Subtopic: Planning, design and layout of surface and sub-surface drainage systems
Question Statement:
A tile drainage system having 200 mm diameter lateral of 400 m length is used to drain an area with a drainage coefficient of 40 mm. Manning’s roughness coefficient for the drain pipe is 0.01. Drain pipes are laid at 0.3% slope. The spacing of the tile drain in m is __________.
Official Answer Key:
118 to 129
Step-by-Step Solution & Explanation
For the pipe flowing full, hydraulic radius R = D/4 = 0.05 m.
Manning's velocity: V = (1/n)·R^(2/3)·S^(1/2) = (1/0.01)(0.05)^(2/3)(0.003)^(0.5)
(0.05)^(2/3) = 0.1357; (0.003)^0.5 = 0.05477.
V = 100 × 0.1357 × 0.05477 = 0.7433 m/s.
Full-pipe discharge, Q = V·A = 0.7433 × (π/4)(0.2)² = 0.7433 × 0.031416 = 0.023352 m³/s = 2017.7 m³/day.
The drain must remove a depth equal to the drainage coefficient (q = 0.04 m/day) over the area served (spacing S × lateral length L): Q = q·S·L
S = Q/(q·L) = 2017.7/(0.04 × 400) = 2017.7/16 = 126.1 m, within the accepted range.
Groundwater Hydrology
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