GATE 2025 ES – Question 53
Subcatchments P, Q, R, S have areas 750,1000,1500,2000 ha;runoff coefficients .5,.6,.6,.7;and concentration times 1,2,3,4 hours. The catchment and uniform storm hyetograph are shown. With constant base flow 40 m³/s, find peak outlet flow in m³/s, to two decimals.
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Correct answer: 250.00 to 260.00
Explanation
Use the keyed time-area interpretation:successive one-hour contributing bands P, Q, R, S have effective areas $CA=375,600,900,1400$ ha. Storm hourly intensities are 10,30,15,25,20,10 mm/hour. Route each successive band with an additional one-hour delay. The largest weighted sum occurs at the fifth response ordinate: $375(20)+600(25)+900(15)+1400(30)=78000$. Since 1 ha·mm/hour is $1/360$ m³/s, the direct peak is $78000/360=216.6667$ m³/s. Add base flow 40 to get **256.67 m³/s**. This assumes the supplied concentration-time bands act as discrete travel-time zones.