Question Bank • QB_EXP_SWCE_INF_001 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Infiltration, Evaporation & Hydrologic Losses

Subtopic: Horton infiltration rate

Question Statement:

The infiltration capacity of a watershed follows Horton's equation: $f_t = f_c + (f_0 - f_c) e^{-k t}$. Given initial infiltration capacity $f_0 = 40\text{ mm/h}$, final steady capacity $f_c = 10\text{ mm/h}$, and decay constant $k = 0.5\text{ h}^{-1}$, the infiltration capacity at time $t = 2\text{ h}$ is ________ $\text{mm/h}$ (round off to two decimal places).

Answer Key:

21.04

Step-by-Step Solution & Explanation

Substituting into Horton's equation: $f_t = 10 + (40 - 10) e^{-0.5 \times 2} = 10 + 30 e^{-1.0} = 10 + 30(0.36788) = 10 + 11.036 = 21.04\text{ mm/h}$.
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