Question

Measured infiltration rates, f, in cm/hour, for every hour from t = 0, when the rainfall just commenced to t = 8 hours are given in the table below. The rainfall lasts over 8 hours. Calculate the total infiltration quantity during 8 hours using Horton's equation (take Horton's constant $k=4da{y}^{-1}$).

$\begin{array}{cc}\text{Time (hour)}& \text{f(cm/hour)}\\ 0& 2.00\\ 1& 1.10\\ 2& 0.75\\ 3& 0.65\\ 4& 0.55\\ 5& 0.50\\ 6& 0.50\\ 7& 0.50\\ 8& 0.50\end{array}$

• A. 4.38 cm
• B. 29.14 cm
• C. 22.63 cm
• D. 10.63 cm

Answer 1

The correct option is D 10.63 cm

Given,

$f_o=2cm/hr$

$f_c=\text{final constant rate of infiltration}$
$=0.5cm/hr$

$k=4da{y}^{-1}$

$=\frac{4}{24}h{r}^{-1}$

$=\frac{1}{6}h{r}^{-1}$

Horton's infiltration Equation

$f_t=f_c+(f_o–f_c)e^{-kt}$

$=0.5+(2-0.5)e^{-\frac{1}{6}t}$

$=0.5+1.5e^{-\frac{1}{6}t}$

Total infiltration quantity during 8 hour

$=\underset{0}{\overset{8}{\int }}{f}_{t}dt$

$=\underset{0}{\overset{8}{\int }}(0.5+1.5e^{-\frac{1}{6}t})dt$

$=10.628cm$