Question:medium

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:

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In the φ-index method, subtract the φ-index value from daily rainfall to calculate runoff, and then sum for the total.
Updated On: Feb 18, 2026
  • 26 cm
  • 16 cm
  • 11 cm
  • 13 cm
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The Correct Option is B

Solution and Explanation

Step 1: φ-index Explained.
The φ-index method determines direct runoff from a catchment area. Direct runoff equals total rainfall minus the φ-index, multiplied by the number of days.
Step 2: Calculate Total Rainfall.
Total rainfall over five days: \[ 2 + 6 + 9 + 5 + 3 = 25 \, \text{cm} \]
Step 3: Calculate Total Direct Runoff.
For each day, subtract the φ-index (3 cm/day) from the daily rainfall, then sum the results: \[ \text{Total direct runoff} = (2 - 3) + (6 - 3) + (9 - 3) + (5 - 3) + (3 - 3) \] \[ \text{Total direct runoff} = (-1) + 3 + 6 + 2 + 0 = 16 \, \text{cm} \]
Step 4: Conclusion.
The total direct runoff is 16 cm, thus option (2) is correct.

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