GATE 2026 AG – Question 58
A $.80\,\mathrm{km^2}$ watershed has slope .30% and maximum travel length 1 km. Ten-year rainfall depths at durations 5,10,20,30,40,60 minutes are 16,24,39,50,60,65 mm. Half the area is row crops with runoff coefficient .40,and half pasture with .35. Find the ten-year peak flow in $\mathrm{m^3/s}$,to two decimals.
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Correct answer: 7.50 to 7.75
Explanation
Use the Kirpich estimate with length in metres and slope fraction:$t_c=.0195L^{.77}S^{-.385}=.0195(1000)^{.77}(.003)^{-.385}=37.2686$ min. Interpolate rainfall depth between 30 and 40 minutes:$P=50+(60-50)(37.2686-30)/10=57.2686$ mm. Hence intensity $i=60P/t_c\approx92.20$ mm/h. Area-weighted $C=(.40+.35)/2=.375$. The rational formula gives $Q=CiA/3.6=.375(92.20)(.80)/3.6\approx\mathbf{7.68}$ m³/s.