EPA-R2-72-078
October 1972              Environmental Protection Technology Series
               Correlated  Studies  of
                  Vancouver Lake -
               Hydraulic  Model Study

                                 \
                                  Z
                                   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
   4.  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-R2-72-078
                                                      October  1972
           CORRELATED STUDIES OF VANCOUVER LAKE-
                   HYDRAUUU£TO&>fiL  STUDY
                             By

                      John F. Orshorn
                      Project 16080 ERP
                     Project Officer

                Dr. Curtis C. Harlin,  Jr.
    National Water Quality Control Research. Program
           Robert S. Kerr Water Research Center
                    Ada,  Oklahoma  74820
                        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 $1.25

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                 EPA"Revlew Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents neces-
sarily reflect the views and policies of the
Environmental Protection Agency, nor does mention
of trade names or commercial products constitute
endorsement or recommendation for use.
                         ii

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                               ABSTRACT

The effects of possible modifications to the Vancouver Lake-Columbia
River system on the hydraulic characteristics of that system were
tested in a physical hydraulic model.  A mathematical model was devel-
oped for predictive analysis and to expand the results of the hydraulic
model study.  Alternate methods for improving flushing action through
Vancouver Lake by use of a conduit were investigated.

The theories, assumptions, test procedures, data analysis and results
as presented in this report are directed .towards arriving at conclusions
and recommendations regarding proposed hydraulic engineering works and
their effects on the hydraulic regime and water quality conditions in
Vancouver Lake.  The tests were conducted to determine the hydraulic
characteristics and the flushing efficiency of pollutants by tlsing a
fluorescent dye to simulate the soluble conservative pollutants in the
prototype.  In addition, the hydraulic model study provided information
on the dispersion, mixing, dilution rates and detention times which are
important factors influencing water quality.

This is Part 1 of a two-part study entitled "Correlated Studies of
Vancouver Lake, Washington."  The other part of the study is Water
Quality Prediction conducted by the Sanitary Engineering Section of
the College of Engineering Research Division at Washington State Uni-
versity under Project Number 16080 ERQ, details of which are covered
in a separate report.

This report was submitted in fulfillment of Project Number 16080 ERP
under the partial sponsorship of the Environmental Protection Agency.
                                    iii

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                    CONTENTS

                                              Page

Conclusions                                     1

Recommendations                                 3

Introduction                                    5

Description of Model                           15
                                  (
Testing Procedures                             21

Description of Tests and Data Analysis         25

Computer Analysis and Data Extension           37

Acknowledgments                                47

Appendices                                     49

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                                FIGURES
                                                                    Page

 1.   VANCOUVER LAKE--COLUMBIA  RIVER HYDRAULIC  SYSTEM                   6

 2.   VIEW OF  HYDRAULIC MODEL LOOKING  NORTH  (70 FT LONG BY
     40  FT WIDE)--EXISTING CONDITIONS,  COLUMBIA RIVER IN
     THE FOREGROUND                                                   7

 3.   FLOW CHART OF  VANCOUVER LAKE  STUDIES                              8

 4.   GEOMETRIES OF  THE SYSTEM  USED FOR THE  HYDRAULIC ANALYSIS         11

 5.   COMPARISON OF  SINUSOIDAL  AND  ACTUAL TIDES OVER TWO
     COMPLETE TIDAL CYCLES--PROTOTYPE                                12

 6.   HYDRAULIC MODEL AND SAMPLING  STATIONS                            16

 7.   UPSTREAM CHANNEL TEST OF  HYDRAULIC MODEL  WITH  WEST SIDE
     OF  LAKE  DREDGED--STAGE III                                      18

 8.   PROTOTYPE MEASUREMENTS USED TO VERIFY THE PHYSICAL
     HYDRAULIC MODEL-SAMPLE                                          19

 9.   CALIBRATION CURVE FOR B & L SPECTRONIC 20 COLORIMETER
     (RHODAMINE WT DYE)                                               22

10.   STRIP CHARTS FOR THE GAGE STATIONS IN THE VANCOUVER LAKE
     HYDRAULIC MODEL                                                 23

11.   TEST NO. 12:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  27

12.   TEST NO. 15:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  28

13.   TEST NO. 17:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  29

14.   TEST NO. 18:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  30

15.   TEST NO. 19:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  31

16.   TEST NO. 20:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  32

17.   TEST NO. 22:  RELATIVE CONCENTRATION  OF DYE  IN VANCOUVER
     LAKE MODEL AS FUNCTION OF TIME                                  33

                                    vi

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                                                                    Page
18.   SUMMARY OF VANCOUVER LAKE MODEL TESTS FOR POST-
     DEVELOPMENT STUDY                                               34

19.   SURFACE VELOCITY IN LAKE RIVER NEAR FELIDA (NEAR GAGE 3).
     (MODEL MEASUREMENTS CONVERTED TO PROTOTYPE)                     36

20.   SURFACE VELOCITIES AND DIFFERENCES IN ELEVATION FOR
     UPSTREAM CHANNEL.  (MODEL MEASUREMENTS CONVERTED TO
     PROTOTYPE)                                                      36

21.   PROTOTYPE INFLOW-OUTFLOW STAGE AND DISCHARGE RELATIONS
     OBTAINED FROM THE PHYSICAL HYDRAULIC MODEL                      38

22.   TYPICAL EXAMPLE OF UPSTREAM CHANNEL FLOW ANALYSIS FOR
     ONE SET OF WIDTH AND DEPTH CONDITIONS                           39

23.   SIMULATED RESULTS OF UPSTREAM CHANNEL AND LAKE RIVER FLOW
     ANALYSES FOR VARIOUS CHANNEL WIDTHS                             41

