A 40 cm diameter tubewell in a 10 m thick confined aquifer (K=25 m/day); piezometric surface 40 m above impervious stratum at radius of influence 500 m; drawdown = 30 m. If aquifer thickness is doubled and well diameter halved (other parameters unchanged), find the change in discharge. [π=3.14]
Options:
(A) Increased by 83.72%
(B) Decreased by 83.72%
(C) Increased by 82.28%
(D) Decreased by 82.28%
Official Answer Key:
A
Step-by-Step Solution & Explanation
Confined aquifer discharge (Thiem): Q ∝ b/ln(R/rw), where b=aquifer thickness, rw=well radius. Original: b₁=10 m, rw₁=0.20 m ⇒ ln(500/0.20)=7.824 ⇒ Q₁∝10/7.824=1.278. New: b₂=20 m, rw₂=0.10 m ⇒ ln(500/0.10)=8.517 ⇒ Q₂∝20/8.517=2.348. % change = (2.348−1.278)/1.278×100 ≈ 83.72% increase.
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