Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
In Cooper-Jacob's approximation for unsteady radial flow to a well ($s = \frac{Q}{4 \pi T} \ln\frac{2.25 T t}{r^2 S}$), the approximation is valid only when parameter $u = \frac{r^2 S}{4 T t}$ is:
Options:
(A) $u < 0.01$ (or $u < 0.05$)
(B) $u > 1.0$
(C) $u = 1.0$
(D) $u > 10.0$
Answer Key:
A
Step-by-Step Solution & Explanation
The Cooper-Jacob simplified straight-line logarithmic method truncates the infinite Theis well function series after the second term. This truncation introduces negligible error (lt; 1\%$) only when the argument $u = \frac{r^2 S}{4 T t}$ is small, typically $u \le 0.01$ (and reasonably up to $0.05$).