WATER POLLUTION CONTROL RESEARCH SERIES
16010 DMG 12/71
FLUSHING OF SMALL SHALLOW LAKES
U.S. ENVIRONMENTAL PROTECTION AGENCY
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the
results and progress in the control and abatement-of pollution
in our Nation's waters. They provide a central source of
information on the research, development and demonstration
activities in the Environmental Protection Agency, through
inhouse research and grants and contracts with Federal, State,
and local agencies, research institutions, and industrial
organizations.
Inquiries pertaining to Water Pollution Control Research
Reports should be directed to the Chief, Publications Branch
(Water), Research Information Division, R&M, Environmental
Protection Agency, Washington, D,C. 20^60.
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FLUSHING OF SMALL SHALLOW LAKES
by
Claud C. Lomax
John F. Orsborn
The R. L. Albrook Hydraulic Laboratory
College of Engineering Research Division
Washington State University
Pullman, Washington 99163
for the
Office of Research and Monitoring
ENVIRONMENTAL PROTECTION AGENCY
Grant #16010 DMG
December 1971
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, B.C., 20402 - Price 80 cents
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EPA Review Notice
This report has been reviewed by the
Environmental Protection Agency and
approved for publication. Approval
does not signify that the contents
necessarily reflect the view and pol-
icies of the Environmental Protection
Agency, nor does mention of trade
names or commercial products consti-
tute endorsement or recommendation
for use.
ii
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ABSTRACT
Restoration of quality to polluted lakes by inflows of clean water with
simultaneous outflow of polluted water was investigated. Elliptical
basins were used in the laboratory to simulate shallow lakes. The in-
vestigation determined the influence of selected geometric and flow
parameters on the flushing efficiency.
The theoretical analyses are combined with the experimental results to
obtain equations for predicting the flushing curves. Application of
these equations will give the potential flushing efficiency of a pro-
posed flushing scheme.
The width of the basin perpendicular to the axis of flow is an impor-
tant parameter. In general, narrower basins have better flushing
action and less erratic flow patterns than wider basins. The pollution
remaining in a basin after any interval of flushing is primarily depend-
ent on the time of the flushing interval divided by the detention time
of the basin.
This report was submitted in fulfillment of Grant Number 16010DMG, under
the partial sponsorship of the Water Quality Office, Environmental Pro-
tection Agency.
iii
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CONTENTS
Conclusions 1
Recommendations 3
Introduction 5
Experimental Apparatus 13
Test Procedure 15
Data Analysis 17
Test Results 21
Discussion of Test Results 23
Acknowledgments 29
References 31
Appendices 33
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FIGURES
Page
1 NOMENCLATURE AND FLOW ZONE SKETCHES 6
2 RESIDUAL CONCENTRATION AND AVERAGE RATE OF
CONCENTRATION REMOVAL 7
3 GENERALIZED BOUNDARY CONDITIONS FOR FLUSHING
EFFICIENCY 7
4 SMOOTHED OUTFLOW CONCENTGRAPH 8
5 PREDICTED VALUES, CR/CQ 10
6 FLUSHING PARAMETER, td/t , AS A FUNCTION OF
ASPECT RATIO, Y/X, AND INLET WIDTH, Wj_ 11
7 SCHEMATIC OF TEST APPARATUS 13
8 TYPICAL OUTFLOW HYDROGRAPH, C/CQ VERSUS t/td 17
9 CONCENTRATION VERSUS TIME 18
10 FLUSHING CURVES FOR 10-FOOT BY 4-FOOT BASIN 21
11 FLUSHING CURVES FOR 10-FOOT BY 6-FOOT BASIN 21
12 FLUSHING CURVES FOR 10-FOOT BY 10-FOOT BASIN 22
13 FLUSHING CURVES FOR 6-FOOT BY 10-FOOT BASIN 22
14 IDENTICAL RUN COMPARISON. RUNS 60 AND 61 24
15 EXAMPLE OF WELL-DIFFUSED JET 26
16 COMPARISON OF AVERAGE FLUSHING CURVES 27
VI
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TABLES
NO. Pa?e
1 Predicted Values, CR/CQ , from Eqs. 9 and 14 10
2 Summary of Test Conditions 15
3 Data and Computed Values 19
4 Data Summary for 10-Foot by 4-Foot Basin 36
5 Data Summary for 10-Foot by 6-Foot Basin 37
6 Data Summary for 10-Foot by 10-Foot Basin 38
7 Data Summary for 6-Foot by 10-Foot Basin 39
Vll
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CONCLUSIONS
1. The most important parameter in determining the shape of the flush-
ing curve, CR/C0 versus t/td, is the variable behavior of the inflow
jet.
2. Inlet velocity and depth of flow have no separable effects on the
flushing curves.
3. For a predictable jet behavior, the residual concentrations are
primarily a function of the time ratio, t/td, and the basin shape (as-
pect ratio, Y/X).
4. The theoretical flushing efficiency as measured by ts/td is influ-
enced directly by the inlet width, V^, inversely by the aspect ratio,
Y/X (Eq. 2),
5. Although the results presented have been derived to apply to flush-
ing pollutants from a lake, the same information can be used to evalu-
ate the degree of increased pollution versus time where a polluted
stream (inflow) is permitted to enter a lake.
6. Perhaps the most significant conclusion reached in this study is
that a jet entering a shallow basin with a solid boundary (the bottom)
and an air-water interface (the free surface), does not follow predicted
patterns for a jet discharging into an infinite medium (1). Considerable
work remains to be done to describe the behavior of such a jet includ-
ing the influences of density differentials.
