Highway 80 Gage
Historical Peaks
Bridges
Weirs
HEC-2 Computer Model
The Golder Evaluation
CONSIDERATIONS AND COMPUTATIONS FOR
FLOOD CONTROL LAKE
IN JACKSON MISSISSIPPI
For conceptual purposes,
while studying the feasibility of using a lake through Jackson for Flood control our
initial calculations were made using an average Pearl River cross section.
And the Chezy-Manning Hydraulic Equation:
Q = AV
V= C (rs)1/2
r = A/p
s = h/l
Where:
Q = Flow rate (ft3/sec)
A = Cross sectional area (ft2)
V = Velocity (ft/sec)
r = Hydraulic radius (ft)
p = Wetted perimeter (ft)
s = Slope of water surface (ft/ft)
l = Distance (ft)
h = Drop in water level (ft)
C is found using the kutter formula
C = 41.6 + 1.1811/n + 0.000281/s
1 + (41.6 + 0.00281/s) n/(r)1/2
Where:
n = Manning roughness coefficient
This was much less
cumbersome than using the HEC-2 program with its many cross sections and data points. This
way we could get a feel for what it would take by simply changing a few numbers. This
would get us in the ball park of what it would take and later we could use a more accepted
computer model.
Present Condition
The first step was to take historical flood
levels vs flow rates and generate a pre-downtown levee/structure curve and a post
levee/structure curve.

When plotting the Pearl River
Jackson Gage data of pre 1963 annual flows and post 1969 annual peak flows, one must go
back to the period of 1874 - 1935 in order to have any significant amount of flood data
which could compare to the 1979 and 1983 floods. By using all of the available yearly peak
flow information, excluding the period in which the levees were constructed, and assuming
that the information is somewhat accurate, it can clearly be seen that there is a
difference in magnitude of the gage readings taken before 1963 compared to those taken
after 1969 (approximately 3 feet at this location). It should be noted that the gauge
readings were taken downstream of the cutoff channel. All that may be concluded from this
information due to the long span of time it covers is that the combination of bridges,
levees, landfills and other encroachments (see map on following page) seem to have an
increase in water levels for this location for the higher magnitude floods.

| Year |
Date |
Gage
Height (ft-HGVD) |
Discharge
(cfs) |
Notes |
Year |
Date |
Gage
Height (ft-HGVD) |
Discharge
(cfs) |
Notes |
|
|
|
|
|
|
|
|
|
|
| 1874 |
4-25-74 |
37.00 |
80000 |
1 |
1947 |
1-22-47 |
30.66 |
26000 |
|
| 1881 |
12-05-80 |
36.50 |
70000 |
1 |
1948 |
3-11-48 |
30.63 |
25600 |
|
| 1900 |
4-24-00 |
36.70 |
35000 |
|
1949 |
1-12-49 |
33.11 |
38300 |
|
| 1901 |
01 |
|
24000 |
|
1950 |
1-14-50 |
33.90 |
44700 |
|
| 1902 |
3-31-02 |
37.50 |
85000 |
|
1951 |
4-04-51 |
34.36 |
49100 |
|
| 1903 |
2-14-03 |
33.70 |
43600 |
|
1952 |
3-16-52 |
17.51 |
6600 |
|
| 1904 |
4-11-04 |
11.10 |
5295 |
|
1953 |
5-09-53 |
31.65 |
28500 |
|
| 1905 |
2-17-05 |
29.20 |
24880 |
|
1954 |
5-12-54 |
23.25 |
10600 |
|
| 1906 |
3-29-06 |
29.80 |
26000 |
|
1955 |
4-20-55 |
31.50 |
27500 |
|
| 1907 |
10-13-06 |
30.10 |
26600 |
|
1956 |
4-14-56 |
31.78 |
29300 |
|
| 1908 |
2-23-08 |
29.08 |
26000 |
|
1957 |
4-11-57 |
30.32 |
22100 |
|
| 1909 |
5-30-09 |
35.30 |
58300 |
|
1958 |
5-08-58 |
34.23 |
38900 |
|
| 1910 |
4-20-10 |
16.40 |
9020 |
|
1959 |
2-20-59 |
26.52 |
13600 |
|
| 1911 |
4-16-11 |
22.60 |
14600 |
|
1960 |
3-11-60 |
30.29 |
22600 |
|
| 1912 |
4-23-12 |
31.70 |
29600 |
|
1961 |
3-01-61 |
35.00 |
46000 |
|
| 1913 |
3-18-13 |
29.00 |
24600 |
|
1962 |
12-21-62 |
37.24 |
66100 |
2 * |
| 1914 |
4-09-14 |
31.10 |
29900 |
|
1963 |
3-19-63 |
17.74 |
6440 |
2 ** |
| 1915 |
2-09-15 |
26.70 |
20200 |
|
1964 |
3-23-64 |
31.00 |
24000 |
2 |
| 1916 |
1-09-16 |
26.70 |
20200 |
|
1965 |
2-17-65 |
32.02 |
28800 |
2 |
| 1917 |
4-11-17 |
26.50 |
19800 |
|
1966 |
2-18-66 |
30.99 |
26700 |
2 |
| 1918 |
5-04-18 |
22.90 |
15300 |
|
1967 |
2-25-67 |
20.16 |
8130 |
2 |
| 1919 |
3-19-19 |
27.60 |
21800 |
|
1968 |
12-23-67 |
31.43 |
29900 |
2 |
| 1920 |
12-14-19 |
30.50 |
28100 |
