ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
Problem 14.1.3
Determine the 2-, 10-, 25-, and 100-year precipitation depths at Miami, Florida, for 15 minute duration.
How much larger are these values than the corresponding values for St. Louis? Why is the precipitation
depth in Miami greater than St. Louis?
The 2 year and 100 year depths for Miami and St. Louis comes directly from Figure 14.1.2(c), and Figure
14.1.2(d)
They are:
Miami
2 year/15 Minute Precipitation Depth: 1.36 in
100 year/15 Minute Precipitation Depth: 2.20 in
St. Louis
2 year/15 Minute Precipitation Depth: 0.90 in
100 year/15 Minute Precipitation Depth: 1.75 in
The 10 and 25 year depths will come from the following interpolation equation:
𝑃𝑇 𝑦𝑟 = 𝑎𝑃2 𝑦𝑟 + 𝑏𝑃100 𝑦𝑟
a and b coefficient values for interpolating design precipitation depths are:
10 year; a = 0.496, b = 0.449
25 year; a = 0.293, b = 0.669
Miami
10 year/15 Minute Precipitation Depth:
𝑃10 𝑦𝑟 = 0.496(1.36 𝑖𝑛) + 0.449(2.20 𝑖𝑛)
𝑃10 𝑦𝑟 = 1.66 in
25 year/15 Minute Precipitation Depth:
𝑃25 𝑦𝑟 = 0.293(1.36 𝑖𝑛) + 0.669(2.20 𝑖𝑛)
𝑃25 𝑦𝑟 = 1.87 in
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ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
St. Louis
10 year/15 Minute Precipitation Depth:
𝑃10 𝑦𝑟 = 0.496(0.90 𝑖𝑛) + 0.449(1.75 𝑖𝑛)
𝑃10 𝑦𝑟 = 1.23 in
25 year/15 Minute Precipitation Depth:
𝑃25 𝑦𝑟 = 0.293(0.90 𝑖𝑛) + 0.669(1.75 𝑖𝑛)
𝑃25 𝑦𝑟 = 1.43 in
15 minute Duration
Miami, Florida
St. Louis, Missouri
2 year
1.36
0.90
10 year
1.66
1.23
25 year
1.87
1.43
100 year
2.20
1.75
The precipitation in Miami is greater than the precipitation in St. Louis because of regional weather
patterns and close proximity to large water body (Atlantic Ocean and Gulf of Mexico, Convectional Type
events).
2
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
Problem 14.3.1
Use the 100-year 24-hour precipitation map for the United States and the SCS storm distribution pattern
to develop a 100-year 24-hour design storm hyetograph for Washington, D.C.
100-year 24 hour precipitation for Washington D.C = 8 in (but you got to be kidding me, eyes are
straining)!!
Washington, D.C is in a Type II Distribution Area
Precipitation Intensity is Taken from the Pt value calculated and time increment (note Pt is cumulative).
Hour t
Type II
(Pt/P24)
Pt (in)
Precipitation
Intensity
(in/hr)
0.00
0.000
0
0
2.00
0.022
0.176
0.088
4.00
0.048
0.384
0.104
6.00
0.080
0.64
0.128
7.00
0.098
0.784
0.144
8.00
0.120
0.96
0.176
8.50
0.133
1.064
0.208
9.00
0.147
1.176
0.224
9.50
0.163
1.304
0.256
9.75
0.172
1.376
0.288
10.00
0.181
1.448
0.288
10.50
0.204
1.632
0.368
11.00
0.235
1.88
0.496
11.50
0.283
2.264
0.768
11.75
0.357
2.856
2.368
12.00
0.663
5.304
9.792
12.50
0.735
5.88
1.152
13.00
0.772
6.176
0.592
13.50
0.799
6.392
0.432
14.00
0.820
6.56
0.336
16.00
0.880
7.04
0.24
20.00
0.952
7.616
0.144
24.00
1.000
8
0.096
Table 12.1 100-yr/24-hr Design Storm Hyetograph Results
3
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
Precipitation Intensity (in/hr)
100-yr/24-hr Design Storm Hyetograph
10
9
8
7
6
5
4
3
2
1
0
0.00
5.00
10.00
15.00
20.00
25.00
Time (min)
Figure 12.1 100-yr/24-hr Design Storm Hyetograph
Problem 14.3.2
Determine a triangular hyetograph for the design of a culvert in Philadelphia. The design return period
is 10 year and the duration is 60 minutes. The value of r is given in Table 14.3.2.
