Pumping test (confined aquifer) – compute soil permeability from observed drawdowns In a constant-discharge pumping test, a discharge of 2.91 litres/s is maintained. Observation wells at r1 = 3 m and r2 = 6.184 m from the pumped well show steady drawdowns s1 = 2.6 m and s2 = 0.3 m, respectively. If the aquifer thickness (overall depth) b = 16 m, estimate the coefficient of permeability k (cm/s), assuming confined, steady radial flow.

Introduction / Context:
Pumping tests allow estimation of aquifer properties by relating discharge, drawdown, and geometry. For confined aquifers under steady conditions, the Thiem equation connects discharge to transmissivity and observed heads (or drawdowns) at different radii.

Given Data / Assumptions:

• Constant discharge Q = 2.91 L/s = 0.00291 m^3/s.
• Observation radii r1 = 3 m, r2 = 6.184 m.
• Drawdowns s1 = 2.6 m, s2 = 0.3 m.
• Confined aquifer of thickness b = 16 m; transmissivity T = k * b.
• Steady, horizontal, radial flow; Dupuit–Thiem assumptions apply.

Concept / Approach:
Thiem (confined) equation in natural log form: Q = 2 * π * k * b * (s1 - s2) / ln(r2 / r1). Solve for k and convert to cm/s. The larger drawdown near the well and the logarithmic radial term govern the estimate.

Step-by-Step Solution:
Compute ln(r2/r1) = ln(6.184 / 3) ≈ ln(2.0613) ≈ 0.724.Compute numerator factor: 2 * π * b * (s1 - s2) = 6.283 * 16 * (2.6 - 0.3) = 6.283 * 16 * 2.3 ≈ 231.2.Rearrange for k: k = Q * ln(r2/r1) / [2 * π * b * (s1 - s2)] = 0.00291 * 0.724 / 231.2 ≈ 9.1 × 10^-6 m/s.Convert to cm/s: 9.1 × 10^-6 m/s × 100 = 9.1 × 10^-4 cm/s ≈ 0.001 cm/s.

Verification / Alternative check:
Check order of magnitude: Typical sandy aquifers have k from 10^-4 to 10^-2 cm/s; the computed 10^-3 cm/s is plausible for fine sand/silty sand, validating the result.

Why Other Options Are Wrong:

• 0.0005 cm/s and 0.002 cm/s bracket the computed value but do not match the calculation.
• 0.01 cm/s is an order of magnitude too high for the given drawdown behavior at small radii.

Common Pitfalls:
Using (s1/s2) instead of (s1 − s2) for confined Thiem, or forgetting to convert litres/s to m^3/s and m/s to cm/s.

Final Answer:
0.001 cm/s