|
1969 |
4-20-69 |
34.55 |
44800 |
2 |
| 1921 |
4-21-21 |
32.90 |
37800 |
|
1970 |
5-03-70 |
27.43 |
18300 |
2 |
| 1922 |
3-11-22 |
28.80 |
24200 |
|
1971 |
5-15-71 |
32.67 |
32100 |
2 |
| 1923 |
2-16-23 |
30.70 |
28700 |
|
1972 |
1-17-72 |
32.56 |
31600 |
2 |
| 1924 |
3-08-24 |
26.80 |
20400 |
|
1973 |
4-19-73 |
32.99 |
33400 |
2 |
| 1925 |
1-25-25 |
28.80 |
24200 |
|
1974 |
4-18-74 |
34.36 |
40300 |
2 |
| 1926 |
3-17-26 |
27.00 |
20700 |
|
1975 |
3-20-75 |
32.43 |
34400 |
2 |
| 1927 |
2-24-27 |
30.00 |
26800 |
|
1976 |
4-03-76 |
35.74 |
50400 |
2 |
| 1928 |
4-30-28 |
29.80 |
26300 |
|
1977 |
4-09-77 |
35.57 |
48900 |
2 |
| 1929 |
3-24-29 |
32.30 |
30600 |
|
1978 |
5-14-78 |
31.80 |
27400 |
2 |
| 1930 |
5-28-30 |
31.90 |
29400 |
|
1979 |
4-17-79 |
43.28 |
128000 |
2,3,4 |
| 1931 |
8-05-31 |
26.40 |
15100 |
|
1980 |
4-13-80 |
35.50 |
50900 |
|
| 1932 |
2-28-32 |
29.10 |
21300 |
|
1981 |
4-05-81 |
30.10 |
24600 |
|
| 1933 |
12-19-32 |
35.20 |
60000 |
|
1982 |
12-02-82 |
36.00 |
46600 |
|
| 1934 |
3-13-34 |
28.00 |
18600 |
|
1983 |
5-23-83 |
39.50 |
78600 |
|
| 1935 |
3-12-35 |
35.18 |
56700 |
|
1984 |
3-06-84 |
28.40 |
20800 |
|
| 1936 |
2-12-36 |
32.46 |
34400 |
|
1985 |
2-07-85 |
29.00 |
23800 |
|
| 1937 |
1-29-37 |
30.00 |
22800 |
|
1986 |
11-29-86 |
29.40 |
25300 |
|
| 1938 |
4-09-38 |
32.07 |
32100 |
|
1987 |
2-28-87 |
32.60 |
39100 |
|
| 1939 |
2-15-39 |
28.93 |
19200 |
|
1988 |
4-03-88 |
27.70 |
19700 |
|
| 1940 |
7-18-40 |
31.94 |
30100 |
|
1989 |
1-17-89 |
30.20 |
24000 |
|
| 1941 |
12-29-41 |
25.17 |
12700 |
|
1990 |
1-25-90 |
33.70 |
38900 |
|
| 1942 |
3-17-42 |
19.41 |
7720 |
|
1991 |
5-05-91 |
35.00 |
45500 |
|
| 1943 |
3-30-43 |
28.43 |
19200 |
|
|
|
|
|
|
| 1944 |
4-04-44 |
34.03 |
46700 |
|
|
|
|
|
|
| 1945 |
3-01-45 |
32.58 |
36900 |
|
|
|
|
|
|
| 1946 |
2-17-46 |
34.44 |
49600 |
|
|
|
|
|
|
1 - Historic peaks outside period of record
2 - Flow regulated since 27 Sep61 by Ross Barnett Reservoir, 15 miles upstream
3 - Estimated discharge of 145,000 cfs used in frequency study to account for flood
control regulation at Ross Barnett Dam, 15 miles upstream of gage
4 - Highest peak since 1874
* - Reservoir constructed
** - Levees constructed
Using the Chezy equation,
an average cross section, historical slopes, and flood data friction factors were derived
to get this cross section to fit the pre-levee/structure curve at various flow rates.
Main Body of Lake
Now a much narrower more efficient cross section (or
lake) was derived that would handle the 1979 flood at the safe flood levels assuming the
water levels south of the lake would remain the same for either situation.

The cleared and graded lake with 2000 foot wide
dredged flow course now has friction factors similar to or better than the original river
channel. Various channel depths were used until through iteration the derived water level
and hydraulic gradient could be achieved.
From an engineering stand point it could be
considered that we are designing a flow course that would have the ability to handle
128,000 cubic feet per second with a rise of about three feet over a length of 11 miles.
Bridges
The next question is what to do at the bridges? Most
of the Pearl River bridges in Jackson have a span of at least 1000 feet. The Highway 80
bridge for example has a span of 1170 feet.

If a 1000 feet wide flow course was dredged down to
the top of the pile caps over a l000 foot length, the resulting cross section would have
the same hydraulic gradient as the rest of the lake.
In the event that any of the bridges are not
constructed in a manner that would lend itself to this depth of dredging, side pilings
could be driven with a concrete band poured around them and the existing piling tying them
all together in order to obtain the proper safety factors. It would also be possible not
to dredge as deep directly under the bridge. Limestone could then be added to prevent
washing. The area under the bridge would act as a small weir and would not cause a
significant change in the water level.
