CEE 350 HW 3
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School
University of Illinois, Urbana Champaign *
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Course
350
Subject
Geography
Date
Dec 6, 2023
Type
Pages
4
Uploaded by GrandOryxMaster958
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
excess of 5.15 cm. The first graph will be interpolated for a 15 min event, where it is multiplied
by 5.15 cm, and then this hydrograph is then added to the same hydrograph shifted forward by
15 min. This looks like
2) The 15 min unit hydrograph (UH) for a 2.1-km2 catchment is given in the previous
problem. Determine the S-Hydrograph (20 points).
i.e.
Calculate the 50-min UH for the catchment. (40 points)
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This was found by developing S(t-50) and interpolating between S(t-45) and S(t-60).