Tile drain spacing, Biratnagar rainfall

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 = 12 m, depth of drain = 2 m, depth of highest water table = 1.5 m (all below ground)
• $K$ = 0.01 cm/s = 0.0001 m/s
• Rainfall 2000 mm; 2 % to be drained in 48 hours

Step 1: Drainage rate

$$q = \frac{2}{100}\times\frac{2000}{1000}\ \text{m} \Big/ (48\times3600\ \text{s}) = 2.315\times10^{-7}\ \text{m/s}$$

Step 2: Heights above the impervious layer

$$\begin{aligned} a &= 12-2 = 10\ \text{m} \\ b &= 12-1.5 = 10.5\ \text{m} \end{aligned}$$

Step 3: Spacing

$$\begin{aligned} S^2 &= \frac{4\times0.0001\times(10.5^2-10^2)}{2.315\times10^{-7}} \\ &= \frac{4\times0.0001\times10.25}{2.315\times10^{-7}} = 17712\ \text{m}^2 \\ S &= 133.1\ \text{m} \end{aligned}$$

Here $K$ = 1 × 10⁻⁴ m/s = 0.01 cm/s, and 2 % of 2000 mm = 40 mm is drained in 2 days = 48 h.

Answer: spacing of the tile drains ≈ 133.1 m (say 133 m).