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RECOMMENDATIONS
Although this program was conducted under controlled laboratory condi-
tions, valuable information has been developed for planning the enhance-
ment of water quality in polluted lakes situated within reasonable dis-
tances of flushing water sources. Factors such as wind and tidal action
were not considered in this program, but their relative effects can be
relatively estimated. Wind action would tend to promote more complete
mixing in shallow lakes, and tidal action would tend to oppose the
flushing action. Temperature differentials between the inflow and the
lake were not investigated.
Therefore, field pilot studies under natural conditions are an obvious
recommendation. Many natural situations ,of various sizes already exist
which could be monitored. Care should be taken to avoid systems which
are so large that automatic, continuous monitoring becomes too expensive.
A system analysis study should be conducted, using the results of this
study combined with natural physical and climatological factors, to de-
velop an optimum pilot investigation plan. This analysis should be con-
ducted prior to the initiation of any field experiments. Based on the
hydraulic and quality parameters of the flow system, the system analysis
would be used to determine required sampling location and density, data
types and probable scaling factors to be evaluated as a result of dif-
ferent system sizes.
The results of these pilot tests would provide a significant contribu-
tion to water resources system design information for the enhancement of
quality in polluted lakes as guided by results of this laboratory study.
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INTRODUCTION
Flushing of a lake means reducing the pollution by clean inflow with an
equivalent outflow of polluted water. In the process the clean water
both displaces and mixes with the polluted water.
Many factors influence the effectiveness of the cleansing stream. This
study was conducted to investigate those parameters believed to be most
important and manageable under laboratory conditions. The parameters
selected for study were: 1) the inlet velocity, 2) the inlet width,
3) the depth, and 4) the basin shape. Testing was conducted on two
depths, two inlet widths, three inlet velocities, and four elliptical
basins. The primary purpose of the project was to evaluate the various
parameters to determine their influences on flushing efficiency, and
to develop prediction equations based on the geometric and flow charac-
teristics of the systems tested.
Analyses were completed to: 1) develop a test program, 2) analyze the
system for comparison with experimental results, and 3) develop pre-
diction equations which incorporate the analytical and experimental re-
sults of the study.
A dimensional analysis of the various geometric, flow, and fluid parame-
ters was completed to isolate the more important variables as a guide
for establishing the test program. The average rate of removal of pol-
lutant, Qr, was of primary interest and is a varying percent of the in-
flow rate, Q.|_, as a function of time. The following set of dimension-
less ratios was developed:
V ' Y ' X ' d
Terms are defined in Figure 1 and in the Nomenclature. Fluid properties
such as density and viscosity were considered constant throughout the
system.
Grouping the first four dimensionless terms in Eq. 1 yields an expression
for the average rate of soluble pollutant removal during passage of some
time, t, such that
W?X
(2)
K' is a dimensionless coefficient containing 4/TT for elliptical basins
and is a function of not only the geometric and flow parameters, but
also time. K1 was found to be independent of the jet momentum force, T?±,
and the Reynolds number.
For the general case of flushing lakes for various geometric conditions,
Qr should approach Qt as Wt approaches Y. Also, as X becomes very
-------
large with respect to W^
and Y, Qr should approach
Qi-
The coefficient K' is used
to relate Qr to the actual
flushing curve at any rela-
tive flushing time, t/td,
in Figure 2 for a particular
lake geometry. An important
time ratio for evaluating
flushing efficiency is ts/td,
or the relative time at
which the real flushing
curve departs from the ideal
flushing curve.
Noting that the volume of the
lake is V = 0.25irXYd and hold-
ing d constant in Eq. 2, it
would be expected that as W^
approaches Y, the average
rate of pollutant removal Qj.
approaches Q^. At the other
extreme, W^ approaches zero,
Qi> Qr and the flushing effi-
ciency should all tend towards
zero. These general boundary
conditions are shown graphi-
cally in Figure 3.
It was found in these tests
that for small values of
and low inflow discharges,
the flushing action can move
through the basin as a wave
front and be quite efficient.
As long as Q^ is finite, the
actual flushing curve will
follow the ideal flushing
curve for a time, ts/td, if
external mixing forces such
as wind are neglected.
10 feet maximum
(a) Plan View of a Longitudinal Basin-
Hydraulically Long Lake
(b) Elevation, Common to (a) and (c)
Developing Developed
Jet Zone-, £L2°™ ,-SinkZone
(c) Plan View of a Transverse Basin-
Hydraulically Short Lake
Fig. 1. Nomenclature and Flow
Zone Sketches
A theoretical analysis of the flushing was developed to relate concen-
tration to time. The displacement phase of pollutant removal continues
for a time interval, tg/td, with the outflow concentration equal to
C/C0 = 1.0. The remaining outflow concentration is assumed to follow
some form of an exponential expression. Figure 4 shows the assumed
curve. The area under the curves to any time, t/td, is proportional to
the pollutant removed from the basin.
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Qr = QO between
1.0 2.0 3.0
t/td, Relative Length of Flushing Time
Fig. 2. Residual Concentration and Average Rate
of Concentration Removal
4.0
1.0
0.8
« ^ 0.6
» 5 O-4
o ^
0.2
•Wj/B
/
/
_/
/
Y/X-
General parameter being a
function of lake shape and
equal to K1 at t/tj = 1.0.
ASSUMED:
Volume of lake constant.
Depth of water constant
in lake, inlet and outlet.
l
0 1.0
•Relative Inlet Width, Wj/Y ^
-Aspect Ratio, Y/X, for Small, Constant Inlet Width, Wj-
Fig. 3. Generalized Boundary Conditions
for Flushing Efficiency
2.0
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Ideal Flushing Curve
Smoothed Outflow Concentgraph
The initial quantity of dye in the basin equals 1.0 KV, where K is a dye
removal coefficient. The area under the curve from t = 0 to t = °° must
equal KV. Integrating the equations to find the area and determine "a",
f Is- + f
L d »*-
•-<
;a(t-ts)/td d(_t_;
(3)
On the right side of Eq. 3, K is multiplied by td to obtain the correct
units for new time base. Within the brackets, the first term, tg/tj*
accounts for area under the horizontal part of the curve; that is, where
C/CO = 1.0. The^area under the exponential decay part of the curve is
determined by Jt /t,. Eliminating K and dividing by Q.^ to get
V.
