Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Soil loss estimation
Question Statement:
The ratio of soil loss from the field plot length to that from the unit plot with a slope length of 22.13 m is 0.5. If the slope length from the watershed divide is 600 m and the slope gradient is 8%, the topographic factor in the Universal Soil Loss Equation is __________. [round off to two decimal places]
Official Answer Key:
4.35 to 4.45
Step-by-Step Solution & Explanation
• USLE topographic (LS) factor: LS = (λ/22.13)^m × (65.41 sin²θ + 4.56 sinθ + 0.065); the given ratio 0.5 confirms exponent m = 0.5, consistent with the standard value for slope gradient ≥ 5%.
• λ = 600 m, slope = 8% ⟹ tanθ = 0.08, θ = 4.574°, sinθ = 0.07968
• (600/22.13)^0.5 = (27.114)^0.5 = 5.207
• 65.41(0.07968)² + 4.56(0.07968) + 0.065 = 0.4153 + 0.3633 + 0.065 = 0.8436
• LS = 5.207 × 0.8436 = 4.39
Computed value: 4.39 (within official range 4.35–4.45)
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