Question Bank • QB_DIAG_S5_001 MSQ • 2 Marks

Section 5: Irrigation and Drainage Engineering

Agricultural Drainage

Subtopic: Drainage coefficient

Question Statement:

Referring to the subsurface tile drainage cross-section shown in the accompanying diagram, parallel pipe drains are installed at spacing $S$ above an impermeable layer. The hydraulic head midway between the drains is $m$ and the steady drainage recharge rate is $q$. Which of the following statements regarding Hooghoudt's equation $S^2 = \frac{8 K_2 d m + 4 K_1 m^2}{q}$ are TRUE?

Options:

  • (A) $K_1$ is the hydraulic conductivity of the soil layer above the drain level
  • (B) $K_2$ is the hydraulic conductivity of the soil layer below the drain level
  • (C) The equivalent depth $d$ is smaller than the actual barrier depth $D$ to compensate for radial flow convergence near the drains
  • (D) When the water table is below the drain level ($m < 0$), subsurface drainage discharge continues to increase

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

1. $K_1$ is the conductivity of soil above the plane of the drains ($m$ zone). (Statement A True) 2. $K_2$ is the conductivity of soil below drain level down to impermeable barrier. (Statement B True) 3. The Hooghoudt equivalent depth $d < D$ mathematically accounts for extra energy loss due to convergence of flow lines entering finite-radius drain pipes. (Statement C True) 4. If water table falls below the drains, gravitational drainage stops ($q = 0$). (Statement D False)
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