24.   DETENTION TIME AS A FUNCTION OF FRICTION FACTOR AND
     DEPTH OF LAKE                                                   42

25.   DETENTION TIME VERSUS WIDTH OF UPSTREAM CHANNEL USING
     THE COLUMBIA RIVER TIDAL AMPLITUDE AS A PARAMETER               42

26.   DETENTION TIME VERSUS NUMBER OF 10-FT DIAMETER.CULVERT
     USING THE COLUMBIA RIVER TIDAL AMPLITUDE AS A PARAMETER         43

27.   LAKE DETENTION TIME AND AVERAGE INFLOW THROUGH ANY KIND
     OF CONDUIT(S)                                                   44

28.   DETENTION TIME VERSUS LENGTH OF CULVERT FOR VARIOUS
     CULVERT DIAMETERS                                               45

29.   AVERAGE DISCHARGE THROUGH ONE CULVERT VERSUS DIAMETER
     OF THE CULVERT                                                  46

30.   FLOW CHART FOR HYDRODYNAMIC AND/OR DO COMPUTER MODELS           60
                                    vii

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                          TABLES
                                                             Page

1.  Model Scale Ratios Used in the Vancouver Lake             1?
    Model Study

2.  Summary of Test Conditions and Data  Acquisition           25

3.  Comparison of Results between Predicted Values
    and Those of the Hydraulic Model                         37
                           viii

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                             CONCLUSIONS

1.  On the basis of five progressive stages of model investigations,
technically feasible prototype modifications for enhancement of the
Vancouver Lake system have been developed.

2.  Fluorescent dyes were used in the hydraulic model to simulate con-
servative prototype pollutants, and these tests furnished information on
the flushing efficiency of the Vancouver Lake system under a variety of
existing and modified conditions.

3.  Dredging of Vancouver Lake and its outlet into Lake River will delay
the accumulation processes from which the lake is currently suffering,
but this modification by itself will not enhance water quality in the
lake because it will increase the volume of the lake and therefore the
detention time.

4.  The introduction of flushing water from the Columbia River through
a conduit, a general term for water conveyance structures, either an
open channel and/or buried culverts, into the southwest quadrant (up-
stream end) of Vancouver Lake is a necessary step for enhancing the
quality of Vancouver Lake.
5.  An open channel or closed conduit (culverts) may be used, but the
open channel has the disadvantages of high construction cost, the trans-
port of floating trash and debris into the lake and interference with
land transportation.
6.  The use of culverts for the introduction of the Columbia River water
into the southwest quadrant of Vancouver Lake has the advantages of less
ground surface disturbance, fewer construction problems and the culverts
can be equipped with counterbalanced gates to keep Vancouver Lake water
from returning directly to the Columbia River during ebb tide.
7.  The use of culverts with gates allows the flushing of the system to
be one-directional, i.e., from south to north out of Vancouver Lake by
way of Lake River, rejoining the Columbia River near Ridgefield.
8.  The construction of a downstream channel near Post Office Lake.
between the Columbia River and Lake River has detrimental effects on
the flushing efficiency and the flow in Lake River.

9.  Small islands could be used for aligning the inflow to reduce stag-
nation areas around the shores of the lake,  but they do not significant-
ly improve the gross flushing characteristics in the system.
10.  The hydrodynamic mathematical model developed from field and physi-
cal hydraulic model data accurately simulates prototype conditions and
was used to significantly extend the analysis of alternatives beyond
conditions tested in the physical model.  The hydrodynamic model pro-
vided the basis for the water quality prediction model in project number
16080 ERQ and was linked to the dissolved oxygen parameter through
detention time of the flushing flow.

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                          RECOMMENDATIONS

This study has included an evaluation of the relative efficiency of
flushing Vancouver Lake under existing and modified conditions.  The
comparison of the advantages and disadvantages of the alternatives is
directed towards developing a set of guidelines for engineering design
and decision-making.  Some combinations of the first three alterna-
tives must be developed in order to optimize the enhancement of the
Vancouver Lake system.

Enactment of only one, or even two, of the first three recommendations
will not achieve the potential project benefits.

1.  Dredge Vancouver Lake to remove nutrient-rich bottom sediments and
to increase the volume of the lake; dredging will increase the poten-
tial use of the lake for recreation.

2.  Introduce the Columbia River water into the southwest quadrant by
the use of culverts equipped with counterbalanced gates on the lake end.

3.  Curtail existing and future pollution entering Vancouver Lake from
upland portions of  the drainage basin.

4.  During and after any modification to the system, a carefully designed
monitoring program  should be initiated for future use including the
evaluation of this  study and for the improved design of similar projects.

It should be emphasized that dredging will increase the detention time
of the lake.  The lake quality will not be enhanced if flushing water
is not introduced and pollution sources are not curtailed.

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                             INTRODUCTION

This report describes a series of experiments conducted with a hydraulic
model of portions of the Vancouver Lake-Columbia River system shown in
Fig. 1.  The major objective of the investigation was to provide  infor-
mation on mixing and flushing characteristics of Vancouver Lake and the
effect of certain proposed modifications on the hydraulic regimen of the
system.  Emphasis was placed on the determination of the hydraulic be-
havior and relative "flushing efficiency" under different geometric and
flow conditions.  The flushing efficiency was measured in terms of the
percentage of dye concentration remaining at various sampling stations
in the lake as time elapsed.  This information was supplied to project
number 16080 ERQ for water quality prediction.

