EPA R2-72-037
Environmental Protection Technology Series
August 1972
Flow into a Stratified Reservoir
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington. DC 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
1. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
standards..
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EPA-R2-72-037
August 1972
FLOW INTO A STRATIFIED RESERVOIR
By
University of California
Berkeley, California 9^720
Project 15014-0 EJZ
Project Officer
William M. Thurston
EPA - Region IX
100 California Street
San Francisco, California
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office. Washington, D.C. 20402 - Price M cents
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EPA Review Notice
This rencrt has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessarily
reflect the viev;s and policies of the Environmental
Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommenda-
tion for use.
11
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ABSTRACT
This report describes the results of an experimental study of the
flow caused by a line source discharging into a stagnant, linearly
density stratified reservoir. The flow enters the reservoir as a
horizontal line jet but immediately passes through an internal
hydraulic jump and forms a slowly m®ving wedge of fluid composed
partly of the injected fluid and partly of fluid mixed into the injection
by the jump. Ahead of this mixed layer the inflow pushes a wide
layer termed the entering layer, which extends to the opposite end
of the reservoir and consists of fluid already in the reservoir before
the jet was begun. The inflow also induces a series of layers of flow
in alternating directions above and below the entering layer.
Experiments are described in which the mixed layer was made visible
by mixing blue dye into the supply fluid. The length, thickness, and
tip speed of the mixed layer were measured as a function of time,
and an empirical scaling relationship was derived to relate the dif-
fering experimental conditions. Use of the scaling factors allows the
results to be applied to prototype reservoirs to predict the extent of
mixed layers which might occur, for instance, during the pumping
phase in a pump-storage reservoir.
This report was submitted in fulfillment of Project Number 15040 EJZ,
under the sponsorship of the Water Quality Office, Environmental
Protection Agency.
ill
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CONTENTS
Section Page
I Conclusions 1
II Recommendations 3
III Introduction 5
IV Description of the Experiment 7
The Experimental Tank 7
The Salinity Probe 7
Establishment of a Linear Density Profile 12
The Injection System 12
Experimental Procedure 15
Details of Experimental Procedure 16
V Experimental Results and Analysis 19
Basic Data for the Experiments 19
General Current Pattern 19
Mixed Layer Length 21
Discussion of Figure 9 21
Discussion of Figure 10 24
Maximum Horizontal Velocity of Front 26
Tip of Mixed Layer
Mixed Layer Thickness 26
Entrainment 30
Discussion of Figure 13 30
Discussion of Figure 14 30
Equation for Y 33
m
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CONTENTS (Continued)
Section Page
VI Discussion of Results 35
Temperature Changes 35
Outlet or Injection Level Depth 35
Linear Density Gradient 35
Effect of the Side Walls 37
Blocking Effect of End Wall 37
VII Acknowledgments 39
VIII References kl
IX Symbols 43
X Appendix 1^5
vi
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FIGURES
PAGE
1 GENERAL LAYOUT OF EXPERIMENTAL TANK 8
2 PHOTOGRAPH OF EXPERIMENTAL TANK 9
3 CONDUCTIVITY PROBE 10
4 TYPICAL CALIBRATION CURVE 11
5 TYPICAL DENSITY PROFILE 13
6 INJECTION SYSTEM ]A
7 GENERAL CURRENT PATTERN 20
8 DEFINITION OF THE VARIABLES INVOLVED 22
9 HORIZONTAL DISTANCE VS. TIME 23
10 SCALED HORIZONTAL DISTANCE x* VS. SCALED
TIME t* 25
11 TYPICAL PROFILE THICKNESS 2?
12 SECONDARY LAYER DESCRIPTION 29
13 ENTRAINMENT VS. TIME 31
14 SCALED ENTRAINMENT E* VS. SCALED TIME t* 32
15 DENSITY PROFILE SHIFT 36
16 MIXED LAYER NEAR THE END WALL 38
vii
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SECTION I
CONCLUSIONS
An experimental study was made of the effects of an entering discharge
into a stagnant, density-stratified reservoir. The discharge entered
as a line jet with the same density as the surrounding fluid at the dis-
charge elevation. The jet immediately passed through an internal
hydraulic jump, after which the mixed flow of entering and entrained
fluid moved forward as a wedge. With respect to this mixed layer the
following conclusions have been established:
1. The maximum scaled horizontal velocity of the front tip of the
mixed layer in a tank of infinite length may be given by
max
where K = 3. 16 x 10 2 and U and t are scaled velocity and time.
2. The thickness of the mixed layer may be given by:
Y/Y = 1 - (x/x,)1/2
m i
3. The scaled entrainment may be given by:
E* = KI (tV/4
where Kj depends on Froude number at inlet conditions.
4. The appropriate scaling factors for time and horizontal distance
are
t = t(eg)1 ' 2
*
x =
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SECTION II
RECOMMENDATIONS
The following extensions of this study are recommended:
a) This study was conducted using the simplest geometry. Future
studies might include: 1) sloping bottom, 2) different locations of
source, 3) more complex, characteristic boundaries.
b) A study of the general current pattern induced by the source
throughout the entire model should be made which should include
the velocity profiles, streamlines, etc. to provide information on
the rate of vertical mixing throughout the reservoir.
c) Both steady and unsteady current patterns should be investigated
for the model, including the retarding effects of the end wall.
d) Future studies should include buoyant sources and three-dimensional
sources.
e) Theoretical and experimental investigations of the internal jump
formed near the source and correlation with the inlet densimetric
Froude number should be made.
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SECTION III
INTRODUCTION
The traditional role of surface water reservoirs is as a storage basin
for a given quantity of water, prLmarlly for water supply or flood
control. Only in recent years have engineers become aware that
reservoirs also play an important and delicate role in the management
of water quality. Properly managed, reservoirs can provide a useful
means of regulating the quality of water in a stream, including its
temperature, dissolved oxygen, and other constituents, in whatever
way will be most beneficial to the downstream users. Improperly
managed a reservoir can contribute to the destruction of a river environ-
ment by permanently changing its temperature, oxygen content, and
turbidity. Much remains to be learned about how the flow in a reservoir
can be controlled to produce the desired quality of outflow. In the
report describing the research conducted by this project for the pre-
vious year, Imberger and Fischer (1970) described the withdrawal
layer which forms when water is removed from a stratified reservoir.
The present report describes the reverse problem, the flow which
results when water is injected into a stratified reservoir.
The injection problem is important in two ways. Firstly, the research
described herein is directly applicable to water quality management in
reservoirs used as part of pump-storage projects, in which water is
pumped into the reservoir during a part of the cycle. Secondly, the
flow patterns observed in this experiment are likely to be similar to
the flow caused by a river discharge into a reservoir, because the
river discharge normally sinks to a level equal to its own density
before flowing in a layer into the reservoir. The total flow created by
the inflow from a river and the discharge through the dam is more
complex than the one studied here, but the study presented herein may
be seen as a first step in identifying the flow patterns caused by an
injection into a stratified reservoir. A complete understanding of the
mechanics of stratified flow in reservoirs and the resulting effects on
water quality management remains a long term goal which will require
considerable further study.
