cveen 4410 hydrology homework 1 - university of...

CVEEN 4410 Hydrology Homework 1

Spring 2013

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.


Spring 2013

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


Spring 2013

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.


Spring 2013

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


Spring 2013

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


Spring 2013

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


Spring 2013

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


Spring 2013

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


Spring 2013

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


Spring 2013

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


Spring 2013

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

cveen 4410 hydrology homework 1 - university of...

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