Problem 59104. Design a capture zone

One approach to remediating a contaminated site is to pump and treat the contaminated groundwater. If the site has background flow, then an extraction well will create a capture zone. In other words, there will be a streamline that divides the water pumped by the well from the water that continues downgradient (i.e., downstream) of the well.
If the background flow (with flow per unit width* Q') is left to right, then the coordinates (xc, yc) of a point on the capture zone are given by xc = yc/tan(yc/x0), where the well is at (0,0) and x0 is the distance to the stagnation point downstream of the well. The distance x0 can be determined by finding the distance at which the specific discharge of the background flow equals the specific discharge of the well.
Write a function that takes the coordinates of a contaminated area and the background flow per unit width and determines the pumping rate needed to capture the entire area.
*Recall that specific discharge v is flow per area over which the flow is occurring. Then flow per unit width is Q' = vb, where b is the thickness of the confined aquifer.
Capture zone
Solve

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18.18% Correct | 81.82% Incorrect
Last Solution submitted on Oct 24, 2025

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