Question

The total observed runoff volume during a $6 \, \text{hr}$ storm with a uniform intensity of $1.5 \, \text{cm/hr}$ is $21.6 \times 10^6 \, \text{m}^3$. What will be the average infiltration rate of the basin if the area of the basin is $300 \, \text{km}^2$?

• A. 2.4 mm/hr
• B. 3 mm/hr
• C. 1.2 mm/hr
• D. 4 mm/hr

Hint:

For infiltration problems, always ensure rainfall, runoff, and basin area are expressed in consistent units before calculating f = I − R.

Answer 1

The Correct Option is B

The infiltration rate ($f$) is determined by:
\[f = I - R\]
where:
$I =$ Total rainfall intensity;
$R =$ Runoff, calculated as the ratio of runoff volume to area: $\frac{21.6 \times 10^6}{300 \times 10^6} = 0.072 \, \text{m/hr}$, which converts to 72 mm/hr.
The total rainfall intensity over 6 hours is:
\[I = 1.5 \, \text{cm/hr} \times 6 = 9 \, \text{cm} = 90 \, \text{mm}.\]
The runoff, expressed in mm/hr, is:
\[R = 72 \, \text{mm/hr}.\]
The infiltration rate is then:
\[f = 90 - 72 = 18 \, \text{mm/hr over 6 hours}.\]
The average infiltration rate is:
\[f_{\text{avg}} = \frac{18}{6} = 3 \, \text{mm/hr}.\]