---
title: "Tile drain spacing: rainfall 1000 mm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-rainfall-1000-1pct"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-1000-1pct
site: BCT Engineering
---

# Tile drain spacing: rainfall 1000 mm

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

- Asked in: 2081 Chaitra, 8 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-1000-1pct
- 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 10 m below the ground level and the average annual rainfall in the area is 1000 mm. 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 the ground level, determine the spacing of the drain pipes. Take K = 0.001 cm/sec.

## Short answer

Donnan's formula: K=1×10⁻⁵ m/s, q = 1% of 1000 mm in 24 h = 1.157×10⁻⁷ m/s, a=10−1.5=8.5 m, b=10−1=9 m. Spacing S = 55.0 m (adopt 55 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 = 10 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 1000 mm; 1 % to be drained in 24 hours

#### Step 1: Drainage rate
$$
q = \frac{1}{100}\times\frac{1000}{1000}\ \text{m} \Big/ (24\times3600\ \text{s}) = 1.157\times10^{-7}\ \text{m/s}
$$

#### Step 2: Heights above the impervious layer
$$
\begin{aligned} a &= 10-1.5 = 8.5\ \text{m} \\ b &= 10-1 = 9\ \text{m} \end{aligned}
$$

#### Step 3: Spacing
$$
\begin{aligned} S^2 &= \frac{4\times1\times10^{-5}\times(9^2-8.5^2)}{1.157\times10^{-7}} \\ &= \frac{4\times1\times10^{-5}\times8.75}{1.157\times10^{-7}} = 3024\ \text{m}^2 \\ S &= 55.0\ \text{m} \end{aligned}
$$

**Answer: spacing of the tile drains ≈ 55.0 m (say 55 m).**

## Check yourself

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

1. Drain centres are 1.5 m below ground and the water table is held 1 m below ground. What does the formula need?
   A. a = 10 - 1.5 = 8.5 m and b = 10 - 1 = 9 m, heights above the impervious layer
   B. a = 1.5 m and b = 1 m
   C. a = 8.5 m and b = 10 m
   D. a = 9 m and b = 8.5 m
   Answer: A. The impervious layer is 10 m deep, so subtract each depth from 10 m. (Key point: Reading the data)

2. What is q for 1% of 1000 mm in 24 hours?
   A. 1.157 x 10^-6 m/s
   B. 1.157 x 10^-7 m/s (10 mm/day)
   C. 1.0 x 10^-7 m/s
   D. 1.157 x 10^-5 m/s
   Answer: B. q = 0.01 x 1 m / 86400 s = 1.157e-7 m/s. (Key point: Drainage rate)

3. What is b^2 - a^2?
   A. 0.5 m^2
   B. 9.0 m^2
   C. 81 - 72.25 = 8.75 m^2
   D. (9 - 8.5)^2 = 0.25 m^2
   Answer: C. Squares are subtracted: 9^2 - 8.5^2 = 8.75. (Key point: b^2 - a^2)

4. What spacing results?
   A. About 5.5 m
   B. About 3024 m
   C. About 30 m
   D. About 55.0 m
   Answer: D. S^2 = 4e-5 x 8.75/1.157e-7 = 3024, so S = 55.0 m. (Key point: Spacing)

## Close variants set in other exams

- [Tile drain spacing: rainfall 80 cm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atile-drain-rainfall-80cm-impervious9) — Irrigation and Drainage Engineering, chapter 9, asked 2×

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