Coppell Industrial-CS001227Graham Associates, Inc.
CONSULTING ENGINEERS & PLANNERS
Centerpoint Two Suite 400/616 Six Flags Drive
Arlington, Texas 76011 - Metro 640-8535
December 27, 2000
Mr. Mike Martin, P.E.
City of Coppell - Engineering
P.O. Box 478
Coppell, Texas 75019 ..
Re: Coppell Industrial Addition - TradePoint Full Development
Proposed by Champion Partners
Dear Mr. Martin,
Please consider this letter as our technical hydrologic calculatians for the p~oposed
distribution facility on Bethel Road north of the USPS facility. This design assnmes an
agreement has been reached with the downstream property owner, Duke Weeks Realty,
allowing a gravity pond outlet to be constructed.
The City's stated criteria is to have the developed condition 100-year flood discharge no
larger than 150 cfs, based on the existing condition (nndeveloped) discharge. Also, the
City has siated the proposed conditions discharges can not exceeded the existing 2 and
5--year stO~TnS. Unlike the Phase 1 design (previously sent to the City on November 14,
2000), we propose to empty the full development detention t~ond tl;m a gravity cutlet,
which drains into the downstream lake be~:'.g proposed by others. Our detention ~ond
analysis is based on the rational method (Q=CIA) and the City of Dallas's detemion
calculation procedure.
For the proposed, fid! development condition, thc weighted C v/as calculateri using the
drainage basin map, shown as Exhibit 1, and the following;
Developed area = 90.72 ac ~ C = 0.90
Pond area= 6.9 ac(~C:l.00
Bethel d~.tch area = 1.28 ac ~) C -- 9.70 ~
Total area =- 98.9 ac
Weigleed C = (90.72 x .9 + 46.9 x 1.0 + i.28 x .7) / 9~.9
C = 0.9044
For the fh!l development co~dition, xve propose to construct a long, on-site detention
pond as st~own u:,. tl~e gradi.,3g plan, Exhibit !. Tl:is 'pond' will be normally wet, having
a normal pool of 50[4.0, which is 2' above the I;hase ! normal pool elevation The full
development flood storage volume calculations are shown on Table 1. We have included
the elevation verses storage graph for our proposed detenlior~ pond as Figure 1. No flood
storage volume was counted below elevation 508.0, even though the actual bottom of the
pond is elevation 504.0.
Figure 2 shows generalized inflow and outflow hydrographs for a detention pond with a
simple gravity outlet. The difference between the 2 hydrographs represents the necessary
storage volume needed to not exceed the desired outlet discharge, Qo.
Ss = 60 x [ (Qi x Td) - Qo x (Td + Tc) / 2]
Where;
Ss is the required storage, in cubic feet, for a simple outlet
Qi is the maximum discharge into the detention, in cfs
Qo is the discharge out of the detention, in cfs
Td is the stom~ duration, in min.
Tc is the time to the peak inlet discharge, in min.
The discharge into the detention pond, Qi, can be calculated from Qi = C x I x A, where
A is the drainage area in acres, C is the weighted runoff coefficient and I is the rainfall
rate, in inches per hour, and is a function of the storm duration, Td. For our design, Tc is
10 minutes. The equation, Ss = ...., will be used to calculate storage volumes for the 5
and 2-year storm.
100-year calculations
The above equation (Ss =. .... ) is valid only xvhen the outlet is governed by a single
hydraulic equation thereby creating an outflow hydrograph with a rising leg that is
reasonably straight. Hoxvever, our proposed outlet has 2 tow level outlets at elevation
508, plus an overflow weir at elevation 513. This outlet is a little more complex and has
a point of inflection on the rising leg of the outflow hydrograph. This point of inflection
marks the time when the xvater starts flowing over the weir. Figure 3 shows the inflow
and outflow hydrographs for a detention pond with a complex gravity outlet. The
difference between the 2 hydrographs is the necessary storage volume needed to not
exceed the design storm outlet discharge, Qo.
Sc = 60x[Qi x Td - (Tp x Qp / 2) - (Qo x Tc x Qo / Qi / 2) -
((Td + Tc - Tc x Qo / Qi - Tp) x (Qo + Qp) / 2)]
Sc = 60x[Qi x Td - (Tp x Qp / 2) - (Qo^2 x Tc / Qi / 2) -
((Td + Tc - Tc x Qo / Qi - Tp) x (Qo + Qp) / 2)]
Where
Qi, Tc and Td are defined above and;
Qo for the 100 year condition is 150 cfs
Sc is the required storage, in cubic feet, for a complex outlet
Qp is the discharge thru the lower openings for a water level at the weir crest
Tp is the time needed to fill the pond up to the weir crest.
