CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 1
Problem 1: Rainfall Averaging (8 pts) Using the following watershed and gage precipitation depths, find the average rainfall over the entire
watershed. Use the following methods:
A. averaging (1 pt)
B. Thiessen polygon (3 pts)
C. Isohyetal (3 pts).
Which method is likely the most accurate? (1 pt)
SOLUTION
Averaging
Gage Depth (in)
B 2.02
C 2.10
D 2.88
E 2.94
average 2.49
Thiessen
Gage Depth (in) Area area/total area
Area Frac * Precip
A 1.49 8 0.03 0.04
B 2.02 47 0.18 0.36
C 2.10 75 0.28 0.59
D 2.88 37 0.14 0.40
E 2.94 96 0.36 1.06
Gage Depth (in)
A 1.49
B 2.02
C 2.10
D 2.88
E 2.94
F 4.21
If the student used all of
the rain gages, it is
acceptable.
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 2
F 4.21 3 0.01 0.05
Total 266 1.00 2.50
Isohyetal
depth area area/total area
Area Frac * Precip
1.5 46 0.17 0.26
2.5 154 0.57 1.43
3.5 69 0.26 0.90
269 1.00 2.59
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 3
Note: all of these methods will have some variance. The areas will likely differ, as well at the final answer.
For the most accurate, both Thiessen and Isohyetal are both acceptable.
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 4
Problem 2: Moisture Relationships Related to Precipitation (8 pts) Use the saturation vapor pressure equation listed below to complete the following exercises:
Make a plot of saturation vapor pressure versus temperature, for temperatures ranging from -30°C –
50°C. Use the plot (2 pts) to answer the following questions.
A. Which of the following samples of air are saturated? (2 pts)
a. T = 20°C, P = 10 mb
b. T = 20°C, P = 25 mb
c. T = 37°C, P = 60 mb
d. T = 15°C, P = 18 mb
B. Given a sample of air at T = 30°C and P = 20 mb, what are the: (2 pts)
a. Dew Point
b. Saturation Vapor Pressure
C. Repeat part B for the following sample of air: T = 10°, P = 20 mb (2 pts)
SOLUTION
Part A:
0
20
40
60
80
100
120
140
-40 -30 -20 -10 0 10 20 30 40 50 60
e(s
) =W
ate
r V
apo
r P
ress
ure
(m
b)
Temp (C)
Saturation Vapor Pressure vs. Temp temp C e(s)
-30 0.509021
-20 1.255143
-10 2.86402
0 6.105834
10 12.26035
20 23.34634
30 42.40596
40 73.84191
50 123.8013
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 5
For Parts A-C see the plot below with annotations.
All points below the line are un-saturated, the points on the line are saturated, and points above the line
are over-saturated.
Saturated samples are: b & d
Part B:
Dew Point ~= 18°C; Sat vapor pressure = 42.4 mb
Part C:
Dew Point ~= 18°C; Sat vapor pressure = 12.3 mb
Problem 3: Reading IDF curves (10 pts) Use NOAA Atlas 14 to find the following rainfall intensities: (4 pts)
A. Utah, Hogle Zoo, 10 year, 12 hour
B. Utah, Manti, 2 year, 2 hour
C. Utah, Price, 100 year, 24 hour
CVEEN 4410 Hydrology Homework 1
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D. Utah, Moab, 2 year, 15 minute
Which of the above storms could be used as a SCS design storm? (1 pt)
What would be the storms total volume of rain for the Moab storm above? (1 pt)
Use TP-40 to find the rainfall depth for the following storms: (4 pts)
A. Texas, Houston, 50 year, 1 hour
B. Texas Houston, 1 year, 3 hour
C. Maine, Augusta, 100 year, 24 hour
D. Maine, Augusta, 1 year, 30 minute
SOLUTION
Intensities:
A. 0.153 in/hr
B. 0.264 in/hr
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 7
C. 0.097 in/hr
D. 1.02 in/hr
The Price 24 hour storm could be used for SCS.
