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GATE 2024 AG – Question 31

Soil and Water Conservation Engineering · Soil and Water Erosion · 1 mark · Numerical answer

An area of 6% slope has its slope length halved with all other factors unchanged. Find the percentage reduction in annual soil loss, to two decimals.

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Correct answer: 29.00 to 29.50

Explanation

In the conventional USLE slope-length relation,$L\propto\lambda^m$ and m=.5 for slopes above 5%. Halving length makes predicted loss $A_2/A_1=(1/2)^{.5}=.7071068$. Reduction is $100(1-.7071068)=\mathbf{29.29\%}$. This uses the conventional USLE exponent intended by the problem.

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