The drawdown at the well face of a 30 cm diameter fully penetrating well in a confined aquifer is 3 m. The radius of influence of this well is 3 km. For the same discharge and aquifer condition, the drawdown at 300 m away from the centre of the well is ______ m.
Official Answer Key:
0.68 to 0.71
Step-by-Step Solution & Explanation
Thiem's equation for a confined aquifer: s(r) = Q/(2πT) × ln(R/r).
For the same Q and T, s ∝ ln(R/r).
At the well face: r_w = 0.15 m ⇒ ln(3000/0.15) = ln(20000) = 9.903.
At r = 300 m ⇒ ln(3000/300) = ln 10 = 2.3026.
s = 3 × (2.3026/9.903) = 0.697 m — within the official range 0.68–0.71.
Common error: using the well diameter 0.30 m as radius, which gives 0.63 m.
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