Homework #3
1) The 15 min Unit Hydrograph for a 2.1-km2 urban catchment is given by:
a) Verify that the unit hydrograph is consistent with a 1-cm rainfall excess (10 points)
Since the time increment is 30 mins in other words, 30*60 = 1800 s, the area under the unit
hydrograph is
𝐴
ℎ
= 1800(1. 4 + 3. 2 + 1. 5 + 1. 2 + 1. 1 + 1 + 0. 66 + 0. 49 + 0. 36 + 0. 28 + 0. 25 + 0. 17) = 20898 𝑚
2
Since the catchment area is also 2.1 km^2 = 2.1 E 6 m^2, we can determine h, the rainfall excess
as
ℎ =
20898
2.1 𝐸 6
= 0. 995 𝑐𝑚 ≈ 1 𝑐𝑚
Therefore, the given hydrograph qualifies as a unit hydrograph since it has a rainfall excess of 1
cm.
b) estimate the runoff hydrograph for a 15 min rainfall excess of 2.8 cm (10 points)
We estimate the runoff hydrograph by multiplying the ordinates of the unit graph by the excess.
As a result, the new runoff hydrograph looks like:
c) estimate the runoff hydrograph for a 30-min rainfall excess of 10.3 cm (10 points).
The runoff hydrograph for 30-min rainfall excess of 10.3 cm can be calculated by adding the
runoff hydrographs from two consecutive 15 min events, where those correspond to a rainfall
