In agricultural land drainage design, which of the following statements regarding the Drainage Coefficient ($q$) and Hooghoudt's equation are TRUE?
Options:
(A) Drainage coefficient is defined as the depth of water to be removed from the drainage area in a 24-hour period (expressed in $\text{mm/day}$ or $\text{m/day}$)
(B) Hooghoudt's equation assumes steady-state recharge with horizontal flow below the drain level and radial flow approaching the drains
(C) In Hooghoudt's equation $S^2 = \frac{8 K_2 d m + 4 K_1 m^2}{q}$, the equivalent depth $d$ accounts for radial flow resistance near the drain pipes
(D) Doubling the drainage coefficient $q$ while maintaining the same water table elevation requires doubling the drain spacing $S$
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Drainage coefficient $q$ is the design rate of water removal per unit drainage area per day (typically $5-25\text{ mm/day}$). (Statement A True)
2. Hooghoudt's equation is derived under steady-state conditions using Dupuit-Forchheimer horizontal flow assumptions adjusted for radial convergence. (Statement B True)
3. The equivalent depth parameter $d$ replaces the actual distance to the impervious floor $D$ to account for radial flow resistance into finite pipe perforations. (Statement C True)
4. From $S^2 \propto \frac{1}{q}$, doubling $q$ requires reducing drain spacing by $\frac{1}{\sqrt{2}} \approx 0.707$, not doubling it. (Statement D False)