Question Bank • QB_EXP_IDE_UNS_002 MCQ • 1 Mark

Section 5: Irrigation and Drainage Engineering

Unsteady Flow to Wells: Theis & Cooper-Jacob Solutions

Subtopic: Condition of validity for Cooper-Jacob approximation

Question Statement:

The Cooper-Jacob simplified straight-line method is valid only when the parameter $u = \frac{r^2 S}{4 T t}$ satisfies:

Options:

  • (A) $u \le 0.01$ (or $u \le 0.05$ with minimal error)
  • (B) $u \ge 1.0$
  • (C) $u = 0.5$
  • (D) $u \ge 10.0$

Answer Key:

A

Step-by-Step Solution & Explanation

The Theis well function series expansion is $W(u) = -0.5772 - \ln u + u - \frac{u^2}{2 \cdot 2!} + \dots$. When $u \le 0.01$, terms beyond the logarithmic term become negligibly small (
lt; 1\%$ error), allowing the Cooper-Jacob approximation.
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