Question

The rainfall on five successive days on a catchment was 2 cm, 6 cm, 9 cm, 5 cm, and 3 cm. If the φ-index for the storm is taken as 3 cm/day, the total direct runoff from the catchment will be:

• A. 26 cm
• B. 16 cm
• C. 11 cm
• D. 13 cm

Hint:

In the φ-index method, subtract the φ-index value from daily rainfall to calculate runoff, and then sum for the total.

Answer 1

The Correct Option is B

Step 1: Understanding φ-index.
The φ-index method is used to calculate the direct runoff from the catchment. The direct runoff is the total rainfall minus the φ-index, multiplied by the number of days.
Step 2: Calculating the total rainfall.
The total rainfall for the five days is: \[ 2 + 6 + 9 + 5 + 3 = 25 \, \text{cm} \]
Step 3: Calculating the total direct runoff.
For each day, subtract the φ-index (3 cm/day) from the daily rainfall, and then sum the values: \[ \text{Total direct runoff} = (2 - 3) + (6 - 3) + (9 - 3) + (5 - 3) + (3 - 3) \] \[ \text{Total direct runoff} = (-1) + 3 + 6 + 2 + 0 = 16 \, \text{cm} \]
Step 4: Conclusion.
Thus, the total direct runoff from the catchment is 16 cm, making option (2) the correct answer.

Final Answer: \[ \boxed{16 \, \text{cm}} \]