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SECTION IV
DESCRIPTION OF THE EXPERIMENT
The Experimental Tank
The experiments were performed in a 42 feet long by 4. 00 feet deep
by 1. 25 feet wide tank located at the University of California Richmond
Field Station. The walls and bottom were constructed of tempered
plate glass set in a steel framework. The tank is shown schematically
in Figure 1 and photographically in Figure 2.
Two trolleys were placed on rails on top of the tank. One served as
a mounting platform for the stratifying apparatus while the other held
the salinity probe and the associated vacuum pump. Mounting the
salinity probe on the trolley allowed the same probe to be used to
measure both the density variations of the receiving fluid and the den-
sity of the supply fluid. The injection system was located at one end
of the tank. Vertical measuring tapes were installed at 22 predeter-
mined points measured horizontally from the injection end of the tank.
The Salinity Probe
Thompson (1968) gives a detailed explanation of design of the type of
conductivity probe used throughout this study.
The probe shown in Figure 3 was calibrated at the beginning of every
run. The calibration was sensitive to the water temperature. Standard
solutions whose specific gravities were measured with a hydrometer,
were prepared and used to calibrate the probe after these solutions
had reached the temperature of the water in the tank; this was accom-
plished by stirring the solutions since most of the time their temperature
was lower than that of the water in the tank.
The difference between the temperature of tank water and the temper-
ature at which the specific gravities were measured was always less
than 2°C. Since only the density gradient of the tank water is required,
no compensation was made for this temperature difference. Furthermore,
the temperature distribution of the water inside the tank was uniform
with depth.
Figure 4 shows a typical calibration curve. The calibration curves
were nearly linear, with a slight decrease in sensitivity for the larger
concentrations. Data were taken with a Brush Dual strain gage
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PROBE STAND
00
DEPTH SCALE
CRANK
(to adjust depth
of probe )
-TROLLEY
CALIBRATION
MIXTURE
PLATES TO
STRATIFY TANK
TROLLEY
SALINITY
PROBE
FLYWHEEL
DISCHARGE SLOTS
FIG. I GENERAL LAYOUT OF EXPERIMENTAL TANK
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, -^*i***
FIG. 2 EXPERIMENTAL TANK
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FIG. 3 CONDUCTIVITY PROBE
10
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1.025
1.000
456
BRUSH - RECORDER READINGS
8
FIG. 4 TYPICAL CALIBRATION CURVE
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amplifier and a Brush Mark 220 recorder. Drift, presumably due
to the amplifier, frequently made it necessary to balance the bridge.
Establishment of a Linear Density Profile
A linear density profile can be established by several methods.
Slotta (1969) has used a special technique to obtain a linear density
profile. However the authors have chosen the technique reported by
Clark et al. (1967) and successfully used by Imberger (1970).
The tank was first filled with fresh water, which was allowed to come
to room temperature. A gated partition consisting of a piece of
plywood with 9" hinged flaps at the bottom and top, was then introduced
vertically into the center of the tank. The partition was sealed to the
glass walls with a soft rubber spacer. This was sufficient to stop any
transfer of water from one side to the other.
An appropriate amount of salt was then placed and thoroughly mixed
in one half of the partitioned tank. The salt used was an ordinary kiln
dried fine commercial product. The uniform mixture was allowed to
come to rest, while some of the entrapped air surfaced. The flaps of
the partition were then opened very slightly to allow the salt water to
flow beneath the fresh water and the fresh water to flow over the salt
water. About one half hour elapsed before the whole tank had a two
layer stratification in it with a sharp interface between them. The
partition was then carefully removed.
To obtain a linear profile, a series of two plates, mounted on the
trolley, were then briskly moved through the interface with a crank
and pulley arrangement at the end of the tank. The largest plate moved
directly through the interface while the smaller one stirred up the
bottom layer. The wakes behind the plates created sufficient turbu-
lence to allow mixing. After internal oscillations ceased, a density
profile measurement was taken with the conductivity probe. If the
profile was not quite linear then a broom was moved up and down all
along the tank. A typical density profile is given in Figure 5. The
stratification procedure took one day, including washing the tank,
filling it and preparing the linear profile. Once the desirable profile
was obtained, the tank was allowed to stand overnight, ensuring a
static condition for the run the following morning.
The Injection System
The injection system is shown schematically in Figure 6 and the main
elements are described in the following lines.
12
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10
15
-E 20
Q_
UJ
O
25
30
35
40
INJECTION POINT
I
I
1.00 1.000
1.010 1.015
SPECIFIC GRAVITY
1.020 1.025
FIG. 5 TYPICAL DENSITY PROFILE
13
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OVERFLOW
OVERFLOW-
CONSTANT HEAD TANK
Lt-
STORAGE TANK
DISCHARGE METER
MODEL RESERVOIR
) *- INJECTION POINT
PUMP
FIG. 6 INJECTION SYSTEM
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The storage tank is a cylindrical tank made out of stainless steel. Di-
mensions are 4 feet diameter by 2. 5 feet deep. The bottom of the
storage tank has a 0. 75 inch opening. The bottom opening is connected
to the suction pump through a 0. 75 inch plastic hose. At the top of the
tank is the terminal end of a hose that brings into the storage tank the
overflow from the constant head tank, so that the solution that is not
injected into the model tank is recycled.
The suction pump is of the centrifuge type and it is moved by a 1. 5
hp AC motor. The water is pumped into the constant head tank which
is 10 feet above the storage tank.
The constant head tank is required so that the entering discharge into
the model tank can be kept constant for the full length of each run. A
0. 75 inch plastic hose carries the chosen discharge from the constant
head tank into the discharge meter. This hose has two filters: one
near the constant head tank and the other near the entrance to the dis-
charge meter. Both filters were needed to keep larger particles from
going into the discharge meter. The filters could be removed from the
main line so they could be cleaned. The filter screens had openings of
2 square mm and were cleaned before each run.
Measurements of flow rates were made by means of a rotameter. The
rotameter, originally calibrated for sea water with a specific gravity
of 1. 025, had to be re-calibrated for the range of specific gravity
values used in this study. Although the re-calibration indicates a small
density influence on the flow rate, it was small enough relative to the
error inherent in reading the rotameter that it may be ignored. The
rotameter had a maximum capacity of 95 gph providing a good range
for the chosen discharge values.
The entering device consists of a 3/4 inch diameter stainless steel
pipe, 35 inches long overall with a continuous horizontal 1/32 inch
deep slot which extends over the width of model reservoir. The-
entering device is located half way between the top and the bottom of
the model tank, and discharges horizontally into the tank. In all the
experiments the inlet depth was 50 cm below the water surface.
Experimental Procedure
After the linear profile was obtained, the specific gravity at the
injection level was measured in the model tank. A solution of salty
water with a specific gravity equal to that at the injection level in the
storage tank was prepared. This solution was colored with
A-Concentrate Blue Dye purchased from Chroma-color Company,
Hollywood, California.
15
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The temperature of the solution in the storage tank was kept •within
2°C of the temperature of the water in the model tank. A continuous
recycle was then allowed for about 15 minutes to assure a good mixed
colored solution. Then the solution was allowed to enter into the
density stratified fluid by opening an adjusting valve until the desired
discharge was obtained.
As the front tip of mixed layer reached each one of the stations a mark
was made on the running tape of the Brush Mark 220 recorder. The
tape was running at a velocity of 1 mm per sec. The time taken by the
front tip to reach each station was measured by taking the length
between marks.
