GATE 2023 AG – Question 62
A .30 m diameter well fully penetrates an unconfined aquifer initially 40 m saturated. After eight hours pumping.03 m³/s, observation drawdowns are3 m at 20 m radius and 2 m at 50 m. Find pumping-well drawdown in m, to one decimal;π=3.14.
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Correct answer: 8.6 to 8.8
Explanation
Using the steady unconfined Dupuit–Thiem approximation, observation heads are37 and 38 m. Squared head varies linearly with ln r: $$h_w^2=37^2-\frac{38^2-37^2}{\ln(50/20)}\ln(20/.15)=968.51\ldots.$$ This gives $h_w\approx31.1209$ m and drawdown **8.9 m**. The official accepted range is 8.6–8.8 m, which does not contain that rounded result. Transient modeling would need storage/time information beyond the supplied observation relation. Official grading is retained with this calculation/key discrepancy explicit.