The infiltration capacity of a soil follows Horton's equation

$$\n f(t)=f_c+(f_0-f_c)\,e^{-k t},\n$$

where $f(t)$ is the infiltration capacity (mm h$^{-1}$) at time $t$ (h), $f_0$ is the initial capacity, $f_c$ the steady‑state capacity and $k$ the decay constant.

For a particular site $f_0=30$ mm h$^{-1}$ and $f_c=5$ mm h$^{-1}$. After 2 h the measured capacity is $12$ mm h$^{-1}$.

(a) Determine the decay constant $k$ (to two decimal places).

(b) Using this value of $k$, calculate the cumulative infiltration $I$ after 4 h, where

$$\n I(t)=\int_{0}^{t} f(\tau)\,d\tau .\n$$

Give $I$ to one decimal place (mm).

Question

The infiltration capacity of a soil follows Horton's equation

$$\n f(t)=f_c+(f_0-f_c)\,e^{-k t},\n$$

where $f(t)$ is the infiltration capacity (mm h$^{-1}$) at time $t$ (h), $f_0$ is the initial capacity, $f_c$ the steady‑state capacity and $k$ the decay constant.

For a particular site $f_0=30$ mm h$^{-1}$ and $f_c=5$ mm h$^{-1}$. After 2 h the measured capacity is $12$ mm h$^{-1}$.

(a) Determine the decay constant $k$ (to two decimal places).

(b) Using this value of $k$, calculate the cumulative infiltration $I$ after 4 h, where

$$\n I(t)=\int_{0}^{t} f(\tau)\,d\tau .\n$$

Give $I$ to one decimal place (mm).

Accepted Answer

k = 0.64 h⁻¹, cumulative infiltration I = 56.2 mm

Gce Model Questions Vol1 2019 Geography Question 22

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