The mixed layer profile was measured at various times by reading the
measuring tapes. The general current pattern in the model reservoir
was observed by dropping into the model reservoir little crystals of
potassium permanganate.
Details of Experimental Procedure
1. The model tank was filled with tap water and allowed to stand
for several hours.
2. The wooden partition was inserted at the center of the tank.
3. The required amount of salt was inserted into one side.
4. The salt was mixed by agitating the water with a push-broom
until uniform. After the mixture was uniform it was allowed to
come to rest.
5. The flaps on the partition were opened about 1 in. After half
an hour the partition was removed, and the interface was allowed
to come to rest.
6. The stratification plates were pulled through the interface.
7. Calibration solutions were prepared and their temperature was
checked against that of the model tank water.
8. The probe was calibrated and then used to obtain a density
profile of the model tank water.
9- If the density profile was not approximately linear then a broom
•was carefully moved up and down at several points along the model
tank. The stratified fluid was allowed to stand overnight.
16
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10. The specific gravity of the salt water in the model tank was
measured at the level of injection. A solution of the same specific
gravity was then prepared in the storage tank.
11. The storage tank solution was colored with deep blue dye. Ten
spoons were usually enough.
12. The solution was recycled for 15 minutes by turning the
centrifugal pump on.
13. The temperature of water in the storage tank and that of the
water in the model tank were taken and compared.
14. The adjusting valve at the discharge meter was set to yield
the required flow.
15. The time that the front tip of the mixed layer took to reach
each station •was recorded.
16. Profiles of the mixed layer were taken at various times.
17. Small crystals of potassium permanganate were thrown into the
model tank from the top in order to visualize the general current
pattern within the model tank.
18. Pictures were taken of streaks left by the falling crystals of
potassium permanganate.
19- The adjusting valve was usually turned off by the time the front
tip of the mixed layer was close to the end wall.
ZO. The model tank was drained overnight.
21. The procedure started at (1) the following morning.
17
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SECTION V
EXPERIMENTAL RESULTS AND ANALYSIS
Basic Data for the Experiments
Twelve experimental runs were performed with the apparatus and
procedure described in Section IV. The values of the pertinent physical
parameters involved are listed in Table 1 of the Appendix.
General Current Pattern
The general current pattern existing in the model reservoir during a
test run is indicated in Figure 7. As water was discharged into the
stagnant, density-stratified model tank, an entering layer formed. The
entering discharge, qm, caused a hydraulic jump which created a zone
of intense turbulence and entrainment. The hydraulic jump acted as a
mixing mechanism between the entering fluid and the layers of tank
fluid in contact with the hydraulic jump above and below. In this mixing
process amounts of fluid from the adjacent fluid were drawn into the
hydraulic jump creating reverse currents called qz[ as shown in Figure
7. An eddy was consistently formed in the vicinity of the entrance where
the mixing between qjn and qzi took place. It was possible to observe
the mixing zone because the entering fluid had a deep blue color. After
the hydraulic jump took place the flow became laminar and stable.
At this point an important distinction should be made between the
entering layer and the mixed layer. The entering layer is the flow layer
moving in and ahead of the mixed layer. The motion of the entering
layer is induced by the entering discharge as it pushes its way into the
tank fluid. The thickness of the entering layer increases with horizontal
distance from the entering device. The entering layer is formed almost
instantaneously as the source is switched on and is the response of the
stratified fluid to the sudden increase of pressure created when the
source is switched on. The entering layer's thickness grows and its
velocity decreases as it moves away from the entrance due to viscous
forces.
The mixed layer is a part of the entering layer and consists of fluid
mixed by the hydraulic jump. It is therefore a combination of the
entering discharge fluid and the ambient fluid. The mixed layer can
be distinguished visually from the remainder of the entering layer by
dying the discharge fluid; however, the motion of the mixed layer is
contiguous to the entering layer and hydr©dynamically no distinction
can be made.
19
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•IN
HYDRAULIC JUMP ZONE
MIXED LAYER 0.
INTENSIVE TURBULENCE
ZONE
FORWARD.
LAYER
SYMBOLS: q_. .... REVERSE CURRENTS
*• i •• ~'i*• i°
*- DIRECTION OF FLOW IN CURRENT
Not to scale
L =1,2,3, THE RELATIVE LEVEL OF EACH CURRENT
Figure 7 A typical flow distribution observed
in the laboratory tank.
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From a pollution control point of view the mixed layer is probably
more important than the entering layer because the mixed layer is
an indicator of the degree of dilution a contaminant would receive
by entraining reservoir fluid. This work is concerned with the mixed
layer only and deals with the following aspects:
1. The mixed layer length, x,, for a given time t.
2. The maximum horizontal velocity, U
7 max
3. Mixed layer thickness, Y, as a function of x and time t.
4. Amount of entrainment, E, taken place up to a given time t.
Figure 8 explains graphically the meaning of the above variables. The
following sections report the experimental results concerning the
above variables.
Mixed Layer Length
The time taken for the front tip of the mixed layer to reach each one of
the 22 established stations was recorded following the procedure
described in Section IV. The results for all test runs are listed in
Table 2 of the Appendix. The data of Table 2 are plotted in Figure 9
in the form x,. vs. t.
Discussion of Figure 9
Figure 9 shows on log-log paper the relationship between horizontal
distance in cms and time in sec that it took for the front tip of the
mixed layer to reach each station. The plotted results show that for
each test run there is a well-defined, smooth curve that fits most of
the points. The typical curve is approximately linear over the range
of points, except for some curvature at the ends. The average slope
of the straight line portion of the curves in Figure .9 is . 74, with
values ranging from . 72 to . 79- The authors suggest it be taken as
. 75, or 3/4.
It is thought that the scatter at the lower end (near the source) is due
to experimental errors. At the lower end, an error of ± 1 sec at a
point significantly changes the location of that point. The nonlinearity
at the upper end is believed to be due to the increased retarding
effect of the end wall. The retardation requires a longer time for the
front tip to travel a unit distance.
Figure 9 shows that the relationship between the horizontal distance
traveled by the front tip of the mixed layer, and time, is parametric
with the entering discharge, qin, the linear density gradient, e, and
the water kinematic viscosity, v.
21
-------
N5
N5
^INITIAL (imediat"ely d/s of jump)
-MIXED LAYER
laminar zone
Zone of
Hydraulic jump
and turbulence
(a) X,y COORDINATES SIDE VIEW
TOWARD END
WALL
U
PLAN VIEW
SIDE VIEW
DEFINITION OF UMAX
FIG. 8 DEFINITION OF THE VARIABLES INVOLVED
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10,000
••
:-
•
1000
ui
u
2
."
•'
I I
:
•
•
100
100 1000
TIME i, ( SECS)
0,000
FIG. 9 HORIZONTAL DISTANCE vs TIME
-------
The above three factors were combined to form two dimensionless
groups. Of the groups tried, it was found that the following two
were the ones that best fitted the experimental results.
* _ X(&g)5/ 12 v 11 /I 8
qg2/9
and
t* =t(eg)i/z (2)
* *
The x and t values are listed in Table 3 in the Appendix. The above
values were plotted in Figure 10 on log-log paper.