Qi
J_Id a(t-ts)/td
a t
(4)
Divide by td. The lower limit gives one and the upper limit gives zero
for "e" raised to its power. Therefore,
1 = ~d+~
Solve for
a =
-1
1 -
(5)
(6)
-------
Residual in Basin = Total at the start minus that removed.
'ts/td
Substitute limits and cancel K. Divide by Q^ to get td = V/Q., and
divide by tj. 1
(8)
Now substitute a = -l/[l-(tg/td)] and simplify.
co
This equation applies for t/td > tg/td. To obtain CR/CQ when t/td <
ts/t, use
sd
CR
The most significant time ratio in the right side of Eq. 9 is t /tH.
Expressing this ratio in terms of the geometric and flow parameters, and
inverting to give whole numbers leads to
The experimental value of tg is equal to the X distance divided by the
average velocity of the fastest flow-through element. If
v = bVi (12)
then for elliptical basins, Eq. 11 becomes
Eq. 13, when inverted and simplified, gives
tg 4bWt
~d = ~W~ '
In this form, b can be selected to fit any condition.
It is feasible to assume a value of b for Eq. 14 and compute .t /tH and
the values of CR/CO can then be computed for values of t/t, using Eq. 9
First the limits will be examined. If ts/td = 1.0, then the polluted
water is all displaced by the clean inflow and the ideal flushing curve
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is followed. Obviously, tg/t^ cannot exceed 1.0. Assuming instantane-
ous mixing of the inflow with the basin water, ts/tj =0, and the expo-
nential curve starts at t/t^ = 0. The assumption of an exponential decay
curve implies perfect mixing. This curve and the ideal flushing curve
are plotted for Figure 5. It is apparent that any value of tg/t^ be-
tween zero and one will give a curve lying between these two curves.
100
_ 80
2 S
60
4- C
a o
& 1 40
O m
O O
20
a
J Ideal Mixing
t,/td = 0
Ideal Flushing
- t,/td - 1.0
1.0 2.0 3.0
t/tj, Relative Length of Flushing Time
Fig. 5. Predicted Values, CR/C0
4.0
Table 1 gives the values calculated for predicting CR/CO for various
t/tj and ts/td values. Although Table 1 gives valid limits for the
assumed conditions, there are other possibilities which are amenable to
theoretical analysis. Conditions may change with time so flushing may
Table 1.
Predicted Values, CR/CO, from Eqs. 9 and 14
t/td
£d
(1)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
(2)
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1
(3)
0.368
0.331
0.294
0.258
0.221
0.184
0.147
0.110
0.074
0.037
0.000
2
W
0.135
0.109
0.084
0.062
0.042
0.025
0.012
0.004
0.001
0.000
0.000
3
(5)
0.050
0.036
0.024
0.015
0.008
0.003
0.001
0.000
0.000
0.000
0.000
4
(6)
0.018
0.012
0.007
0.004
0.002
0.001
0.000
0.000
0.000
0.000
0.000
10
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be either: 1) displacement, 2) near perfect mixing, or 3) very poor
mixing to the extent of clean water short circuiting through the basin
to the exit. The experimental values cannot be below the ideal flush-
ing curve in the lower limit curve as given by values in Table 1. Each
curve consists of a short section of the ideal flushing curve plus an
ideal mixing curve which starts at tg/td. It is recognized that neither
ideal mixing nor a perfect short circuit (upper limit of no flushing)
are possible. Variability in the experimental values of t /td can be
attributed to: 1) the jet expansion and 2) the type of start, "static"
or "running."
Examination of the limits of Eq. 14 reveals some of the complexity of
establishing b values. td/tg cannot be less than unity. When Y/W£ = 1,
td/ts - 1 and b must equal 4/ir. The minimum value of Y/X also occurs
when Y = W^. If Y = °°, then Y/W^ = °°, td = °°, and td/ts = <». However,
ts is finite. If V^ =0, ts = 0, td = <*>, and td/ts = °o. In this case,
Eq. 14 is not valid.
The experimental data have been plotted in Figure 6 to show the depend-
ence of td/tg on aspect ratio Y/X and inlet width Wj_. These data are
averages for the combined data (4
from two depths and three ve-
locities. Within each group
there is random scatter of ±10
percent except for two readings
which were ±25 percent from the
average. It should be noted
that the running start data
gave t,j/ts values which were
from two to five times those
for the static starts.
The curves shown in Figure 6
can be combined with Eq. 14. ~
TJ
10Y
= 8 in.) (16)
with Wi, X, and Y in feet. In
Eqs. 15 and 16, b = 0.29X and
0.24X, respectively, for a
typical jet expansion rate.
Considerably more data, pref-
erably under natural condi-
tions, are required to extend
with confidence Eq. 15 beyond
the limits of these tests.
td
Limit Ideal Flushing — =1.0
Fig. 6. Flushing Parameter, td/ts, as a
Function of Aspect Ratio, Y/X,
and Inlet Width, WA
11
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EXPERIMENTAL APPARATUS
Figure 7 is a schematic of the test apparatus. The test basins were
constructed on a 12-foot by 12-foot wood platform. The entrance still-
ing box, gate, and depth measuring piezometer tap were common for all
tests. At the exit, the mixer, Fluorometer tap, control gate, and
measuring weir were common. The sides of each basin were fabricated
with sheet metal fastened to a plywood template of the desired ellipti-
cal shape. The entrance and exit sections were faired to the elliptical
basins by a 2-inch radius. Sections were provided for an 8-inch exit
width and for both an 8-inch and a 4-inch entrance width for each basin.
