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 ------- 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.. ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 = ------- 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. ------- 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. ------- 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 ------- 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 ------- , -^*i*** FIG. 2 EXPERIMENTAL TANK ------- FIG. 3 CONDUCTIVITY PROBE 10 ------- 1.025 1.000 456 BRUSH - RECORDER READINGS 8 FIG. 4 TYPICAL CALIBRATION CURVE ------- 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 ------- 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 ------- OVERFLOW OVERFLOW- CONSTANT HEAD TANK Lt- STORAGE TANK DISCHARGE METER MODEL RESERVOIR ) *- INJECTION POINT PUMP FIG. 6 INJECTION SYSTEM ------- 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 ------- 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 ------- 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 ------- 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 ------- •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. ------- 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 ------- 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 ------- 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 ------- |