GATE 2025 ES – Question 52
The shown storm hyetograph produces 12.5 mm direct runoff. Find its φ-index in mm/hour, to two decimals.
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Correct answer: 15.00 to 15.00
Explanation
Half-hour intensities are 10,30,15,25,5,10 mm/hour. For $\phi=15$,only the 30 and 25 mm/hour blocks have positive excess. Their runoff depths total $.5(30-15)+.5(25-15)=7.5+5=12.5$ mm, as specified. All lower blocks produce zero excess. Thus **15.00 mm/hour**. Using total rainfall divided by full duration would incorrectly charge losses during low-intensity intervals above their actual rainfall.