Allied & ICAR Exam Bank • ALLIED_1183 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology and Runoff

Subtopic: Infiltration Capacity

Question Statement:

In Horton's infiltration equation $f_p = f_c + (f_0 - f_c) e^{-k t}$, initial infiltration capacity is $f_0 = 10\text{ cm/h}$ and ultimate steady capacity is $f_c = 2\text{ cm/h}$. If the decay constant is $k = 0.5\text{ h}^{-1}$, the infiltration capacity at $t = 2.0\text{ hours}$ (given $e^{-1} \approx 0.368$) in cm/h is:

Answer Key:

4.94

Step-by-Step Solution & Explanation

$f_p = 2 + (10 - 2) e^{-0.5 \times 2} = 2 + 8 e^{-1} = 2 + 8(0.3679) = 2 + 2.943 = 4.943\text{ cm/h}$.
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