GATE AG 2021 • Q56 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Runoff estimation

Question Statement:

A small watershed receives rainfall of 90 mm in a day. For this watershed, irrespective of the land use, the amount of initial abstraction can be considered as 25% of the potential maximum retention (S) of soil. Initially, the entire watershed was under forest with S = 136 mm, which was converted into cultivated land with S = 64 mm. The change in the daily runoff volume due to this land use alteration for this specific rainfall event in percent is ______. [round off to one decimal place]

Official Answer Key:

142.9 to 143.6

Step-by-Step Solution & Explanation

SCS-CN runoff equation with Ia = 0.25S: Q = (P − 0.25S)²/(P + 0.75S). Forest (S=136 mm): P−Ia = 90−34 = 56; P+0.75S = 90+102 = 192; Q_forest = 56²/192 = 3136/192 = 16.33 mm. Cultivated (S=64 mm): P−Ia = 90−16 = 74; P+0.75S = 90+48 = 138; Q_cult = 74²/138 = 5476/138 = 39.68 mm. % change = (39.68−16.33)/16.33 × 100 = 143.0%.

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