Well Drawdown Calculator

It computes the dimensionless parameter u = r²S / (4Tt) from your inputs and checks it against 0.05. Below that threshold, the Cooper-Jacob straight-line formula is an accurate simplification of the Theis solution and gets used directly. At or above it, the calculator switches to a truncated series expansion of the full Theis well function instead, since Cooper-Jacob would no longer be reliable. The reported 'Calculation Method' output tells you which path was taken.

Time enters both the numerator and denominator relationships in u and in the drawdown formulas, so its effect isn't purely one-directional in this model — increasing t generally increases the log argument (2.25Tt / r²S) in Cooper-Jacob, which increases drawdown, but it also shrinks u, which can flip which formula is used. In practice, for a given well and aquifer, drawdown grows more slowly as pumping continues, which is exactly the physical behavior the logarithmic Cooper-Jacob term captures.

The calculator reports radius of influence as R = √(2.25Tt / S), the distance from the well at which the Cooper-Jacob formula's drawdown mathematically reaches zero. In real aquifers drawdown actually approaches zero asymptotically rather than hitting it at a sharp boundary, so treat this figure as a practical outer limit of measurable effect rather than a hard physical edge.

Both formulas assume a confined, homogeneous, isotropic aquifer of infinite lateral extent, a fully penetrating well, and a constant pumping rate. If your aquifer is unconfined, layered, bounded by a recharge or barrier boundary nearby, or the well only partially penetrates the aquifer, actual drawdown can deviate substantially from these idealized values — the calculator has no way to detect or correct for those conditions from the five inputs alone.