Engineering fromAndhra 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 ofWater Environment Federation /American Water Works Association.

yaping chi, North Dakota State University

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

G. Padmanabhan, North Dakota State University

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

c©American Society for Engineering Education, 2011

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

Abstract A simple experiment was developed for an undergraduate civil engineering fluid mechanics laboratory course to teach flownet concepts in groundwater flow using electrical analogy. The basic differential equation governing steady flow of a fluid through an isotropic and homogeneous soil, flow of heat, flow of magnetic flux, flow of current in a conducting medium, is Laplace equation. This allows a steady-state groundwater flow problem to be viewed as an analogous electrical current flow problem. Principles of flownet can be taught in a laboratory setting easily using this analogy. Construction of a flow net is an indirect way of obtaining the solution to Laplace equation with appropriate boundary conditions. The experiment consisted of using a plexiglass tray, mildly-ionized water, electrodes, voltmeter, and a voltage probe to obtain flownets for electrically analogous flow situations of selected groundwater problems with different boundary conditions. Students were asked to study and understand the selected physical groundwater problems first. Next, they were asked to conceive the corresponding electrically analogous problem for solving which they could use the experimental set up. Then, students had to study and understand the mathematical formulation in the differential and difference forms of the problem. The idea of using an electrically conducting medium to illustrate electrical analogy is not new. However, the emphasis in this paper is to give the students an idea of flownets and electrical analogy of groundwater problems. Students learned that flow net is a pictorial or graphical representation of flow patterns consisting of equipotential lines and flow lines. By definition, flow lines and equipotential lines are orthogonal to one another. Students learned Laplace equation involved in the groundwater problem and understood that the equation can be easily solved for problems with geometrically regular boundaries, but not with irregular boundaries. However, the electrical analogy experiment provided a method for the students to solve groundwater flow problems, including the ones with geometrically irregular boundaries. Students understood the analogy between electrical current flow and the groundwater flow. Student work and the results of a student perception survey on the effectiveness of the approach are presented. Introduction Flownets are convenient graphical representations of flow patterns of steady flow of a fluid through an isotropic and homogeneous soil, flow of heat in a conducting medium, flow of magnetic flux, flow of electrical current in a conducting medium, or laminar flow of fluids. The net consists of equipotential lines and stream or flow lines. Equipotential lines are lines along which a constant potential exists. Flow lines are lines along which the velocity vectors are tangents. By definition flow lines and equipotential lines must be orthogonal to one another. In order to simplify flow calculations, these two families of curves are usually drawn to form a pattern of curvilinear squares (Figures 1and 2). Flownet concept is applicable to all steady state flow situations in which flow of any flux is driven by a potential difference and thereby the governing equation is LaPlace equation. This property of flownet makes it amenable to be used for solving a problem in one discipline as an analogous problem in another discipline having LaPlace equation as the governing equation.

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Figure 1. An example of a flownet

(a)

(b)

Figure 2. Flow nets showing stream lines and potential lines for (a) a discharging well in an aquifer bounded by a stream parallel to an impermeable barrier (plan view) (slightly modified1), and (b) groundwater flow beneath a dam with a cutoff wall (sectional view).

Dam

Cutoff wall

Equipotential lines

Stream lines

Equipotential Lines Flow

Lines

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Laboratory course The flownet experiment was included as one of the twelve experiments for Laboratory course (CE 310), a 1-curriculum . The description and the theory behindmanual2. Background information on comparable groundwater flow equationaddition they are introduced at the be familiar with the electrical part of the experiment2010 Spring and Fall semesters. Each semesterstudents per section. Each section wassessions of each experiment, students learn to setup the experiment and Students are also required to preparediscuss the reports with the students and provide feedback. Experimental Setup The experimental setup consisted of transformer, a voltmeter, a voltage probewith tap water to form a thin sheet of water to serve as the conducting medium. The boundary conditions could be varied by changing the geometry and by using conducting and nonconducting material for the boundary. appropriate boundary configurations. Athe coordinate points of voltage readingssetup allows measurements of potential for mapping e

Figure 3. Materials used in the electrical analogygroundwater flow scenarios Experiments Students were presented with five differentconceive and prepare the corresponding electrical analogy setspatial distribution of voltage. The five flow situations are:

