GATE 2025 AG – Question 51
An 8 ha watershed receives successive half-hour rainfall intensities 2.5,3.6,5.4,3.3,2.6,1.2 cm/hour. Surface runoff is 4800 m³. Neglect initial abstractions and find W-index in cm/hour, to two decimals.
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Correct answer: 1.08 to 1.12
Explanation
Runoff depth is $4800/80000=.06$ m=6 cm. Total rainfall is $.5(2.5+3.6+5.4+3.3+2.6+1.2)=9.3$ cm. Thus total loss is 3.3 cm over 3 hours and $W=3.3/3=\mathbf{1.10}$ cm/hour. This is below even the lowest rainfall intensity 1.2,so all six intervals contribute rainfall excess and the assumed full duration is consistent.