GATE 2019 CE (CE1) – Question 59
The hyetograph shows a 140-minute storm with successive 20-minute rainfall intensities 4, 8, 15, 10, 8, 3 and 1 mm/h. Infiltration capacity begins at 17 mm/h, decreases linearly to 10 mm/h at 40 minutes, then linearly to 4 mm/h at 100 minutes, and remains constant until the storm ends. Find the φ-index (mm/h), to two decimal places.
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Correct answer: 7 to 7.3
Explanation
Each rainfall bar lasts 1/3 h. Rain exceeds infiltration only from 40 to 100 min, when average infiltration is (10 + 4)/2 = 7 mm/h. Total runoff is $(15+10+8)/3-7(1)=4$ mm. A constant φ between 4 and 8 applies excess to the four bars 8, 15, 10 and 8. Thus $(41-4\phi)/3=4$, giving **φ = 7.25 mm/h**.