The following three pages show the calculations using the Chezy
equations for the original river channel, the lake itself, and the dredged channels that
could be used under the bridges.
|
water level
|
272
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
32
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
26.0
|
7.0
|
-2.0
|
|
|
straight line down floodplain) |
|
width (ft)
|
200
|
3800
|
12000
|
|
264.4
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
276.4
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
4.72
|
0.45
|
0.00
|
|
|
|
|
flowrate (cubic ft/sec)
|
24535
|
11981
|
0
|
|
|
|
|
total flow (cubic ft/sec)
|
|
36515
|
36515
|
|
|
|
|
|
|
|
|
|
|
|
The above calculations are for an average cross-section of the Pearl River in
Jackson as it existed before the levees, bridges, or any other structures were built. For
calculation purposes the cross-section is located at River Mile 294 which is roughly at
the half way point of the upper lake. Different water levels and their resulting flowrates
can be compared to the historical Jackson gage readings to make sure we are in the ball
park with our friction factors and cross-sectional shape. The extrapolated water levels
are based on reach distance rather than river miles.
|
|
|
|
Average
|
water level
|
274
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
34
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
28.0
|
9.0
|
0.0
|
|
|
straight line down floodplane)
|
|
width (ft)
|
200
|
3800
|
12000
|
|
266.4
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
278.4
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
4.95
|
0.56
|
0.00
|
|
|
|
|
flowrate (cubic ft/sec)
|
27709
|
19315
|
0
|
|
|
|
|
total flow (cubic ft/sec)
|
|
47024
|
47024
|
|
|
|
|
|
|
|
|
|
|
|
The average water level is increased in two ft. increments and will be placed
on a curve that shows the historical data
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Average
|
water level
|
276
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
36
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
30.0
|
11.0
|
2.0
|
|
|
straight line down floodplane)
|
|
width (ft)
|
200
|
3800
|
12000
|
|
268.4
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
280.4
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
5.17
|
0.68
|
0.14
|
|
|
|
|
flowrate (cubic ft/sec)
|
31025
|
28229
|
3401
|
|
|
|
|
total flow (cubic ft/sec)
|
|
59253
|
62655
|
|
|
|
|
|
|
|
|
|
|
|
It is also interesting to note that the extrapolated water levels at RM284.5
and RM301.7 are within a foot of the before
|
|
levee HEC-2 study that we did using many cross-sections. This is accurate
enough for conceptual purposes to
|
|
come up with rough dimensions and
water levels of a flood control lake. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Average
|
water level
|
278
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
38
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
32.0
|
13.0
|
4.0
|
|
|
straight line down floodplain) |
|
width (ft)
|
200
|
3800
|
12000
|
|
270.4
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
282.4
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
5.39
|
0.78
|
0.27
|
|
|
|
|
flowrate (cubic ft/sec)
|
34477
|
38664
|
13001
|
|
|
|
|
total flow (cubic ft/sec)
|
|
73141
|
86142
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Average
|
water level
|
280
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
40
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
34.0
|
15.0
|
6.0
|
|
|
straight line down floodplain) |
|
width (ft)
|
200
|
3800
|
12000
|
|
272.4
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
284.4
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
5.60
|
0.89
|
0.39
|
|
|
|
|
flowrate (cubic ft/sec)
|
38063
|
50569
|
28288
|
|
|
|
|
total flow (cubic ft/sec)
|
|
88632
|
116920
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Average
|
water level
|
280.6
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
265
|
274
|
|
40.6
|
ft equiv. gage reading
|
|
rise (ft)
|
12.00
|
12.00
|
12.00
|
|
0.70
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
1.00
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
34.6
|
15.6
|
6.6
|
|
|
straight line down floodplain) |
|
width (ft)
|
200
|
3800
|
12000
|
|
273.1
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.2
|
0.2
|
|
285.1
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
5.66
|
0.92
|
0.43
|
|
|
|
|
flowrate (cubic ft/sec)
|
39213
|
54597
|
34195
|
|
|
|
|
total flow (cubic ft/sec)
|
|
93811
|
128006
|
|
|
|
|
|
|
|
|
|
|
|
The flowrate in this situation is the same as that of the 1979(200year) flood
but the water levels are that of a cross-section from the earlier part of this century.
|
|
|
|
|
|
|
|
|
Below is the same graph of historical peak flowrates vs. gage readings as
shown earlier except that it has the above calculated information added on the graph.
|
|
|
|
|

|
Average
|
water level
|
275.1
|
ft elev
|
@R.M.294
|
|
|
channel
|
river bottom
|
flat woods
|
|
|
|
av.bottom (elevation)
|
246
|
259
|
264
|
|
35.1
|
ft equiv. gage reading
|
|
rise (ft)
|
3.19
|
3.19
|
3.19
|
|
0.19
|
ft rise per river mile
|
|
run (ft)
|
90800
|
63500
|
63500
|
|
0.27
|
ft rise per reach mile(somewhat
|
|
height (ft)
|
29.1
|
16.1
|
11.1
|
|
|
straight line down floodplain) |
|
width (ft)
|
200
|
2000
|
1200
|
|
273.1
|
ft water surface-RM284.5
|
|
n (friction coef.)
|
0.03
|
0.03
|
0.03
|
|
276.3
|
ft water surface-RM301.7
|
|
velocity (ft/sec)
|
3.19
|
2.59
|
1.96
|
|
|
|
|
flowrate (cubic ft/sec)
|
18540
|
83364
|
26103
|
|
|
|
|
total flow (cubic ft/sec)
|
|
101904
|
128007
|
|
|
|
|
|
|
|
|
|
|
|
Here is the 1979 flood again except the dredged lake is in place. You can see
that there is only a three foot rise over a linear distance of 11 miles(16.5 river miles).