The model, constructed of a cement-vermiculite mixture, covered a sur-
face area of  approximately 2100 sq ft.  The test program was comprised
of five progressive stages:  1) existing conditions; 2) upstream  channel
and turning basin in the lake excavated; 3) Vancouver Lake dredged
uniformly; 4) downstream channel excavated; and 5) Lake River dredged
and widened.

By distorting the model (distortion index 10:1) in the vertical direc-
tion, more accurate depth and velocity measurement could be made.
Principles covering the effects of distortion on dispersion were  con-
sidered in designing the model.  The  lake is so large compared to the
amount of inflow, and tidal action creates such uniform mixing during
ebb flow, that good prototype prediction is anticipated.  A view  of the
hydraulic model looking north is shown in Fig. 2.

Certain areas of the model were sealed with a plastic paint to improve
flow visualization and photographic records, and to prevent the dye from
being absorbed by the model.  A fluorescent dye was used to simulate the
soluble pollutants in the lake.  The  water samples were taken with
syringes at eight sampling stations (see Fig. 6, page 16), and the cor-
responding times were recorded.  A precalibrated colorimeter was  used
to determine the dye concentration of the samples.  Most of the tests
were conducted with river flows which occur in the summertime because
this is the critical period for water quantity and quality conditions.

Sinusoidal tides were generated in the hydraulic model and the stage
hydrographs were obtained with automatic level recorders.  The operation
of the model was verified against prototype data for water surface tidal
fluctuations and discharges at various points in the system.  Following
model verification, tests were run to determine the influences of the
various modifications on velocities,  flow patterns, tidal effects, and
dilution throughout the system.

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Lake Rtv.  and Columbia Rlv.
  Join near Ridgefield
                                               LEGEND


                                           •  Automatic water
                                               level recorders

                                           A  Water quality
                                               stations

                                          	Model outline
                                              SCALE  IN MILES

                                            oe====S=^=f^=^^=^
Fig.  1.   Vancouver Lake-Columbia River Hydraulic  System

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          Fig. 2.  View of Hydraulic Model Looking North (70 ft
                   long by 40 ft wide)—Existing Conditions,
                   Columbia River in the Foreground
A mathematical model, the hydrodynamic computer model, was formulated
as a basis for the theoretical analysis of the flow regime in the system
before and after the dredging of the lake and the construction of the
flushing water conduit.  Simulated results were obtained by numerical
solution of the mathematical model with a digital computer.  The validity
of the hydrodynamic computer model was verified with the available data
from the Vancouver Lake Hydrographic Study.  Figure 3 shows the flow
chart of all pertinent Vancouver Lake studies.

Predictive analyses were made with the hydrodynamic computer model to
cover reasonable variations in width and length of an open channel;
size, number, type and length of culverts; tidal amplitude of the Colum-
bia River; and dredging depth of Vancouver Lake.  Applications of the
mathematical model are discussed in the section entitled "Computer
Analysis and Data Extension" beginning on page 37.  The computer program
description is given in Appendix B.  The response of water levels in
Vancouver Lake to changes in river and creek discharges can be expressed
by a water budget.  For conservation of mass the change in volume of the
lake must equal the net flux to the lake.  This yields a continuity
equation for the lake given by
    =  Q. -
dt      i
Q  +P
 o    r
                                          +Q.  -Q
                                        v    in    ou
(1)

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   LOCAL & FEDERAL AGENCIES
(CONCEPTUAL & PLANNING STUDIES)
   COLLEGE OF  ENGINEERING
     RESEARCH  DIVISION
WASHINGTON STATE  UNIVERSITY
(BASIC INFORMATION STUDIES)
   U.S.C.E,  EARLIER FLOOD
   AND NAVIGATION STUDIES
    (ALSO U.S.G.S,  DATA)
      Circa:  1952. 1966.  ...
       F.A.I.R,  STUDY
    Port of Vancouver:  1966
        ST&R COMPLEX
      DEVELOPMENT PLAN
    Port of Vancouver:  1967
         CLARK COUNTY
      REGIONAL PLANNING
       COUNCIL STUDIES
      CURRENT AND FUTURE
      U.S.C.E,FLOOD AND
      NAVIGATION STUDIES
       HYDROCLIMATIC
           STUDY
       EPA:  May, 1968
        HYDROGRAPHIC
            AND
         HYDROLOGIC
          STUDIES
  Port of Vancouver: 1969-1971
   HYDRAULIC MODEL STUDY
       EPA:   1969-1971
       WATER QUALITY
      PREDICTION STUDY
       EPA:   1969-1971
                           FUTURE DESIGN
                          AND DEVELOPMENT
                              STUDIES
           Fig. 3.  Flow Chart of Vancouver Lake  Studies

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in which V is the total lake volume, t  is  time, Q-^  the  inflow rate  to
the lake, Qo the outflow rate from  the  lake, Q^n and Qou  are  local  in-
flow and outflow rates via ground-water seepage, Pr the precipitation
rate onto the lake, and Ev the evaporation rate from the  lake.  An  aver-
age EV value for the study area based on available  data was used  for
each incremental period.

The inflow and outflow rates are those  from Burnt Bridge  Creek, Lake
River, and a man-made conduit, expressed as Qg, Q^, and Qc, respectively,
and Eq. (1) becomes
                     On t Q, ± Q  + Q.  +P-E-Q
                     XB   XL   xc   xin    r    v   xou
              dt
in which the positive sign means  influx to the lake, H is depth of the
lake, and A is the area of lake water surface.  For existing prototype
conditions, Qc is equal to zero,  Qg  is small compared to QL and assumed
to be 50 cfs, Qin is estimated to be about 20 cfs, and Qou is assumed
to balance Q^n due to lack of information.  The volume of the lake at a
depth of 6 ft is approximately 640xl0^ft^ and the annual flow from Burnt
Bridge Creek used in this model amounts to 1578xl0^ft^.  This indicates
an average flushing time to be about five months for complete mixing and,
if storage were available to release QJJ, at a constant rate.

