Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
A well fully penetrates a 30 m thick confined aquifer. After a long period of pumping at a constant rate of 0.06 m³·s⁻¹, drawdowns of 3.6 m and 2.0 m are found at distances 60 m and 120 m away from the well respectively. The hydraulic conductivity of the aquifer is n × 10⁻⁴ m·s⁻¹. The value of n is ________ (Rounded off to two decimal places)
Official Answer Key:
1.36 to 1.39
Step-by-Step Solution & Explanation
For steady radial flow to a fully penetrating well in a confined aquifer of thickness b, Thiem’s equation applies:
Q = 2πkb(s₁ − s₂)/ln(r₂/r₁)
where s₁, s₂ are drawdowns at radii r₁, r₂ (drawdown decreases outward).
Rearranging for k:
k = Q ln(r₂/r₁)/[2πb(s₁ − s₂)]
Substituting Q = 0.06 m³·s⁻¹, r₂/r₁ = 120/60 = 2, b = 30 m, (s₁ − s₂) = 3.6 − 2.0 = 1.6 m:
k = (0.06 × ln 2)/(2π × 30 × 1.6)
= (0.06 × 0.6931)/301.59
= 0.041589/301.59
= 1.379 × 10⁻⁴ m·s⁻¹
Hence n = 1.38.
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