Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
A 0.30 m diameter well penetrates an unconfined aquifer with a saturated depth of 40 m. After 8 hours of pumping at a steady rate of 0.03 m³ s⁻¹, the drawdown in two observation wells located at 20 m and 50 m away from the pumping well are found to be 3 m and 2 m, respectively. The drawdown in the pumping well in m is ___________ (rounded off to 1 decimal place, Consider π = 3.14).
Official Answer Key:
8.6 to 8.8
Step-by-Step Solution & Explanation
Thiem equation for steady radial flow in an unconfined aquifer: Q = πK(h₂²−h₁²)/ln(r₂/r₁), with h = saturated thickness at radius r (h = b−s, b=40 m).
At r₁=20 m: h₁ = 40−3 = 37 m. At r₂=50 m: h₂ = 40−2 = 38 m.
K = Q×ln(r₂/r₁)/[π(h₂²−h₁²)] = 0.03×ln(2.5)/[π(38²−37²)] = 0.03×0.9163/[π×75] = 0.02749/235.6 = 1.167×10⁻⁴ m/s.
Apply Thiem again between the near observation well (r₁=20, h₁=37) and the pumping well (r_w=0.15 m):
h_w² = h₁² − Q·ln(r₁/r_w)/(πK) = 37² − 0.03×ln(20/0.15)/(π×1.167×10⁻⁴) = 1369 − 0.03×4.893/0.0003665 = 1369−400.4 = 968.6
h_w = √968.6 = 31.12 m → drawdown s_w = 40−31.12 = 8.88 m. This is close to — but slightly above — the official range (8.6–8.8 m); the small residual gap is likely attributable to intermediate rounding differences (e.g. of π or K) in the official solution rather than a different method, since the standard two-observation-well Thiem approach is the well-established procedure for this exact problem type.
Section 6 — Agricultural Process Engineering
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