The flow rate in Lake River, Q^,  is  calculated by using the Manning
formula for open channels.  As a  first approximation, the water-surface
slope was used instead of the energy slope to evaluate the flow rate in
Lake River as
                                                                     (3)
where W£ is the width of Lake River, Z and H the water depth of Lake
River and Vancouver Lake, respectively, n£ the Manning roughness factor
in Lake River, R  is the average hydraulic radius and SW2  is the average
slope of the water surface.  Hydraulic radius is defined as the ratio of
the water flow area to its wetted perimeter.  Considering  an equivalent
rectangular channel to the actual cross-sectional geometry of Lake River,
RZ=W2Z/(W2+2Z).  As W2 becomes  large, 2Z becomes less important, i.e.,
W£»-2Z, RZ-»Z.  The hydraulic radius  is defined by


                                                                     (4)

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for a wide channel and


                                 Z   - H
where Zw and E^ are the water levels of Lake River and Vancouver  Lake
above mean sea level, and L2 is  length of the reach.  A wide,  open chan-
nel is defined as a rectangular  channel whose width  is greater than ten
times the depth of flow.  Figure 4 shows the prototype geometries used
in this analysis.  Substitution  of Eqs. (4) and  (5)  in Eq.  (3)  yields
                            W2              S/3          1/2
                                       + H)5/3(Z  - H)              (6)
                               1/2
                           (L2)
with the first approximated value, (QL)]> velocities in the upstream and
downstream ends of the reach are calculated as follows
                    uu = -7-    and   ud = —-                   (7)
in which Au and A^ are the cross-sectional areas at the upstream and
downstream ends of the reach.  Therefore, the second approximation of
the energy slope can be evaluated by


                        (Z  - H ) + (u 2 - uJ2)/2g
                      m iw	wL_J_u	dJli
                   a *7              T                                N
                   ez              j_irt
and then the final calculation of the flow rate becomes
                  Q  .  [w  -L±mi^\ R 2/3    1/2
                  XT —  I ™ O   O   I I      I"     ^       *              V-/J
                   L    I  2   2   l\  TLJ  I  z     ez


By the same token, the flow rate  for the upstream channel  for  introducing
flushing water, Qch, is given by
                                  10

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Willamette
River
                                                                N
                                                           Lake
                                                           River
                         Burnt  Bridge  Creek

             (a)  The Columbia River-Vancouver Lake System
            Vancouver Lake
     Lake River
V^ ' H f HW


f
/ • i,/i ill f 1 //ill*1 > '~7^,
»Hb

' /"^- — '
J i »T
Z V i7h
u
frTJj 77V / /TTTTTTnTTT?
                                                           msl
             (b)  Section A-A (before dredging of the lake)
            Columbia
             River
Vancouver
  Lake
                                                           msl
                     Cut
                   Channel
             (c)  Section B-B (after cutting a channel and
                         dredging of the lake)
  Fig. 4.  Geometries of the System Used for the Hydraulic Analysis
                                 11

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                                         R
                                         R
                                                  1/2
                                               "ec
                                                            (10)
where Y is the depth in the channel.  Both Rc, the hydraulic radius of
the channel, and Sec, the energy slope in the channel, have similar
definitions as defined in Eqs. (4) and (8).  Sinusoidal tide cycles in
the Columbia River and Lake River were assumed and used in the hydraulic
model and for the prediction studies as follows.
                       Y = Yn + a, sin(4Tt)
                                                            (ID
                       Z = Z  +82 sin(4irt)
                                                            (12)
where a^ and a£ are half of the tidal amplitudes of the Columbia River
and Lake River respectively, and YQ and Zo are respectively the mean
initial depth in the channel and Lake River.   Magnitudes of the mean
tidal amplitude were obtained by statistical analysis of the field hydro-
graphic data.  Figure 5 presents the comparison between sinusoidal and
actual tides over two complete tidal cycles (about 25 hrs).
                             Assumed sinusoidal
                             tide stage—7
                                     S
r o
Q)
         -2
                                                        Mean
                                                        initial
                                                        depth
                                    Actual tide stage
                                    I	I	I
                                   12
                                Time, hrs
                                    18
24
         Fig. 5.  Comparison of Sinusoidal and Actual Tides
                  over Two Complete Tidal Cycles--Prototype

An alternative for introducing flushing water is a submerged culvert
system.  The flow through a culvert system was analyzed by the Darcy-
Weisbach equation as
                    AH =
                                                                   (13)
                                  12

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in which  AH is the continuously changing  difference  in water  level
between the Columbia River and Vancouver Lake,  Dc  is  the  inside  diameter
of culvert, LC the length of culvert, Ke the  entrance loss  coefficient
of 0.5, K^ the exit loss coefficient of  1.0,  and  f the friction  factor
in the culvert.  Rearranging Eq. (13) and  solving  for the average veloc-
ity in the culvert yields
Therefore, the total flow rate  through any number of  culverts, N , into
the lake, when the water surface  in  the river rises above Vancouver
Lake, is expressed by
                            Q    = N A V                             (15)
                             cu    c c                              ^

where A  is the cross-sectional  area of  a  culvert.
       c

Note that for the upstream  channel, if Yw  is greater  than EL^, Qch is
positive and inflow  to  the  lake  occurs (or if  it  is negative, outflow
occurs).  For culvert construction, Qcu  is always positive because  of
the flap gates on the Vancouver  Lake end.   Therefore,  if AH  is negative,
i.e., when the river falls  below Vancouver Lake,  the  gates will auto-
matically close and Qcu becomes  zero.