Discussion of Figure 10
Figure 10 shows on a log-log plot that a well defined relationship exists
between x and t . For all runs, a considerable part of the x vs. t
curves can be synthesized to a single straight line, after "which each
curve starts to deviate from the straight line portion as it approaches
the scaled tank length L .
From (1),
L* =
qg2/9
where L = fixed tank length.
Equation (3) shows that the scaled tank length L was different for every
run, through the dependence of the horizontal scaling factor on q and £.
^r ^f
As a result, each x vs. t curve starts to bend from the straight line
portion at a different point, until it becomes horizontal at x = L .
The bending is due to the presence of the end wall, which implies that
for a tank with an infinite length, the x* vs. t* curve must fall on the
linear portion of Figure 10. The same figure shows that the end wall
effect starts at:
* Xs
x , = . 6 L* (4)
b
24
-------
•
i
n
fM
CT>
, 5/12 ''/IB
X L(€g) I/
t*= t (eg)
FIG. 10 SCALED HORIZONTAL DISTANCE X* VS SCALED TIME
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The straight line portion of Figure 10 is expressed by Equation
(5):
x* =K (t*)3/4 (5)
where K is a constant equal to 3. 16 x 10~ . Equation (5) is valid for
0 < x < . 6 L ; for larger values of x*, the actual curve on Figure 10
should be followed.
Maximum Horizontal Velocity of Front Tip
of Mixed Layer
U = or U*
max dt max dt
From Equation (5),
U* =3/4K(tV/4 (6)
max ' * '
Equation (6) shows that the velocity decreases with time.
Mixed Layer Thickness
The ideal method of taking the mixed layer profile at a certain time,
would have been a photographic one. In the absence of such equipment
the profile thickness was measured directly with a measuring tape.
In so doing it was impossible to obtain an instantaneous profile.
Starting at a given position xf of the front tip of mixed layer, the thick-
ness of the mixed layer was taken at various stations x such that
0 ^ x ^ xf. The time for each reading was recorded. As the front tip
advanced into a new position xf + £ x, a new set of readings was
taken. From the above two profiles an "instantaneous" profile was
obtained by a linear interpolation of both Xf and time.
The resulting mixed layer thickness at each station for a given position
of the mixed layer front tip are listed in Table 4 in the Appendix.
There is one table for each run. The values listed in Table 4 are
plotted in the form Y vs. xf, where Y and X£ were defined in Figure 8.
Figure 11 shows a typical thickness profile.
The main conclusions derived from a thickness profile plot are:
26
-------
ro
0
SECONDARY LAYER
2 3 4 5 67
HORIZONTAL DISTANCE, Xf , IN METERS
8
FIG. I I TYPICAL PROFILE THICKNESS
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1. The slope of the thickness profile curve decreases with time.
2. For a given horizontal distance x, the thickness at that point
increases as a function of time.
3. For a given Ym and Xf the thickness Y at a point x such that
0 £ x £ xf may be expressed by a parabolic equation of the form
Y = Y^ - (Ym/xf1/ 2) x1/2 (7)
or
Y =Ym(l - (x/x^M (8)
or in a dimensionless form,
Y/Y = 1 - (x/x.)1/2 (9)
m I
An expression for Y^ is given under Entrainment below.
4. The volume in the profile can be expressed Ln terms of Ym and xf
as: volume = 2/3 Ym xf , where Ym and xf were defined in Figure 8.
$ ^
5. Conclusions (3) and (4) are valid for values x < . 6 L .
For larger values a practical problem developed in measuring the
thickness profile. For x* > . 6 L , a so-called "secondary layer" on
top of the main profile, and as shown on Figure 11, started to develop.
The secondary layer thickness is not uniform throughout the cross-
sectional area of the mixed layer. Instead it is formed by particles
of dye being deposited near the side walls. Figure 12 shows schemat-
ically the secondary layer. The velocity profile of the secondary layer
is the reverse of that in the main layer.
It is thought that the secondary layer is related to currents occurring
in the Z -direction. These currents take place due to a difference in
temperature between the side walls of the tank and shear in the
transverse direction. These local currents are responsible for taking
some dye particles from the main mixed layer up against the side
walls and therefore carried by the main stream of the reverse currents
towards the inlet.
28
-------
t-o
SECONDARY MIXED LAYER
MAIN MIXED LAYER
SECONDARY LAYER
>—MAIN
LAYER
(a) SIDE V! EW
(b) CROSS-SECTION A-A
FIG.12 "SECONDARY LAYER" DESCRIPTION
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Entrainment
The amount of entrainment, E, in the mixed layer at a given time t
is given by:
E = volume in the mixed layer - q t. (10)
The volume in the mixed layer was measured from thickness profiles.
Table 5 in the Appendix includes the entrainment values for each run,
These values are plotted in Figure 13.
Discussion of Figure 13
Figure 13 shows that on a log-log plot a well-defined relationship exists
between ehtrainment and time. This relationship is parametric with the
unit discharge q, the density gradient &, and the viscosity v. For each
run the points fall on a straight line whose slope is 3/4.
The parametric influence of q,£, and v upon the entrainment has been
reduced by plotting the results of Table 5 in the form E vs. t*.
* E (eg)*73 y"
q3/2 g2/9
and, * .
t =t(eg)1/2 (12)
* *
Figure 14 shows E vs. t .
Discussion of Figure 14
The points on Figure 14 fall along two curves, depending upon the
outlet conditions Froude number,
F=—3
where h = 0. 063 cms (slot depth).
For F values between 2. 10 x 102 and 9. 85 x 102 the points fall on
curve A. For F values between . 61 x 102 and 1. 05 x 102 the points
fall on curve B. For a given value of t* curve A gives higher values
of E*.
30
-------
10
(VI
E
o
LU
no'
Q
LU
a:
h-
LU
10
10'
I I
I03 I04
TIME, t, sec
R- I
R-2
R-3
R-4 -
R-5
R-6
R-7
R-8
R-9
R-IO
R- I I
R- 12
_| L_L
FIG. 13 ENTRAINMENT VS TIME
31
-------
u>
N)
00
\
~7^
rO
LU
w i n
a1 I U
II
LU
1.0
T~T
T—r
x
A
D
O
o-
+0
R- I
R-2
R-3
R-4
R-5
R-6
R-7
R-8
R-IO
R- II
R-12
CURVE A-
40
CURVE B
I I I
o
io3
1/2
I I
10'
FIG. 14 SCALED ENTRAINMENT E* VS SCALED TIME t*
-------
The Froude number is a measure of the Intensity of the turbulence
produced by the hydraulic jump. The turbulence, in turn, produces
entrainment. As a result the entrainment must increase as the Froude
number increases.
Curves A and B may be expressed by an equation of the form,
E* =K! (t*)3/4
(13)
where
or
! = 5. 6 x 102 for 2. 10 x 102 < F< 9. 85 x 102
: = 2. 5 x 102 for 0. 61 x 102 < F < 1. 05 x 102
Equation (13) shows that for a strong hydraulic jump the entrainment
is about twice that of a weak jump for the same t*.
Equation for Y
m
An equation for Ym is suggested now from entrainment considerations.
