Problem 59109. Check a scheme to dewater a construction area

In addition to supplying water and capturing contaminants, wells can be used to lower the water table in a construction area. In such applications, the water table must be lowered from the initial elevation H at least a value smin over the whole area. That is, the water table elevation relative to the bottom of the aquifer must be no greater than hmax = H - smin.
The wells will be set back from the boundaries of the construction area to allow for excavation. The water table elevation can be computed with
h = sqrt(H^2 - (1/(pi K) sum(Qj ln(R/rj))
where K is the hydraulic conductivity, Qj is the pumping rate of the jth well, R is the radius of influence, and rj is the distance from the jth well to the point in question.
Write a function that takes the coordinates of the wells and their pumping rates, as well as the dimensions of a rectangular construction area and properties of the aquifer, and assesses whether the minimum drawdown is achieved everywhere in the construction area. The origin will be at the center of the left side, as shown by the black X below. In addition to a logical variable that indicates whether the well system works, the function should return the minimum drawdown achieved by the well system and the coordinates of the minimum drawdown.
dewatering scheme

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50.0% Correct | 50.0% Incorrect
Last Solution submitted on Jan 01, 2024

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