Subtopic: Hooghoudt spacing for drains on impermeable barrier
Question Statement:
Subsurface pipe drains are laid directly on an impermeable horizontal floor ($d = 0$). The hydraulic conductivity of the soil is $K = 1.0\text{ m/day}$ and the steady drainage design recharge rate is $q = 5\text{ mm/day}$ ($0.005\text{ m/day}$). To prevent the water table at midpoint from rising more than $h = 0.80\text{ m}$ above the drains, the required drain spacing $S$ is ________ $\text{m}$ (round off to one decimal place).
Answer Key:
22.6
Step-by-Step Solution & Explanation
When drains rest on the impermeable layer, Hooghoudt's equation simplifies to:
$S^2 = \frac{4 K h^2}{q}$
Given $K = 1.0\text{ m/day}$, $h = 0.80\text{ m}$, $q = 0.005\text{ m/day}$:
$S^2 = \frac{4 \times 1.0 \times (0.80)^2}{0.005} = \frac{4 \times 0.6400}{0.005} = 512.0\text{ m}^2$
$S = \sqrt{512.0} = 22.6\text{ m}$