---
title: "Tile drain spacing with drainage coefficient 0.012"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-spacing-drainage-coeff-0012"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-spacing-drainage-coeff-0012
site: BCT Engineering
---

# Tile drain spacing with drainage coefficient 0.012

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

- Asked in: 2062 Kartik (old course), 8 marks
- 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/tile-drain-spacing-drainage-coeff-0012
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

Find the spacing of tile drains with following data: annual rainfall = 900 mm; drainage coefficient = 0.012; depth of impervious layer below GL = 9 m; depth of tile drains below GL = 1.6 m; depth of highest position of water table below GL = 1.2 m; coefficient of permeability = 0.012 cm/sec.

## Short answer

Use Donnan's formula. Drainage coefficient 0.012 means 1.2% of900 mm in24 h so q=1.25×10⁻⁷ m/s; K=0.012 cm/s=1.2×10⁻⁴ m/s, a=7.4 m, b=7.8 m. Spacing S ≈152.8 m (say 150 m).

## Answer

Tile drain spacing follows from Donnan's formula for steady flow to parallel drains above an impervious layer:

$$
S=\sqrt{\frac{4K\,(b^2-a^2)}{q}}
$$

The drainage coefficient is given as a pure number, 0.012, so it is taken as the fraction of the annual rainfall to be drained in 24 hours (1.2 %, as in the usual "x % of annual rainfall in 24 h" problems). This uses the given annual rainfall of 900 mm.

#### Data
- $q$ = 0.012 × 0.900 m = 0.0108 m/day = 0.0108/86400 = $1.25\times10^{-7}$ m/s
- $K$ = 0.012 cm/s = 0.00012 m/s
- $a$ = 9 − 1.6 = 7.4 m (drain above the impervious layer)
- $b$ = 9 − 1.2 = 7.8 m (highest water table above the impervious layer)

#### Calculation
$$
\begin{aligned} S^2 &= \frac{4\times0.00012\times(7.8^2-7.4^2)}{1.25\times10^{-7}} \\ &= \frac{4\times0.00012\times6.08}{1.25\times10^{-7}} = 23347\ \text{m}^2 \\ S &= 152.8\ \text{m} \end{aligned}
$$

Note: if the drainage coefficient is instead read as a depth of 0.012 m/day (12 mm/day), then $q = 1.389\times10^{-7}$ m/s, $S^2$ = 21012 m² and $S$ ≈ 145 m.

**Answer: spacing of the tile drains ≈ 152.8 m (say 150 m).**

## Check yourself

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

1. How is the drainage coefficient 0.012 used?
   A. As q directly (0.012 m/day), so the annual rainfall of 900 mm is not needed
   B. It multiplies 900 mm to give q
   C. It is the permeability
   D. It is a percent of rainfall drained in 24 hours
   Answer: A. The drainage coefficient is the drainage rate itself, taken as 12 mm/day. (Key point: Given drainage coefficient)

2. What is q in m/s?
   A. 1.389 x 10^-5 m/s
   B. 0.012/86400 = 1.389 x 10^-7 m/s
   C. 0.012 m/s
   D. 1.2 x 10^-4 m/s
   Answer: B. Divide m/day by 86400 seconds per day. (Key point: q in SI units)

3. What are K, a and b?
   A. K = 1.2 x 10^-2 m/s, a = 7.4 m, b = 7.8 m
   B. K = 1.2 x 10^-4 m/s, a = 1.6 m, b = 1.2 m
   C. K = 1.2 x 10^-4 m/s, a = 7.4 m, b = 7.8 m
   D. K = 1.2 x 10^-4 m/s, a = 7.8 m, b = 7.4 m
   Answer: C. 0.012 cm/s = 1.2e-4 m/s; a = 9 - 1.6, b = 9 - 1.2. (Key point: K and heights)

4. What is the spacing?
   A. About 14.5 m
   B. About 45 m
   C. About 21012 m
   D. About 145 m
   Answer: D. S^2 = 4 x 1.2e-4 x 6.08/1.389e-7 = 21012, so S = 145 m. (Key point: Spacing)

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