Both the mathematical and physical hydraulic models were important  tools
in the analysis of the  effects of alternative modifications  to the  Van-
couver Lake-Columbia River  System.  In addition,  the  laboratory and
predicted results are providing  guidelines for design and decision  making
to achieve the enhancement  of Vancouver  Lake.  The methodology developed
in this study will provide  a useful experience record for others wishing
to improve the quality  of some of the thousands of lakes which can  be
restored through dredging,  flushing and  curtailment of pollution sources.
                                   13

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                         DESCRIPTION OF MODEL

The area modeled included the Columbia River from near the Vancouver
Bridge, Vancouver Lake, and Lake River downstream to just below Post
Office Lake.  The confluences and short sections of the Willamette
River, Burnt Bridge Creek, and Salmon Creek were included in the model.
Figure 6 shows the model and monitoring stations in the model and proto-
type lakes.  In order that dynamic similarity be maintained it is
necessary to satisfy the Froude model law, i.e., the Froude number must
be equal in model and prototype.  By this relationship it is possible
to establish the various geometric, kinematic and dynamic similitude
relationships between the model and the prototype.

By definition, the Froude number F can be expressed as


                             F = V//iD                              (16)

where V is the average  longitudinal velocity in a cross section, D is
the characteristic depth, and g is the gravitational acceleration.  Let
the subscript r denote  prototype-to-model ratios, and m and p refer to
model and prototype, respectively.  Then

                             F  = F                                 (17)
                              p    m


or                      (VA/gD)  = (V/JiD)m                          (18)

                                    1/2
and therefore                Vr = Dr                                (19^

If A  represents a cross-sectional area and L is a characteristic length,
the discharge and time  ratios can be expressed as
                               Q   = A  V
                               r    r r
                                           (Dr)1/2
 or                            Qr = W                           <20>


 and                           Tr = Lr/Vr


                               Tr =Lr/(Dr)1/2                       (21)
                                     15

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                                               LEGEND

                                           Automatic water level
                                           recorders in the field

                                           Taps for stage sensing
                                           in the  hydraulic model

                                           Sampling  stations  in
                                           the hydraulic model
                                           Calibration tubes and
                                           pressure cells in model
                            \Felida __
                                           Gates for model tests only
                             VANCOUVER,
                             WASHINGTON
Willamette
River
           PORTLAND,
           OREGON
             Fig. 6.  Hydraulic Model and Sampling Stations
                                 16

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When model scales in  length and  depth  are  chosen,  then the  other  related
similitude ratios can be calculated.   Table  1  shows  the prototype-to-
model ratios used in  the Vancouver Lake model  study.


                  Table 1.   Model Scale Ratios Used in  the
                         Vancouver Lake Model Study
Item
Horizontal length
Vertical depth
Velocity
Discharge
Time
Distortion ratio
Definition
Lr
Dr
vr
Qr
Tr
Lr/Dr
Relation
Lr
Dr
Dr1/2
LrDr3/2
L D ~1/2
LrDr
Lr/Dr
Scale Ratio
600:1
60:1
7.75:1
279,000:1
77.5:1
10:1
The model  topography was  constructed  of vermiculite concrete.  A base
pour was made,  contours  laid out  on this  base,  small (s 1/4"  <$>) metal
rods were  driven  into  the base  and cut  to proper  elevation, the shaping
pour was made,  and  the model was  then sealed with a neat cement paste.

The Columbia and  Willamette  river head  tanks were designed to minimize
large-scale turbulence at their entrances.  The tail tank and tide
generators were designed  as  a unit.   The  tide generator consisted of a
hydraulic motor coupled to a camshaft with reduction gears and chain
drives.  The cam  lifted a vertical gate to generate the tidal water
level change at the tail  tank by  raising  and lowering  the crest over
which the  outflow passed.  Separate tide  gates  and power takeoffs were
used for the Columbia  and Lake  Rivers.  The height of  the crest, the
time of a  cycle,  and the  cam throws were  variable.  The cam used for
these studies provided a  sine wave motion to the  tide  gates.  The pool
upstream of the tide gate for Lake River  was provided  with a  source of
make-up water to  insure flow over the tide gate during a rising tide
cycle.  The large amount  of  flow  in the Columbia  River made such a con-
trol unnecessary  there.   The Columbia and Lake  River tides could be
generated  independently except  for the  time of  the cycle, which was
common.

Flows for  the Columbia and Willamette Rivers were measured with magnetic
flowmeters.  Burnt  Bridge Creek and Salmon Creek  flows were measured
with "Rotometer"  units and a propeller meter.   The water levels in the
model were measured with  Consolidated 4-312 ±5  psid pressure  cells. The
signal conditioning and recording were  done on  Brush equipment.
                                   17

-------
Rhodamine WT dye was used for pollution tracing and concentrations were
measured with a B & L Spectronic 20 colorimeter.  The dye was photo-
graphed to provide visual dispersion records not possible to obtain with
concentration sampling techniques.  In those areas where photographs of
the dye were needed, the model was painted with white epoxy paint to
increase visibility and reduce staining of the topography.  A Statham
0.5 psid pressure cell was used to obtain differences in water levels
between the Columbia River Gage 1 and the Vancouver Lake Gage 2.

The modifications to the construction of the model were comprised of
five progressive stages:

Stage I was for existing conditions in the prototype for model verifi-
cation.

