Two Lakes : Dreams Realized

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.

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

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.

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

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.

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.

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<

Computations