The total volume, V, of the mixed layer up to time, t, may be expressed
by Equation (14):
V = q t + E
V = (2/3) Ym xf
(14)
(15)
Combining Equations (1), (2), and (5)
q t =
qi/4 g2/9 K
4/3
Combining Equations (11), (12), and (13),
(16)
E =
K (eg)1/4
(17)
33
-------
Equation (14) becomes:
Z/3 Y =x.1/3
m f
(eg)1/24v
ql/4 g 2/9 K
4/3
(18)
K (eg)
The interesting feature about Equation (18) is that its second term is
independent of Xf which means that when Xf = 0 then:
3K,
m
2 K (eg)
(19)
The relationship between Equation (19) and the hydraulic jump height
should be more carefully studied. At this point it is not possible for
theauthorsto say that YQ in Equation (19) is the hydraulic jump height.
Since no careful record was kept of the jump height, no conclusion
can be drawn.
34
-------
SECTION VI
DISCUSSION OF RESULTS
The average elapsed time required for the front tip of the mixed layer
to travel from the injection point to the end wall of the model reservoir
was approximately two hours. During that period several factors that
were assumed to be constants varied by small amounts. These factors
which probably affected the results of Section V are analyzed below.
Temperature Changes
The experiments were conducted in a building whose heating system
was incapable of holding the air temperature constant. The changes
in the ambient air temperature caused changes in the temperature and
kinematic viscosity of the water in the model reservoir. Changes in
viscosity introduced changes in the velocity of the front tip. The tem-
perature used herein was the one recorded at the beginning of each
experiment. This initial temperature was a crucial one in matching
the density of the model tank water at the level of injection to the density
of the entering fluid.
Outlet or Injection Level Depth
No outflow from the model tank occurred during each run. The free
surface elevation increased at a constant rate given by dh/dt = q/c
where c is the surface area of the model tank. The maximum change in
free surface elevation was 5 cms which was considered small compared
to the initial 50 cms height of the free surface above the injection level.
It is believed that any error introduced by the variations in depth is
negligible.
Linear Density Gradient
In formulating all the equations in Section V, the value of £ used was
the one recorded at the beginning of each run. Figure 15 shows the
density profile before and after a typical run. Figure 15 shows that
the density becomes uniform around the injection level, and that local
variations in e exist. It is not known yet to what extent these local
variations affect the experimental results.
35
-------
40
1.00
1.005 1.010 1.015
SPECIFIC GRAVITY
1.020
FIG. 15 DENSITY PROFILE SHIFT
36
-------
Effect of the Side Walls
A true two-dimensional flow in the laboratory tank could not be
achieved because of the wall effects. In the area of interest, a
parabolic velocity distribution was created across the tank. The
shearing force in a horizontal plane produced by the side wall effect
was not insignificant in comparison to the shearing force in a vertical
plane produced by the reverse currents. The width of the tank was
38 cms while the greatest thickness observed in the mixed layer was
approximately 15 cms. A linear approximation of the velocity gives a
vertical velocity gradient that is about three times the horizontal
velocity gradient.
Blocking Effect of End Wall
As the mixed layer approached the end of the tank, its forward movement
was impeded by the end wall. As the blocking effect of the end wall
became stronger and stronger, the maximum horizontal velocity of the
mixed layer decreased and its thickness increased. As the mixed layer
approaches the end wall it seemed to break into a three-dimensional
flow. Figure 16 shows some of the patterns observed when the mixed
layer was approximately one meter away from the end wall. These
patterns were not consistent.
37
-------
MIXED LAYER
[D
TOP
MIXED LAYER
UJ
c»
BOTTOM
Q PLAN VIEW
b SIDE VIEW
FIG 4-2o MIXED LAYER (RUN-3) NEAR THE END WALL
TOP
•
•
•*
^
\
V
\
«v
/
- MIXED LAYER
ItK
MIXED LAYER
BOTTOM
Q PLAN VIEW
SIDE VIEW
FIG. 16 MIXED LAYER (RUN-2) NEAR THE END WALL
-------
SECTION VII
ACKNOWLEDGMENTS
This report is based on a thesis submitted in partial fulfillment
of the requirements for the degree of Master of Science by
Antonio A. Zuluaga-Angel. The report was revised and prepared
for publication by R. B. Darden. The research described in this
report was under the supervision of Drs. Jorg Imberger and
Hugo B. Fischer.
39
-------
SECTION VIII
REFERENCES
1. Brooks, N. H. , and Koh, R. C. Y. "Selective Withdrawal From
Density-Stratified Reservoirs, " Proceedings of the Specialty
Conference on Current Research into the Effect of Reservoirs
on Water Quality, sponsored by ASCE, Portland, Oreg. , 22-24
Jan. , 1968, Technical Report No. 17, Department of Environ-
mental and Water Resources Engineering, Vanderbilt University,
(1968).
2. Clark, C. B. , Stockhausen, P. J. , and Kennedy, J. F. "A
Method for Generating Linear Density Profiles in Laboratory
Tanks, " J. of Geophys ical Research, 72, No. 4, pp. 1393-95,
(1967).
3. Ellison, T. H. , and Turner, J. S. "Turbulent Entrainment in
Stratified Flows, " JFM, 6, part 3, p. 423, (1959).
4. Harleman, D. R. F. , and Elder, R. A. "Withdrawal From Two -
Layer Stratified Flows, " J. of the Hydraulics Division, ASCE,
21, No. HY4, Proc. paper 4398, pp. 43-58, (1965).
5. Imberger, J. "Selective Withdrawal From a Stratified Reservoir,
Ph.D. thesis, Univ. of Calif. , Berkeley, (1970).
6. Imberger, J. , and Fischer, H. B. Selective Withdrawal From a
Stratified Reservoir. A Report for the Environmental Pro-
tection Agency. Project Number 15040 EJZ, (1970).
7. Koh, R. C. Y. "Viscous Stratified Flow Towards a Sink, "
J. of Fluid Mechanics, 24, part 3, pp. 555-575, (1966).
8. Sharp, J. J. "Spread of Buoyant Jets at the Free Surface, "
J. of the Hydraulic Division, ASCE, 95, No. HY3, Proc. paper
6538, (1969).
9. Slotta, L. S. , Elwin, E. H. , Mercier, H. T. , and Terry, M. D.
"Stratified Reservoir Currents, " Oregon State Univ. , Eng. Exp.
Station, Bull. No. 44, (1969).
10. Thompson, E. F. "The Mixing of a Layer of Fresh Water With
Underlying Salt Water Under the Influence of Wind, " Master's
thesis, Univ. of Calif. , Berkeley, (1968).
11. Wood, I. R. "Selective Withdrawal From a Stably Stratified
Fluid." J. of Fluid Mechanics, 32, part 2, pp. 209-223, (1968).
41
-------
E
F
g
h
L
L*
q, q.
in
t
u
u
max
*
rnax
x
Y
SECTION IX
SYMBOLS
Entrainment
Scaled entrainment
Source Froude number based on slot depth, h
Acceleration due to gravity
0. 063 cms (slot depth)
Tank length
Scaled tank length
Discharge measured at inlet
Reverse flows in the model tank, i = 1,2,...
