Question

The hyetograph of a storm event of duration 140 minutes is shown in the figure.



The infiltration capacity at the start of this event (t = 0) is 17 mm/hour, which linearly decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration rate further drops down linearly to attain a value of 4 mm/hour at t = 100 minutes and remains constant thereafter till the end of the storm event. The value of the infiltration index, $\varphi$(in mm/hour, round off to 2 decimal places), is

• A. 5
• B. 7.25
• C. 8.5
• D. 12

Answer 1

The correct option is B 7.25


Depth of infiltration = Area of hyetograph above Horton's curve
$=(15\times \frac{20}{60}+10\times \frac{20}{60}+8\times \frac{20}{60})-\frac{10+4}{2}\times \frac{60}{60}$

= 4 mm

Now, assuming
$4\le \varphi \le 8$


$(8-\varphi )\times \frac{20}{60}+(15-\varphi )+\frac{20}{60}+(10-\varphi )\times \frac{20}{60}$

$+(8-\varphi )\times \frac{20}{60}=4$

$41-4\varphi =12$

$\Rightarrow \varphi =7.25mm/hr$