Surface drainage design, 40 ha Terai field

Surface drainage of the 40 ha Terai field is designed from the design rainfall, the permissible ponding of the rice crop, and Manning's formula for the drain.

Step 1: Design rainfall and drainage rate

Design 3-day rainfall $R$ = 50 mm (16.7 mm/day). Assume the initial water depth in the bunded field $h_0$ = 50 mm (not given).

The water level at the end of the storm without drainage = 50 + 50 = 100 mm. This is below the permissible 300 mm and also below 200 mm, so the crop limits are met even without drainage. To avoid accumulation over later storms, the 3-day rainfall is removed within the same 3 days:

$$D = \frac{R}{3} = \frac{50}{3} = 16.7\ \text{mm/day} = 16.7\times\frac{10}{86.4} = 1.93\ \text{l/s/ha}$$

Step 2: Design discharge

$$Q = D\,A = 1.93\times40 = 77.2\ \text{l/s} = 0.0772\ \text{m}^3/\text{s}$$

Step 3: Section of the drain

Assume an earthen trapezoidal drain, side slope 1:1, $n$ = 0.025 (given), slope $S$ = 1/400 (given), bed width $b$ = 0.5 m.

$$Q=\frac{1}{n}AR^{2/3}S^{1/2}$$

By trial: depth $d$ = 0.208 m (say 0.21 m), $A=(b+d)d$ = 0.147 m², $P=b+2\sqrt{2}d$ = 1.088 m, $R$ = 0.135 m; check $Q$ = (1/0.025) × 0.147 × 0.135^(2/3) × (1/400)^0.5 = 0.0776 m³/s ≈ 0.0772 m³/s.

$V$ = 0.0772/0.147 = 0.53 m/s, which is non-silting (> 0.3 m/s) and non-scouring (< 0.6 m/s for earth).

Provide a free board of 0.15 m: total depth = 0.21 + 0.15 = 0.36 m; adopt 0.40 m.

Step 4: Layout

Field drains (laterals) run along the slope into one collector drain along the lower edge of the 40 ha block; the collector discharges into the natural drain through an outlet structure with its sill 0.3 m below the lowest field level. The drain is made deep enough for the field outlets to discharge freely, with the drain water level at least 0.3 m below the field outlets.

Answer: D = 16.7 mm/day (1.93 l/s/ha), Q = 77.2 l/s; trapezoidal drain with bed width 0.5 m, flow depth 0.21 m (total 0.40 m), side slopes 1:1, slope 1 in 400.