1. Groundwater flow between two constant head boundaries

• Steel cylinder

• Aluminum sheet

• Aluminum cylinder

• Wooden block

• Mildly ionized water

• Voltage meter & probe

• Step-down transformer

included as one of the twelve experiments for the Fl-credit required course for Civil Engineering undergraduate

The description and the theory behind the experiment are included in theBackground information on electrical current flow equations and analogously

water flow equations are included in the laboratory instruction manual. In at the beginning of the class because all incoming students may not

be familiar with the electrical part of the experiment. Data for this paper was collected during the Each semester, 4 sections of the course are offered

Each section was divided into 3 groups of four students. During 2each experiment, students learn to setup the experiment and record observations

are also required to prepare and submit reports in the following week. Instructors discuss the reports with the students and provide feedback.

experimental setup consisted of a plexiglass tray, electrodes (aluminum sheets)voltmeter, a voltage probe, and a graphing paper (Figure 3). The tray was filled

water to form a thin sheet of water to serve as the conducting medium. The boundary varied by changing the geometry and by using conducting and non

conducting material for the boundary. Additional pieces of plexiglass can be used for cappropriate boundary configurations. A graphing paper was placed underneath the tray to locate

voltage readings so the spatial distribution of voltage can be plottedmeasurements of potential for mapping equipotential lines in two dimensions.

electrical analogy setup to develop flownets for various

five different groundwater flow situations and were asked to conceive and prepare the corresponding electrical analogy set-up and take measurements of spatial distribution of voltage. The five flow situations are:

Groundwater flow between two constant head boundaries

Plexiglass tank Graphing paper

Fluid Mechanics for Civil Engineering undergraduate

the experiment are included in the laboratory lectrical current flow equations and analogously

laboratory instruction manual. In because all incoming students may not

Data for this paper was collected during the of the course are offered with 12

During 2-hour record observations.

Instructors

(aluminum sheets), a step-down The tray was filled

water to form a thin sheet of water to serve as the conducting medium. The boundary varied by changing the geometry and by using conducting and non-

glass can be used for creating graphing paper was placed underneath the tray to locate so the spatial distribution of voltage can be plotted. The

quipotential lines in two dimensions.

setup to develop flownets for various

and were asked to up and take measurements of

Plexiglass tank

Graphing paper

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2. Groundwater flow between two constant head boundaries with an “impermeable barrier” in between the boundaries

3. Groundwater flow between two constant head boundaries with a “permeable barrier” in between the boundaries

4. Groundwater flow converging to a pumping well situated between an impermeable boundary and a recharge boundary

5. Seepage beneath a dam The scenarios for this lab exercise were designed to gradually introduce the complexity involved in the groundwater flow. In the first scenario, the groundwater flow through a homogeneous soil between two constant head boundaries at different elevations was simulated. This scenario could be an example for groundwater flowing between two lakes at different elevations or two ditches at different elevations in an agricultural field or infiltration of water from the bottom of a pond to an unconfined aquifer. While keeping the constant head boundaries same, an impermeable barrier was added in between the two boundaries in the second scenario. This scenario represents the grout/slurry walls that divert the groundwater flow from a contaminated zone. In the third scenario, the impermeable barrier was replaced by a semi-permeable barrier. This scenario simulates the flow in a permeable reactive barrier system for groundwater treatment. In the fourth scenario, a pumping well was introduced close to one of the constant head boundaries. In the fifth scenario, seepage underneath a dam was simulated by separating the two constant head boundaries by a small distance on one side of the plexiglass tray. The constant head boundaries in the first, second, third and the fifth scenarios were simulated by applying a high voltage to one aluminum sheet and a low voltage to the other aluminum sheet. In the fourth scenario, the low voltage was applied to an aluminum cylinder to simulate well pumping situation. Coordinates of constant voltage points were identified on a graph sheet placed below the plexiglass tank. The voltage was recorded using a volt meter and a probe. Most of the scenarios were developed with straight and/or rectangular edge boundaries. With few modifications to one of the scenarios, the setup was also used to simulate irregular boundary conditions. Scenario 1: Groundwater flow between two constant head boundaries In this scenario, groundwater flow between two constant head boundaries was considered. Groundwater flow in an aquifer between two rivers or two lakes or two ditches in an agricultural field or infiltration of surface water from a pond/lake towards an unconfined aquifer could be the examples for this scenario. Two sub scenarios were studied.