Stage II consisted of construction of an upstream channel 400 ft wide
between the Columbia River and Vancouver Lake (see Fig. 6).   An area was
deepened in the proposed docking and turning area along the  west shore
of Vancouver Lake.

For Stage III the channel was narrowed to 200 ft.  The bottom of the chan-
nel and the "dredged" area in the lake were maintained at -10 ft msl as
shown in Fig. 7.
        Fig.  7.   Upstream Channel  Test of Hydraulic Model
                 with West Side of Lake Dredged--Stage III

                                 18

-------
For Stage IV  the  entire Vancouver Lake was  " dredged" to -10 ft msl.
An island was installed in Vancouver Lake  to evaluate the feasibility
of using such an  island for improving circulation within the lake.
No significant improvement was observed.  A  10-ft diameter (prototype)
culvert was  tested in lieu of the upstream channel to evaluate its
relative effectiveness in flushing the lake.

Stage V consisted of additional "dredging" and widening of Lake River
to a downstream channel from Lake River  to the Columbia River (see
Fig. 6).  This channel was constructed just  upstream of Post Office
Lake.  The width  was 200 ft and beds were excavated to -10 ft msl for
both Lake River and channel cross sections.
The model was verified by comparing model  gage  heights  versus time with
prototype data for the same discharge  conditions  under  which the field
data  were taken (Fig. 8).  Gage data of Vancouver Bridge were obtained
from  the USGS and others were taken by visual observation of staff
gages by Clark College (Vancouver, Washington)  students under the direc-
tion  of the project hydrologist.  The  verification was  considered ac-
ceptable for the available range of prototype data and  the sinusoidal
model tide generation.
              Columbia R. discharge
     W Farmhouse
     A Marina
       Craig
 •Felida
 QLake R. belov
  Salmon Cr.
                  JL
                                      220
                                      200-
                                      180
                                      160
                                      140 -g
                                         «
                                         •rl
                                         a
                                      120
                                      100
                                       80
          10
  AM
  12      14
torch 19, 1970
 Time, hrs
16
PK
                             Fig.  8.   Prototype measure-
                                      ments Used to Verify
                                      the Physical Model-
                                      Sample
                                    19

-------
                          TESTING PROCEDURES

Testing was restricted to the most severe  conditions  available  from
examination of the prototype data.  The  extreme  tide  variation  for the
Columbia Gage 1 was selected and the concurrent  streamflows were
determined.  Model streamflows were established  and the  tide  generator
adjusted to produce the desired tide range.   Some  additional  adjustment
in phasing and range was necessary on  the  Lake River  tide  system.  With
these controls all set, the model was  ready for  testing  in the  Stage I
condition.  For subsequent conditions, the control settings were not
changed.  This was required to establish a controlled basis in  the model
for evaluating effects for future conditions  (i.e., the  dredged upstream
channel).

Data taken included photographs, samples of the  water, velocity measure-
ments, flow rates, and recorded stages.  All  data  were related  on a com-
mon time base.  Velocities were low and  their measurement  was restricted
to timing the movement of floats or dye.   Velocities  were  taken through-
out a tide cycle, and three locations  were selected for measurements:
1) in Lake River downstream of the lake  outlet near Felida; 2)  in the
upstream channel, and 3) in the downstream channel.

In general it was necessary to run through five  or six tide cycles
before stable repetitive water levels  were achieved.  A  testing modifi-
cation was necessary for reliable pollution tracing.  For  the modified
conditions with channels, temporary gates  were used in the upstream
channel and Lake River to isolate the  Vancouver  Lake  pollution.  The
isolated area was filled and mixed uniformly  with  dyed water  to a depth
consistent with the test conditions.   The  water  levels were selected so
there was no differential head across  the  gates.   At  the null point
where the tide was starting to rise and  there was  no  movement of water
in or out of Vancouver Lake, the gates were removed.

Eight sampling points were selected in the Vancouver  Lake  area  and
samples were taken with syringes at the  end of the ebb tide cycle
(Fig. 6).  The corresponding times were  recorded.  A  precalibrated
B & L Spectronic 20 colorimeter was used to read the  percent  of trans-
mittance.  By using the calibration curve  the relative concentration
of each sample was determined.  The calibration  curve was  obtained by
the following steps:  1) consider the  initial concentration Co  of dye
water in the lake to be 100 percent corresponding  to  percentage of
transmittance To (note that the clearer  the water, the higher is To);
2) by successive dilution to the desired concentration C,  the percent
of transmittance T was read from the colorimeter;  and 3) plot C versus T
to one of the curves using To as a parameter  as  shown in Fig. 9.
                                  21

-------
   100
    80
    60
  u
  d
  o 40
    20
      0
-  To is the initial percent
   of transraittance cor-
   responding to C0 (1007.)
      20
              40              60
                       Transmittance,
80
100
           Fig. 9.
             Calibration Curve for B & L Spectronic 20
             Colorimeter (Rhodamine WT Dye)
Photographs were taken to record the changes in lake color, and stages
were recorded continuously.  Figure 10 presents strip charts for gage
stations in Vancouver Lake model.  Differential water stages between
the Columbia Gage 1 and the Vancouver Lake Gage 2 were recorded for one
tide cycle.

In the "as-is condition," without the channels being open, additional
pollution studies were made by injecting dye into Burnt Bridge Creek
and Salmon Creek flows.  Samples were taken at Felida and two locations
in the lake.  Dye injection was started or commenced to be concurrent
with the highest, lowest or intermediate level of Vancouver Lake water
stage, with the lake being initially clean for those exploratory tests.

