Question Bank • QB_IDE_002 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Groundwater Hydrology

Subtopic: Steady and unsteady flow in confined and unconfined aquifers

Question Statement:

A fully penetrating well of radius $0.20\text{ m}$ taps a confined aquifer of thickness $20\text{ m}$. Hydraulic conductivity of the aquifer is $15\text{ m/day}$. During pumping, the steady state drawdowns measured at radial distances of $10\text{ m}$ and $50\text{ m}$ from the well centre are $3.0\text{ m}$ and $1.0\text{ m}$, respectively. The steady pumping discharge $Q$ in $\text{m}^3\text{/day}$ is ________ (round off to 1 decimal place). Take $\pi = 3.1416$.

Answer Key:

1172.5

Step-by-Step Solution & Explanation

For steady radial flow in a confined aquifer (Thiem's equation): $Q = \frac{2 \pi K b (s_1 - s_2)}{\ln(r_2 / r_1)}$ Where: • $K = 15\text{ m/day}$ • Confined aquifer thickness $b = 20\text{ m}$ • Drawdown $s_1 = 3.0\text{ m}$ at $r_1 = 10\text{ m}$ • Drawdown $s_2 = 1.0\text{ m}$ at $r_2 = 50\text{ m}$ • $s_1 - s_2 = 3.0 - 1.0 = 2.0\text{ m}$ • $\ln(r_2/r_1) = \ln(50/10) = \ln(5) \approx 1.6094$ $Q = \frac{2 \times 3.1416 \times 15 \times 20 \times 2.0}{1.6094} = \frac{3769.9}{1.6094} \approx 1172.5\text{ m}^3\text{/day}$
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