Question Bank • QB_DIAG_S5_002 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Wells and Pumps

Subtopic: Types of wells

Question Statement:

Referring to the unconfined aquifer steady-state pumping well radial flow diagram shown below, the initial saturated thickness of the aquifer is $H = 25\text{ m}$. At steady discharge, the water depth at the well face ($r_w = 0.15\text{ m}$) is $h_w = 20\text{ m}$. The radius of influence is $R = 300\text{ m}$. If the hydraulic conductivity is $K = 15\text{ m/day}$, the steady discharge $Q$ of the well is ________ $\text{m}^3\text{/day}$ (round off to the nearest integer).

Answer Key:

1395

Step-by-Step Solution & Explanation

For an unconfined aquifer under steady-state radial flow, Dupuit-Thiem equation is: $Q = \frac{\pi K (H^2 - h_w^2)}{\ln(R / r_w)}$ Given: - $K = 15\text{ m/day}$ - $H = 25\text{ m} \implies H^2 = 625\text{ m}^2$ - $h_w = 20\text{ m} \implies h_w^2 = 400\text{ m}^2 \implies H^2 - h_w^2 = 225\text{ m}^2$ - $R = 300\text{ m}, r_w = 0.15\text{ m} \implies R/r_w = 2000$ - $\ln(2000) \approx 7.6009$ $Q = \frac{3.14159 \times 15 \times 225}{7.6009} = \frac{10602.87}{7.6009} \approx 1394.95\text{ m}^3\text{/day}$ Rounded to the nearest integer: $1395\text{ m}^3\text{/day}$.
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