Time
Scaled time
Maximum horizontal velocity of front tip of
mixed layer
Scaled maximum horizontal velocity of front
tip of mixed layer
Mixed layer length, measured immediately down-
stream of hydraulic jump
Scaled mixed layer length
Horizontal distance from inlet
Scaled horizontal distance from inlet
Mixed layer thickness
43
-------
Y = Initial thickness of mixed layer
m
p = Density of fluid
p = Density at injection level
Density gradient 1/p ( A p/A y) ( Ay = a difference in
° elevation)
v = Kinematic viscosity
H = Dynamic viscosity
-------
SECTION X
APPENDIX
Page No.
Table 1: Summary of Basic Experimental
Parameters for Each Run ^6
Table 2: Time Taken by the Front Tip of Mixed
Layer to Reach each Station ^7
# *
Table 3: x vs. t values
Table 4: Series Profile Values 53
5: Entrainment Values 62
45
-------
TABLE 1
SUMMARY OF BASIC EXPERIMENTAL PARAMETERS
FOR EACH RUN
Unit
Run
No.
1
2
3
4
5
6
7
8
9
10
11
12
Discharge
Measured
At Inlet
q
cm2 /sec
1. 93
1. 38
1. 38
1. 38
0. 83
0. 89
0. 83
0. 83
0. 83
0.29
0. 277
0. 277
Density
Gradient
&
10"5cm"1
10. 75
5.0
16. 8
Z2. 8
12. 92
2. 94
8. 24
27. 5
10. 2
4. 9
51. 7
17. 75
Temp.
T
w
°F
62
68
66
64
68
69
68
73
69
68
69
67
Kinematic
Viscosity
V
10"5cm2 /s<
1100
1014
1043
1072
1014
995
1014
942
995
1014
995
1028
NOTES:
1. Unit discharge = total discharge measured volumetrically/
width of tank.
? r L_ _l£_
2- e" P_ dy
46
-------
TABLE 2
TIME TAKEN BY THE FRONT TIP OF MIXED LAYER
TO REACH EACH STATION
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
1Z
13
14
15
16
17
18
19
20
21
END WALL
Horizontal
Distance x.
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
R-l
-
6
14
23
32
57
83
110
138
198
263
328
398
475
595
722
867
1037
1222
1473
1915
2873
3848
R-2
3. 5
13
23
34
48
84
116
159
194
274
365
453
549
651
829
1030
1249
1527
1894
2354
3064
4099
5309
R-3
3. 5
12. 7
24. 7
38
54
84
119
156
194
276
-
475
585
697
905
1136
1418
1778
2229
2792
3612
5707
-
R-4
3
12
23
36
51
88
127
164
205
293
389
490
604
733
980
1282
1646
2259
2496
2996
3781
5248
7408
R-5
3
13. 3
40
65
92
147
212
282
357
521
702
899
1121
1355
1755
2249
2833
3609
4637
6115
9205
-
-
R-6
4
11
30
50
77
122
187
259
335
490
655
827
1007
1212
1651
2131
2755
3312
4500
-
-
-
-
47
-------
TABLE 2 (Continued)
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
END WALL
AiUX L^JUllLCLX
Distance x,
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
R-7
2.5
17.5
-
-
-
164
226
308
384
541
711
901
1081
-
1693
2143
2732
3550
-
-
-
-
-
R-8
3. 5
19
33
49
70
108
149
186
231
332
450
592
760
941
1222
1610
2056
2666
3455
5375
7055
10600
-
R-9
14
112
172
241
311
465
615
775
935
1278
1654
2069
2522
2965
-
4802
5895
6928
8240
98711
-
-
-
R-10
11
62
210
354
523
865
1240
1670
2119
3142
4276
-
-
7703
-
-
13916
16600
-
-
-
-
-
R-ll
18
118
217
272
-
709
986
1279
1579
2221
2914
3645
4479
5209
6529
8359
-
-
-
-
-
-
-
R-12
-
-
-
348
-
811
1147
-
1839
-
3384
-
5147
6120
7694
9500
11557
-
16832
19802
-
-
-
48
-------
TABLE 3
x" AND t VALUES
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
ID WALL
R
*
X
. 025
. 068
. 11
. 16
. 20
. 28
. 37
.46
. 54
. 72
. 89
1. 06
1/24
1. 41
1. 66
1. 93
2. 19
2.45
2. 70
2. 97
3. 22
3. 49
3. 64
-1
*
t
-
1. 94
4. 2
7. 45
10. 4
18. 5
26. 9
35. 6
44. 7
64. 0
85. 5
106
129
154
193
234
281
336
395
476
620
930
1250
*
X
. 024
. 065
. 105
. 150
. 19
. 27
. 35
. 43
. 52
. 68
. 85
1. 01
1. 18
1. 34
1. 58
1. 84
2. 08
2. 33
2. 58
2. 82
3. 07
3. 31
3. 46
R-2
*
t
. 776
2. 88
5. 1
7. 55
10. 65
18. 6
25. 8
35. 3
43. 0
61
81
100
122
144
184
228
277
340
420
524
680
910
1 175
R
#
X
. 041
. 109
. 177
. 250
. 318
. 455
. 596
. 732
. 874
1. 15
1. 43
1. 71
1. 98
2. 26
2. 67
3. 09
3. 50
3.93
4. 34
4. 75
5. 17
5.59
5. 82
-3
*
t
1.42
5. 15
10. 0
15.4
21. 8
34
48
63
78. 5
112
-
192
237
283
367
461
575
720
900
1132
1465
2320
_
49
-------
TABLE 3 (Continued)
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
1Z
13
14
15
16
17
18
19
20
21
END WALL
*
X
. 048
. 127
.207
.291
. 371
. 53
.69
. 85
1.02
1. 34
1.66
1.99
2. 31
2. 63
3. 10
3. 60
4.08
4. 57
5.06
5. 54
6. 02
6. 51
6. 78
R-4
*
t
1.41
5. 65
10. 8
17
24
41. 5
60
77.4
96. 6
138
183
230
285
346
461
605
776
1065
1180
1410
1780
2470
3500
*
X
.060
. 16
.26
.37
.47
. 67
. 87
1.07
1.28
1. 68
2.09
2. 50
2. 90
3. 30
3.90
4.53
5. 13
5175
6. 35
6.96
7.57
8. 18
8.52
R-5
*
t
1.06
4.7
14. 1
23
32.5
52
75
100
126
185
248
318
390
480
620
795
1000
1275
1640
2160
3260
-
-
R-6
*
X
. 032
. 086
. 14
. 198
.25
.36
. 47
. 58
. 69
.91
1. 13
1. 35
1. 57
1. 78
2. 11
2.45
2. 77
3. 11
3.43
376
4.09
4.42
4. 61
*
t
. 68
1. 87
5. 1
8. 5
13. 1
20. 8
31. 8
44
57
83.4
111
141
171
206
282
363
470
564
765
-
-
-
-
50
-------
TABLE 3 (Continued)
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
END WALL
#
X
. 049
. 132
. 214
. 302
. 38
. 55
. 72
. 88
1. 056
1. 39
1. 72
2. 06
2. 40
2. 73
3.22
3. 74
4. 23
4. 75
5. 25
5. 75
6. 25
6. 75
7. 04
R-7
*
t