This would lower the 200 year flood about 12 feet from present conditions at the
reservoir.
|
|
|
|
|
|
|
|
|
|
Average
|
water level
|
275.1
|
ft elev
|
|
|
|
|
channel
|
|
|
|
|
|
|
av.bottom (elevation)
|
243
|
|
|
|
35.1
|
ft equiv. gage reading
|
|
rise (ft)
|
0.05
|
|
|
|
0.26
|
ft rise per mile
|
|
run (ft)
|
1000
|
|
|
|
|
|
|
height (ft)
|
32.1
|
|
|
|
|
|
|
width (ft)
|
1000
|
|
|
|
275.08
|
ft water surface-south
|
|
n (friction coef.)
|
0.03
|
|
|
|
275.12
|
ft water surface-north
|
|
velocity (ft/sec)
|
3.99
|
|
|
|
|
|
|
flowrate (cubic ft/sec)
|
128001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Here is an example of what could be done under the bridges. They could be
dredged down to a level which would would not harm the bridge piles over a width of one
thousand feet and have similar flow characteristics(water levels & gradients) as the
lake itself. They would not silt back up because the water velocity of the lake would not
be enough to carry sand.
|


Weirs
There are two weirs or low head dams on the lake. The southern most
weir would hold a lake level of about 260 feet. The upper weir would hold the main body of
the lake at a level of about 270 feet. The energy equation was used for the preliminary
design of the weirs.

WEIR OBSERVATIONS
During major floods, such as
the one that occurred in 1979, the flood control lakes will act as a river which is
flowing on a grade. In order to understand what effect the submerged weirs will have when
the flood control lakes are flowing on a grade, the pump house weir in the city of Jackson
was studied and observed at various flow velocities and submergence heights.
The example of actual flow
over the pump house weir, shown in the charts below, is used in this report because the
rate of flow per foot of weir (82.2 cubic feet per second) is almost identical to the rate
of flow per foot of weir that will occur over the lower flood control lake weir during a
1979 flood (85.3 cubic feet per second).
A person would not need to
understand weir formulas to safely adjudge that an identical volume of water will pass
over the lower lake weir with less elevation difference than will pass over the pump house
weir. This is because the same rate of water passing over the pump house weir (which is
8.2 feet deep) has 12.6 feet of depth with which to pass over the lower lake weir.
Velocity is, therefore, much
less over the lower lake weir than at the observed pump house weir and, because velocity
effects are exponential, calculations show that the upstream elevation increase, caused by
the lower lake weir, will be approximately 0.26 feet, or, approximately one-half the
effect observed at the pump house weir (0.57 feet).
WeirObservations
JACKSON, MISSISSIPPI
WATER INTAKE DAM
(LOCATED ON PEARL RIVER)

LOWER LAKE WEIR

MEMORANDUM
TO: Matt Lamar (McGowan Working Partners) DATE: November 9, 1999
FROM: Gary Lake (Golder Associates
Inc.)
RE:
UPPER AND LOWER WEIR CALCULATIONS FOR FLOOD
CONTROL LAKE IN MISSISSIPPI
In your e-mail message to Mike Jacobs of
Golder Associates Inc. (Lakewood, Colorado) on November 2, 1999, you requested that a
hydraulics evaluation be made for two weir sites located on a flood control lake in
Mississippi. Specifically, four situations were presented by you for Golder to calculate
flood water levels above the two weir sites (designated as Lower Lake Weir and Upper Lake
Weir) based on the hydraulics information and data you provided on Sheets 1 through 4
included with your e-mail message. Also, Golder understands that the calculated water
surface elevations may be used in further HEC-2 computer model runs to be made by McGowan
Working Partners. In addressing your request, two situations at each weir site were
evaluated by Golder using the principles of submerged weir flow hydraulics for low dams.
The four flood situations you indicated are
represented by water surfaces downstream of the weirs that are higher than the crest
elevations for each situation and where the tailwater depths are so high that the
characteristic "train" of surface waves at the weir site would be flattened out
and disappear except for a dip in the water surface over the downstream side of the weir
itself. Thus, the weirs are said to be submerged or drowned, and the water below the weirs
is termed tailwater. The depth of submergence is the difference in elevation between a
given tailwater surface and the crest of the weir. The discharge over a submerged weir is
related to the head on the upstream side of the weir, the head at the downstream side, and
the height of the weir crest above the channel bottom.
The following equation developed by Du Buat
(discussed in Elements of Hydraulic Engineering, D.S. Ellis, 1947) was used to
estimate flood water levels above the weir sites for the four weir flow situations,
denoted as Cases 1 through 4 below. This submerged weir flow equation historically has
primarily been used for establishing designs of regulating weirs on river systems and
gives reliable results for evaluating existing river regulating weir systems under
submerged flow conditions.
 
where:
d = submerged water depth, in feet;
H = upstream head depth on weir crest;
L = length of weir, in feet;
C = coefficient determined from tests on
submerged weirs as used for river regulation and control, dimensionless; values of C for
the following values of d/H are noted below; and
|
d/H
Value
|
C
Value
|
0.000 |
3.74 |
0.100 |
3.70 |
0.200 |
3.70 |
0.300 |
3.75 |
0.400 |
3.82 |
0.500 |
3.93 |
0.600 |
4.18 |
0.700 |
4.61 |
0.800 |
5.36 |
0.900 |
6.64 |
0.985* |
9.19* |
* upper limit of test data
Q = total discharge of 128,000 cfs.
Several iteration analyses were made to
calculate a value of H for each case. A summary of the calculated upstream water levels
for the weir sites (Cases 1 through 4, two cases for Upper Lake Weir site and two cases
for Lower Lake Weir site) is presented below. The calculations are based solely on using
the physical and hydraulics data you provided, and assuming the downstream water levels
you cited represent the tailwater conditions, either as measured or calculated by others.
Case 1 (Lower Lake Weir)
Given:
weir crest elevation @ 260 ft.
weir length @ 1500 ft.
downstream water level elevation @ 273.30 ft.
channel bottom elevation @ 250 ft.
