---
title: "Tile drain spacing: rainfall 1600 mm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-rainfall-1600-impervious9"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-1600-impervious9
site: BCT Engineering
---

# Tile drain spacing: rainfall 1600 mm

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

- Asked in: 2071 Magh, 5 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-1600-impervious9
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

Calculate the spacing of the tile drains for an area having average annual rainfall of 1600 mm, if 1.5% is to be drained in 24 hrs. From ground level, depth of impervious stratum is 9 m, depth of drains is 2.0 m and depth of highest position of water table is 1.0 m. Coefficient of permeability = 0.001 cm/sec.

## Short answer

Apply Donnan's formula: q = 1.5% of 1600 mm in 24 h = 2.778×10⁻⁷ m/s, a=7 m, b=8 m, K=1×10⁻⁵ m/s. Spacing S = sqrt[4K(b²-a²)/q] = 46.5 m (say 46 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 = 2 m, depth of highest water table = 1 m (all below ground)
- $K$ = 0.001 cm/s = $1\times10^{-5}$ m/s
- Rainfall 1600 mm; 1.5 % to be drained in 24 hours

#### Step 1: Drainage rate
$$
q = \frac{1.5}{100}\times\frac{1600}{1000}\ \text{m} \Big/ (24\times3600\ \text{s}) = 2.778\times10^{-7}\ \text{m/s}
$$

#### Step 2: Heights above the impervious layer
$$
\begin{aligned} a &= 9-2 = 7\ \text{m} \\ b &= 9-1 = 8\ \text{m} \end{aligned}
$$

#### Step 3: Spacing
$$
\begin{aligned} S^2 &= \frac{4\times1\times10^{-5}\times(8^2-7^2)}{2.778\times10^{-7}} \\ &= \frac{4\times1\times10^{-5}\times15.00}{2.778\times10^{-7}} = 2160\ \text{m}^2 \\ S &= 46.5\ \text{m} \end{aligned}
$$

**Answer: spacing of the tile drains ≈ 46.5 m (say 46 m).**

## Check yourself

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

1. How is K = 0.001 cm/s expressed in the formula?
   A. 1 x 10^-5 m/s
   B. 1 x 10^-3 m/s
   C. 1 x 10^-7 m/s
   D. 0.001 m/s
   Answer: A. Divide cm/s by 100 to get m/s: 0.001 cm/s = 1e-5 m/s. (Key point: Permeability units)

2. What is q for 1.5% of 1600 mm in 24 hours?
   A. 2.778 x 10^-5 m/s
   B. 2.778 x 10^-7 m/s (24 mm/day)
   C. 1.5 x 10^-7 m/s
   D. 2.4 x 10^-7 m/s
   Answer: B. q = 0.015 x 1.6 / 86400 = 2.778e-7 m/s. (Key point: Drainage rate)

3. What are a and b with impervious layer 9 m, drains 2 m, water table 1 m deep?
   A. a = 2 m, b = 1 m
   B. a = 8 m, b = 7 m
   C. a = 7 m, b = 8 m
   D. a = 7 m, b = 9 m
   Answer: C. a = 9 - 2 = 7 m and b = 9 - 1 = 8 m; b is larger because the water table is higher than the drain. (Key point: Heights above impervious layer)

4. What is the spacing?
   A. About 4.65 m
   B. About 2160 m
   C. About 93 m
   D. About 46.5 m
   Answer: D. S^2 = 4e-5 x (64 - 49)/2.778e-7 = 2160, so S = 46.5 m. (Key point: Spacing)

## Close variants set in other exams

- [Tile drain spacing: rainfall 1700 mm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atile-drain-rainfall-1700-impervious10) — Irrigation and Drainage Engineering, chapter 9, asked 2×
- [Tile drain spacing: rainfall 1400 mm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atile-drain-rainfall-1400-1pct) — Irrigation and Drainage Engineering, chapter 9, asked 2×

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