Question

The rate of rainfall for successive $30minutes$ period of a $4-hour$ storm are as follows:
$3.5,6.5,8.5,7.5,6.4,4.0,4.0,6.0cm/hr.$ If the value of $\varphi -index$ is $4.5cm/hr$, then the value of W- index (cm/hr) is

• A. 5.5
• B. 4.13
• C. 4.25
• D. 3.9

Answer 1

The correct option is C 4.25


Rainfall excess is shown by hatched area.
Total rainfall
$P=(3.5+6.5+8.5+7.5+6.4+4.0+4.0+6.0)\times \frac{30}{60}$

$=23.2cm$

Total rainfall excess,
$R=\left[\right(6.5-4.5)+(8.5-4.5)+(7.5-4.5)+(6.4-4.5)+(6.0-4.5\left)\right]\times \frac{30}{60}$

$(2+4+3+1.9+1.5)\times \frac{1}{2}=6.2cm$

$\text{W- index}=\frac{P-R}{t}=\frac{23.2-6.2}{4}=4.25cm/hour$