A constant head tank supplied the clean water. After the desired flow
rate was established with regulating valves, a shut-off valve could be
closed and reopened without affecting the flow rate. Flow rates were
measured with the 90° V-notch weir. Repeated readings on the point gage
established the constancy of flow rate during a test run. A tail-water
gate at the exit of the discharge channel controlled the depth. Time-
lapse, motion pictures in color were taken at intervals. Rates of one
picture per second, per two seconds, or per four seconds were used.
Samples of the outlet channel flow were pumped at a constant rate through
a heat exchanger for temperature stabilization, then through the Fluorom-
eter. The Fluorometer readings were recorded with a strip chart recorder.
Temperatures were sensed at the outlet of the flow-through door with a
thermistor and recorded whenever changes occurred. The inlet and outlet
temperatures of the basin were monitored for a few of the final tests.
The water in the basin was usually warmer than the inlet supply by 2 to
5 degrees Celsius. The flow was warmed about 1.5 degrees Celsius by
heat from the air and lighting during passage through the basin.
TEMPERATURE
INDICATOR
PUMP
CHILLER
12" GRID
RECORDER
FLUOROMETER
/ CONSTANT
TEMPERATURE
BATH
, 'i i — HEAT
P J EXCHANGER
TAIL-WATER!
CONTROL—'
"BAFFLES
1—ENTRANCE BOX
PLAN VIEW
Fig. 7. Schematic of Test Apparatus
13
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TEST PROCEDURE
1. A flow rate was established with the upstream regulating valves.
2. The tailgate was adjusted to establish the desired depth.
3. Flow was shut off without disturbing the regulating valves.
4. The basin was filled to the test depth with water polluted with
fluorescent (Rhodamine WT) dye. This dyed water extended to the control
gates in the inlet and outlet channels.
5. The entrance box was filled to the necessary depth with clean water.
6. After the basin water became quiescent the upstream control gate was
opened.
7. The shutoff valve and the downstream control gate were opened simul-
taneously.
8. The Fluororaeter, timing, and camera systems were started with the
start of flow into the entrance channel.
At the beginning of each test the basin concentration was adjusted to be
within the range 85 to 100 percent on the Fluorometer scale being used.
The test was terminated when the outflow percentage reached about five
percent. Table 2 summarizes the parameters studied in this investigation.
Table 2. Summary of Test Conditions
Variable
(1)
Inlet width, /
in inches X
Inlet velocity, f
in feet per <
second I
Depth, in f
inches L
Running Start
also tested
Basin Size, in feet, Y by X
4 by 10
(2)
4.0
8.0
0.1
0.2
0.4
2.0
4.0
No
6 by 10
(3)
4.0
8.0
0.1
0.2
0.4
2,0
4.0
Yes
10 by 10
(4)
8.0
0.1
0.2
0.4
2.0
4.0
No
10 by 6
(5)
4.0
8.0
0.1
0.2
0.4
2.0
4.0
No
15
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DATA ANALYSIS
The raw data from the strip charts were corrected for temperature vari-
ations in the sample temperature by the technique given by Cobb and
Bailey (2). Time adjustments were made to correct the raw data for
transit time in the inlet, and the delay due to passage through the out-
let channel and the tube leading to the Fluorometer. Although a small
error exists due to instrument response lag, no correction was made for
it.
In Figure 8 the data were reduced to a common comparison base by using
the relative concentration; that is, measured concentration divided by
initial concentration and multiplied by 100 to return to percentages.
A dimensionless time equal to the time from the start of flushing (when
clean water enters the basin) divided by the basin detention time has
also been used for all comparisons and evaluations. Figure 8 may be
thought of as a dimensionless hydrograph of the outflow concentration.
i i i i 1 i i ill ii
0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2
Fig. 8. Typical Outflow Hydrograph, C/CQ Versus t/td
The area under the curve when multiplied by the proper factors gives the
quantity of dye removed. This subtracted from the initial quantity gives
the residual concentration. Considerable local variation from this aver-
age value will occur throughout the basin.
17
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Referring to the simplified concentration versus time curve in Figure 9:
Initial quantity of dye = KG V
dt
Dye removed = K/ Q.C
t «•
Residual quantity of dye = KCRV = K(CDV - f Q.C
R / i n
dt)
Basin volume
V = 0.257rXYd
Basin detention time = t. = —- =
(17)
(18)
(19)
(20)
(21)
Fig. 9. Concentration Versus Time
Eliminate K, substitute Q^d for V, divide by Co and introduce td into
the third term of Eq. 19 to obtain:
fC0
= k
tn/td
t0/td
(f-) (22)
Simplify to:
(23)
When multiplying by 100 to get the relative concentration on a percentage
basis, Eq. 23 is applicable to the curve shown in Figure 8.
Because the experimental Cn versus t curve is not mathematically defin-
able, discrete steps as shown in Figure 9 must be summed to obtain the
area under the curve. Equation 24 shows this summation as it was used
in the computer program to obtain the relative residual concentration,
CR/C0.
18
-------
CR
(7-) 100
uo
={l-
o,
Wl
i
100 (24)
The required time and temperature corrections were applied to the data
read from the strip chart before they were entered into a program on the
GE 235. Table 3 is a printout from this program. The first two columns
are the inputs of time and fluorescence concentration in the outflow.
The third column shows the relative fluorescence of the outflow, (100C/CO).
The fourth column gives the ratio of time to detention time, and the
last column shows the mean residual relative concentration in the basin,
(100CR/C0).
The residual concentration calculated for the terminal time can be com-
pared with the residual measured with the Fluorometer after thoroughly
mixing the basin contents at the end of the test. The measured value
was four percent and the calculated value was one percent for this example.
Table 3. Data and Computed Values
t, In
seconds
(1)
•
68.