. 71
5
-
-
-
46. 5
64.4
87. 5
109
154
202
256
307
-
480
610
775
1000
-
-
-
-
_
*
X
. 078
. 21
. 34
. 48
. 61
. 87
1. 14
1.40
1. 67
2. 20
2. 73
3. 26
3. 79
4. 31
5. 10
5. 90
6. 70
7. 51
8. 3
9. 1
9.9
10. 7
11. 19
R-8
*
t
1. 85
9.9
17. 0
30
50
70
130
170
170
260
360
500
640
680
840
1000
1300
1550
2100
3500
4200
6000
8300
*
X
. 12
. 32
. 52
. 73
. 93
1. 33
1. 74
2. 14
2. 55
3. 36
4. 18
4. 98
5. 80
6. 60
7. 80
9. 00
10. 24
11. 48
12. 69
13. 90
15. 11
16. 33
17. 02
R-10
*
t
2.4
13. 6
46
77. 5
114
190
272
366
465
690
940
-
-
1690
-
-
3040
3630
-
-
-
-
_
51
-------
TABLE 3 (Continued)
Station
Number
1
2
3
3a
4
5
6
7
8
9
10
11
1Z
13
14
15
16
17
18
19
ZO
Zl
END WALL
*
X
. 32
. 85
1. 38
1.95
2.48
3. 54
4. 64
5. 70
6. 80
8. 96
11. 11
13. 27
15.4
17. 6
20. 74
24. 1
Z7. 2
30. 6
33. 8
37
40. 2
43. 5
45. 3
R-ll
*
t
12. 8
84
1545
193
-
505
700
910
1123
1580
2075
2600
3190
3710
4650
5950
-
-
-
-
-
-
—
#
X
. 21
. 55
. 90
1. 26
1. 61
2. 3
3. 0
3. 7
4. 4
5. 8
7. 2
8. 6
10. 0
11.4
13. 5
15. 6
17. 7
19. 8
21.9
24
26
28.2
29.4
R-12
t
_
-
-
145
-
339
478
-
767
-
1410
-
2150
2560
3210
3970
4825
-
7030
8260
-
-
_
52
-------
TABLE 4
SERIES PROFILE VALUES
R-l
Profile Time
sec
265
600
1050
1350
Horizontal
Distance
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1 136
1228
1280
Thickness
cms
12. 05
12. 05
12. 05
12. 05
12. 70
12. 25
11. 15
9. 20
10. 50
9. 20
7. 00
4. 10
0. 0
13. 95
13. 95
13. 95
13. 95
13. 65
12.40
12. 10
12. 10
11.45
10. 65
9. 85
8. 90
8. 30
7. 05
4. 45
0. 0
_
-
14. 25
14. 25
14. 60
13. 70
12. 75
13. 05
12. 70
12.25
11.45
11. 10
10. 65
10.00
8. 75
7. 30
5. 75
2. 85
0.0
_
-
16. 25
16. 25
16. 50
14. 30
14. 30
15. 00
14. 30
13. 50
12. 75
12. 10
11. 80
11. 45
10. 50
9. 55
8. 25
7. 30
5. 25
0. 0
53
-------
TABLE 4 (Continued)
R-2
Profile Time
sec
1500
2000
3200
Horizontal
Distance
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
Thickness
cms
-
11. 60
11.20
10. 7
10. 6
10. 2
9. 85
9.36
9. 00
8. 25
7. 97
6. 75
5. 5
2. 8
0. 0
-
11. 80
11. 7
11. 6
11. 6
11. 2
11. 0
10. 9
10.4
9. 90
9. 5
8. 6
7. 5
6. 5
5.4
0. 0
-
-
14. 8
14.4
14. 6
14. 0
14. 2
13. 5
13. 3
13. 2
12.4
12.0
22.5
10. 6
10.4
9.5
8.2
0.0
54
-------
TABLE 4 (Continued)
R-3
Profile Time
sec
590
900
1450
Z300
3450
Horizontal
Distance
cms
9
24 -
39
55
1
1
70
100
131
161
192
253
314
375
436
586
680
770
863
954
045
136
-
8.20 8.
7. 70 8.
7. 00 7.
6. 35 7.
5.26 7.
4. 33 6.
1.31 5.
0. 0 4.
3.
0.
Thickness
cms
70
20
94
48
00
36
1
67
70
0
-
9.
9.
8.
8.
8.
7.
7.
6.
5.
4.
3.
0.
60
15
80
30
10
72
00
50
82
40
20
0
_
10.
10.
10.
9.
9-
8.
8.
8.
7.
5.
4.
3.
0.
80
70
20
60
10
73
50
03
05
93
63
13
0
_
1
1
1
1
1
1
1
1
1
1228
1
280
2.
1.
1.
1.
1.
1.
0.
0.
0.
9.
8.
8.
7.
5.
4.
0.
30
73
65
65
53
15
62
64
20
55
74
00
10
45
35
0
55
-------
TABLE 4 (Continued)
R-4
Profile Time
sec
710
1250
2000
3500
Horizontal Thickness
Distance
cms
cms
9 _
24 -
39 - - -
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
8. 10
8. 30
8. 10 8. 20
8. 00 8. 00
7. 10 8. 20
6. 62 7. 87
5. 93 7. 52
4. 88 7. 00
3. 75 6. 54
1.56 6.39
0.0 4.98
2.40
0. 0
-
9. 30
9.21
9. 17
9. 00
8. 87
8. 71
8. 25
8. 20
7. 97
7. 14
6. 70
5. 66
2. 54
0. 0
-
-
10. 80
10. 70
10. 70
10. 67
10.45
10.40
10. 12
10.0
9. 73
9.28
8. 67
7. 70
7. 55
6. 15
4.03
0. 0
56
-------
TABLE 4 (Continued)
R-5
Profile Time
sec
700
1150
Z2ZO
3600
9000
Horizontal
Distance
cms
9 7. 8
24 7. 7
39 7. 6
55 7. 5
70 7. 4
100 7.0
131 6.4
161 5.8
192 5.2
253 3.4
314 0.0
375
436
496
586
680
770
863
954
1045
1136
1228
1280
Thickness
cms
8.0
7.9
7. 8
7. 7
7. 6
7.4
7. 0
6. 8
6. 3
5. 5
4. 6
3. 0
0. 0
8. 5
8. 4
8. 4
8. 3
8. 3
8. 2
8. 2
8.0
7.9
7. 4
6. 8
6.4
5. 8
5. 0
3. 8
0. 0
9. 5
9. 5
9.4
9-4
9. 3
9. 3
9. 2
9. 1
9. 0
8. 8
8. 4
8. 0
7. 4
7. 0
6. 3
5. 8
4. 5
0. 0
14. 1
14. 1
14. 0
14. 0
13. 9
13. 8
13. 7
13. 4
13. 3
13. 1
12. 8
12. 6
12. 5
12. 0
11. 6
11. 0
10. 2
9. 6
8. 4
6. 5
0. 0
57
-------
TABLE 4 (Continued)
R-6
Profile Time
sec
830
1200
Z700
4600
Horizontal
Distance
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
Thickness
cms
-
9.00 9.2
8. 25 8. 6
7. 5 8. 4
6. 70 7. 9
6. 23 7. 7
4. 90 6. 50
1. 60 5. 80
0.0 4.20
3. 20
0. 0
-
10. 7
10. 6
10.20
10. 3
10.0
9.4
8. 6
8. 10
7. 50
7.20
5. 70
3.90
0. 0
-
-
11.0
11.00
11.0
11. 0
10. 60
10. 30
10. 10
10. 20
9.25
8. 75
8.25
7. 30
4. 60
0.0
58
-------
TABLE 4 (Continued)
R-7
Profile Time
sec
900
1650
2600
3500
Horizontal
Distance
cms
9
24
39
55
70
100
131
161
192
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
Thickness
cms
12. 40
10. 85
11.40
11. 1
10. 8
9. 6
8. 6
8. 0
7. 4
6.4
5. 0
0. 0
12. 60
12. 50
12. 3
12. 0
11. 8
11. 2
10. 8
10. 4
9. 6
8. 6
7. 7
6. 7
6. 1
5. 0
0. 0
13. 6
13. 5
13.4
13.3
13. 2
13. 0
12.9
12. 5
12. 4
11. 0
10. 5
9.0
8.4
7. 35
7. 0
4. 75
15. 0
14. 8
14. 7
14. 6
14.4
14. 3
13. 8
13. 6
13. 0
12. 5
11. 3
10. 5
10. 0
9.0
8. 0
7. 0
6.0
0.0
59
-------
TABLE 4 (Continued)
R-10
Profile Time
sec
880
2150
4300
7600
1400
Horizontal „. . .
