CE 4200 Hydrology
Frank T.-C. Tsai
9/16/10
Exam 1
(12:10-1:30pm)
(four problems)
Problem 1 (25 points)
A rainfall record contains 59 years of measurements. The annual-maximum rainfall amounts (in
inches) of 5 min, 15 min, and 30 min are ranked in the foll
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #2 Solution
Problem 1:
Solution
For each time interval there are n = 50 ranked rainfall amounts of annual maxima. The
relationship between the rank, m, and the return period, T, is given by Weibull formula:
T =
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #1 Solution
Problem 1:
Solution
S = 2120 km3
Q = 44700 km3/yr
Tr=2120 km3/44700 km3/yr = 0.0474 yr = 17.3 days.
Problem 2:
Solution
(1) Storage at the beginning of August (or end of July):
S July S Jan (3 5
30)
Return Blue Book and question sheet(s)
CE 4200 Hydrology
Frank T.-C. Tsai
9/16/14
9:00-10:20 am
Exam 1
(4 problems, 100 points)
Problem 1 (25 points)
Use the Chen method to estimate total rainfall depth (inches) for the 25-year, 8-hour storm for a
10
city
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CE 4200 Hydrology
Frank T.-C. Tsai
10/21/2014
9:00-10:20am
Exam 2
(4 problems, 100 points)
Problem 1 (25 points)
The annual-maximum 24-hour rainfall data of an area show a mean of 22 cm and a standard
deviation of 12 cm.
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CE 4200 Hydrology
Frank T.-C. Tsai
9/18/12
12:00-1:20pm
Exam 1 and solution
(7 problems, 100 points)
Problem 1 (15 points)
Use the Chen method to estimate total rainfall depth (inches) for
the 10-year 1-hour storm fo
Probability Distribution Functions:
1. Discrete probability distributions
a. Basic properties
b. Exceedance probability
c. Mean, variance, skewness
2. Return Period = Average number of years between
exceedances.
3. Probability functions
a. Binominal (Bern
CE 4200 Hydrology
Frank T.-C. Tsai
Introduction
Hydrologic Cycle and System Concept
Hydrology
Current research topics in hydrology
Hydrologic data
Hydrologic cycle
Hydrologic Cycle
Hydrologic Cycle and System Concept
1
Hydrology
Hydrology is the science
CE 4200 Hydrology
Frank T-C. Tsai
8/26/04
Lecture 2
Hydrologic Processes
Water Balance Equation
Linear Reservoir System
Discrete Water Balance Equation
Hydrologic Processes
2-1
Water Balance Equation
I (t )
S (t )
Q(t )
I (t ) : volumetric inflow rate
Q
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #9 Solution
Problem 1 Solution:
2
2
x2 x2 e y 1 302 1522 e y 1 y 0.195 .
x e
(y
2
y
2
)
152 e
2
( y 0.195 )
2
y 5.00 .
For T=100 years, the exceedance probability is 0.01. The cumulative probability is 0
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #1 Solution
Problem 1:
Solution
(1) Storage at the beginning of August (or end of July):
S July S Jan (3 5
30) (6 8
20)
S July 60 59 65 S July 54
(2) Storage at the end of August
S Aug S July 15 13
S July 54
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #3
Problem 1 Solution:
1
Problem 2 Solution:
In Baton Rouge, Louisiana, 24-hour storms are characterized by Type III rainfall, and the
hyetograph is determined by multiplying the ordinates of the Type III hyetog
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CE 4200 Hydrology
Frank T.-C. Tsai
9/15/15
9:00-10:20 am
Exam 1
(4 problems, 100 points)
Problem 1 (25 points)
Hydrologic data over a 2-year period (1986-1987) for a mountain basin containing a lake are given
in the
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CE 4200 Hydrology
Frank T.-C. Tsai
10/22/2015
9:00-10:20am
Exam 2
(5 problems, 100 points)
Problem 1 (20 points)
The storage capacity of a forest canopy covering a catchment is 9 mm, the leaf-area index is 8,
and the
Runoff Models
(1)
Time of concentration
a. Kinematic-wave equation (turbulent flow and laminar
flow)
b. NRCS method
c. Kirpich equation
d. Izzard equation
e. Kerby equation
f. Channel flow
(2)
Peak-runoff models
a. Rational method
b. NRCS-TR55 method
cm
5. Probable Maximum Precipitation
Example 5.7
(1) Statistical Method
Estimate t-hour PMP: Pm P km p
P : mean of annual-maximum rainfall depths for a given
duration
p : standard deviation of annual-maximum rainfall depths for a
given duration
km : frequen
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #3
Problem 1 Solution:
1
Problem 2 Solution:
In Baton Rouge, Louisiana, 24-hour storms are characterized by Type III rainfall, and the
hyetograph is determined by multiplying the ordinates of the Type III hyetog
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #4
Problem 1 Solution:
0-20 min:
P=20 mm/h*20min*1h/60min=6.67 mm
P
6.67
I S 1 e S KEt 9(1 e 9 ) 8(0.5)(20) / 60 6.04 mm
20-40 min:
P=50 mm/h*20min*1h/60min=16.67 mm
P
16.67
I S 1 e S KEt 9(1 e 9 ) 8(0.5)(20
CE 4200 Hydrology
Frank T.-C. Tsai
Homework #2 Solution
Problem 1:
Solution
For each time interval there are n = 50 ranked rainfall amounts of annual maxima. The
relationship between the rank, m, and the return period, T, is given by Weibull formula:
T =
CE 4200 Hydrology
Frank T.-C. Tsai
Due: 11/12/2015
Homework #6
Problem 1
Consider one-hour rainfall intensity below for an area. The area has a curve number CN = 70.86.
Time
(min)
0-12
12-24
24-36
36-48
48-60
Rainfall Intensity
(in/hr)
1.143
1.893
7.375
2
CE 4200 Hydrology
Frank T.-C. Tsai
Due: 11/19/2015
Homework #7
Problem 1
The 10-min unit hydrograph for a watershed is given below.
Time
0
10
20
30
40
50
(min)
u10min(t) 0
10
20
50
20
10
3
(m /s)
Determine the peak runoff (m3/s) for the 50-minute unit hyd
CE 4200 Hydrology
Frank T.-C. Tsai
Due: 10/15/2015
Homework #5
1. The 10-year IDF curve for Baton Rouge is given as follow:
i
60.86
(t 6.75)0.72
where i is the rainfall intensity in in/hr and t is the rainfall duration in minutes. If soil type
for an area
CE 4200 Hydrology
Frank T.-C. Tsai
Due: 10/8/2015
Homework #4
Problem 1
The 10-year IDF curve for Baton Rouge is given as follow:
i
60.86
(t 6.75)0.72
where i is the rainfall intensity in in/hr and t is the rainfall duration in minutes. If the infiltratio