Question

The infiltration capacity of soil in a small watershed was found to be 6.6 cm/h before a rainfall event. It was found to be 1.2 cm/h at the end of storm. If the total infiltration during the 8 hours period of storm was 15 cm, then the value of decay coefficient $k_h$ in Horton's infiltration capacity equation will be ___________ hr${}^{-1}$.

• A. 1
• B. 3.2
• C. 4.18
• D. 0.06

Answer 1

The correct option is A 1

Horton's equation is
$f_p=f_c+(f_0-f_c)e^{-k_{h}t}$

$\therefore$ Total infiltration,
$F_P={\int }_0^t{f}_{p}t$

$={\int }_0^5[f_c+(f_0-f_c\left)e^{-k_{h}t}\right]dt$

$=f_{c}t+(f_0-f_c){\int }_0^t{e}^{-k_{h}t}dt$

${\begin{array}{c}{f}_{c}t-\left(\frac{f_0-f_c}{k_h}\right)e^{-k_{h}t}\end{array}|}_0^8$

$=f_{c}t-\left(\frac{f_0-f_c}{k_h}\right)\{e^{-8k_h}-1\}$

Assuming
$\frac{1}{e^{8k_h}}\to 0$

So,
$F_p=f_{c}t+\frac{f_0-f_c}{k_h}$
$\Rightarrow 15=(1.2\times 8)+\frac{6.6-1.2}{k_h}$
$\Rightarrow k_h=\frac{5.4}{5.4}{h}^{-1}$

So,
$k_h=1h^{-1}$