Problem 57452. Design a well field in an infinite aquifer
A well field provides water for a community. The design of a well field involves a goal to meet a specified service demand (i.e., volume of water per time) with the constraint of lowering the water table by no more than , the maximum drawdown. Inputs to the design are properties of the aquifer (the hydraulic conductivity K, the specific yield , and the initial saturated thickness b) and the radius of the well.
The Gupta/Chin method for designing a well field has the following steps:
- Compute , an initial estimate of the pumping rate, such that the drawdown at one well (i.e., at a distance ) is . Compute the transmissivity to be . Evaluate the drawdown at a time 1 year. Realize that for small values of the unconfined well function* can be approximated and compute the pumping rate from where and .
- Compute the number of wells by dividing the demand by the initial estimate of the pumping rate and rounding up to the nearest integer:
- Set the pumping rate to .
- Arrange the wells so that they are equidistant from the central well.
- Determine the distance R between the central well and others so that the total drawdown at the central well is . In other words, add the drawdown from the central well to the drawdown from the other wells. If , then
Write a function to design a well field using this method.
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