Total volume rain for Moab = 1.02 in/hr(15/60 hr) = 0.255 in
Depths
A. ~4.3 in
B. ~2.7 in
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 8
C. ~6.0 in
D. ~0.6 in
Problem 4: Constant Intensity Design Storm (3 pts) Determine the constant intensity design storm for a Price, Utah watershed that has a 42 minute
time of concentration. The local standards specify a 100 year design storm. Show your calculations.
Draw the hyetograph.
SOLUTION
Will fall
between these
two values
CVEEN 4410 Hydrology Homework 1
Spring 2013 Page 9
Intensity ~= 2.0 in/hr
Problem 5: SCS Design Storm (5 pts) Determine the 8 hour, 50 year design storm using the SCS dimensionless hyetograph procedure for a
detention basin design project in St George. Use the Type 2 storm hyetograph shown below. Turn in
your table (3 pts) and hyetograph (2 pts). Use a bar plot for the hyetograph.
Time Type II Time Type II Time Type II Time Type II Time Type II
(hrs) Incremental (hrs) Incremental (hrs) Incremental (hrs) Incremental (hrs) Incremental
0.0 0.0000 5.0 0.0077 10.0 0.0183 15.0 0.0158 20.0 0.0073
0.5 0.0053 5.5 0.0080 10.5 0.0234 15.5 0.0138 20.5 0.0069
1.0 0.0055 6.0 0.0085 11.0 0.0309 16.0 0.0125 21.0 0.0065
1.5 0.0056 6.5 0.0090 11.5 0.0482 16.5 0.0113 21.5 0.0064
2.0 0.0059 7.0 0.0097 12.0 0.3799 17.0 0.0105 22.0 0.0060
2.5 0.0061 7.5 0.0105 12.5 0.0719 17.5 0.0096 22.5 0.0059
3.0 0.0063 8.0 0.0114 13.0 0.0373 18.0 0.0091 23.0 0.0056
3.5 0.0067 8.5 0.0125 13.5 0.0265 18.5 0.0085 23.5 0.0055
CVEEN 4410 Hydrology Homework 1
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4.0 0.0069 9.0 0.0139 14.0 0.0208 19.0 0.0080 24.0 0.0053
4.5 0.0072 9.5 0.0158 14.5 0.0183 19.5 0.0075
SOLUTION
50 year, 24 hour storm for St George is 2.23 in.
Design Storm: 50-yr, 24-hr 2.23
Type II
Time Type II Incremental
(hrs) Incremental Design Storm
0.0 0.0000
0.5 0.0053
1.0 0.0055
1.5 0.0056
2.0 0.0059
2.5 0.0061
3.0 0.0063
3.5 0.0067
4.0 0.0069
4.5 0.0072
5.0 0.0077
5.5 0.0080
6.0 0.0085
6.5 0.0090
7.0 0.0097
7.5 0.0105
8.0 0.0114
8.5 0.0125 0.0279
9.0 0.0139 0.0310
9.5 0.0158 0.0352
10.0 0.0183 0.0408
CVEEN 4410 Hydrology Homework 1
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10.5 0.0234 0.0522
11.0 0.0309 0.0689
11.5 0.0482 0.1075
12.0 0.3799 0.8472
12.5 0.0719 0.1603
13.0 0.0373 0.0832
13.5 0.0265 0.0591
14.0 0.0208 0.0464
14.5 0.0183 0.0408
15.0 0.0158 0.0352
15.5 0.0138 0.0308
16.0 0.0125 0.0279
16.5 0.0113
17.0 0.0105
17.5 0.0096
18.0 0.0091
18.5 0.0085
19.0 0.0080
19.5 0.0075
20.0 0.0073
20.5 0.0069
21.0 0.0065
21.5 0.0064
22.0 0.0060
22.5 0.0059
23.0 0.0056
23.5 0.0055
24.0 0.0053
1.6355
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
Rai
n In
ten
sity
(in
/hr)
Time (hrs)
St George, UT 50 year 8 hour Hyetograph