77.
79.
82.
85.
88.
90.
95.
98.
101.
103.
105.
106.
108.
110.
112.
113.
115.
118.
120.
122.
126.
131.
166.
182.
200.
240.
348.
368.
434.
469.
478.
C, tn
percent
(2)
94.
94.
92.
90.
88.
86.
84.
82.
80.
78.
76.
74.
72.
70.
68.
66.
64.
62.
60.
58.
56.
54.
52.
50.
50.
48.
46.
44.
44.
42.
42.
40.
38.
c/c0
(3)
100.
100.
98.
96.
94.
91.
89.
87.
85.
83.
81.
79.
77.
74.
72.
70.
68.
66.
64.
62.
60.
57.
55.
53.
53.
51.
49.
47.
47.
45.
45.
43.
40.
t/*d
(4)
.00
.09
.10
.11
.11
.12
.12
.12
.13
.13
.14
.14
.14
.14
.15
.15
.15
.15
.16
.16
.16
.17
.17
.18
.23
.25
.27
.33
.47
.50
.59
.64
.65
CR/CO t, in
seconds
(5) (1)
100. 648.
91. 660.
90. 691.
89. 725.
89. 743.
89. 767.
88. 814.
88. 855.
87. 910.
87. 960.
87. 980.
86. 1008.
86. 1071.
86. 1160.
86. 1182.
86. 1304.
86. 1312.
85. 1427.
85. 1481.
85. 1555.
85. 1602.
85. 1638.
84. 1713.
84. 1780.
82. 1955.
80. 2004.
79. 2266.
77. 2340.
70. 2677.
68. 2837.
64. 2965.
62. 3000.
62. 3305.
C, in
percent
(2)
38.
36.
34.
32.
30.
30.
28.
28.
26.
26.
24.
24.
22.
22.
20.
20.
18.
16.
16.
14.
14.
12.
12.
10.
10.
8.
8.
6.
6.
4.
4.
3.
3.
C/C0
(3)
40.
38.
36.
34.
32.
32.
30.
30.
28.
28.
26.
26.
23.
23.
21.
21.
19.
17.
17.
15.
15.
13.
13.
11.
11.
9.
9.
6.
6.
4.
4.
3.
3.
t/'d
(4)
. .88
.90
.94
.98
1.01
1.04
1.10
1.16
1.23
1.30
1.33
1.37
1.45
1.57
1.60
1.77
1.78
1.94
2.01
2.11
2.17
2.22
2.32
2.42
2.65
2.72
3.07
3.18
3.63
3.85
4.02
4.07
4.48
CR/CO
(5)
53.
52.
50.
49.
48.
47.
45.
43.
41.
39.
39.
38.
35.
33.
32.
28.
28."
25.
24.
23.
22.
21.
20.
19.
16.
15.
12.
12.
9.
8.
7.
7.
5.
19
-------
TEST RESULTS
The computed values for each run were plotted and the smooth curves
shown in Figures 10 through 13 were drawn. The solid line was drawn
through the visual average of the data. The dashed lines show the
range for two identical runs having the greatest spread, and the dotted
lines border the inclusive field for all data taken on the basin.
100
DESCRIPTION
Visual average of all data
Inclusive field for all data
Identical runs with, widest spread
Idea! "|
Flushing^
Curve J
o
1.0 2.0 3.0 3.8
Relative Length of Flushing Time
Flushing Curves for 10-Foot by 4-Foot Basin (X-Y)
100
DESCRIPTION
Visual average of all data
Inclusive field for all data
Identical runs with widest spread
Ideal 1
Flushing}-
Curve J
1.0 2.0 3.0 3.8
, Relative Length of Flushing Time
11. Flushing Curves for 10-Foot by 6-Foot Basin (X-Y)
21
-------
100
80
60
i §
40
O
>
"5 o
5
40
c
a>
8
a
20
0
Fig.
CURVE
DESCRIPTION
Visual average of all data
Inclusive field for all data
Identical runs with widest spread
Ideal 1
Flushing^
Curve J
i i
3.0 3.8
13. Flushing Curves for 6-Foot by 10-Foot Basin (X-Y)
1.0 2.0
t Relative Length of Flushing Time
Most of the testing was done by introducing a clean stream into a pol-
luted static basin and removing an equal quantity of polluted flow at
the opposite end of the basin. However, several running starts were
made. Flow through the basin was established and dye fed into the in-
flow. When the concentrations of dye in the outflow, basin, and inflow
were the same, the dye feed was stopped to start the run. During the
running starts the basin circulation pattern was established by the time
the clean water was introduced. Therefore, the transit time across the
basin was much shorter and, consequently, the initial flushing was less
efficient for the running starts than for the static starts. The time
required to reach a Cjj/Co value of five percent was essentially the
same for both types of starting.
22
-------
With a data spread for identical conditions nearly as great as the in-
clusive field for all tests of a basin, the effect of the test parame-
ters is either completely masked or barely discernible.
Motion pictures of identical conditions show completely different jet
behavior. Selected frames from the motion pictures do not show the com-
plete jet action and the dispersion with time but they do indicate stages
of the dispersion and jet movement and permit comparisons to be made.
Figure 14 shows the persistence of "hot" islands of pollutant for Run I
that do not occur in identical Run II.
In the first run of another test, the inflow jet spread laterally almost
across the basin, mixed with the dye, and swept the pollution toward the
outlets in a "front." In an identical run the inflow jet remained iso-
lated and mixed only at the edges so that a clean or slightly mixed
stream penetrated to the outlet. Whether such jet behavior is a random
phenomena or is triggered by subtle differences in the test conditions
remains to be determined.