Dye tracing was done photographically to determine:  1) under what con-
ditions the Willamette River would enter the upstream channel; 2) the
flow rate from Salmon Creek which causes reversal of the Lake River flow
back into Vancouver Lake during ebb tide; 3) flow patterns with the
island; and 4) various other flow patterns in the model.
                                   22

-------
          Time, min

                        rh=d==±==^==i==4==±^=i==J^t-~l-^=h


                                                 Columbia R. at
                                             -3^ Blurock Landing
                                             -7^-_._,	,	. _,1_-r_T--«={
                                            S—:-^vi—Jtrl^j:
                                    t=±=±=.±=t:r.
                                    1	L	L	i	1—


                               ^4^£^EESE^ Lake River
                               ••^/^%£^~4~"^	'	"-rfEZK


                                         	j__j^_i ,  , __^	 * 	 	_,_^,
Conditions:   Run No.  18.
Downstream  channel openrjrE-]
Qc-145,000  cfs
Qw-8,900  cfs

                                                    Lake River   -
Note:  Chart speed (horizontal)  lcm-2min (model time)
       Chart scale (vertical  lcm-1ft  (prototype)

 Fig.  10.   Strip Charts  for the Gage Stations  in
            the Vancouver Lake Hydraulic Model

                          23

-------
                   DESCRIPTION OF  TESTS  AND  DATA ANALYSIS
Prior  to  initiating the test  program, the hydraulic model was verified
against prototype conditions  for  water  surface tidal  fluctuations and
discharges at various  points  in the  system.   Following model  verifica-
tion,  tests  were conducted to determine the  influences of the various
test conditions  on  velocities,  flushing action,  and dilution  throughout
the system.   Table  2 summarizes the  conditions for the various tests.

                      TABLE 2  .  SUMMARY OF TEST  CONDITIONS AND DATA ACQUISITION

TEST
NO.

1
2
3
it
5
6
7
8
9a
9b
9c
9d
1O
lla
lib
lie
lid
12a
12b
12c
12d
13
Ik
11;
*.?
Ifi
.LM
17
18
19
20
21
22
FLOW CONDITIONS
HIViB FLOWS (cfs)
Columbia

Willamette
•v
Preliminary Tests 1
on Burnt Bridge >
and Salmon Creeks J



11*5000
11*5000
75000
50000
25000
H5OOO
11*5000
75000
50000
25000
1145000
11*5000
3118000
232000
11(5000
VOID
11*5000
11*5000
11*5000
11(5000
11*5000
11*5000
11*5000
11*5000
\
>
J
7500
5000
75000
1OOOOO
125000
5OOO
5COO
75000
100000
125000
7000
7000
50000
26000
7500
—
9*i OO
I j\j\j
7soo
(JW
8900
8900
8900
7000
7000
7000
Burnt Bridge
1037
1031
1037
1037



0.2



















500
500
500

Salmon




2565
2565
2510
1.6









A
5230T












CHANNELS
OPEN3
U L C







'(00
1*00
1*00
1*00
1)00
200
200
200
200
200
200
200
200
200
200

200 200
POO
f\AJ
•
200 o
200 200

200
200
I AKF
JurllVCj
CONDITIONS'3
H DO D LB





















Island









DATA MEASUREMENTS
DYE STATIONS0
Source
BBC
BBC
BBC
BBC
sc
so
sc
U
»
VR
CD
1
VL

VR
PD
UK
*
VL

-
_
U

VL
» Ju
VI
V&j
VL
VL
VL
VL
VL
VL
Sampled
1
1,3
1,3
1,3
1,3
1.3
1.3
1.3.7




1-8




1-8





1-8
X w
1-8
i«-U
1-8
1-8
1-8
1-8
1-8
1-8
VELOCITIES
0 F L












• •




• •








•
• •

•
•
PHOTO-
GRAPHS6
U F L





















•




•
•



TID£f
































AHS
































SCHANNELS OPEN: U, upstream channel near Blurock Landing opposit Willamette River
L, downstream channel south of Post Office Lake ear mouth of Salmon Creek
              Cj  10-ft diameter single culvert placed in upstream channel position
              For location of channels, see Fig. 6
              200 and 400 are channel widths in feet
 bLAKE CONDITIONS:   S,  natural existing conditions
               DD,  docking area dredged along west shore of lake (15 ft)
                 D,  Vancouver Lake dredged to 15-ft depth (-12 ft msl)
               LR,  Lake River widened to 200 ft and dredged to 15 ft
 CDYE STATIONS: Source: BBC, Burnt Bridge Creek; SC, Salmon Creek; U, upstream channel;
                    CR, Columbia River; WR, Willamette River
             Sampled: Stations 1 through 8 as shorn in Fig. 6
 ^VELOCITIES measured at:  F, Felida in Lake River; D, upstream channel; L, downstream channel

 ePhotographs taken at same locations as in Note d above
 fIIDE means the tides for Columbia River and Lake River were generated in the model
 8&H means that the differential elevation between water surfaces in the Columbia River and
  Vancouver Lake was  recorded
 tMinimum flood flow  at  which Salmon Creek moves upstream in Lake River and enters Vancouver
  Lake against an ebb tide
                                            25

-------
Tests in the hydraulic model are divided according to different modifi-
cation stages as follows:

Stage I (Tests Nos. 1-7):  Preliminary tests on Burnt Bridge and Salmon
Creeks — the introduction of larger than average flows was to simulate
flood-flow effects and possible future storage released from Salmon
and/or Burnt Bridge Creeks.  Continuous dye was injected at Salmon and
Burnt Bridge Creeks in order to trace their flows into and out of the
lake.

