Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Vegetative waterways
Question Statement:
A triangular shaped grassed waterway with a longitudinal slope of 2.5% is to carry a discharge of 1.5 m³ s⁻¹ with a permissible velocity of 1.2 m s⁻¹. The side slope of the channel is 1.5:1 (Horizontal:Vertical). Without considering free board, the top width of the channel in m is _________.
Official Answer Key:
2.70 to 2.75
Step-by-Step Solution & Explanation
Required flow area, A = Q/V = 1.5/1.2 = 1.25 m².
For a symmetric triangular channel with side slope z (H:V) = 1.5, cross-sectional area in terms of flow depth y: A = z·y² (both sides combined) → 1.25 = 1.5y² ⇒ y² = 0.8333 ⇒ y = 0.9129 m.
Top width, T = 2×z×y = 2 × 1.5 × 0.9129 = 2.739 m, within the accepted range.
Section 5
Soil-Water-Plant Relationship
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