DISCUSSION OF TEST RESULTS
Two distinct yet related flushing actions take place. Initially, the
clean water, displaces polluted water and this is the most efficient
flushing possible. In fact, if a barrier could isolate the clean water
from the polluted water and prevent mixing as the jet spread laterally,
the basin would be cleansed in a time, t/tj = 1.0. Figures 10 through
13 show this ideal flushing curve as a straight line between Cn/Co = 100,
t/td = 0.0; and CR/CO - 0.0, t/td = 1.0. The efficiency of the flushing
can be judged by how close the experimental curve comes to this ideal
curve.
However, mixing does occur and this modifies the flushing curve. Ideally,
the incoming water should spread across the basin and mix uniformly at
the front. This would accomplish two desirable objectives: 1) the time
of the displacement phase would be long, and 2) there would be no iso-
lated islands of highly polluted water left in the basin.
Figure 15 shows the strong demarcation that occurs between the original
basin water and the inflow when the jet diffuses across the basin later-
ally. This run had a long initial displacement time, t
Figure 16 shows a reproduction of the average curves for the basins
studied. The wider the basin, the greater the relative time, t/t^, re-
quired to reach a given relative residual concentration. The time dur-
ing which the flushing curve coincides with the ideal flushing curve is
inversely proportional to the width of the basin.
23
-------
Run I
Run II
CS
^ ..__
360 SECS.
Fig. 14. Identical Run Comparison, Runs 60 and 61
X by Y = 6 ft by 10 ft,
Wi =8 in., d ••-- 2 in., v - 0.1 fps.
Note dye islands in Run I.
Arrows indicate circulation
24
-------
Run I
Run II
. 6
1300 SECS.
DYE ISLANDS FORMED
i H
•
L DYE i:
i
• *
Hm
2420 SECS.
DYE ISLAND PERSISTS
1670 SECS.
NO ISLAN.
Fig. 14. (continued)
25
-------
50 SECS.
3 SECS.
193 SECS.
260 SECS.
Fig. 15. Example of Well-Diffused Jet
26
-------
100
_ 80
o
ZJ
•o
£
240
c
-------
ACKNOWLEDGMENTS
The co-investigators on this project were Claud C. Lomax and John F.
Orsborn. A significant contribution to the analysis and data reduction
was made by S. T. Chen and C. Y. Eric Shih, Research Assistants in the
Albrook Hydraulic Laboratory. This study was performed under Grant
16010 DMG by the Federal Water Quality Administration with grantee con-
tributions by the College of Engineering Research Division of Washington
State University, Pullman, Washington. The Project Officer was Charles
F. Powers, Pacific Northwest Water Laboratory, Water Quality Office,
Environmental Protection Agency, Corvallis, Oregon.
29
-------
REFERENCES
1. Abramovich, G. N., The Theory of Turbulent Jets. M.I.T. Press
Cambridge, Mass., 1963.
2. Cobb, E. D., and Bailey, J. F., "Measurement of Discharge by
Dye-Dilution Methods, " Hydraulic Measurement and Computation.
Book 1, Chapter 14 (Supplement No. 1), U.S. Department of the
Interior, Geological Survey Publication, 1965.
3. Albertson, M. D., et al.. "Diffusion of Submerged Jets," Trans ->-"
actions of the American Society of Civil Engineers. Vol. 115
1950, pp. 639-664. '
4. Abraham, G., "Jet Diffusion in Stagnant Ambient Fluid," Delft
Hydraulic Laboratory Publication 29. Delft, The Netherlands,
July, 1963.
5. Abraham, G., "Entrainment Principle and Its Restrictions to ,/-
Solve Problems of Jets, " Journal of Hydraulic Research. IAHR
Vol. 3, No. 2, 1965, pp. I^23~.
6. Abraham, G., "Horizontal Jets in Stagnant Fluid of Other Density,"
Journal of the Hydraulics Division. ASCE, Vol. 94, No. HY4, July
1965, pp. 139-154. '
7. Daily, J. W., and Harleman, D.R.F., "Turbulent Jets and Dif-
fusion Processes," Fluid Dynamics, Addison -Wesley Pub. Co.,
Reading, Mass., 1966.
31
-------
APPENDICES
A. Notation . .
B. Data Summary
Table 4: Data Summary for 10-Foot by
4-Foot Basin
Table 5: Data Summary for 10-Foot by
6-Foot Basin
Table 6: Data Summary for 10-Foot by
10-Foot Basin
Table 7: Data Summary for 6-Foot by
10-Foot Basin
Page No,
34
36
36
37
38
39
33
-------
APPENDIX A. NOTATION
The following symbols are used in this paper:
a coefficient in exponential equation
b coefficient for ratio of transit velocity to inlet velocity
C concentration, in percent
C outflow concentration at time, t , in percent
C initial concentration in the basin, in percent
CL residual concentration in the basin, in percent
K
d depth of flow or depth of lake, in feet
e 2.718
f function of
F. momentum force in inflow, in pounds
K coefficient used to obtain the absolute amount of dye
removed from the concentration measured, in percent
K1 general pollutant removal coefficient used in Eq. 4
Q flow entrained by jet
Q. inflow rate, in cubic feet per second (Qo)
Q outflow rate, cubic feet per second
Q removal rate, in cubic feet per second
Q average removal rate, cubic feet per second
Q Q. + Q , in cubic feet per second
R aspect ratio
t time, in seconds
t^ basin detention time = V/Q., in seconds
tQ time measured from start of clean flow into basin,
in seconds
tQ time zero
34
-------
ts basin transmit time (time from the start of clean flow into
basin until the outflow concentration shows its effect in
that Cn is less than C0), in seconds
v mean basin flow through velocity = v^/2, in feet per second
ve entrainment velocity, in feet per second
Vf velocity in the inflow channel, in feet per second
V volume of basin, in cubic feet
W.j_ width in inlet, in feet
W0 width in outlet, in feet
X length of ellipse parallel to the direction of flow, in feet
Y width of ellipse perpendicular to the direction of flow,
in feet
AC change in concentration in time integral At
At time integral
y absolute viscosity of liquid, assumed constant, in
pound-second per square foot
p mass density of liquid, assumed constant for inflow and
lake, in slugs per cubic foot
35
-------
U)
Table 4.
