Question 01 (10 pts) [will be graded]
The infiltration rate for excess rain on a small site was observed to be 10 cm/hr at the beginning
of rain and it decreased exponentially toward an ultimate infiltration rate of 1.2 cm/hr. A total of 33 cm
of water infiltrated during the 10-hr interval. Assuming the Horton’s infiltration model is appropriate,
what is the value of k in Horton equation? Utilize the “Excel” with “Trial & Error” technique as well as
“Solver” function to solve for “k” (Submit separately with HW 5 submission).
SOLUTION:
Infiltration rate, f = fc + (fo -fc) e ^(-kt)
Given, fo = 10 cm/hr and fc = 1.2 cm/hr
Cumulative infiltration volume = F
= ∫ fc + (fo-fc) e ^(-kt) dt
= fc*t + (fo-fc)/k (1-e^(-kt))
Given, F = 33 cm at t = 10 hrs
Substitute F into the integrated equation and solve for k by trial and error technique described in the
class,
k = 0.412/hr.
SEE EXCEL FOR SOLUTION
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Figure 1 - EXCEL SOLUTIONS
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DEPARTMENT OF CIVIL ENGIEERING
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Question 02 (10 pts) [will be graded]
The parameters for Horton’s equation are f0 = 3.0 in/hr. fc = 0.5 in/hr, and K = 4.0 h-1
. Determine
the infiltration rate and cumulative infiltration at 0.25-hr increments up to 4 hr from the beginning of
infiltration. Assume continuous ponding. Plot the graph between time and infiltration rate.
SOLUTION:
Time (hrs) ft (in/hr) F (in)
0 0.000 0
0.25 1.420 0.520
0.5 0.838 0.790
0.75 0.624 0.969
1 0.546 1.114
1.25 0.517 1.246
1.50 0.506 1.33
1.75 0.502 1.499
2.0 0.501 1.625
2.25 0.500 1.750
2.5 0.500 1.875
3 0.500 2.000
3.25 0.500 2.250
3.5 0.500 2.375
3.75 0.500 2.500
4 0.500 2.625
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
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THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Question 03 (20 pts) [will be graded]
Assuming an average soil moisture condition on hydrologic soils group C, calculate the runoff
volume (cm) for a 40.5 ha suburban development with the following land use if rainfall is 100 mm. Use
the SCS method.
Land use % of land
Residential 40
Condominium 20
Commercial 25
Open space, grass cover=85% 15
What is the area of retention (no outlet) or percolation basin in ha to store the runoff water if the
maximum depth of storage is 1.52 m, excluding debris storage and freeboard?
Solution: Using table 5.14 for CN
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Question 04 (20 pts) [will be graded]
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Use the NRCS (SCS) method to estimate rainfall excess for an area before and after
development. The rainfall is estimated at 15 cm. The hydrologic soil type is A. The pre-development
condition is open space with grass on above 50% of the area with fair condition. The postdevelopment condition is residential with a 38% impervious cover.
If the watershed were 10.1 ha, how many m3 of ponding is necessary to store all the rainfall excess
from post-development?
SOLUTION:
Using table 5.14 for CN
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Figure 2 - CN table used for problem 3 and 4
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Question 05 (20 pts) [will be graded]
An urban catchment with an asphalt surface has an average slope of 0.5%, and the distance
from the catchment boundary to the outlet is 90 m. For a 20 minutes’ storm with an effective rainfall
rate of 75 mm/h, estimate the time of concentration using the Izzard equation. Please check the validity
of utilizing the Izzard equation for calculating the time of concentration.
Solution:
Izzard Equations:
? =
2.8 ? 10−6
?? + ??
??
1/3
; ?? =
530??
1/3
??
2/3
; ?ℎ??? ??? < 3.9 ?2 ℎ? Table: Values for cr in the Izzard Equation Surface cr Very smooth asphalt 0.0070 Tar and sand pavement 0.0075 Crushed-slate rook 0.0082 Concrete 0.012 Closely clipped sod 0.016 Tar and gravel pavement 0.017 Dense bluegrass 0.060 Given: Slope (S0) = 0.5% = 0.0005 L = 90m Cr (from table Asphalt) = 0.007 ie = 75 mm/hr Solution: ? = 2.8 ? 10−6 ?? + ?? ?? 1/3 = 2.8 ? 10−6 ∗ (75) + (0.007) (0.005) 1/3 = 0.0422 ?? = 530?? 1/3 ?? 2/3 = 530 ∗ (0.0422) ∗ 901/3 752/3 = 6 ???? ?ℎ??? ???????? => ??? = (0.075
?
ℎ?
) ∗ (90?) = 6.75
?2
ℎ?
6.75
?2
ℎ?
3.9
?2
ℎ?
,?ℎ??????? ?????? ???????? ?? ??? ??????????
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
DEPARTMENT OF CIVIL ENGIEERING
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Question 06 (20 pts) [will be graded]
The subject watershed is located in Baltimore, Maryland. A developer wants to develop a
subdivision of 2 acres in the watershed. The proposed subdivision will consist of (i) 50% of the
subdivision with single-family residential areas, (ii) 25% of the subdivision will be left as parks and (iii)
25% of the area will be converted into pavement made of brick. Estimate the peak discharge (runoff)
for a 2-hour 100-year storm for the proposed condition utilizing RATIONAL METHOD. Use the IDF
curve.
Clearly show with arrows in the IDF how you obtain the rainfall intensity (in/hr).
SOLUTION:
Using table 5.21 to get runoff coefficient
(i) 50% of the subdivision with single-family residential areas
a. Average of 0.30+0.5 = 0.4
(ii) 25% of the subdivision will be left as parks
a. Average of 0.10+0.25=0.175
(iii) 25% of the area will be converted into pavement made of brick
a. Average of 0.70+0.85 = 0.775
THE UNIVERSITY OF THE DISTRICT OF COLUMBIA (UDC)
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SOLUTION:
Using formula for peak flow by Rational formula:
? = ???
? =
∑ ????
??
C = 0.5∗0.4+0.25∗0.175+0.25∗0.775
0.5+0.25+0.25
= 0.4375
i= 2 in/hr (from IDF curve below)
A = 2 acres
? = 0.4375 ∗ 2
??
ℎ?
∗ 2 ????? ∗
1 ??
12 ??
∗
1 ℎ?
36000 ???
∗
43,560 ??2
1 ????
= 1.765
??3
???
(???)
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Sample Solution