r value from table is 0.414
Philadelphia
10 year/60 Minute Precipitation Depth:
𝑃10 𝑦𝑟 = 0.496(1.40 𝑖𝑛) + 0.449(3.0 𝑖𝑛)
𝑃10 𝑦𝑟 = 2.04 in
The Peak Intensity is calculated using (14.3.1) with Td = 60 min
ℎ=
2𝑃
2(2.04)
𝑖𝑛
=
= 4.08
𝑇𝑑
1 ℎ𝑟
ℎ𝑟
The time ta to the peak intensity is calculated by (14.3.2):
𝑡𝑎 = 𝑟𝑇𝑑 = 0.414 ∗ 60 𝑚𝑖𝑛 = 24.8 𝑚𝑖𝑛
The recession time tb is
𝑡𝑏 = 𝑇𝑑 − 𝑡𝑎 = 60 − 24.8 = 35.2 𝑚𝑖𝑛
4
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
Precipitation intensity (in/hr)
Triangular Design Hyetograph
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
60
70
Time (min)
Figure 12.2 10-yr/1-hr Triangular Design Hyetograph
Problem 4
For the monitored catchment from the Pluvia Munda study, generate a 2 year design hydrograph
utilizing the SCS small watershed step function. Proviede the time to peak (tp), the peak flow, the runoff
duration, the time of concentration, and the runoff volume. Neatly and clearly plot the hydrograph and
provide resulting information and list all assumptions made solving the problem. Use SI units (L,min) to
present final results
From the Source Area Catchment slide within the course documents of this class the total surface area
for the runoff is A = 7,200 ft2 or 0.17 Acres
From the slopes and graphical observation it is seen that the hydraulically most distant point is from the
most North Eastern portion (most North row of pavement section) of the topo map. Time of
concentration is calculated from this point: 280 ft at a 3% slope and 60 ft at a 1.5% slope using the
Kirpich equation:
For Run 1:
𝑡𝑐 = 0.0078 ∗ 2800.77 ∗ 0. 03−0.385 = 2.3 𝑚𝑖𝑛
L1 = 280 ft
S1 = 0.03
5
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
For Run 2:
𝑡𝑐 = 0.0078 ∗ 600.77 ∗ 0. 015−0.385 = 0.92 𝑚𝑖𝑛
L2 = 60 ft
S2 = 0.015
Sum of tc = 3.22 min
The minimum IDF time of concentration value is 8 minutes, for our watershed we will assume a
minimum time of concentration value of 10 minutes.
From the IDF curves provided for the city of Gainesville a 2 year Design storm with a time of
concentration of 10 minutes results in an Intensity of 5.8 in/hr
The total volume of the runoff is taken from the watershed data provided to be; V = 31,268 L. The
watershed data also provides a total rainfall amount of rain, depth = 2.91 in. The Curve number value
can be taken from the equation:
𝐶=
𝑅𝑎𝑖𝑛𝑓𝑎𝑙𝑙
2.91 𝑖𝑛 ∗ 7,200 𝑓𝑡
0.24 𝑓𝑡 ∗ 7,200 𝑓𝑡
=
=
𝑅𝑢𝑛𝑜𝑓𝑓
31,268 𝐿
1104 𝑐𝑢 𝑓𝑡
= 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 1 𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑤𝑒 𝑤𝑖𝑙𝑙 𝑎𝑠𝑠𝑢𝑚𝑒 𝑎 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 0.95
From graph given on slide 12 of notes Time to Peak = 22 min.
Peak flow rate is determined from the Rational Method:
𝑄𝑝 = 𝐶𝐼𝐴
𝑄𝑃 = 0.95 × (5.8 𝑖𝑛/ℎ𝑟) × (0.17 𝐴𝑐)
𝑄𝑝 = 0.94 𝑐𝑓𝑠 = 1597 L/min
The Equations below will produce the Inflow Design Hydrograph
𝑄=
𝑄𝑃
𝛱
[1 − 𝑐𝑜𝑠 ( )] 𝑓𝑜𝑟 0 ≤ 𝑡 < 1.25𝑡𝑝
2
𝑡𝑝
𝑡
𝑄 = 4.34𝑄𝑝 𝑒𝑥𝑝 [−1.30 ( )] 𝑓𝑜𝑟 𝑡 > 1.25𝑡𝑝
𝑡𝑝
6
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Time (min)
In-Flow, Q
(L/min)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
0.00
32.34
126.76
275.59
466.79
684.86
912.14
1130.21
1321.41
1470.24
1564.66
1597.00
1564.66
1470.24
1325.06
1177.36
1046.12
929.52
825.91
733.85
652.05
579.37
514.79
457.41
406.42
361.12
320.87
285.10
253.32
225.09
200.00
177.70
157.90
140.30
124.66
110.76
98.42
87.45
Ryan Locicero #50779799
7
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
76
77.70
78
69.04
80
61.34
82
54.51
84
48.43
86
43.03
88
38.24
90
33.97
92
30.19
94
26.82
96
23.83
98
21.18
100
18.82
102
16.72
104
14.85
106
13.20
108
11.73
110
10.42
112
9.26
114
8.23
116
7.31
118
6.49
120
5.77
122
5.13
124
4.56
126
4.05
128
3.60
130
3.20
132
2.84
134
2.52
136
2.24
138
1.99
140
1.77
142
1.57
162
0.00
Table 12.2 2-yr Design Storm Inflow Hydrograph Results
8
ENV 6932 Advanced Env Hydrology
Homework # 12 12/09/09
Ryan Locicero #50779799
Design Inflow Hydrograph
1800
1600
Flow Rate, Q (L/min)
1400
1200
1000
800
600
400
200
0
0
20
40
60
80
100
Time (min)
Figure 12.3 2-yr Design Inflow Hydrograph
Time of
Time to
Concentration Peak
(min)
(min)
2-yr Design
Storm
10
22
Peak Flow
(L/min)
1597
Area of
Catchment
(Acre)
0.17
Intensity
(in/hr)
Depth of
Runoff
(in)
Volume
of Runoff
(L)
5.8
2.91
31,268
9