Distance Thicknesa
cms cms
9 6.40 8.0 7.4
24 7. 05 7. 8 7. 3
39 6. 5 7. 8 7. 1
55 5.4 7. 7 7. 0
70 4. 6 7. 5 6. 9
100 0.0 6.1 6.8
131 5.3 6.7
161 4.0 6.5
192 0.0 6.2
253 6. 0
314 0.0
375
436
496
586
680
770
863
954
1045
1136
1228
1280
8. 6
8. 3
8. 1
7. 8
7. 7
7. 6
7. 5
7.4
7. 3
6.9
6.5
6.3
6. 1
0.0
8.3
8.2
8.4
8. 3
8. 2
8. 1
8.0
7. 8
7. 7
7. 6
7. 5
7.4
7. 1
6.5
5.5
5.0
0. 0
60
-------
TABLE 4 (Continued)
R-ll
Profile Time
sec
1550
2300
3600
5600
Horizontal
Distance
cms
9 3. 8
24 3. 7
39 3.5
55 3.4
70 3.2
100 2.9
131 2.2
161 1. 60
192 0.0
253
314
375
436
496
586
680
770
863
954
1045
1136
1228
1280
Thickness
cms
4.15 4.5
4. 1 4. 5
4. 0 4. 4
3. 7 4. 3
3. 7 4. 1
3.3 4.0
2. 7 3. 9
2.4 3.5
2.0 2. 7
0.0 2.5
2. 2
0. 0
4. 8
4. 7
4. 6
4. 5
4.4
4. 3
4. 2
4. 1
3. 8
3. 5
3. 0
2.5
2. 2
0. 0
61
-------
TABLE 5
ENTRAINMENT VALUES
R-l
F=9. 45 x 102
R-Z
F=9. 85 x 102
R-3
F=5. 40 x 102
R-4
F= 4. 65 x 102
E
cm2
1440
3100
5600
6500
9300
1500
4600
6000
9000
1400
2200
2850
3900
5000
1050
1800
2300
3000
4300
E
1. 55
3. 3
6.0
7. 0
10. 0
1. 55
4. 4
6. 0
8. 6
3.4
5. 3
6. 8
9. 5
12. 5
3. 0
4. 8
7.4
10. 0
15. 5
t
sec
265
600
1050
1350
1810
365
1500
2000
3200
590
900
1450
2300
3450
390
710
1250
2000
3500
88
220
330
420
640
83
340
480
700
245
380
590
900
1450
195
350
600
1050
1750
62
-------
TABLE 5 (Continued)
R-5
F=3. 72 x 102
R-6
F=7. 75 x 102
R-7
F=4. 65 x 102
R-8
F=2. 52 x 102
E
cm2
1060
1350
2Z20
3200
5400
1500
2000
3500
4600
1350
2100
2800
3500
930
1200
1530
3070
E
4. 6
5. 6
9. 6
13
23
2.4
2. 9
5. 1
6. 7
4. 3
6. 7
9. 0
11.2
6. 7
8. 6
11
22
t
sec
700
1150
2220
3600
9000
830
820
2700
4600
900
1650
2600
3500
1060
1600
1920
6000
330
400
810
1280
2800
150
205
480
770
260
520
770
960
550
830
1000
3100
63
-------
TABLE 5 (Continued)
R-10
F=2. 10 x 102
R-ll
F=. 61 x 102
R-12
F=l. 05 x 102
E
cm2
270
560
850
1200
2200
73
90
140
240
210
270
500
600
750
E
3.0
6. 10
9.20
12.0
23.0
4. 1
5.0
7.9
12.0
5.9
7.2
13. 0
15. 0
19.0
t
sec
880
2150
4300
7600
14000
1550
2300
3600
5600
3500
5000
9300
11500
17000
T
210
450
830
1000
3100
1100
1650
2650
5800
1800
2500
5200
7000
8000
64
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
/. Report No.
3. Accession No.
w
4. Title
Flow into a Stratified Reservoir
7. Author(s) Antonio A. Zuluaga-Angel,
Rufus Benton Darden,
Hugo B. Fischer
9. Organization
University of California
Berkeley, Calif. 94720
5. Report Date
6.
*. Performing Organization
Report No.
10. Project No.
150&Q EJZ
12. Sponsoring Organization
IS. Supplementary Notes
11. Contract I Giant No.
13. Type of Report and
Period Covered
Environmental Protection Agency report
number EPA-R2-T2-037j August 1972.
16. Abstract
This report describes the results of an experimental study of the flow caused by
a line source discharging into a stagnant, linearly density stratified reservoir.
The flow enters the reservoir as a horizontal line jet but immediately passes
through an internal hydraulic jump and forms a slowly moving wedge of fluid composed
partly of the injected fluid and partly of fluid mixed into the injection by the
jump. Ahead of this mixed layer the inflow pushes a wide layer termed the entering
layer, which extends to the opposite end of the reservoir and consists of fluid
already in the reservoir before the jet was begun. The inflow also induces a series
of layers of flow in alternating directions above and below the entering layer.
Experiments are described in which the mixed layer was made visible by mixing
blue dye into the supply fluid. The length, thickness, and tip speed of the mixed
layer were measured as a function of time, and an empirical scaling relationship
was derived to relate the differing experimental conditions. Use of the scaling
factors allows the results to be applied to prototype reservoirs to predict the
extent of mixed layers which might occur, for instance, during the pumping phase
in a pump-storage reservoir.
17a. Descriptors
Reservoirs, Stratified Flow, Water Quality Management
I7b. Identioers
17c. COWRR Field & Group
18. Availability
19. Security Class.
(Report)
20. Security Class.
(Page)
Abstractor
B. Fischer
21. No. of
Pages
Send To:
22. Price
Institution
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C. 20240
University of Ca 1 -i fnttHa
WRSIC 102 (REV. JUNE 1971)
4U. S. GOVERNMENT PRINTING OFFICE : 1972-514-146 (20)
GPO 913.261
------- |