1. Constant head boundary with a higher head on one end and with a lower head on the

opposite end (Figure 4a), and 2. Constant head boundary with a higher head on one side and with a lower head on

other sides of the tank ((Figure 4b). The electrical analogies for these two sub scenarios were setup as shown in Figure 5. For the first sub scenario (Case 1 in Figure 5), electrodes (aluminum sheets) were placed on the opposite ends of the plexiglass tray. For the sub scenario 2 (Case 2 in Figure 5), the tray walls were covered on three sides with connecting aluminum sheets to make the three sides as one electrode. The fourth

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wall of the tray was covered with another aluminum sheet with small gaps between this fourth side and its adjacent sides. A voltage difference of 20 volts was maintained between the two electrodes. Coordinates of constant voltage points were identified on a graph sheet placed below the plexiglass tank.

(a) (b) Figure 4. Examples for groundwater flow between two constant head boundaries: a) groundwater flow between two ditches in an agricultural field and b) seepage of surface water from the bottom of a pond towards an unconfined aquifer.

Figure 5. Electrical analogy set up for Scenario 1. Scenario 2: Groundwater flow around an impermeable barrier Groundwater vertical barrier walls are often used for waste containment by restricting the flow of uncontaminated groundwater from passing through a contaminated site, thus limiting the flow of contaminants off of the contaminated site. The walls are typically straight, curved, or enclosed, and constructed of grout, clay slurry, and plastic or steel sheet piling, which are known for their

Unconfined aquifer

Pond Ditches

Groundwater level

Step-down Transformers

Volt meter V

Alu

min

um s

heet

s

Plexiglass tank

Case 1 Case 2

V

Probe

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low permeability. Figure 6 illustrates the groundwater flow stream lines around a curved slurry wall.

Figure 6. Ground water flow diverted from a contaminant zone. The electrical analogy was setup as shown in Figure 7. A wooden block was used as an impermeable material to electrical current, which is analogous to impermeable grout wall in case of groundwater flow. Aluminum sheets (electrodes) were placed on opposite ends of the electrolytic tank and the wooden block was placed in the center of the tank. A voltage difference of 20 volts was maintained between the two electrodes. Constant voltage locations were identified similar to the previous experiment.

Figure 7. Electrical analogy set up for Scenario 2. Scenario 3: Groundwater flow through a permeable barrier Permeable reactive barrier (PRB) system is an in situ remediation technology to treat contaminated ground water that combines a passive chemical or biological treatment zone with subsurface groundwater flow management3. One of the typical configurations of PRBs include low permeable grout/slurry walls that direct the groundwater flow towards a higher permeable

Cut-off wall

Contaminant zone

Groundwater flow

Step-down transformer

V

Probe

Volt meter

Aluminum sheets

Plexiglass tank

Wooden block

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reactive zone, where the contaminated water is treated using chemical or biological reactive materials (Figure 8). These configurations are called as funnel and gate systems, in which low-permeable walls (slurry walls) act as funnels and PRB acts as a gate that allows that groundwater to pass through it.

Figure 8. Ground water flow through a permeable reactive barrier (adapted4). The funnel and gate system was simplified in the present experiments. A steel cylinder which has higher electrical conductivity than the surrounding water was assumed to analogously represent the PRB. The electrical analogy setup for this flow situation is illustrated in Figure 9. A voltage difference of 20 volts was maintained between the two electrodes. The steel cylinder was placed at the center of the tank. Constant voltage locations were identified similar to the previous experiments.

