Question

The intensity of the rainfall for successive 1 hr period of a 6 hr storm are 2, 6, 8, 9, 7 and 3 cm/hr. The runoff is 4 cm/hr. Calculate the $\varphi -index$ (in cm/hr).

• A. 2.5
• B. 3.5
• C. 4.6
• D. 7.67

Answer 1

The correct option is B 3.5

Given that:
Duration of storm = 6 hr.
Runoff = 4 cm/hr.

$\therefore \text{Total surface runoff}=4\times 6=24\text{cm}$

Hyetograph for the given intensity of rainfall.



$\text{Assume}\varphi -\text{index to be lower than 2 cm/hr.}$

$\therefore \sum (i-\varphi )\times t=\text{Surface runoff}$

$(2-\varphi )\times 1+(6-\varphi )\times 1+(8-\varphi )\times 1+(9-\varphi )\times 1+(7-\varphi )\times 1+(3-\varphi )\times 1=24$
$35-6\varphi =24$
$6\varphi =3.5-24$
$\varphi =\frac{11}{6}=1.833\text{cm/hr}\text{<(2 cm/hr)}$
Our assumption is correct.

$\text{Hence,}\varphi \text{-index}=1.833\text{cm/hr.}$