Soil and Water Erosion: Mechanics of soil erosion - wind and water erosion: soil erosion types, factors affecting erosion; soil loss estimation; biological and engineering measures to control erosion; terraces and bunds; vegetative waterways; gully control structures, drop, drop inlet and chute spillways; earthen dams.
A parabolic grassed water channel 8 m wide at the top and 60 cm deep is laid on a slope of 3%. Assuming Manning's 'n' = 0.04 m⁻¹ᐟ³s, the discharge capacity (m³ s⁻¹) of the channel (rounded to 2 decimals) is ______.
Official Answer Key:
7.35 to 7.55
Step-by-Step Solution & Explanation
For a parabolic channel section with top width T and depth y:
Area, A = (2/3)Ty = (2/3)(8)(0.6) = 3.20 m².
Wetted perimeter (parabolic approximation), P ≈ T + (8y²)/(3T) = 8 + (8×0.36)/(24) = 8 + 0.12 = 8.12 m.
Hydraulic radius, R = A/P = 3.20/8.12 = 0.3941 m.
Manning's equation: Q = (1/n) A R^(2/3) S^(1/2)
Q = (1/0.04) × 3.20 × (0.3941)^(2/3) × (0.03)^(0.5)
= 25 × 3.20 × 0.5388 × 0.1732
= 7.448 ≈ 7.45 m³/s. Answer: within 7.35–7.55.
Section 5 — Irrigation and Drainage Engineering
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