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

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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

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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

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•
 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

-------
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

-------
                            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

-------