---
title: "Tile drain spacing: rainfall 80 cm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-rainfall-80cm-impervious9"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-80cm-impervious9
site: BCT Engineering
---

# Tile drain spacing: rainfall 80 cm

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

- Asked in: 2080 Chaitra, 6 marks
- Video: [Unit:7 | Water logging & Drainage | Numerical | Irrigation Engineering | BE Civil | TU,PU,KU,PoU |](https://www.youtube.com/watch?v=csVF08cgXmc) — Prashant YT
- 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-rainfall-80cm-impervious9
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

In a tile drainage system, the drains are laid with their centers 1.5 m below the ground level. The impervious layer is 9.0 m below the ground level and the average annual rainfall in the area is 80 cm. If 1% of the annual rainfall is to be drained in 24 hours to keep the highest position of the water table to 1 m below ground level, determine the spacing of the drain pipes. The coefficient of permeability is 0.001 cm/sec.

## Short answer

Donnan's formula: with 80 cm = 800 mm, 1% in 24 h gives q=9.259×10⁻⁸ m/s, a=9−1.5=7.5 m, b=9−1=8 m, K=1×10⁻⁵ m/s. Spacing S ≈ 57.9 m (say 58 m).

## Answer

Tile drain spacing is found from Donnan's (Dupuit–Forchheimer) formula for steady flow towards parallel drains over an impervious layer:

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

where $S$ = spacing, $K$ = permeability, $q$ = drainage rate (discharge per unit area), $b$ = height of the water table above the impervious layer at the mid-point, $a$ = height of the drain above the impervious layer.

#### Data
- Depth of impervious layer = 9 m, depth of drain = 1.5 m, depth of highest water table = 1 m (all below ground)
- $K$ = 0.001 cm/s = $1\times10^{-5}$ m/s
- Rainfall 800 mm; 1 % to be drained in 24 hours

#### Step 1: Drainage rate
$$
q = \frac{1}{100}\times\frac{800}{1000}\ \text{m} \Big/ (24\times3600\ \text{s}) = 9.259\times10^{-8}\ \text{m/s}
$$

#### Step 2: Heights above the impervious layer
$$
\begin{aligned} a &= 9-1.5 = 7.5\ \text{m} \\ b &= 9-1 = 8\ \text{m} \end{aligned}
$$

#### Step 3: Spacing
$$
\begin{aligned} S^2 &= \frac{4\times1\times10^{-5}\times(8^2-7.5^2)}{9.259\times10^{-8}} \\ &= \frac{4\times1\times10^{-5}\times7.75}{9.259\times10^{-8}} = 3348\ \text{m}^2 \\ S &= 57.9\ \text{m} \end{aligned}
$$

Rainfall 80 cm = 800 mm.

**Answer: spacing of the tile drains ≈ 57.9 m (say 58 m).**

## Check yourself

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

1. How is the annual rainfall of 80 cm used?
   A. Converted to 800 mm = 0.8 m before taking 1%
   B. Used as 80 m
   C. Used as 8 mm
   D. Used as 0.08 m
   Answer: A. 80 cm = 0.8 m; 1% of it (8 mm) is drained in 24 hours. (Key point: Unit conversion)

2. What is q?
   A. 9.259 x 10^-6 m/s
   B. 9.259 x 10^-8 m/s
   C. 1.157 x 10^-7 m/s
   D. 9.259 x 10^-10 m/s
   Answer: B. q = 0.01 x 0.8 / 86400 = 9.259e-8 m/s. (Key point: Drainage rate)

3. With impervious layer 9 m, drains 1.5 m and water table 1 m below ground, what are a and b?
   A. a = 1.5 m, b = 1 m
   B. a = 8 m, b = 7.5 m
   C. a = 7.5 m, b = 8 m
   D. a = 7.5 m, b = 9 m
   Answer: C. a = 9 - 1.5 and b = 9 - 1, giving b^2 - a^2 = 64 - 56.25 = 7.75. (Key point: Heights)

4. What is the spacing?
   A. About 5.8 m
   B. About 3348 m
   C. About 100 m
   D. About 57.9 m
   Answer: D. S^2 = 4e-5 x 7.75/9.259e-8 = 3348, so S = 57.9 m. (Key point: Spacing)

## Close variants set in other exams

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