Tp = (Vi / 60 + 5 x Qi) / (Qi - Qp / 2)
Where Vi is the detention storage volume at the weir crest elevation of 513.0. For the
proposed ultimate pond, the storage volume at 513.0 is 810,227 cuft (see Table 1),
therefore Vi = 810,227.
The maximum discharge into the pond can be calculated using Qi = C x A x I, where
A = 98.9, C = .9044 and I = 99.5 / ((6.5 + Td)^.7537) for the 100 year storm, as discussed
in our 11-14-00 letter. Therefore,
Qi = .9044 x 98.9 x 99.5 / ((6.5 + Td)^.7537) for the 100 year storm.
In our proposed design we use 2 - 3 foot wide by 1 foot tall openings having a flowline of
508.0. We can calculate the flow thru the openings using the orifice equation;
Q = C x Ax (2 x g x h)^.5
where ;A is the orifice opening, in square feet, for our design a = 6
g is the gravitational constant, 32.2
h is the water height, in feet, above the center of the orifice
C is an orifice coefficient. We used 0.6 based on King and Brater's
Handbook of Hydraulics, table 4-6.
For a pond water level of 513.0, h = 513.0 - 508.5 = 4.5, therefore;
Qp = 0.6 x 6 x (2 x 32.2 x 4.5)^.5 = 61.3 cfs
Of the variables in the equation,
Sc = 60x[Qi x Td - (Tp x Qp / 2) - (Qo^2 x Tc / Qi / 2) -
((Td + Tc - Tc x Qo / Qi - Tp) x (Qo + Qp) / 2)],
Tc =10, Qo = 150, and Qp = 61.3. Qi is a functions of Td and can be found using;
Qi = .9044 x 98.9 x 99.5 / ((6.5 + Td)^.7537)
Tp is also a functions of Td and can be found using;
Tp -- (Vi / 60 + 5 x Qi) / (Qi - Qp / 2)
With Vi -- 810,227.
Therefore, by solving these equations for various Td we can find a worst case condition
that maximizes the required storage, Sc. Determining the critical duration Td is a trial
and error calculation. (The City of Dallas uses this sort of methodology in their manual.)
Our calculations are presented in the following table.
trial Td
in min.
80.
100.
110.
112.
113.
114.
120.
140.
calc. Qi
in ch
308.64
263.86
246.60
243.45
241.92
240.40
231.76
.. 207.49
calc. Tp
in min.
54.13
63.56
68.24
69.18
69.64
70.11
72.91
82.23
calc. Sc
in ch
1163471
1182329
1185145
1185283
1185303
1185291
1184579
1175360
Maximum
To achieve a storage volume of 1,185,303 cubic feet, the water level in the pond must be
at 514.7, as shown on the elevation / storage graph (see Figure 1). For a pond at this
level, we can calculate the orifice head, h = 514.7 - 508.5 -- 6.2' and the orifice discharge
Q = .6 x 6 x (2 x 32.2 x 6.2)^.5 -- 71.9 cfs. In order to satisfy Qo: 150, the weir Q must
be 150 - 71.9, or 78.1 cfs. Solving the weir equation for L we get;
L=Q/(CxH^I.5), or L=78.1/(3x(514.7-513)^1.5)=11.75'
where; Q is the discharge over the weir, in cfs L is the weir width, in feet
H is the water height above the weir crest
C is a weir coefficient. We used 3.0 based on King and Brater's
Handbook of Hydraulics, table 5-3.
We can now calculate the flow over the weir using the weir equation for any pond
elevation between 513 and 517. Our hydraulic calculations for our proposed outlet,
including both the ~veir and the orifices, are presented on Table 2 and as Figure 4, which
is a graph of elevation verses discharge.
2 and 5-year calculations
For our project, the existing condition 2 and 5-year discharges are 67.8 and 88.8 cfs,
respectively, as calculated in our 11-14-00 letter. These discharges represent upper
design limits; the proposed 2 and 5-year discharges can be less. For the proposed pond
and pond outlet, the exact calculation of non-100 year outlet discharges, Qo, is not an
easy task, however a graphical method can yield a good answer, within + or - 1 cfs. For
this analysis, we assume the 2 and 5-year will discharge thru the orifices only (no weir
flow). In the end, this assumption will be verified by comparing the proposed 2 and 5-
year flood levels to the weir crest elevation. This assumption makes our inflow and
outfloxv hydrographs of the type shown in Figure 2, therefore the required storage can be
calculated using the Ss = .... equation, not the longer Sc = .... equation.
The maximum discharge into the pond can be calculated using Qi = C x A x I, where
A = 98.9, C = .9044 and I -- 74.9 / ((8.5 + Td)^.8069) for the 5 year storm and I = 50.6 /
((6.0 + Td)^.7856) for the 2 year storm as discussed in our 11-14-00 letter. Therefore,
Qi = .9044 x 98.9 x 74.9 / ((8.5 + Td)^.8069) for the 5 year storm.
