GATE 2025 CE (CE2) – Question 58
A 60 cm diameter well completely penetrates a confined aquifer of permeability $5 \times 10^{-4}$ m/s. The length of the strainer (spanning the entire thickness of the aquifer) is 10 m. The drawdown at the well under steady state pumping is 1.0 m. Assume that the radius of influence for this pumping is 300 m.
The discharge from the well (in litres per minute) is ______ (round off to the nearest integer).
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Correct answer: 273
Explanation
For a well in a confined aquifer (Thiem's equation) $Q = \frac{2\pi KTs_w}{\ln(R/r_w)}$. With $K = 5 \times 10^{-4}$ m/s, $T = 10$ m, $s_w = 1$ m, $R = 300$ m and $r_w = 0.3$ m: $Q = \frac{2\pi \times 5 \times 10^{-4} \times 10 \times 1}{\ln 1000} = \frac{0.031416}{6.9078} = 4.548 \times 10^{-3}$ m³/s, which is $4.548 \times 10^{-3} \times 60000 = 273$ litres per minute.