Question

The hyetograph in the figure corresponds to a rainfall event of 3 cm. 

If the rainfall event has produced a direct runoff of 1.6 cm, the \(\phi\)-index of the event (in mm/hour, round off to one decimal place) would be \(\underline{\hspace{1cm}}\).

Hint:

The \( \phi \)-index is calculated as the ratio of direct runoff to total rainfall, multiplied by the rainfall intensity.

Answer 1

Correct Answer: 4.2

The \( \phi \)-index is a measure of the average rainfall intensity that contributes to direct runoff. It can be calculated by the formula: \[ \phi = \frac{\text{Direct Runoff}}{\text{Total Rainfall}} \times \text{Rainfall Intensity} \] Given:
- Total rainfall = 3 cm,
- Direct runoff = 1.6 cm.
From the hyetograph, we need to compute the total rainfall intensity over the period, which is the average of the rain intensities for each interval. Step 1: Calculate the average rainfall intensity over the time intervals: We calculate the total rainfall intensity as the area under the hyetograph, which corresponds to the sum of the area of each rectangle: \[ \text{Total Intensity} = 0.5 \times (12 + 14 + 4.5 + 15 + 7.5 + 4 + 3) = 0.5 \times 60 = 30 \, \text{mm/hour} \] Step 2: Calculate the \( \phi \)-index: Now we use the formula to calculate the \( \phi \)-index: \[ \phi = \frac{1.6}{3} \times 30 = 4.2 \, \text{mm/hour} \] Thus, the \( \phi \)-index of the event is \( \boxed{4.2} \, \text{mm/hour} \).