Question Bank • QB_EXP_IDE_STW_002 MCQ • 1 Mark

Section 5: Irrigation and Drainage Engineering

Steady Flow to Wells: Confined & Unconfined Aquifers

Subtopic: Dupuit equation for unconfined aquifer

Question Statement:

Dupuit's steady-state discharge equation for a fully penetrating well in an unconfined aquifer between radial distances $r_1$ and $r_2$ with phreatic heights $h_1$ and $h_2$ is:

Options:

  • (A) $Q = \frac{\pi K (h_2^2 - h_1^2)}{\ln(r_2 / r_1)}$
  • (B) $Q = \frac{2 \pi K b (h_2 - h_1)}{\ln(r_2 / r_1)}$
  • (C) $Q = \frac{\pi K (h_2 - h_1)^2}{\ln(r_2 / r_1)}$
  • (D) $Q = \frac{2 \pi K (h_2^2 - h_1^2)}{\log_{10}(r_2 / r_1)}$

Answer Key:

A

Step-by-Step Solution & Explanation

Integrating Darcy's law $Q = 2 \pi r h K \frac{dh}{dr}$ from $r_1$ to $r_2$ yields Dupuit's formula: $Q = \frac{\pi K (h_2^2 - h_1^2)}{\ln(r_2 / r_1)}$
← Previous (QB_EXP_IDE_STW_013) Next (QB_EXP_IDE_STW_003) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test