A storm with 12·0 cm precipitation produced a direct runoff of 6·8 cm. The time distribution of the storm is given in the following Table. What is the φ-index ? (Take duration of excess rainfall as 8 hrs) Time from start (hr) – incremental rainfall in each hour (cm): 1 – 0·56; 2 – 0·95; 3 – 1·90; 4 – 2·80; 5 – 2·00; 6 – 1·80; 7 – 1·20; 8 – 0·61
- A0·55 cm/hr
- B0·31 cm/hr
- C0·46 cm/hr
- D0·65 cm/hrCorrect
Solution
Concept
φ-index = average infiltration rate during the period of excess rainfall
Formula
φ = (P − R) / te
Step-by-step solution
1. Total losses = P − R = 12.0 − 6.8 = 5.2 cm. 2. Duration of excess rainfall te = 8 h (as instructed). 3. φ = 5.2 / 8 = 0.65 cm/h.
Explanation
The φ-index is the uniform rate of loss that makes the rainfall in excess of it equal to the direct runoff. Dividing the total loss by the duration of excess rainfall gives the average value.
Why the other options are wrong
0.55, 0.31 and 0.46 cm/h do not follow from (12.0 − 6.8)/8.
Shortcut
φ = (P − R) / t.
Common mistake
Dividing by the total duration of the storm.
Correct answer: D) 0·65 cm/hr