Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
Annual average soil loss from a watershed has been measured as 20 Mg ha⁻¹ year⁻¹. Watershed has 8% land slope and 84 m maximum slope length. Assume all other factors same and dimensionless exponent for slope factor is 0.5. To reduce soil loss from the watershed to 10 Mg ha⁻¹ year⁻¹, the maximum slope length in m should be ______
Official Answer Key:
20.9 to 21.1
Step-by-Step Solution & Explanation
In the USLE slope-length factor, soil loss is proportional to L^m (m = the given exponent, 0.5), all else constant. So SL₂/SL₁ = (L₂/L₁)^m → L₂ = L₁×(SL₂/SL₁)^(1/m) = 84×(10/20)^(1/0.5) = 84×(0.5)² = 84×0.25 = 21.0 m, matching the accepted band 20.9–21.1 exactly.
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