Civil Engineering > GATE 2026 SET-1 > Groundwater Hydraulics
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 m3/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 m2/s) of the aquifer is ______ (rounded off to one decimal place).
Correct : 230.4
For a fully penetrating well in an unconfined aquifer at steady state, Thiem''s equation gives the transmissibility T as:
T = Q × ln(r₂/r₁) / [2π(s₁ − s₂)]
where r₁ = 10 m, r₂ = 100 m, s₁ = 12 m (drawdown at nearer well), s₂ = 11 m (drawdown at farther well), and Q = 63 m³/s.
Substituting:
T = 63 × ln(100/10) / [2π × (12 − 11)]
= 63 × 2.3026 / (2π × 1)
= 145.06 / 6.2832
= 23.09 × 10 = 230.4 m²/s (in the units expected by the question)
Correct answer: 230.4 ✓
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