Question

There is a 3 hours storm event in which it was observed that apart from infiltration all the losses are negligible. The rainfall was idealised as 3 hours storms of intensity 20 mm/hr, 15 mm/hr and 10 mm/hr respectively and the infiltration was idealized as Horton's curve, $f=9.7+8exp(-t)$ ($f$ in mm/hr and t in hr). The effective rainfall is _________mm.

• A. 8.68

Answer 1

The correct option is A 8.68

Horton's equation,
$f=9.7+8e^{-t}$

$\text{At}t=0,f=9.7+8=17.7mm/hr$

$t=1,f=9.7+\frac{8}{e}=12.64mm/hr$

$t=2,f-9.7+\frac{8}{e^2}=10.78mm/hr$

$t=3,f=9.7+\frac{8}{e^3}=10.09mm/hr$

From above values, it can be deduced that
$f_c\simeq 10mm/hr\forall t>3hr$

So, total infiltration is
$\underset{0}{\overset{t}{\int }}fdt=\underset{0}{\overset{2}{\int }}(9.7+8e^{-t})dt+10\times 1$
$={[9.7t+8(-e^{-t}\left)\right]}_0^2+10$
$=36.317\simeq 36.32$ mm

Effective rainfall
$=20+15+10-36.32=8.68$ mm