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Tile drain spacing with drainage coefficient 0.012

Short answer

Use Donnan's formula. Drainage coefficient 0.012 means 1.2% of900 mm in24 h so q=1.25×10⁻⁷ m/s; K=0.012 cm/s=1.2×10⁻⁴ m/s, a=7.4 m, b=7.8 m. Spacing S ≈152.8 m (say 150 m).

Find the spacing of tile drains with following data: annual rainfall = 900 mm; drainage coefficient = 0.012; depth of impervious layer below GL = 9 m; depth of tile drains below GL = 1.6 m; depth of highest position of water table below GL = 1.2 m; coefficient of permeability = 0.012 cm/sec.

Tile drain spacing follows from Donnan's formula for steady flow to parallel drains above an impervious layer:

S=4K (b2−a2)qS=\sqrt{\frac{4K\,(b^2-a^2)}{q}}

The drainage coefficient is given as a pure number, 0.012, so it is taken as the fraction of the annual rainfall to be drained in 24 hours (1.2 %, as in the usual "x % of annual rainfall in 24 h" problems). This uses the given annual rainfall of 900 mm.

Data

  • qq = 0.012 × 0.900 m = 0.0108 m/day = 0.0108/86400 = 1.25×10−71.25\times10^{-7} m/s
  • KK = 0.012 cm/s = 0.00012 m/s
  • aa = 9 − 1.6 = 7.4 m (drain above the impervious layer)
  • bb = 9 − 1.2 = 7.8 m (highest water table above the impervious layer)

Calculation

S2=4×0.00012×(7.82−7.42)1.25×10−7=4×0.00012×6.081.25×10−7=23347 m2S=152.8 m\begin{aligned} S^2 &= \frac{4\times0.00012\times(7.8^2-7.4^2)}{1.25\times10^{-7}} \\ &= \frac{4\times0.00012\times6.08}{1.25\times10^{-7}} = 23347\ \text{m}^2 \\ S &= 152.8\ \text{m} \end{aligned}

Note: if the drainage coefficient is instead read as a depth of 0.012 m/day (12 mm/day), then q=1.389×10−7q = 1.389\times10^{-7} m/s, S2S^2 = 21012 m² and SS ≈ 145 m.

Answer: spacing of the tile drains ≈ 152.8 m (say 150 m).

✓ Answer checked by Claude Opus 5.5 (high effort)

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