Figure 9. Electrical analogy set up for Scenario 3. Scenario 4: Groundwater flow near a pumping well In this scenario, the effect of a pumping well situated near a perennial stream was simulated (Figure 10a). The electrical analogy for this experiment is shown in Figures 10b and 10c. An aluminum cylinder was used as analogous to the pumping well, while aluminum sheet(s) were used to simulate perennial stream(s) condition. The tank was filled with mildly conducting water to simulate homogeneous aquifer soil condition. The higher voltage of 20V was applied to the

Treated groundwater

Contaminated groundwater

Slurry walls

Permeable Reactive Barrier

Step-down Transformer

V

Probe

Volt meter

Aluminum sheets

Plexiglass tank Steel cylinder

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aluminum sheet and the lower voltage of 0V was applied to the aluminum cylinder to simulate the pumping (or discharging). For two constant head boundaries, a second step-down transformer was used and a constant voltage of 10V was applied to the second constant head boundary. Constant voltage locations were identified similar to the previous experiments.

(a)

(b) (c) Figure 10. (a) Schematic of a pumping well near a perennial stream and its electrical analogy setup for well with (b) one constant head boundary and (c) two constant head boundaries. Scenario 5: Seepage beneath a dam Groundwater flow beneath a dam occurs due to difference in water elevations upstream and downstream of a dam (Figure2b). In the present scenario, however, the dam without a cut-off wall was analogously simulated. Two sub scenarios were considered, one with homogeneous soil layer and with an irregular impervious soil layer within a homogeneous soil layer. The electrical analogy was setup as shown in Figure 11. Aluminum sheets (electrodes) were placed on the same side of the plexiglass tray with a gap in between them. For the second sub scenario, a Styrofoam

Discharging well

Non pumping

Perennial stream

Aquifer Aquifer

Pumping water level Impermeable layer

Step-down transformer

V Probe

Volt meter

Aluminum sheet

Plexiglass tank Aluminum cylinder

Step-down transformer

V Probe

Volt meter

Aluminum sheet

Plexiglass tank Aluminum cylinder

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was used to analogously represent the irregular impervious soil layer (Figure 11b). Electrical current was supplied to the electrodes and a voltage difference of 20 volts was maintained between the two electrodes. Constant voltage locations were identified similar to the previous experiments.

(a) (b) Figure 11. Electrical analogy set up for Scenario 5. Results Obtained by Students Typical results obtained by the students are presented in Figures 12 to 17 and are discussed in this section. The flownets for groundwater flow between two constant head boundaries are presented in Figures 12 and 13. Figure 12 illustrates the flownets for groundwater flow between two ditches in an agricultural field (Scenario 1 - Case 1). In this scenario, the equipotential lines are generally parallel to each other. The flownets for this scenario were easily constructed by drawing stream lines perpendicular to the equipotential lines. The flownets for infiltration from a pond towards an unconfined aquifer are presented in Figure 13. The equipothential lines are closer to each other near the boundary where a pond is located, which indicates higher flow rate, than the other boundary where an unconfined aquifer is located. Results for flownets constructed for groundwater flow around an impermeable barrier are presented in Figure 14. This scenario is very similar to Scenario 1 - Case 1, except that an impermeable barrier was added in between the constant head boundaries (ditches). The equipotential lines bent towards the barrier near the barrier boundary, which indicates a buildup of head near the barrier boundary. The flow lines were bending away from the barrier in this scenario. On the other hand, the equipotential lines bent away from the barrier for a permeable barrier and the flow lines were bent into the barrier (Figure 15). Due to higher conducting nature of the barrier (steel cylinder) than the surrounding medium (mildly ionized water), the flow lines (current) have a tendency to pass through the highly-permeable material. The flownets results for a pumping well with one constant head boundary and two constant head boundaries are presented in Figure 16. Equipotential lines obtained for the scenario for pumping

Step-down Transformers

V

Aluminum sheets

V

Probe

Volt meter

Plexiglass tank Styrofoam

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well with one constant head boundary indicate that the well was directly drawing water from the stream (20V in Figure 16a). On the other hand, the well was drawing water from the stream (20V in Figure 16b) and the aquifer as well for the scenario with two constant head boundaries. In this scenario, the water in the aquifer was replenished by the second constant head boundary, i.e. voltage potential of 13V (Figure 16b).

Figure 12. Flownets for groundwater flow between two constant head boundaries (Scenario 1 – Case 1). Example scenario for two ditches in an agricultural field.