Data Summary for 10-Foot by 4-Foot Basin
In order of
Hour-Day-
Honth-Year
(1)
1420-16-5-69
1555-16-5-69
0850-20-5-69
0950-20-5-69
0855-27-5-69
1000-27-5-69
0910-4-6-69
1545-4-6-69
1315-6-6-69
1530-6-6-69
1555-9-6-69
1135-10-6-69
1400-10-6-69
1145-13-6-69
1350-13-6-69
1445-17-6-69
1613-17-6-69
Run
Num-
ber
(2)
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
x,
in
feet
(3)
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
Y,
in
feet
(4)
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
"i,
in
inches
(5)
8
8
8
8
8
8
8
8
8
8
8
8
8
4
4
4
4
d,
in
inches
(6)
2
2
2
2
2
2
4
4
4
4
4
2
2
2
2
2
2
v§ In
feet
per
second
(7)
0.1
0.1
0.2
0.2
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.1
0.1
Ql,in
cubic
feet
per
second
(8)
0.011
0.011
0.022
0.022
0.040
0.040
0.044
0.044
0.044
0.044
0.044
0.022
0.022
0.022
0.022
0.0056
0.0056
ts>
in
seconds
(9)
202
242
93
100
60
61
110
120
124
103
77
109
105
65
74
345
310
*
in
seconds
.(10)
472
458**
224**
222**
130
134**
250**
250**
236**
236**
221**
225**
221**
262**
247
828
828
Relative Residual Concen-
tration, CR/CO, in percent
Terminal
Meas-
ured
(ID
2
4
3
4
2
3
2
i
1
2
2
2
3
4
3
3
4
Calcu-
lated
(12)
2
4
3
4
1
3
2
1
1
2
2
3
3
4
4
2
3
* Maximum
Extrapolated Minimum
**
Adjusted Average
Spread
At t/td -
2.5
(13)
3
3*
10
11
9
10
5
5
5
9
7
6
5
14
13
6
7
14
3
8
11
3.0
(14)
2*
2*
6
8
6
7
3
3
3
6
4
4
4
10
9
3
4
10
2
5
8
3.5
(15)
1*
1*
4
5
3
6
2*
2
1
4
3
2*
2*
6
6
2*
3*
6
1
3
5
4.0
(16)
1*
1*
3*
3*
2
5
1*
1
1*
3
1*
1*
1*
5
• 4
1*
2*
5
1
2
4
-------
Table 5.
Data Summary for 10-Foot by 6-Foot Basin
In order of
Hour -Day -
Month-Year
(1)
1030-5-8-69
1500-5-8-69
1445-6-8-69
0845-12-8-69
1115-12-8-69
1345-12-8-69
1600-14-8-69
0900-15-8-69
1030-15-8-69
1340-15-8-69
1445-15-8-69
1000-2-9-69
1130-2-9-69
1430-2-9-69
1600-3-9-69
1045-4-9-69
1420-4-9-69
0900-5-9-69
1125-5-9-69
1020-8-9-69
1355-8-9-69
Run
Sum-
[>er
(2)
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
x,
in
feet
(3)
10
10
10
10
10
10
10
. 10
10
10
10
10
10
10
10
10
10
10
10
10
10
Y/
in
feet
(4)
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
vit
in
inches
(5)
8
8
8
8
8
8
8
8
8
8
8
4
4
4
4
4
4
4
4
4
4
d
in
inches
(6)
2
2
2
2
2
2
2
2
2
4
4
2
2
2
2
4
4
2
2
2
2
v. in
feet
per
second
(7)
0.2
0.2
0.2
0.1
0.1
0.1
0.4
0.4
0.4
0.2
0.2
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.1
0.1
Qi> in
cubic
feet
per
second
(8)
0.0222
0.0222
0.0222
0.0111
0.0111
0.0111
0.0444
0.0444
0.0444
0.0444
0.0444
0.0222
0.0222
0.0222
0.0222
0.0222
0.0222
0.0111
0.0111
0.0055
0.0055
ts,
in
seconds
(9)
107
99
39**
220
200
58**
55
55
27**
111
66**
77
77
20**
72
217
159
145
150
405
335
td,
in
seconds
(10)
342
-342
342
722
722
722
176
176
176
352
352
381
381
402
402
804
804
701
701
1512
1676
Relative Residual Concen-
tration, CR/CO, in percent
Terminal
Meas-
ured
(11)
7
6
5
5
6
4
4
2
5
3
4
5
7
4
4
8
5
5
6
5
5
Calcu-
lated
(L2)
2
2
6
7
5
4
2
1
4
9
7
3
5
1
5
5
0
5
6
6
6
^ Maximum
Extrapolated Minimum
** Average
Running Start gprcad
At t/td =
2.5
(13)
16
18
18
10
8
10
11
13
20
13
20
12
13
13
13
11
13
15
13
7
9
20
7
13
13
3.0
(14)
12
14
14
7
5
7
7
9
15
11
14
9
9
8
8
7
8
10
8
4*
6*
15
4
9
11
3.5
(15)
9
11
11
4*
3*
4
4
6
11
9
10
5
5
5
6
4*
5
6
6*
3*
4*
11
3
6
8
4.0
(16)
7
8
8
3*
2*
3*
3
3
8
6*
8
3
2*
2
2*
3*
3
3*
2*
2*
3*
8
2
4
6
-------
00
Table 6.
