Solution Homework 3
Hydraulic Engineering Design
Spring 2014
Prepared by Carlos Galdeano
1. Consider the storm drain inlet at the corner of Dean Keaton St and San Jacinto
Blvd. How large is this? Assuming the same drainage area you worked with in
Problem 1 of Homework 2, determine the design discharge and the top width
of the spread of the water across the street at this location. The best estimate
that I can make of the elevations on the road from the airborne LIDAR data at
this location is 533.6 ft above datum at the curb and 534.5 ft above datum at
the center of the road off the median strip, which is 45 ft from the curb. Will
the spread of the water across the road satisfy the City of Austin’s Design
Criteria in a 2 year storm? In a 25 year storm? What proportion of the flow
bypasses the inlet during these events?
𝐼𝑛𝑙𝑒𝑡 𝐿𝑒𝑛𝑔𝑡ℎ = 11.9 𝑓𝑡
Estimating the slope from the center of the road to the gutter:
𝑆𝑥 =
(534.5 − 533.6) 0.9
𝑓𝑡
=
= 0.02
45
45
𝑓𝑡
From previous homework, we know that the slope along the gutter is:
𝑆𝑜 =
14.57
𝑓𝑡
= 0.0424
343
𝑓𝑡
Estimating the design discharge capacity and top width spread
The time of concentration is 5 minutes as estimated in Homework 2.
Intensities from table 2-4 and C from table 2-1 of the Drainage Criteria
Manual of the City of Austin:
𝑖𝑛
𝑄2 𝑦𝑒𝑎𝑟 = 𝐶 𝑖 𝐴 = (0.73)(5.76)(0.292) = 1.2614 𝑎𝑐𝑟𝑒
= 1.274 𝑐𝑓𝑠
ℎ𝑟𝑎
𝑖𝑛
𝑄25 𝑦𝑒𝑎𝑟 = 𝐶 𝑖 𝐴 = (0.86)(10.1)(0.292) = 2.6058 𝑎𝑐𝑟𝑒
= 2.632 𝑐𝑓𝑠
ℎ𝑟𝑎
From the Gutter Flow formula
𝑄=
𝐶𝑓 5 8 1
𝑆 3 𝑇 3 𝑆0 2
𝑛 𝑥
Where
Q = flow in gutter (cfs)
Cf = coefficient (0.56 for US units, 0.376 for SI units)
So = longitudinal slope
T = spread (ft)
Sx = transverse slope
𝑇2
𝑇25
𝑦𝑒𝑎𝑟
𝑦𝑒𝑎𝑟
= (𝑄
= (𝑄
𝑛
3
8
= (1.274
)
5
𝐶𝑓 𝑆𝑥 3 𝑆0 0.5
𝑛
3
8
0.016
5
) = 6.03 𝑓𝑡
0.56(0.02)3 (0.042)0.5
3
8
)
5
𝐶𝑓 𝑆𝑥 3 𝑆0 0.5
= (2.632
0.016
5
3
8
) = 7.917 𝑓𝑡
0.56(0.02)3 (0.042)0.5
According to Table 3-1 of the Drainage Criteria Manual of the City of Austin
the minimum clear width of roadway design when gutter is flowing full is
12 ft in each direction. The distance of the center of the road and the inlet
is 45 ft, so 𝑇 ≤ 33. In both cases this criteria is satisfied.
