Question

Following is the set of observed data for successive 15 minutes period of 90 minutes storm in a catchment

If the value of $\varphi$ index is 3 cm/hr , the value of W-index will be _______cm/hr

$\begin{array}{ccccccc}Duration\left(min\right)& 15& 30& 45& 60& 75& 90\\ Rainfall\left(cm/hr\right)& 2.0& 2.0& 8.0& 7.0& 1.25& 1.25\end{array}$

• A. 2.08

Answer 1

The correct option is A 2.08

Hatched portion shows the total runoff and dotted portion shows the total infiltration.
$\therefore$ Total runoff = $(8-3)\times \frac{15}{60}+(7-3)\times \frac{15}{60}$
$=\left[\right(8-3)+(7-3\left)\right]\times \frac{15}{60}=2.25cm$
Total precipitation$=2\times \frac{15}{60}+2\times \frac{15}{60}+8\times \frac{15}{60}+7\times \frac{15}{60}+1.25\times \frac{15}{60}+1.25\times \frac{15}{60}$
$=(2+2+8+7+1.25+1.25)\times \frac{15}{60}=5.375cm$
$W-index=\frac{Totalprecipitation-Runoff}{Durationofrainfallinhr}=\frac{5.375-2.25}{90/60}$
=2.083 cm/hr $\simeq$ 2.08 cm/hr