GATE 2024 CE (CE1) – Question 35
A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the drawdowns in two observation wells located at 10 m and 100 m from the pumping well are 5 m and 1 m, respectively. The corresponding pumping rate (in m$^3$/day) from the well is _____________ (rounded off to 2 decimal places).
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Correct answer: 1846.27 to 1864.83
Explanation
For a well in an unconfined aquifer, $Q = \frac{\pi K(h_2^2 - h_1^2)}{\ln(r_2/r_1)}$. The water depths in the observation wells are $h_1 = 20 - 5 = 15$ m at $r_1 = 10$ m and $h_2 = 20 - 1 = 19$ m at $r_2 = 100$ m. So $Q = \frac{\pi \times 10 \times (361 - 225)}{\ln 10} = \frac{4272.57}{2.3026} = 1855.55$ m³/day.