Qi = .9044 x 98.9 x 50.5 / ((6.0 + Td)^.7856) for the 2 year storm.
The discharge out of the pond in unknown, but is related to the pond's storage / elevation
and the outlet's discharge / elevation characteristics.
We calculated the required storage usin'g;
Ss = 60 x [ (Qi x Td) - Qo x (Td + Tc) / 2]
for several different Qo's, ranging from 20 to 70 cfs, and we tried several valves of Td
such that Sc was maximized. We considered the proposed time of concentration, Tc, to
be 10 minutes. A summary of the results of these calculations, for both the 2 and 5-year
storm, are presented as Table 3 and a graph of the maximum storage vs. outlet discharge
is shown as Figure 5.
We noxv have 3 graphs, Figures 1, 4 and 5, that are related to each other. By adding a
fourth graph, showing elevation vs. elevation, to be used as a turning line, and by plotting
these related graphs at the same scales, we have arrange these graphs so that their axis
align and form a rectangle as shown on Figure 6. This figure shows only that part of
Figures 1 and 4 needed for our analysis. In this way the scale is expanded to increase the
accuracy of our graphical analysis. By selecting a trial pond elevation on the elevation
vs. storage graph, and projecting this elevation horizontally to the turning. Then
projecting this elevation vertically to the outlet discharge vs. elevation graph, then
projecting this discharge horizontally to the storage vs. outlet discharge graph (either the
2 or 5-year), then projecting this storage vertically back to the elevation vs. storage graph.
If the final projected elevation matches the trial elevation, then this is the answer. If not,
repeat the process with a new trial elevation. Figure 6 shows the projected lines for the 2
and 5-year storms. The projected lines also show the outlet discharges for the proposed 2
and 5-year condition.
The graphic solution technique result in maximum discharges of 51 and 58.5 cfs for the 2
and 5-year storms, respectively. These discharges correspond to storm durations of
approximately 122 and 134 minutes for the 2 and 5-year storms, respectively. Using the
full development, elevation verses storage graph, our proposed design has water levels in
the detention pond of 511.6, 512.6 and 514.7 for the 2, 5 and 100-year storms.
Please feel free to call myself or Chuck Stark with any questions you may have.
Sincerely, ·.
Neal Chisholm P.E.
Graham Associates, Inc.
cc; Kerry Borden - Champion Partners
David Meinhardt - Meinhardt & Quintang
Table 1
Champion - Tradepoint Proj¢ct
Full Development Detention Storage Calculations
Elevation
504.0 ..
505.0
506.0
507.0
508.0
509.0
510.0
511.0
512.0
513.0
514.0
515.0
516.0
517.0
Area
(sO
644
19,750
55,474
102,547
119,341
136,266
153,321
170,507
187,824
205,273
222,855
240,571
258,421
276,405
Incremental
Volume (cO
10,179.
37,612.
79,011.
110,944.
127,804.
144,794.
161,914.
179,166.
196,549.
214,064.
231,713.
249,496.
267,413.
Cumul~ive *
Volume (cO
0
0
0
0
0
127,804
272,598
434,512
613,678
810,227
1,024,291
1,256,004
1,505,500
1,772,913
* Above elevation 508.0
Table 2
Champion - Tradepoint Project
Outlet Hydraulic Information
Elevation
I Orifice 2-3'x1'
I C=0.6 A=6
508.0 0.0
508.5 0.0
509.0 0.5
509.5 1.0
510.0 1.5
510.5 2.0
511.0 2.5
511.5 3.0
512.0 3.5
512.5 4.0
513.0 4.5
513.5 5.0
514.0 5.5
514.5 6.0
514.7 6.2
515.0 6.5
515.5 7.0
516.0 7.5
516.5 8.0
517.0 8.5
II
II
II
.11.
