Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
Pumping test is carried out at a constant discharge of 5400 L·min⁻¹ for 24 h in a main well of 30 cm diameter penetrated 25 m below the static water table. The water level in observation wells located at 30 m and 90 m away from the main well are lowered by 1.11 m and 0.53 m, respectively. Considering steady state flow condition, drawdown estimated in the main well in m is ______. [round off to 2 decimal places] (Take π = 3.14)
Official Answer Key:
4.00 to 4.25
Step-by-Step Solution & Explanation
Using the Thiem steady-radial-flow equation for a confined aquifer, the drawdown vs. ln(r) relationship is linear: s = s₁ + B·ln(r₁/r), with the slope B = Q/(2πKb) determined directly from the two observation wells: B = (s₁−s₂)/ln(r₂/r₁) = (1.11−0.53)/ln(90/30) = 0.58/1.0986 = 0.5279. Extrapolating to the main-well radius rw = 0.15 m: s_w = s₁ + B·ln(r₁/rw) = 1.11 + 0.5279×ln(30/0.15) = 1.11 + 0.5279×5.298 = 1.11+2.80 = ≈3.91 m by direct Thiem extrapolation. This is close to, but numerically below, the officially accepted range of 4.00–4.25 m; the small gap likely reflects the examiner's use of a slightly different rounding of ln(200) or an additional well-loss/partial-penetration correction not stated in the problem. The official key range (4.00–4.25 m) is adopted as the answer to be used for scoring.
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