Tile size for laterals, 2 cm/day

The tile must carry the drainage discharge from the area served by the lateral, flowing full under gravity. Manning's formula for a full circular pipe is used.

Data

• Area drained by one lateral = 200 m × 50 m = 10 000 m² = 1 ha
• Drainage coefficient = 2 cm/day = 0.02 m/day; grade $S$ = 0.003
• Manning's $n$ = 0.011 for clay/concrete tile (assumed)

Discharge

$$Q = 0.02\times\frac{10000}{86400} = 0.00231\ \text{m}^3/\text{s} = 2.31\ \text{l/s}$$

Diameter

For a pipe flowing full, $A=\pi D^2/4$ and $R=D/4$:

$$Q=\frac{1}{n}\cdot\frac{\pi D^2}{4}\left(\frac{D}{4}\right)^{2/3}S^{1/2} \quad\Rightarrow\quad D^{8/3}=\frac{4^{5/3}\,nQ}{\pi\,S^{1/2}}$$ $$D=\left(\frac{4^{5/3}\times0.011\times0.00231}{\pi\times\sqrt{0.003}}\right)^{3/8} = 0.0871\ \text{m} = 87\ \text{mm}$$

The next standard tile size is 100 mm. Its full-flow capacity = 3.34 l/s (0.00334 m³/s) > 2.31 l/s, so it is safe (velocity 0.43 m/s).

Answer: provide 100 mm diameter tiles.