o.o II
o.o II
20.4 II
28.9 II
35.4 II
40.9 II
45.7 11
50.0 II
54.0 II
57.8 II
61.3 II
64.6 II
67.8 II
7o.8 11
71.9 II
73.7 IJ
76.4 II
79.1 II
81.7 II
84.2 Il
II
Weir L = 11.75'
C = 3.0
H Q
0.0 0.0
0.5 12.5
1.0 35.3
1.5 64.8
1.7 78.1
2.0 99.7
2.5 139.3
3.0 183.2
3.5 230.8
4.0 282.0
Total
cfs
0.0
0.0
20.4
28.9
35.4
40.9
45.7
50.0
54.0
57.8
61.3
77.1
103.1
135.6
150.0
173.4
268.4
310.1
354.9
402.4
Q=CxAx(2xgxh)^-5 II Q=CxLxH^l.5
Td
120
122
123
124
128
108
109
110
111
112
98
99
100
101
105
85
91
92
93
95
Table 3
Champion - Tradepoint Project
* =Maximum
Full Development Detention Storage Calculations
For 2 and 5-year Storms
2 - YEAR STORM
5 - YEAR STORM
11
Qo = 50 cfs Il Qo = 50 cfs
calc. Qi I calc. Ss II Td I calc. Qi [ calc. Ss
cfs [ cfs II min. ] cfs [ cfs
10'1'.3 534439 150 112.4 771760
100.1 534478 159 107.5 772222
99.5 534480 * 160 107.0 772227 *
98.9 534472 161 106.5 772224
96.5 534336 165 104.5 772125
2 - YEAR STORM
Qo = 55 cfs
109.6 515496
108.8 515520
108.1 515531 *
107.4 515529
106.7 515513
2- YEAR STORM
Qo = 60 ch
117.8 498233
116.9 498260
116.0 498271 *
115.2 498265
111.9 498O86
2 - YEAR STORM
Qo = 65 cfs
130.8 481947
124.4 482398
123.4 482401*
122.4 482385
120.5 482298
2- YEAR STORM
Qo = 70 ch
II 5 - YEAR STORM
11 Qo = 55 ch
140 118.5 747795
144 116.0 747910
145 115.4 747911 *
146 114.8 747902
150 112.4 747760
Il 5 - YEAR STORM
II Qo = 60 c~
120 133.2 724732
131 124.6 725700
132 123.9 725704 *
133 123.2 725696
140 118.5 725295
YEAR STORM
Qo = 65 cfs
84 132.0 467697
85 130.8 467698*
86 129.7 467676
118 134.9 705162
120 133.2 705232
· :121 132.3 705243 *
122 1.3J:5 705239
124 129.9 705186
105
111
112
113
120
YEAR STORM
Qo = 70 cfs
147.2
141.2
140.2
139.3
133.2
685763
686240
686253 *
686247
685732
Td
min.
355
357
358
359
365
215
220
221
222
228
155
157
158
159
164
135
137
138
139
145
Table 3
Champion - Tradepoint Project
Full Development Detention Storage Calculations
For 2 and 5-year Storms
2 - YEAR STORM
II 5 - YEAR STORM
Qo = 20 cfs [1 Qo = 20 cfs
I calc. Qi I calc. Ss II Td I calc. Qi
'1 c£s I crs II min. I cfs
44.3 724864 440 48.57
44.1 724870 445 48.13
44.0 724872 * 446 48.05
43.9 724871 447 47.96
43.4 724842 450 47.71
calc. Ss
cfs
1012140
1012162
1012162 *
1012162
1O12154
2 - YEAR STORM [I 5 - YEAR STORM
Qo = 30 cfs I1 Qo = 30 cfs
65.2 638009 260 73.5 903167
64.0 638072 280 69.3 903813
63.8 638074 * 281 69.1 903814 *
63.6 638072 283 68.8 903812
62.3 637992 290 67.5 903695
2 - YEAR STORM 11 5 - YEAR STORM
Qo = 40 cfs II Qo = 40 cfs
83.6 579155 200 90.1 829268
82.8 579185 203 89.1 829308
82.4 579190 * 204 88.7 829311 *
82.0 579188 205 88.4 829308
80.1 579083 210 86.8 829216
2 - YEAR STORM I[ " 5 - YEAR STORM
Qo = 45 cfs Il Qo = 45 cfs
92.7 555467 175 99.9 799068
91.7 555508 178 98.6 799129
91.2 555515* 179 98.2 799136 *
90.7 555513 180 97.7 799135
87.9 555329 185 95.7 799029
* = Maximum
Tradepoint Ultimate Devopment
e.
o
518
517
516
515
514
513
512
511
510
5O9
5O8
5O7
0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 2000000
G') Storage in cubic feet
213 [~Tradepoint Ultimate DevopmentI
HYDROGRAPHS simple outlet
Qo ~
?
?
?
Td
Td+Tc
TIME in min.
INFLOW ~ --OUTFLOW
HYDROGRAPHS complex outlet
Qi
C:
m
QP
TC Tp
Td
TIME in min.
Td+Tc iL_--OUTFLOW
INFLOW
Tradepoint - Outlet for ult. dev.
O
518
517
516
515
514
513
512
511
510
5O9
5O8
507
C:
Ill
0 50 100 150 200 250 300 350 400
Discharge in cfs
-- - Orifice 2-3'x1' -- - Weir 11.75' Combined]
Tradepoint - 11.75' weir
8O
7O
6O
C:
m
4O
3O
2O
400000
500000 600000 700000 800000 900000 1000000 1100000
Storage in cubic feet
YEAR 5 YEAR