2V

20V

18V

10V

14V

6V 0V

Equipotential Lines

Stream Lines

0V

0V

Pond or Lake

Unconfined aquifer

20V 18V 14V 10V 6V 2V 0V

Equipotential Lines

Stream Lines

Drain at a higher elevation

Drain at a lower elevation

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Figure 13. Flownets for groundwater flow between two constant head boundaries (Scenario 1 Case 2). Example scenario for infiltration from a pond towards an unconfined aquifer.

Figure 14. Flownets for groundwater flow around an impermeable barrier.

Figure 15. Flownets for groundwater flow through a

Flownets for groundwater flow between two constant head boundaries (Scenario 1 Case 2). Example scenario for infiltration from a pond towards an unconfined aquifer.

Flownets for groundwater flow around an impermeable barrier.

Flownets for groundwater flow through a highly-permeable barrier.

Equipotential Lines

Stream Lines

Impermeable Barrier

Equipotential Lines

Stream Lines

Highly-Permeable Barrier

Flownets for groundwater flow between two constant head boundaries (Scenario 1 – Case 2). Example scenario for infiltration from a pond towards an unconfined aquifer.

Equipotential

Equipotential

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Figure 16. Flownets for groundwater flow thead boundary and b) located between two constant with higher potential. Figure 17 illustrates the results for flownets obtained for groundwater flow beneath a dam. scenario with an irregular shaped impermeable boundary was obtained by a simple addition of an irregular shaped Styrofoam to the Scenario 5(a).

(a)

(b)

Flownets for groundwater flow towards a pumping well a) located near a constant

head boundary and b) located between two constant head boundaries and closer to the boundary

Figure 17 illustrates the results for flownets obtained for groundwater flow beneath a dam. scenario with an irregular shaped impermeable boundary was obtained by a simple addition of an irregular shaped Styrofoam to the Scenario 5(a). The difference in the flownets due to the

pumping well a) located near a constant head boundaries and closer to the boundary

Figure 17 illustrates the results for flownets obtained for groundwater flow beneath a dam. The scenario with an irregular shaped impermeable boundary was obtained by a simple addition of an

in the flownets due to the

Page 22.1392.13

presence of an irregular shaped boundary (impermeable soil layer in this scenario) can be seen by comparing Figures 17a and 17b. A mathematical solution for the irregular shaped boundary conditions would have been hard to obtain and the electrical analogy had shown a significant reduction of the complexity involved in obtaining solutions for such situations.

Figure 17. Flownets for groundwater beneath the dam with a) a homogeneous soil layer and b) an irregular shaped impermeable soil layer located within a homogeneous soil layer.

(a)

(b)

0V 20V

18V

14V

2V

6V

8V 12V

10V

Upstream Dam Downstream

0V 20V

18V

14V

2V

6V

8V 12V

Impermeable soil layer

10V

Upstream Dam Downstream

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Assessment A short survey (Appendix) consisting of four questions (A-D) was given to the students in order to get their feedback. Question A consisted of four sub-parts designed to elicit Yes/No type answers. The purpose of these questions was to assess whether the students understood the concept of flownets and patterns of groundwater flow under different boundary conditions from electrical analogy experiments. Questions B through D were short answer open ended asking the students to identify the part of the experiment they liked the most, improvements and enhancements to the experiment, and any additional scenarios that they would like to observe with the electrical analogy experiment. A total of 48 students responded in Spring 2010 and 24 students responded in Fall 2010 semesters. Responses to Question A are shown in Figure 17. Almost all the students (more than 95%) indicated that they gained a better understanding of flownet concepts. Responses to Questions B-D are summarized in Table 2. Several students had similar responses. The responses indicate that students enjoyed conducting experiments on the different scenarios chosen and were able to visualize the groundwater flow situations through the analogous comparison. Majority of students did not mention any improvements to the existing experiments or the experimental setup (responses to Question C). A few students felt that more readings at closer intervals would have given them better picture of groundwater flow patterns in complex scenarios such as flow around a barrier. This was included as a recommendation to the teaching assistants in future semesters. Moreover, students also wanted to explore a few other scenarios such as “Beaver Dam” and “Infiltration and inflow into sewer pipes”. These responses are indicative that the analogy experiment stimulated critical and analytical thinking of the students.