Calculated upstream water level elevation @
273.51
Case 2 (Lower Lake Weir)
Given:
weir crest elevation @ 260 ft.
weir length @ 2500 ft.
downstream water level elevation @ 273.30 ft.
channel bottom elevation @ 250 ft.
Calculated upstream water level elevation @
273.37
Case 3 (Upper Lake Weir)
Given:
weir crest elevation @ 269.5 ft.
weir length @ 3500 ft.
downstream water level elevation @ 274.50 ft.
channel bottom elevation @ 251.5 ft.
Calculated upstream water level elevation @
274.95
Case 4 (Upper Lake Weir)
Given:
weir crest elevation @ 266 ft.
weir length @ 3500 ft.
downstream water level elevation @ 274.50 ft.
channel bottom elevation @ 251.5 ft.
Calculated upstream water level elevation @
274.58
The calculated difference between upstream
and downstream water depths for Case 1 (Lower Lake Weir site) is 0.21 foot and the
calculated average approach flow velocity is 3.63 fps for the reported unit discharge of
85.3 cfs/ft width of flow. For Case 2 (Lower Lake Weir site), the reported unit discharge
is 51.2 cfs/ft width of flow and the calculated average approach flow velocity is
2.19 fps. The calculated average approach flow velocities upstream of the Upper Lake Weir
site for Cases 3 and 4 is 1.56 and 1.58 fps, respectively. For the purpose of
modeling the four weir flow cases using the submerged weir flow equation, a reasonableness
check was also made concerning the Pearl River low head dam and the reported water levels
for January 10, 1997. For this low dam, the measured data indicated a 0.57-foot difference
in water levels upstream and downstream of the dam for a reported unit discharge of 82.2
cfs/ft width of flow and average approach flow velocity of 4.29 fps. A calculated C value
using the submerged weir flow equation is 8.09 and is considered very reasonable in
accordance with the C values noted above.
If you should have any questions concerning
these results of the hydraulic analyses presented herein, please contact me at (303)
980-0540 or email glake @golder.com. As we discussed yesterday, Golder shall invoice McGowan
Working Partners in the amount of $1,300.00 for the engineering services rendered. If
Golder Associates can provide further engineering assistance to McGowan Working Partners,
please call Mike Jacobs or myself at the phone number indicated above.
Thank you,
Gary Lake, P.E. |
E1 = E3 – hL(1-3)
For simplicity set E1 = E2 = E3
and E = z + y + V2/2g
Where:
V = Q/Area = q/y
q = flow rate Q ¸ Width of weir channel
g = Gravity = 32.2 ft/sec2
y = Fluid depth
y2 = Critical depth of weir; yc = (q2/gn)1/3
z2 = Height of weir
If the weirs are designed properly, the flow during a 200 year flood
could approach the weir at subcritical flow, pass over the weir at critical flow and
return to subcritical flow with little or no rise above the normal hydraulic gradient of
the lake itself. It was calculated that for an upper weir height of 269.5 feet, it would
take a width of at least 3500 feet to allow 128,000 cubic feet per second to pass through
without causing a significant change in the upstream water surface elevation.
|
3500 FT WEIR TOP AT 269.5
|
|
|
|
|
|
|
|
|
*W.S.elev
|
upstream
|
|
Q
|
q
|
y(crit)
|
(v^2)/2gn
|
E
|
over weir
|
W.S.elev
|
|
128000
|
37
|
3.5
|
1.7
|
5.2
|
273.0
|
274.6
|
|
100000
|
29
|
2.9
|
1.5
|
4.4
|
272.4
|
273.8
|
|
90000
|
26
|
2.7
|
1.4
|
4.1
|
272.2
|
273.6
|
|
80000
|
23
|
2.5
|
1.3
|
3.8
|
272.0
|
273.3
|
|
70000
|
20
|
2.3
|
1.2
|
3.5
|
271.8
|
272.9
|
|
60000
|
17
|
2.1
|
1.0
|
3.1
|
271.6
|
272.6
|
|
50000
|
14
|
1.9
|
0.9
|
2.8
|
271.4
|
272.3
|
|
40000
|
11
|
1.6
|
0.8
|
2.4
|
271.1
|
271.9
|
|
30000
|
9
|
1.3
|
0.7
|
2.0
|
270.8
|
271.5
|
|
20000
|
6
|
1.0
|
0.5
|
1.5
|
270.5
|
271.0
|
|
10000
|
3
|
0.6
|
0.3
|
0.9
|
270.1
|
270.4
|
|
5000
|
1
|
0.4
|
0.2
|
0.6
|
269.9
|
270.1
|
|
1000
|
0
|
0.1
|
0.1
|
0.2
|
269.6
|
269.7
|
|
|
|
|
|
|
|
|
*The flow over the weir has a reduced water surface elevation due to the high
flow rate. When the downstream flow returns to a subcritical flowrate, the water surface
elevation returns to the normal level which can be as high as the upstream level depending
upon the downstream head.
