Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
A fully penetrating tube well in a 30 m deep confined aquifer with hydraulic conductivity of 4×10⁻⁴ m s⁻¹ has 50 L s⁻¹ discharge. The drawdown and radius of influence are 5 m and 250 m, respectively. Diameter of the tube well in mm is ______
Official Answer Key:
262.0 to 268.0
Step-by-Step Solution & Explanation
For steady radial flow to a fully penetrating well in a confined aquifer (Thiem equation): Q = 2π×T×s / ln(R/r_w), where T = K×b is transmissivity, s = drawdown, R = radius of influence, r_w = well radius. T = 4×10⁻⁴×30 = 0.012 m²/s. Rearranging: r_w = R×exp[−2πTs/Q] = 250×exp[−2π×0.012×5/0.05] = 250×exp(−7.540) = 250×0.000531 = 0.1327 m. Diameter = 2×r_w = 0.2655 m = 265.5–265.7 mm, within the accepted band 262.0–268.0.
Section 5 — Irrigation and Drainage Engineering
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