Below is the 30-minute unit hydrograph for a 2.1 km2 urban catchment (runoff res

Question

Below is the 30-minute unit hydrograph for a 2.1 km2 urban catchment (runoff resulting from 30-minute precipitation event). Show one sample of calculations by hand, using Excel, or provide MATLAB scripts 1. Time (min)O 30 60 90 120 150 180 210 UH (m3/s) Time (min) 240 270 300 330 360 390 UH (m3/s) 0.49 0.36 0.28 0.25 0.17 O 0 14 3.2 1.5 1.2 1.1 1.0 0.66 (a) Verify that the values in the table above are consistent with a 30-minute unit hydrograph resulting in 1-cm of rainfall excess (b) Estimate the runoff hydrograph for a 30-minute rainfall excess of 2.8 cm

Explanation / Answer

Answer a

For the values in the table to be consistent with unit hydrograph the rainfall excess would be 1 cm when calculated as follows:

Rainfall excess= Total runoff volume/ Area of catchment

Total runoff volume = Area of given unit hydrograph = (30*60)*(0+1.4+3.2+1.5+1.2+1.1+1+0.66+0.49+0.36+0.28+0.25+0.17+0)= 30*60*11.61= 20898 m3

Area of catchment= 2.1*1000000 m2

Rainfall excess= 20898*100/(2.1*1000000) = 0.995 cm = say 1 cm ( which is in accordance with the excess rainfall that should have been there)

Answer b

Runoff hydrograph for a 30 minute storm of rainfall excess of 2.8 cm can be obtained by multiplying the discharge or ordinates values of unit hydrograph by 2.8 ( using linearity property of hydrograph)

Thus ordinates or discharge values of runoff hydrograph corresponding to time 0,30,60 .....upto 390 min would be 0,3.92,8.96,4.2,3.36, 3.08,2.8,1.848,1.372,1.008,0.784,0.7,0.476 and 0 respectively.

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