Allied & ICAR Exam Bank • ALLIED_1202NAT • 2 Marks
Section 5: Irrigation and Drainage Engineering
Agricultural Drainage and Salinity
Subtopic: Hooghoudt's Drainage Equation
Question Statement:
In a subsurface drainage system on an agricultural field with an impermeable barrier at a large depth, the hydraulic conductivity of the soil is $K = 1.2\text{ m/day}$ and the steady design drainage recharge rate is $q = 0.003\text{ m/day}$. If the maximum water table rise above the drain line at mid-spacing is $h = 1.0\text{ m}$ and equivalent depth is $d = 2.0\text{ m}$, the drain spacing $L$ (in m) using Hooghoudt's equation is:
Answer Key:
89.4
Step-by-Step Solution & Explanation
$q L^2 = 8 K d h + 4 K h^2 = 8(1.2)(2.0)(1.0) + 4(1.2)(1.0)^2 = 19.2 + 4.8 = 24.0$. $L^2 = \frac{24.0}{0.003} = 8000 \implies L = \sqrt{8000} \approx 89.44\text{ m}$.