Question

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 _____. \textit{[Round off to two decimal places]}

Hint:

The topographic factor in the Universal Soil Loss Equation depends on slope length, gradient, and a constant that accounts for the slope length and slope gradient.

Answer 1

Correct Answer: 4.35

The topographic factor \( LS \) in the Universal Soil Loss Equation can be calculated using the formula: \[ LS = \left( \frac{L}{22.13} \right)^m \times (1 + 0.03 \times S)^{1.3} \] where:
- \( L = 600 \, \text{m} \) is the slope length,
- \( S = 8% = 0.08 \) is the slope gradient,
- \( m \) is a constant that depends on the slope length, typically taken as 0.5 for slope lengths greater than 22.13 m.
Substitute the given values into the formula: \[ LS = \left( \frac{600}{22.13} \right)^{0.5} \times (1 + 0.03 \times 0.08)^{1.3} \] \[ LS = \left( 27.14 \right)^{0.5} \times (1 + 0.0024)^{1.3} = 5.2 \times (1.0024)^{1.3} \approx 5.2 \times 1.0031 = 5.22. \] Thus, the topographic factor is approximately \( \boxed{5.22} \).