Question Bank • QB_IDE_DRN_002 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Agricultural Drainage

Subtopic: Planning, design and layout of surface and sub-surface drainage systems

Question Statement:

Parallel agricultural tile drains are placed at spacing $S = 40\text{ m}$ directly upon an impermeable substratum ($d = 0$). Soil hydraulic conductivity is $K = 0.80\text{ m/day}$ and the steady design drainage flux is $q = 0.004\text{ m/day}$. Using Hooghoudt's equation ($S^2 = \frac{4 K h^2}{q}$), the maximum mid-drain water table elevation $h$ above the drain level in metres is ________ (round off to 2 decimal places).

Answer Key:

1.41

Step-by-Step Solution & Explanation

For drains placed directly on the impermeable floor ($d = 0$): $S^2 = \frac{4 K h^2}{q}$ Given: • $S = 40\text{ m} \implies S^2 = 1600$ • $K = 0.80\text{ m/day}$ • $q = 0.004\text{ m/day}$ $1600 = \frac{4 \times 0.80 \times h^2}{0.004} = \frac{3.20}{0.004} h^2 = 800 h^2$ $h^2 = \frac{1600}{800} = 2.0$ $h = \sqrt{2.0} \approx 1.4142\text{ m} \approx 1.41\text{ m}$
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