From the required length formula:
Where
1 0.6
𝐿 𝑇 = 𝐶𝑓 𝑄 0.42 𝑆0 0.3 (
)
𝑛𝑆𝑥
LT = required length to intercept all flow (ft)
Q = flow in gutter (cfs)
Cf = coefficient (0.60 for US units, 0.817 for SI units)
So = longitudinal slope
Sx = transverse slope
0.6
1 0.6
1
𝐿 𝑇2𝑦𝑒𝑎𝑟 = 𝐶𝑓 𝑄 0.42 𝑆0 0.3 (
) = (0.60)(1.274)0.42 (0.042)0.3 (
) = 32.08 𝑓𝑡
(0.016)(0.02)
𝑛𝑆𝑥
0.6
0.6
1
1
0.3
𝐿 𝑇25𝑦𝑒𝑎𝑟 = 𝐶𝑓 𝑄 0.42 𝑆0 (
) = (0.60)(2.64)0.42 (0.042)0.3 (
) = 43.951 𝑓𝑡
(0.016)(0.02)
𝑛𝑆𝑥
Calculating proportion of the flow bypasses the inlet
The proportion of flow captured:
𝐸2𝑦𝑒𝑎𝑟 = 1 − (1 −
𝐿 1.8
11.9 1.8
) = 1 − (1 −
) = 0.566
𝐿𝑇
32.08
𝐿 1.8
11.9 1.8
𝐸25𝑦𝑒𝑎𝑟 = 1 − (1 − ) = 1 − (1 −
) = 0.434
𝐿𝑇
43.951
Therefore, the proportion of flow bypasses the inlet
𝐹𝑙𝑜𝑤 𝑏𝑦𝑝𝑎𝑠𝑠𝑒𝑠2 𝑦𝑒𝑎𝑟 = 100 − 100(𝐸2𝑦𝑒𝑎𝑟 ) = 43.41%
𝐹𝑙𝑜𝑤 𝑏𝑦𝑝𝑎𝑠𝑠𝑒𝑠25 𝑦𝑒𝑎𝑟 = 100 − 100(𝐸25𝑦𝑒𝑎𝑟 ) = 56.64%
2. Continue this study of the storm drainage on Dean Keaton upstream to the
drainage divide near the Student Services Building (Figure 1(b)). How many
storm inlets are there? How large are they? What is the distance between
them? Will this portion of Dean Keaton St satisfy the City of Austin’s Drainage
Criteria for spread of water on the street considering a 2 year storm? A 25
year storm? What proportion of the street flow bypasses the inlets during
these events? If you conclude that the street drainage capacity is not adequate,
what could you do to alter it? A web map is presented at http://bit.ly/1jhywhz
and more information on the corresponding elevations is shown on the next
page.
6 inlets in the area
Figure 1 shows the data obtained from the cross sections and ArcGIS online map
1
b
Z = 562.7
Z = 590. 8
3
307.8 ft
ft
A2
Z = 562
307.4 ft
ft
550 ft
ft
6
Z = 547.45
c
Z = 547.8
5
4
𝐴1 = 362,020.06 ft = 0.8269 Acres
𝐴2 = 20,944.28 𝑓𝑡 = 0.4808 Acres
𝐴3 = 25,563.62 𝑓𝑡 = 0.5869 Acres
Estimating the Slopes:
Relation
Profile
1&a
a&2
3&b
b&4
5&c
c&6
7&d
d&8
1&3
3&5
5&7
2&4
4&6
6&8
cross section
cross section
cross section
cross section
cross section
cross section
cross section
cross section
longitudinal
longitudinal
longitudinal
longitudinal
longitudinal
longitudinal
Length
ft
32.55
32.55
31.75
31.75
35.1
35.1
40
40
550
307.4
342
574.5
307.8
352.2
Slope
Sx
0.052
0.003
0.022
0.028
0.026
0.010
0.018
0.014
-
Slope
So
0.052
0.049
0.038
0.053
0.047
0.038
332.2 ft
ft
A3
Z = 546.9
8
d
Z = 534.6
7
342 ft
Z = 534.05
San Jacinto
Z = 592.4
A1
Z = 561.8
80 ft
a
4
70.2 ft
65.1
2
574.5 ft
ft
63.5
Z = 592.4
Z = 533.9
Estimating the Time of Concentration for each inlet catchment (double click to
enter to excel sheet):
Inlet
Cross
Section
Length
Cross
Section
Slope
Long Length
ft
Long
slope
Tt1
minutes
Tt2
minutes
Tc
minutes
Tc Design
minutes
3
4
5
6
7
8
32.55
32.55
31.75
31.75
35.1
35.1
0.0522
0.0031
0.022
0.0283
0.0256
0.01
550
574.5
307.4
307.8
342
352.2
0.0524
0.0533
0.0491
0.0466
0.0380
0.0380
0.0358
0.1111
0.0495
0.0448
0.0505
0.0737
1.9706
2.0409
1.1371
1.1688
1.4382
1.4804
2.0064
2.1520
1.1867
1.2135
1.4887
1.5541
5
5
5
5
5
5
Estimating the Discharge at each inlet (double click to enter to excel sheet)
Inlet
3
4
5
6
7
8
i
i
C
C
2 year 25 year