|
|
4000 FT WEIR TOP AT 269.5
|
|
|
|
|
|
|
|
|
*W.S.elev
|
upstream
|
|
Q
|
q
|
y(crit)
|
(v^2)/2gn
|
E
|
over weir
|
W.S.elev
|
|
128000
|
32
|
3.2
|
1.6
|
4.8
|
272.7
|
274.2
|
|
100000
|
25
|
2.7
|
1.3
|
4.0
|
272.2
|
273.5
|
|
90000
|
23
|
2.5
|
1.3
|
3.8
|
272.0
|
273.2
|
|
80000
|
20
|
2.3
|
1.2
|
3.5
|
271.8
|
272.9
|
|
70000
|
18
|
2.1
|
1.1
|
3.2
|
271.6
|
272.6
|
|
60000
|
15
|
1.9
|
1.0
|
2.9
|
271.4
|
272.3
|
|
50000
|
13
|
1.7
|
0.8
|
2.5
|
271.2
|
272.0
|
|
40000
|
10
|
1.5
|
0.7
|
2.2
|
271.0
|
271.7
|
|
30000
|
8
|
1.2
|
0.6
|
1.8
|
270.7
|
271.3
|
|
20000
|
5
|
0.9
|
0.5
|
1.4
|
270.4
|
270.9
|
|
10000
|
3
|
0.6
|
0.3
|
0.9
|
270.1
|
270.4
|
|
5000
|
1
|
0.4
|
0.2
|
0.5
|
269.9
|
270.0
|
|
1000
|
0
|
0.1
|
0.1
|
0.2
|
269.6
|
269.7
|
|
|
|
|
|
|
|
|
*The flow over the weir has a reduced water surface elevation due to the high
flow rate. When the downstream flow returns to a subcritical flowrate, the water surface
elevation returns to the normal level which can be as high as the upstream level depending
upon the downstream head.
|
With the southern most weir being at a height of 260, a width of
1000 feet would be adequate. A width of 1500 feet however would hold the lower lake at a
more stable level.
|
1000 FT WEIR TOP AT 260
|
|
|
|
|
|
|
|
|
*W.S.elev
|
upstream
|
|
Q
|
q
|
y(crit)
|
(v^2)/2gn
|
E
|
over weir
|
W.S.elev
|
|
128000
|
128
|
8.0
|
4.0
|
12.0
|
268.0
|
271.4
|
|
100000
|
100
|
6.8
|
3.4
|
10.2
|
266.8
|
269.8
|
|
90000
|
90
|
6.3
|
3.2
|
9.5
|
266.3
|
269.1
|
|
80000
|
80
|
5.8
|
2.9
|
8.8
|
265.8
|
268.5
|
|
70000
|
70
|
5.3
|
2.7
|
8.0
|
265.3
|
267.8
|
|
60000
|
60
|
4.8
|
2.4
|
7.2
|
264.8
|
267.0
|
|
50000
|
50
|
4.3
|
2.1
|
6.4
|
264.3
|
266.3
|
|
40000
|
40
|
3.7
|
1.8
|
5.5
|
263.7
|
265.4
|
|
30000
|
30
|
3.0
|
1.5
|
4.6
|
263.0
|
264.5
|
|
20000
|
20
|
2.3
|
1.2
|
3.5
|
262.3
|
263.4
|
|
10000
|
10
|
1.5
|
0.7
|
2.2
|
261.5
|
262.2
|
|
5000
|
5
|
0.9
|
0.5
|
1.4
|
260.9
|
261.4
|
|
1000
|
1
|
0.3
|
0.2
|
0.5
|
260.3
|
260.5
|
|
|
|
|
|
|
|
|
*The flow over the weir has a reduced water surface elevation due to the high
flow rate. When the downstream flow returns to a subcritical flowrate, the water surface
elevation returns to the normal level which can be as high as the upstream level depending
upon the downstream head.
|
|
1500 FT WEIR TOP AT 260
|
|
|
|
|
|
|
|
|
*W.S.elev
|
upstream
|
|
Q
|
q
|
y(crit)
|
(v^2)/2gn
|
E
|
over weir
|
W.S.elev
|
|
128000
|
85
|
6.1
|
3.0
|
9.1
|
266.1
|
268.8
|
|
100000
|
67
|
5.2
|
2.6
|
7.8
|
265.2
|
267.5
|
|
90000
|
60
|
4.8
|
2.4
|
7.2
|
264.8
|
267.0
|
|
80000
|
53
|
4.5
|
2.2
|
6.7
|
264.5
|
266.5
|
|
70000
|
47
|
4.1
|
2.0
|
6.1
|
264.1
|
266.0
|
|
60000
|
40
|
3.7
|
1.8
|
5.5
|
263.7
|
265.4
|
|
50000
|
33
|
3.3
|
1.6
|
4.9
|
263.3
|
264.8
|
|
40000
|
27
|
2.8
|
1.4
|
4.2
|
262.8
|
264.2
|
|
30000
|
20
|
2.3
|
1.2
|
3.5
|
262.3
|
263.4
|
|
20000
|
13
|
1.8
|
0.9
|
2.7
|
261.8
|
262.6
|
|
10000
|
7
|
1.1
|
0.6
|
1.7
|
261.1
|
261.7
|
|
5000
|
3
|
0.7
|
0.4
|
1.1
|
260.7
|
261.1
|
|
1000
|
1
|
0.2
|
0.1
|
0.4
|
260.2
|
260.4
|
|
|
|
|
|
|
|
|
*The flow over the weir has a reduced water surface elevation due to the high
flow rate. When the downstream flow returns to a subcritical flowrate, the water surface
elevation returns to the normal level which can be as high as the upstream level depending
upon the downstream head.
|
Capacity
The effect of the lost capacity due to this lake is
explained in detail on page 103 of the lake plan.
