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Question

The drainage area of a watershed is 50 km2. The ϕ - index is 0.5 cm/hour and the base flow at the outlet is 10 m3/s. One hour unit hydrograph (unit depth = 1 cm) of the watershed is triangular in shape with a time base of 15 hours. The peak ordinate occurs at 5 hours.
For a storm of depth of 5.5 cm and duration of 1 hour, the peak ordinate (in m3/s ) of the hydrograph is

A
55.00
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B
82.60
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C
92.60
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D
102.60
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Solution

The correct option is D 102.60
Unit hydrograph is a hydrograph of direct runoff resulting from 1 cm of effective rainfall. So volume of water contained inside the unit hydrograph (i.e., area of unit hydrograph) = 1 cm x catchment area


12×a×15 hrs=1 cm×A

12×a×15×3600=0.01×50×106

a=18.52m3/s/cm of effective rainfall

For a storm of 5.5 cm and duration of 1 hour
Effective rainfall = storm depth - ϕ index
=5.50.5=5 cm
Peak ordinate of hydrograph due to 5 cm effective rainfall
=5×peak ordinate of UH + base flow
=5×18.52+10=102.60 m3/s

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