Figure 17. Student responses to Question # A.

0

20

40

60

80

100

A.1 A.2 A.3 A.4

Per

cent

age

of T

otal

Stu

dent

s

Question #

YesNo

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Student Responses to survey questions B, C, & D. Question B. Which part of the experiment did you like the most? “Being able to physically see how current moves.” “Seeing the completed graphs.” “Taking the readings.” “Measurement of potential lines.” “Scenario 4, shows around objects.” “Looking at different scenarios after each one was completed.” “All parts were entertaining.” “Finding the equipotential lines and seeing how they flow through water.” “Seeing how a conducting and a nonconducting barrier changes the flow.” “Seeing the equipotential lines as the experiment went on through the placement of the probe.” “Seeing the final results.” “Probing of the water to examine the electrical potential at the spot and seeing how it changes throughout the water.” “Seeing the different patterns when you mess with medium.” Question C. What could be done to improve and enhance the experiment? “I thought it was well done, don't see much that needs to be improved on.” “More explanation.” “Nothing, I think the experiment was done fine.” “Plot more points for each equipotential drop to get better graphs.” Question D. Are there any other groundwater flow scenarios that you would like to observe with this electrical analogy experiment? “Beaver Dam (High to low current).” “Infiltration and inflow into infrastructure pipes.” “Aquifers.” “Underwater current.” “Cofferdam/dewatering scenarios might be good to see.” Suggestions for further improvement The scope of the experiment can be expanded and the effectiveness of the approach can be improved by a few minor additions/modifications. Also, a more rigorous assessment method can be implemented to evaluate the effectiveness of the approach. The following suggestions are made for future semesters.

1. Include a problem of groundwater flow through a multi-layered soil system. 2. Include spatial heterogeneity in aquifer.

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3. The analogy can be applied for more examples such as multiple pumping wells in an aquifer, and multiple permeable and/or impermeable barriers.

4. A pre- and post- survey can also be included for assessing learning effectiveness rather than the one perception survey after the laboratory experience.

Conclusions In this paper, the experience of the authors with a civil engineering undergraduate fluid mechanics laboratory course to introduce the concepts of flownet using electrical analogy of groundwater flow is presented. A simple experiment was developed and implemented to illustrate flownets for different groundwater flow situations using their analogous problems of flow of current through an electrically conducting medium. The setup was introduced with simple geometric boundaries, however it was demonstrated that with few easy modifications, it can also be applied to various irregular boundaries. Assessment based on student evaluations at the end of the experiment indicated that the students understood the basic idea behind the application of electrical analogy for various groundwater flow situations and the concepts of flownet. Acknowledgements The authors would like to thank the Department of Civil Engineering for providing the necessary funding for the materials. The authors would also like to thank the teaching assistants of this laboratory for their assistance in conducting the experiments. References 1. Ferris, J.G., Knowles, D.B., Brown, R.H., Stallman, R.W., 1962. Theory of Aquifer Tests. U.S. Geological

Survey Water-Supply Paper 1536-E. 2. Padmanabhan, G., 2007. Fluid Mechanics Lab Manual for Civil Engineering Students. Kendall/Hunt Publishing

Company, Debuque, IA, USA. 3. Environmental Protection Agency, 1998. Permeable Reactive Barrier Technologies for Contaminant

Remediation. U.S. EPA Remedial Technology Fact Sheet, EPA 600/R-98/125. 4. K.C. Scott, P.G., Folkes, D. J., 2000. Groundwater modeling of a permeable reactive barrier to enhance system

performance. Proceedings of the 2000 Conference on Hazardous Waste Research, Environmental Challenges and Solutions to Resource Development, Production, and Use, Denver, CO, USA.

Appendix: Flownets Experiment Survey

A. Did the electrical analogy experiment help you understand better the 1. concept of flownet? 2. idea of equipotential lines and flowlines and their relationship? 3. analogy between the flow of groundwater and the flow of current through a

conducting medium? 4. patterns of groundwater flow situations?

B. Which part of the experiment did you like the most? C. What could be done to improve and enhance the experiment? D. Are there any other groundwater flow scenarios that you would like to observe with

this electrical analogy experiment?

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