HEC-2 Computer
Model
In order for any concept such as this lake to be considered it must
be applied to an accepted computer model. This plan was applied to the Corps of Engineers
"HEC-2" stream channel analysis computer program. The results confirmed that the
long hand calculations were in the ball park. A modification must be made on the upper
lake’s weir to get the HEC-2 to have proper water surface elevations. The top of the
weir had to be entered as having an elevation of 267 feet. The true dimensions may be
confirmed with the energy equation or long hand calculations. The hands on HEC-2 guide
states on page 1-2 under limitations that "Profile computations are not allowed To
Pass through critical depth. Sub critical and super critical analyses must be performed
separately". The results of the HEC-2 analysis for a flow rate of 128,000 cubic feet
per second follow
DTLAKE.OUT
FLOODWAY DATA,
PROFILE NO. 2 |
200 YEAR FLOOD |
128000 |
Line 3346 |
Col 1 |
|
--------------------
FLOODWAY -------------------- |
----------
WATER SURFACE ELEVATION ---------- |
| STATION |
WIDTH |
SECTION
AREA |
MEAN
VELOCITY |
WITH
FLOODWAY |
WITHOUT
FLOODWAY |
DIFFERENCE |
| 253.950 |
6976. |
69109. |
1.9 |
251.8 |
251.8 |
.0 |
| 254.820 |
7050. |
73017. |
1.8 |
253.0 |
252.9 |
.1 |
| 54.839 |
9010. |
43290. |
3.0 |
252.6 |
252.5 |
.1 |
| 54.847 |
9017. |
43773. |
2.9 |
252.7 |
252.5 |
.2 |
| 54.865 |
6304. |
69664. |
1.8 |
253.6 |
253.7 |
-.1 |
| 257.050 |
8319. |
91902. |
1.4 |
255.4 |
255.2 |
.2 |
| 59.194 |
9193. |
103056. |
1.2 |
257.0 |
256.8 |
.2 |
| 59.213 |
9236. |
87574. |
1.5 |
257.2 |
257.0 |
.2 |
| 59.221 |
9226. |
87723. |
1.5 |
257.3 |
257.1 |
.2 |
| 259.270 |
6754. |
84234. |
1.5 |
257.3 |
257.1 |
.2 |
| 262.270 |
6610. |
93167. |
1.4 |
259.6 |
259.0 |
.6 |
| 264.450 |
6678. |
94316. |
1.4 |
261.3 |
260.6 |
.7 |
| 266.220 |
11360. |
146590. |
.9 |
262.8 |
262.0 |
.8 |
| 268.870 |
9648. |
118954. |
1.1 |
264.2 |
263.3 |
.9 |
| 270.440 |
1581. |
26125. |
4.9 |
265.3 |
264.4 |
.9 |
| 270.530 |
1581. |
26852. |
4.8 |
265.8 |
264.9 |
.9 |
| 70.584 |
1581. |
26656. |
4.8 |
265.8 |
264.9 |
.9 |
| 70.591 |
1581. |
26673. |
4.8 |
265.8 |
264.9 |
.9 |
| 70.610 |
6171. |
85682. |
1.5 |
267.4 |
266.7 |
.7 |
| 273.310 |
7499. |
96611. |
1.3 |
268.3 |
267.6 |
.7 |
| 277.110 |
10293. |
145400. |
.9 |
270.1 |
269.2 |
.9 |
| 278.980 |
10340. |
104832. |
1.2 |
271.0 |
270.1 |
.9 |
| 282.080 |
9479. |
113419. |
1.1 |
272.9 |
272.1 |
.8 |
| 282.890 |
9922. |
99896. |
1.3 |
273.2 |
272.5 |
.7 |
| 283.610 |
10185. |
175277. |
.7 |
273.8 |
273.1 |
.7 |
| 284.420 |
9772. |
148876. |
.9 |
274.0 |
273.3 |
.7 |
| 284.500 |
7350. |
124586. |
1.0 |
274.0 |
273.3 |
.7 |
| 285.070 |
1500. |
51067. |
2.5 |
274.0 |
273.3 |
.7 |
| 85.087 |
1500. |
22266. |
5.7 |
273.9 |
273.1 |
.8 |
| 85.088 |
1500. |
22267. |
5.7 |
273.9 |
273.1 |
.8 |
| 285.110 |
1500. |
51589. |
2.5 |
274.4 |
273.7 |
.7 |
| 285.350 |
2862. |
64366. |
2.0 |
274.5 |
273.8 |
.7 |
| 286.250 |
959. |
30020. |
4.3 |
274.5 |
273.8 |
.7 |
| 286.630 |
1038. |
31836. |
4.0 |
274.6 |
273.9 |
.7 |
| 286.970 |
998. |
30348. |
4.2 |
274.7 |
274.0 |
.7 |
| 287.370 |
1132. |
32280. |
4.0 |
274.9 |
274.2 |
.7 |
| 287.540 |
3500. |
116246. |
1.1 |
275.2 |
274.5 |
.7 |
| 87.559 |
3500. |
31844. |
4.0 |
275.1 |
274.4 |
.7 |
| 87.560 |
3500. |
31847. |
4.0 |
275.1 |
274.4 |
.7 |
| 87.579 |
3500. |
116909. |
1.1 |
275.4 |
274.8 |
.6 |
|
|
|
|
|
|
|
| DTLAKE.OUT |
|
|
|
|
Line 3393 |
Col 1 |
|
|
|
|
|
|
|
| 87.579 |
3500. |
116909. |
1.1 |
275.4 |
274.8 |
.6 |
| 287.820 |
2871. |
52079. |
2.5 |
275.3 |
274.7 |
.6 |
| 288.230 |
3215. |
29266. |
4.4 |
275.2 |
274.6 |
.6 |
| 288.990 |
5387. |
75360. |
1.7 |
275.7 |
275.0 |
.7 |
| 289.460 |
5390. |
75664. |
1.7 |
275.7 |
275.1 |
.6 |
| 290.080 |
5393. |
75982. |
1.7 |
275.8 |
275.2 |
.6 |
| 290.400 |
5395. |
76142. |
1.7 |
275.8 |
275.2 |
.6 |
| 290.500 |
4870. |
51805. |
2.5 |
275.8 |
275.2 |
.6 |
| 290.530 |
4869. |
51786. |
2.5 |
275.8 |
275.2 |
.6 |
| 290.600 |
5398. |
76414. |
1.7 |
275.9 |
275.3 |
.6 |
| 291.810 |
5590. |
76406. |
1.7 |
276.0 |
275.4 |
.6 |
| 292.340 |
3110. |
49750. |
2.6 |
276.0 |
275.4 |
.6 |
| 92.549 |
1987. |
26658. |
4.8 |
275.9 |
275.3 |
.6 |
| 293.790 |
3389. |
65546. |
2.0 |
276.7 |
276.0 |
.7 |
| 295.190 |
3038. |
54086. |
2.4 |
276.9 |
276.2 |
.7 |
| 295.490 |
3037. |
54255. |
2.4 |
276.9 |
276.2 |
.7 |
| 296.690 |
3419. |
59644. |
2.1 |
277.1 |
276.4 |
.7 |
| 298.310 |
4153. |
72636. |
1.8 |
277.3 |
276.6 |
.7 |
| 299.800 |
2540. |
46080. |
2.8 |
277.4 |
276.7 |
.7 |
| 300.280 |
3431. |
54138. |
2.4 |
277.7 |
276.9 |
.8 |
| 301.290 |
1898. |
33683. |
3.8 |
278.0 |
277.3 |
.7 |
Conclusion
As stated in the lake plan, these figures are by no
means set in stone. This is a concept. If it turns out that these lake dimensions are not
adequate, or more than adequate, the proper depths and widths can be determined.
