Example of Exam Question....(one of 2 or 3 questions -- perhaps with choice of questions): A Boundary-Value Problem |
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Exam questions will be applied practical problems as found in consulting practice. These will require the same skills and techniques presented in lecture and practiced on problem sets. The problems will be solved by analysis and by computer methods, in the G/G PC Teaching Laboratory.
Example of Exam Question....(one of 2 or 3 questions -- perhaps with choice of questions): A Boundary-Value Problem |
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A long linear trench is used as a "recharge barrier" for a contaminant plume on the west side of an alluvial channel aquifer in Oklahoma (Figure 3). The purpose of the recharge barrier is to maintain a constant head in the aquifer that is higher than the river and thus to create a zero-flow (flat) hydraulic gradient between the trench and the aquifer boundary. To do this, the trench is cut to a depth of 5 m and filled continuously with water pumped from the river. The trench is 24 meters long and Q=0.013 m3/s of water is required to keep the trench full of water to elevation. The river stage is h=0 (assume the river gradient is negligible, approximately flat), the elevation of the river water surface. The K of the underlying aquifer is high, at a value of 0.004 m/s. Its thickness (average 17 m) is also relatively great, so that the product does not vary greatly across the aquifer, i.e. it is reasonable to treat the flow regime as artesian (ignore vertical flow and variations of thickness with depth). Because the trench length M is long and parallel to the river, it is reasonable to treat the flow across the channel (from A-A') as one-dimensional (i.e., ignore flow parallel to the river). The storage coefficient (specific yield) is 0.12 in these gravels. The recharge rate on the alluvial aquifer is 12 cm per year of water and is absolutely uniform across the aquifer. Of concern is the water table rise and any wetlands or springs the recharge barrier will create between the river and the barrier, where there are homes.
1) Develop an analytical model for hydraulic head in terms of selected variables in the problem stated above. Assume x=0 is the barrier and x=L is the river. Develop the model for artesian conditions (use the artesian conductance parameter!) and for a time after all water levels have stabilized. DON'T USE NUMBERS; present solution in closed algebraic form.
2) Plot in EXCEL the configuration of the potentiometric surface