---
title: "Location of closed tile drains"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:closed-tile-drain-location-root15"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/closed-tile-drain-location-root15
site: BCT Engineering
---

# Location of closed tile drains

Irrigation and Drainage Engineering · Chapter 9: Water Logging and Drainage

- Asked in: 2078 Poush
- Video: [Tile Drains](https://www.youtube.com/watch?v=GiIAcXWM1KQ) — Coordinator cas
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/closed-tile-drain-location-root15
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

Determine the location of closed tile drains below ground for the following data: Root zone depth = 1.5 m, capillary rise in soil = 0.3 m, coefficient of permeability of soil = 1.5 × 10⁻⁴ m/s, drainage capacity = 0.11 m³/s/km², spacing of drains = 200 m, and depth of impervious stratum below ground = 10.0 m.

## Short answer

Using Donnan's formula, permissible water table is 1.8 m below ground. With impervious layer at 10 m, drain height above impervious layer is 7.74 m, giving drain depth 2.26 m below ground.

## Answer

The drains must be placed so that the water table, midway between the drains, stays below the root zone plus the capillary rise. The depth of the drain then follows from Donnan's formula.

#### Data
- Root zone depth = 1.5 m, capillary rise = 0.3 m
- $K$ = 1.5 × 10⁻⁴ m/s; drain spacing $S$ = 200 m; depth of impervious layer = 10 m below ground
- Drainage capacity = 0.11 m³/s/km² = 0.11/10⁶ = $1.10\times10^{-7}$ m/s

#### Step 1: Highest permissible water table
Depth of the water table below ground at the mid-point = 1.5 + 0.3 = 1.8 m. Its height above the impervious layer:

$$
b = 10 - 1.8 = 8.2\ \text{m}
$$

#### Step 2: Height of the drain above the impervious layer
$$
S^2=\frac{4K(b^2-a^2)}{q} \quad\Rightarrow\quad a^2 = b^2-\frac{qS^2}{4K}
$$

$$
\begin{aligned} a^2 &= 8.2^2-\frac{1.10\times10^{-7}\times200^2}{4\times1.5\times10^{-4}} \\ &= 67.24-7.333 = 59.907 \\ a &= 7.740\ \text{m} \end{aligned}
$$

#### Step 3: Depth of drain below ground
$$
\text{Depth} = 10 - 7.740 = 2.26\ \text{m}
$$

**Answer: lay the drains about 2.26 m (say 2.3 m) below the ground surface, i.e. 7.74 m above the impervious layer.** The water table at the mid-point then stays 1.8 m below the surface, just below the root zone and capillary fringe.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How deep is the highest permissible water table at mid-point?
   A. 1.5 + 0.3 = 1.8 m below ground (root zone plus capillary rise)
   B. 1.5 m
   C. 0.3 m
   D. 1.5 - 0.3 = 1.2 m
   Answer: A. The water table must stay below the root zone and its capillary fringe. (Key point: Water table limit)

2. What is b and what must be found?
   A. b = 1.8 m; unknown S
   B. b = 10 - 1.8 = 8.2 m; unknown a, from a^2 = b^2 - qS^2/(4K)
   C. b = 10 m; unknown K
   D. b = 8.2 m; unknown q
   Answer: B. Spacing is given, so Donnan's formula is rearranged for the drain height a. (Key point: Heights)

3. How is 0.11 m3/s/km2 converted?
   A. Multiply by 10^6
   B. Divide by 10^3
   C. Divide by 10^6 m2 per km2: 1.10 x 10^-7 m/s
   D. Use it as 0.11 m/s
   Answer: C. 1 km2 = 10^6 m2, so q = 1.1e-7 m/s. (Key point: Drainage capacity)

4. What drain depth results?
   A. About 7.74 m below ground
   B. About 1.8 m below ground
   C. About 0.26 m below ground
   D. About 2.26 m below ground (a = 7.74 m)
   Answer: D. a^2 = 67.24 - 7.333 = 59.907, a = 7.74 m, so depth = 10 - 7.74 = 2.26 m. (Key point: Drain depth)

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