2 year 25 year
in/hr in/hr
0.73
0.73
0.73
0.73
0.73
0.73
0.86
0.86
0.86
0.86
0.86
0.86
5.76
5.76
5.76
5.76
5.76
5.76
10.1
10.1
10.1
10.1
10.1
10.1
Q =CiA Q cumulative Q =CiA Q cumulative
2 year
2 year
25 year
25 year
cfs
cfs
cfs
cfs
A
acre
0.413
0.413
0.24
0.24
0.293
0.293
1.76
1.76
1.02
1.02
1.25
1.25
1.76
1.76
1.82
1.86
2.16
2.44
3.63
3.63
2.11
2.11
2.57
2.57
3.63
3.63
4.22
4.29
5.25
5.75
Estimating the top width spread (double click to enter to excel sheet)
Inlet
3
4
5
6
7
8
Q cumulative Q cumulative
2 year
25 year
cfs
cfs
1.76
1.76
1.82
1.86
2.16
2.44
3.63
3.63
4.22
4.29
5.25
5.75
Sx
So
Cf
n
T
2 year
T
25 year
0.022
0.028
0.026
0.010
0.018
0.014
0.052
0.053
0.049
0.047
0.038
0.038
0.56
0.56
0.56
0.56
0.56
0.56
0.016
0.016
0.016
0.016
0.016
0.016
6.141
5.232
5.734
10.539
8.143
9.913
8.061
6.867
7.854
14.402
11.358
13.664
According to Table 3-1 of the Drainage Criteria Manual of the City of Austin the
minimum clear width of roadway design when gutter is flowing full is 12 ft in each
direction. The excel below shows the estimation of the requirement needed for
Inlet
Length
center road
ft
Requirement
City of Austin
T
2 year
T
25 year
3
4
5
6
7
8
31.75
31.75
35.1
35.1
40
40
19.75
19.75
23.1
23.1
28
28
6.141
5.232
5.734
10.539
8.143
9.913
8.061
6.867
7.854
14.402
11.358
13.664
As we can see, in all cases the specification is satisfied ( 𝑇2𝑦𝑒𝑎𝑟 <
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝐶𝑖𝑡𝑦 𝑜𝑓 𝐴𝑢𝑠𝑡𝑖𝑛; 𝑎𝑛𝑑 𝑇2𝑦𝑒𝑎𝑟 < 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝐶𝑖𝑡𝑦 𝑜𝑓 𝐴𝑢𝑠𝑡𝑖𝑛).
The graphs below show a better visualization of the spread along Dean Keaton.
Inlets 3,5 and 7 (Dean Keaton St)
30.000
Spread T (ft)
25.000
20.000
2 year
15.000
25 year
10.000
City of Austin
5.000
0.000
0
500
1000
1500
Long length (ft)
Inlets 4, 6 and 8 (Dean Keaton St)
30.000
Spread T (ft)
25.000
20.000
15.000
2 year
10.000
25 year
City of Austin
5.000
0.000
0
500
1000
1500
Long length (ft)
Estimating required length, inlet efficiencies and the proportion of flow bypasses
the inlets (double click to enter to excel sheet)
Inlet
Inlet
Length
ft
3
4
5
6
7
8
12.2
9.99
10
12
11.87
11.82
Lt
Lt
E
2 year 25 year
2 year
ft
ft
34.52
29.84
31.42
55.03
39.30
47.84
46.82
40.47
44.69
78.08
57.04
68.53
0.54
0.52
0.50
0.36
0.48
0.40
E
25 year
0.42
0.40
0.37
0.26
0.34
0.29
Flow
Bypass
2 year
46%
48%
50%
64%
52%
60%
Flow
Bypass
25 year
58%
60%
63%
74%
66%
71%
As shown in the table above, the flow bypasses by almost 52% on one side of the
Dean Keaton (inlets 3, 5 and 7) for a 2 year event, and 66% for a 25 year event. On
the other hand, flow bypasses by 60 % the other side of Dean Keaton (inlets 4, 6
and 8) for a 2 year event, and 71% for a 25 year event. The T required by the City
of Austin is much higher than the designed, but the proportion of flow that
bypasses is relevant. A way of reducing the percentage of flow bypassing the inlets
is by implementing infiltration trench as the ones in the redevelopment area of
Mueller Airport. It will be interesting to do the same exercise with a 100 and 500
year storm event to see how the system behaves in more extreme conditions.