Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
Water is recharged to an aquifer through a well of 200 mm diameter penetrating up to the base of the aquifer. The hydraulic conductivity of the aquifer is 19 m d⁻¹. During recharge, the water level in the well is 32 m from the base of the aquifer. A constant height of 27 m above the same base is obtained at a distance of 200 m from the well.
Options:
(A) 18.2
(B) 25.2
(C) 28.8
(D) 30.5
Official Answer Key:
A
Step-by-Step Solution & Explanation
For steady radial flow into a confined aquifer (Thiem/Dupuit form, reversed for recharge): Q = 2πKb(hw−h0)/ln(R/rw), where b=20 m (aquifer thickness), hw=32 m, h0=27 m, R=200 m, rw=0.1 m. Q = 2π×19×20×(32−27)/ln(200/0.1) = 2π×19×20×5/ln(2000) = 11,938/7.601 = 1570.6 m³/day. Converting: 1570.6 m³/day × 1000 L/m³ / 86,400 s/day = 18.18 L/s ≈ 18.2 L/s, matching option (A).
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