Theis Equation Calculator

by Glenn M. Duffield, President, HydroSOLVE, Inc.

Drawdown around a pumping well discharging from a nonleaky confined aquifer of infinite extent may be computed with the Theis Equation (Theis 1935):

$s = \frac{Q}{4 π T} w (u) (1)$

$w(u) = -0.5772 - ln(u) + u - \frac{u^{2}}{2 \cdot 2!} + \frac{u^{3}}{3 \cdot 3!} - \frac{u^{4}}{4 \cdot 4!} + \cdot\cdot\cdot (2)$

$u = \frac{r^{2} S}{4 T t} (3)$

where s is drawdown [L], Q is pumping rate [L³/T], r is radial distance from pumping well to observation well [L], S is storativity [-], T is transmissivity [L²/T] and t is elapsed time since start of pumping [T].