The following pages contain a hydraulic evaluation of this lake pan
by Golder Associates. The firm was hired by John McGowan and Mart Lamar to verify the work
that is presented in this plan.
MAXIMUM BENEFITS THAT WILL RESULT FROM THE
FLOOD CONTROL LAKES ALONE WITH NO ADDITIONAL BENEFIT
FROM RESERVOIR REGULATION
Flood benefits at 1979 Flow Rate
350 Year Probability
| Position |
River
Mile
Location |
1979
Actual |
Flood
Lake
Elevation
McGowan
Evaluation |
Flood
Lake
Flood
Benefit
McGowan |
Flood
Lake
Elevation
Golder
Evaluation |
|
|
|
|
|
|
| 1. Richland Flood Plain |
284.5 |
272.9 |
273.3 capacity
effect |
+ 0.4 feet |
(272.9) 128,000 cfs actual |
| 2. Lynch Creek |
286.4 |
276.6 |
273.8 |
- 2.8 |
(273.2) 0.10 ft over lower weir |
| 3. Town Creek |
287.4 |
277.7 |
274.2 |
- 3.5 |
(273.5) |
| 4. Island South End |
288.5 |
281.0 |
275.0 |
- 6.0 |
(274.9)0.89 ft over upper weir |
| 5. Island North End |
292.3 |
283.7 |
275.2 |
- 8.5 |
(275.3) |
| 6. The Quarter |
292.5 |
283.7 |
275.2 |
- 8.5 |
(275.3) |
| 7. Twin Lake Subdivision |
293.0 |
284.0 |
275.7 |
- 9.2 |
(275.8) |
| 8. Canterbury Court SBV |
294.0 |
285.8 |
276.0 |
- 9.8 |
(275.9) |
| 9. Hanging Moss Creek |
295.8 |
286.4 |
276.1 |
-10.3 |
(276.1) |
| 10. McLeod SBV |
296.5 |
286.8 |
276.3 |
-10.5 |
(276.2) |
| 11. Canton Club SBV |
298.0 |
287.1 |
276.5 |
-10.6 |
(276.4) |
| 12. Dam |
301.3 |
288.4 |
277.0 |
-11.4 |
(277.4) |
At the present time
it is very difficult to utilize the flood prevention capabilities of the Barnett
Reservoir. Creation of flood control lakes below the reservoir will enable the reservoir
to prerelease in advance of major storms without flooding homes and businesses in Jackson.
This ability will enable the reservoir to reduce flooding downstream in Richland and
Byram.
MAXIMUM BENEFITS THAT CAN BE DERIVED BY
SUBTRACTING AN
APPROXIMATE ADDITIONAL 1.23 FEET THAT WILL RESULT FROM
IMPROVED REGULATION OF THE RESERVOIR.
Benefits derived from reservoir regulation will
be discounted according to the consistency with which reservoir inflow can be predicted
from rainfall as it is measured on the ground. This discount value will be applied to the
chart below when a computer model for inflow projection has been completed.
| Position |
1979
Actual
Flood
Level |
Flood
Lake
Level
With improved
Discharge |
Cumulative
Flood
Benefits |
|
|
|
|
| 1. Richland Flood Plain |
272.9 |
272.0 |
- 0.9 feet |
| 2. Lynch Creek |
276.6 |
272.6 |
- 4.0 |
| 3. Town Creek |
277.7 |
272.9 |
- 4.8 |
| 4. Island South End |
281.0 |
273.9 |
- 7.1 |
| 5. Island North End |
283.7 |
274.2 |
- 9.5 |
| 6. The Quarter |
283.7 |
274.2 |
- 9.5 |
| 7. Twin Lake Subdivision |
284.0 |
274.7 |
-10.2 |
| 8. Canterbury Court SBV |
285.8 |
275.0 |
-10.8 |
| 9. Hanging Moss Creek |
286.4 |
275.1 |
-11.3 |
| 10. McLeod SBV |
286.8 |
275.3 |
-11.5 |
| 11. Canton Club SBV |
287.1 |
275.5 |
-11.6 |
| 12. Dam |
288.4 |
276.0 |
-12.4 |
|