Question

Following is the set of observed data for successive 15 minutes period of 90 minutes storm in a catchment
$\begin{array}{ccccccc}\text{Duration (min)}& 15& 30& 45& 60& 75& 90\\ \text{Rainfall (cm/hr)}& 2.0& 2.0& 8.0& 7.0& 1.25& 1.25\end{array}$

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

• 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
$\therefore \text{Total runoff}=(8-3)\times \frac{15}{60}+(7-3)\times \frac{15}{60}$
$=\left[\right(8-3)+(7-3\left)\right]\times \frac{15}{60}=2.25cm$
$\text{Total precipitation}=2\times \frac{15}{60}+2\times \frac{15}{60}+8\times \frac{15}{60}+7\times \frac{15}{60}+1.25\times \frac{15}{60}+1.25\times \frac{15}{60}$
= $(2+2+8+7+1.25+1.25)\times \frac{15}{60}=5.375cm$
$\text{W- index}=\frac{\text{Total precipitation -Runoff}}{\text{Duration of rainfall in hr}}=\frac{5.375-2.25}{90/60}$
$=2.083cm/hr\simeq 2.08cm/hr$