---
title: "Tile drain spacing: rainfall 1700 mm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-rainfall-1700-impervious10"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-1700-impervious10
site: BCT Engineering
---

# Tile drain spacing: rainfall 1700 mm

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

- Asked in: 2077 Chaitra, 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-1700-impervious10
- 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 rainfall of 1700 mm, if 1.5% is to be drained in 24 hrs. From ground level, depth of impervious stratum is 10 m, depth of drain is 2.2 m and depth of highest position of water table is 1.2 m, coefficient of permeability = 0.001 cm/sec.

## Short answer

Use Donnan's formula S = sqrt[4K(b²-a²)/q] with K=0.001 cm/s, q from 1.5% of 1700 mm in 24 h = 2.951×10⁻⁷ m/s, a=7.8 m, b=8.8 m. Spacing S ≈ 47.4 m (adopt 47 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 = 2.2 m, depth of highest water table = 1.2 m (all below ground)
- $K$ = 0.001 cm/s = $1\times10^{-5}$ m/s
- Rainfall 1700 mm; 1.5 % to be drained in 24 hours

#### Step 1: Drainage rate
$$
q = \frac{1.5}{100}\times\frac{1700}{1000}\ \text{m} \Big/ (24\times3600\ \text{s}) = 2.951\times10^{-7}\ \text{m/s}
$$

#### Step 2: Heights above the impervious layer
$$
\begin{aligned} a &= 10-2.2 = 7.8\ \text{m} \\ b &= 10-1.2 = 8.8\ \text{m} \end{aligned}
$$

#### Step 3: Spacing
$$
\begin{aligned} S^2 &= \frac{4\times1\times10^{-5}\times(8.8^2-7.8^2)}{2.951\times10^{-7}} \\ &= \frac{4\times1\times10^{-5}\times16.60}{2.951\times10^{-7}} = 2250\ \text{m}^2 \\ S &= 47.4\ \text{m} \end{aligned}
$$

**Answer: spacing of the tile drains ≈ 47.4 m (say 47 m).**

## Check yourself

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

1. Which formula gives tile drain spacing here and what do a and b mean?
   A. S = sqrt(4K(b^2 - a^2)/q); b = mid-point water table height and a = drain height, both above the impervious layer
   B. S = sqrt(4K(b^2 - a^2)/q); a and b are depths below ground
   C. S = 4Kq(b^2 - a^2); b is the drain depth
   D. S = sqrt(q/(4K)) x (b - a)
   Answer: A. Donnan's formula uses heights above the impervious layer, not depths below ground. (Key point: Formula)

2. What is q for 1.5% of 1700 mm drained in 24 hours?
   A. 2.951 x 10^-5 m/s
   B. 2.951 x 10^-7 m/s (25.5 mm/day)
   C. 1.7 x 10^-7 m/s
   D. 25.5 x 10^-7 m/s
   Answer: B. q = 0.015 x 1.7 m / 86400 s = 2.951 x 10^-7 m/s. (Key point: Drainage rate)

3. What are a and b for impervious layer 10 m, drain 2.2 m and water table 1.2 m below ground?
   A. a = 2.2 m, b = 1.2 m
   B. a = 8.8 m, b = 7.8 m
   C. a = 7.8 m, b = 8.8 m
   D. a = 7.8 m, b = 9.8 m
   Answer: C. Subtract the depths from 10 m: a = 10 - 2.2 = 7.8 and b = 10 - 1.2 = 8.8. (Key point: Heights)

4. What spacing results (K = 1e-5 m/s)?
   A. About 22 m
   B. About 474 m
   C. About 2250 m
   D. About 47.4 m
   Answer: D. S^2 = 4 x 1e-5 x 16.6 / 2.951e-7 = 2250 m^2, so S = 47.4 m. (Key point: Spacing)

## Close variants set in other exams

- [Tile drain spacing: rainfall 1600 mm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atile-drain-rainfall-1600-impervious9) — Irrigation and Drainage Engineering, chapter 9, asked 3×

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