GATE 2026 CE (CE1) – Question 53
A fully-penetrating well of 20 cm diameter is provided in an unconfined aquifer. The height of the ground water table is 30 m from the bottom of the aquifer. After a long period of pumping at a rate of 63 m$^3$/s, the drawdown in the observation wells at 10 m and 100 m from the pumped well is 12 m and 11 m, respectively. The transmissibility (in m$^2$/s) of the aquifer is ______ (*rounded off to one decimal place*).
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Correct answer: 37.21 to 37.59
Explanation
The water depths in the two observation wells are $h_1 = 30 - 12 = 18$ m and $h_2 = 30 - 11 = 19$ m. For an unconfined aquifer, $Q = \frac{\pi K(h_2^2 - h_1^2)}{\ln(r_2/r_1)}$, so $K = \frac{63 \times \ln 10}{\pi(361 - 324)} = 1.248$ m/s. The transmissibility is $T = K \times 30 = 37.4$ m$^2$/s.