Allied & ICAR Exam Bank • ALLIED_0404 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Hydrology and Runoff

Subtopic: Hydrology and Runoff

Question Statement:

The total cumulative depth of infiltration $F(t)$ during time duration $t$ according to Horton's equation is:

Options:

  • (A) $F(t) = f_c t + \frac{f_0 - f_c}{k}(1 - e^{-kt})$
  • (B) $F(t) = (f_0 + f_c) t / 2$
  • (C) $F(t) = f_c t + (f_0 - f_c) e^{-kt}$
  • (D) $F(t) = f_0 t - k t^2$

Answer Key:

A

Step-by-Step Solution & Explanation

Integrating $f_p dt$ from $0$ to $t$ gives $F(t) = \int_0^t [f_c + (f_0 - f_c)e^{-kt}] dt = f_c t + \frac{f_0 - f_c}{k}(1 - e^{-kt})$.
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