Question Bank • QB_IDE_EXP_023 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:

Using Hooghoudt's steady-state drainage equation $S^2 = \frac{4 K_1 m^2 + 8 K_2 d m}{q}$, compute the required drain spacing $S$ in meters for an agricultural field with hydraulic conductivity of upper layer $K_1 = 1.0\text{ m/day}$, lower layer $K_2 = 1.0\text{ m/day}$, equivalent depth $d = 2.0\text{ m}$, water table height above drains midway $m = 1.0\text{ m}$, and steady recharge rate $q = 0.005\text{ m/day}$. The drain spacing $S$ in meters is ________ (round off to nearest integer).

Answer Key:

63

Step-by-Step Solution & Explanation

Hooghoudt's equation: $S^2 = \frac{4 K_1 m^2 + 8 K_2 d m}{q}$ Given: • $K_1 = 1.0\text{ m/day}$ • $K_2 = 1.0\text{ m/day}$ • $m = 1.0\text{ m}$ • $d = 2.0\text{ m}$ • $q = 0.005\text{ m/day}$ 1. Numerator: $4(1.0)(1.0)^2 + 8(1.0)(2.0)(1.0) = 4.0 + 16.0 = 20.0$ 2. Denominator: $q = 0.005$ $S^2 = \frac{20.0}{0.005} = 4000$ $S = \sqrt{4000} \approx 63.25\text{ m} \approx 63\text{ m}$
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