Subtopic: Planning, design and layout of surface and sub-surface drainage systems
Question Statement:
Tile drains in soil of permeability 2.3×10⁻³ mm/s. Impermeable stratum at 3.2 m below surface; water table to be kept ≥1.0 m below surface. Average drainage discharge 2.0 mm/day. Drains placed at 1.5 m below surface (equivalent depth = tile depth). The drain spacing in m is: [note: marked "Marks to All" in the official key owing to an ambiguity/error in the original question]
Options:
(A) 10.6
(B) 12.4
(C) 13.9
(D) 19.7
Official Answer Key:
MARKS TO ALL
Step-by-Step Solution & Explanation
• **Official Status:** Marked as **MARKS TO ALL (MTA)** in the official GATE 2012 AG answer key due to specification inconsistencies in drain boundary conditions (equivalent depth vs impermeable stratum depth).
• **Theoretical Hooghoudt Formulation:**
- Steady-state drain discharge $q = 2.0\text{ mm/day} = \frac{0.002}{86400}\text{ m/s} = 2.315 \times 10^{-8}\text{ m/s}$.
- Hydraulic conductivity $K = 2.3 \times 10^{-3}\text{ mm/s} = 2.3 \times 10^{-6}\text{ m/s}$.
- Water table mid-spacing elevation $m = 1.5 - 1.0 = 0.5\text{ m}$.
- Impermeable stratum distance below drains $d = 3.2 - 1.5 = 1.7\text{ m}$.
- Applying Hooghoudt equation $S^2 = \frac{8 K d m + 4 K m^2}{q}$ yields theoretical spacing between $12\text{ m}$ and $14\text{ m}$. Due to competing interpretation of equivalent depth $d_e = 1.5\text{ m}$, full marks were awarded to all candidates.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.