Question

The infiltration capacity of a soil follows Horton's exponential model $f=C_1+C_2{e}^{-kt}$. During an experiment, the initial infiltration capacity was observed to be 200 mm/hr. After a long time the infiltration capacity was reduced to 25 mm/h. If the infiltration capacity after 1 hour was 90 mm/h the value of the decay rate constant k $(in{h}^{-1}$, up to two decimal places) is

• A. 0.99

Answer 1

The correct option is A 0.99

$f=C_1+C_2.e^{-kt}$

$C_1=f_0$
$=25mm/hr$

$C_2=f_1-f_0$
$=200-25$
$=175$

f = 90 mm/hr after 1 hr
Hence,
$90=25+175\times e^{-k\times 1}$
$\Rightarrow e^{-k}=\frac{90-25}{175}=0.3714$
$\Rightarrow -k=lo{g}_e\left(0.3714\right)$
$\Rightarrow -k=-0.99$
$\Rightarrow k=0.99$