Data Summary for 10-Foot by 10-Foot Basin
In order of
Hour-Day-
Month-Year
(1)
1100-26-3-69
1000-1-4-69
0915-2-4-69
1415-3-4-69
1045-4-4-69
1040-11-4-69
1435-14-4-69
1030-16-4-69
1040-18-4-69
1450-18-4-69
1030-25-4-69
Run
Num-
ber
(2)
11
12
13
14
15
16
17
18
19
20
21
x,
in
feet
(3)
10
10
10
10
10
10
10
10
10
10
10
Y,
in
feet
10
10
10
10
10
10
10
10
10
10
10
Wi,
in
inches
(5)
8
8
8
8
8
8
8
8
8
8
8
d,
in
inches
(6)
2
2
4
2
2
2
2
2
4
4
4
v, in
feet
per
second
(7)
0.4
0.4
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.2
Q. in
cubic
feet
per
second
(8)
0.0388
0.0444
0.0444
0.0222
0.0222
0.0111
0.0111
0.0111
0.0222
0.0222
0.0444
tst
in
seconds
(9)
58
50
103
102
106
310
217
218
213
244
105
cd>
in
seconds
(10)
330**
278**
484**
572**
590
1298**
1263**
1274**
1133**
1180
590
Relative Residual Concen-
tration, CR/CQ, in percent
Terminal
Meas-
ured
(11)
7
8
3
6
6
7
8
6
11
9
12
Calcu-
lated
(12)
8
9
3
6
6
6
7
5
11
8
11
# Maximum
Extrapolated Minimum
A"A A \7tf*T" SJCTO
Adjusted Average
J Spread
At t/td =
2.5
<13)
17
17
13
10
10
5
10
7
13
14
25
25
5
1 1
LJ
20
3.0
(14)
13
12
9
7
7
4
7*
5*
10*
10
21
21
4
i n
1U
17
3.5
as)
9
9
6
5*
5*
3*
6*
4*
8*
8*
16
16
3
13
4.0
(16)
8*
8*
5
4*
4*
2*
5*
3*
7*
7*
14
14
2
12
-------
GJ
Table 7.
Data Summary for 6-Foot by 10-Foot Basin
T r\t*Aevv f>£
Hour -Day
Month -Year
(1)
1335-15-9-69
1555-15-9-69
1600-16-9-69
0945-17-9-69
1320-17-9-69
0930-18-9-69
1135-18-9-69
0846-19-9-69
1129-19-9-69
0930-23-9-69
1321-23-9-69
1522-23-9-69
~*
Num-
ber
(2)
60
61
62
63
64
65
66
67
68
69
70
71
X,
"7
in
feet
(3)
6
6
6
6
6
6
6
6
6
6
6
6
y,
* 7
in
feet
(4)
10
10
10
10
10
10
10
10
10
10
10
10
Wtt
" JL9
in
inches
(5)
8
8
8
8
8
8
8
8
8
4
4
4
d.
^* t
in
inches
(6)
2
2
2
2
2
2
2
4
4
2
2
2
v, in
f f-
per
second
(7)
0.1
0.1
0.2
0.2
0.2
0.4
0.4
0.2
0.2
0.2
0.2
0.2
Q
cubic
f
per
second
(8)
0.0111
0.0111
0.0222
0.0222
0.0222
0.0444
0.0444
0.0222
0.0222
0.0111
0.0111
0.0111
t.,
S"
in
seconds
(9)
82
90
47
48
47
24
25
43
54
47
55
68
t A
in
seconds
(10)
687
687
342
342
342
178
178
356
356
737
737
737
Relative Residual Concen-
tration, CR/CQ, in percent
Terminal
Meas-
ured
(11)
7
6
4
2
6
4
9
6
7
6
6
6
Calcu-
lated
(12)
8
1
2
1
1
1
3
8
7
4
6
5
Maximum
Minimum
Average
Spread
At t/t. =
Q
2.5
(13)
34
21
19
27
23
27
28
20
20
18
22
20
34
18
23
16
3.0
(14)
29
14
13
20
17
22
22
16
17
12
16
13
29
12
18
17
3.5
(15)
27
8
9
15
11
17
17
13
12
8
11
10
27
8
13
19
4.0
(16)
26
5
7
11
8
13
13
11
9
6
9
7
26
5
10
21
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1
Accession Number
w
5
2
Subject Field &. Group
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
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College of Engineering Research Division
Albrook Hydraulic Laboratory
Title
Flushing of Small Shallow Lakes
| Q Authors)
Lomax, Claud C.
Orsborn. John F.
16
21
Project Designation
EPA, WQO No.
16010 DMG
Note
22
Citation
23
Descriptors (Starred First)
*Lakes, *Hydraulics, Water Quality, Hydraulic Models,
25
Identifiers (Starred First)
*Inflow, *Flow Characteristics, Enhancement, Tests
27
Restoration of quality to polluted lakes by inflows of clean water with
simultaneous outflow of polluted water was investigated. Elliptical basins were
used in the laboratory to simulate shallow lakes. The investigation determined
the influence of selected geometric and flow parameters on the flushing efficiency,
The theoretical analyses are combined with the experimental results to obtain
equations for predicting the flushing curves. Application of these equations will
give the potential flushing efficiency of a proposed flushing scheme.
The width of the basin perpendicular to the axis of flow is an important
parameter. In general, narrower basins have better flushing action and less
erratic flow patterns than wider basins. The pollution remaining in a basin
after any interval of flushing is primarily dependent on the time of the flushing
interval divided by the detention time of the basin.
The report was submitted in fulfillment of Grant Number 16010 IMS, under
the partial sponsorship of the Water Quality Office, Environmental Protection
Agency.
Abstractor
Ifolin F. Orsborn
Institution
Washington State University
WR:t02 (REV. JULY 1969)
WRSIC
SEND WITH COPY OF DOCUMENT. TOl WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
* SPO: 1970-389-930
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