GATE 2026 ES – Question 56
A 100-minute rainfall event has cumulative rainfall (cm) 0,.5,1.2,2.6,3.3,3.5 at times (min) 0,20,40,60,80,100. Initial loss is .6 cm and the $\phi$-index is .6 cm/hour. Find total surface runoff in cm, to one decimal place.
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Correct answer: 2.5 to 2.5
Explanation
The official answer uses the standard $\phi$-index as a gross average loss rate, including initial abstractions. In each 20-minute interval the indexed loss is $.6(20/60)=.2$ cm; every rainfall increment (.5,.7,1.4,.7,.2) meets or exceeds that amount. Thus total indexed loss is $.6(100/60)=1.0$ cm and runoff is $3.5-1.0=\mathbf{2.5}$ cm. Do not subtract the stated initial loss again under this convention. If .6 cm/hour were intended as an additional post-initial infiltration rate, the problem would require a different interpretation; that is not the official grading convention.