Stage II (Tests Nos. 8-9): Excavation of an upstream channel 400 ft
wide in the vicinity of Blurock Landing in the Columbia River opposite
the mouth of Willamette River to Vancouver Lake, and the dredging of a
docking terminal area along the west shore of the lake to a mean depth
of 15 ft.

Stage III (Tests Nos. 10-11);  Same conditions as Stage II except
reducing the upstream channel to 200 ft of width.

Stage IV (Tests Nos. 12-13);  Dredging of entire Vancouver Lake bottom
to approximately 10 ft below mean sea level and widening of the entrance
to Lake River.  The flow conditions in the Willamette and Columbia
Rivers were tested at which the Willamette would enter the upstream
channel.  (Only when Qw *i Qc.  This condition occurs rarely and only at
times when the Willamette River is in flood.)  A small island was placed
in the lake near the upstream channel outlet to divide the inflow and
observe any changes in flushing pattern.  Test No. 14 was voided.

Stage V (Tests Nos. 15-22);  Additional dredging and widening of Lake
River downstream (north) as far as the second (downstream) by-pass
channel to a width 200 ft and a bottom elevation of 10 ft below mean
sea  level.  Various dye experiments were conducted in the hydraulic
model with the upstream and/or downstream channels in operation and
a single culvert was used as an alternative to the upstream channel.

To display test results, selected data from Tests 12,15,17,18,19,20
and  22 are presented in Figs. 11 through 17.  These show similar
concentration decay curves.  In order to evaluate the relative effective-
ness of each test, comparison was made of the relative "flushing
efficiency" which was measured in terms of the percentage of dye con-
centration remaining in the lake as time elapsed.  The lower the relative
concentration C/C0, the more efficient is the flushing action.  Figure 18
presents the test results (average of all eight sampling stations)
plotted on semilog paper.  A functional relationship between these tests
is given by


                            -£-  = exp(-kt)                          (22)
                                  26

-------
    100
                       Prototype Time, days
                     234
    80
  o
 o
    60
  o
  §
  o
  
-------
ro
oo
              100
               80
               60
             o
             a
             o
            u
             0)
             CO
            I-l
             
-------
                                             Prototype Time,  days

                                                2                  3
N)
VO
IUU

80
o
u
" 60
•%

u
c
o
u
 fj

9- 9- °{r


_

—A
*••• * •*" "* "
A**"" *"""
""^••N.^ ^^"^
A
-
: Test No. 17
Lake dredged, -10 'msl
dredged
culvert installed
of upstream channel*
cfs, Qw 8,900 cfs
*Special conditions compare with
Test Nos.
1 i i
40 50 60
Model, min
12 and 18
i i
70 80 90

                           Fig.  13.  Test No.  17:  Relative Concentration of Dye
                                     in Vancouver Lake Model as Function of Time

-------
                            Prototype Time, days
100
      60
   o
   cs
   o
   co
      40
      20
       0
                                              4
                                             "T
                                                        6
                                                       "T
                                                   Sampling
                                                   Stations
                                                  • 1
                                                  • 2
                                                  o 3
                                                  A 4
                                                 a 5
                                                 
-------
               100
                80
u>
                60
             u
             §
             o
             
-------
Test Series No. 12;  Purposes;   to determine Salmon Creek flood flow
which would block the tidal flow in Lake River from entering and leaving
Vancouver Lake; and to explore the effects of higher flows in the Colum-
bia River on tidal effects for a fully dredged lake.  Results:   Salmon
Creek flood flow determined that would block the tidal action in Lake River,
and model verified for field tide data at higher flows (see Fig. 11 for
results of Test No. 12a).

Test No. 13;  Purpose;  to evaluate effectiveness of island in lake near
outlet of upstream channel on flushing efficiency.   Results; the island
assisted in dividing the flow in such a way as to improve the flow char-
acteristics along the south shore part of the time.  But the path of the
inflow is strongly influenced by the tidal action,  and the amount of in-
flow is so small in comparison to the volume of the lake,  that the use
  100
     0
             Prototype Time, days
         234
1 1 1 1
— |B" QjP" tD~ _QO" Q_

A XXA-""" "*" ^\X
>g(^
A
A A
A A
A
Conditions: Test No. 20
Vancouver Lake dredged,
- 10 'ms 1
Lake River dredged
~ Qc 145,000 cfs
Qw 7,000 cfs
QB 500 cfs*
*Special condition,
_ compare with Test
Nos. 12 and 21.
1 l 1
l l
V D D ~
o 
-------
                 100
                   0
                                  Prototype Time, days
                                  345
                                     6
                                    —j—
                                             8
OJ
UJ
                 80
              O
              o
              o
o
c
o
o

-------
of an island was deemed insignificant in trying to influence flushing
efficiency.

Tests Nos. 15 and 16:  Purposes;  to test downstream channel operating
in conjunction with the upstream channel and test the action of the
downstream channel with the upstream channel closed.  Results:  the
downstream channel short-circuits the Columbia River tidal flow into
Vancouver Lake via Lake River.  Its flow blocks the tidal action coming
up Lake River towards Vancouver Lake and holds back water in the lake.
The downstream channel is detrimental to the flushing of Vancouver Lake
by the upstream channel.  This is obvious when Fig. 12 (Test No. 15) for
both channels open is compared with Fig. 17 with only the upstream chan-
nel being open.
                             Prototype Time,  days
                              3456
                8
          100
    Run #17 (0.0142)*
          #20 (0.0246)
                                             #16  (0.166)
                                                  #18  (0.175)
                                             #15  (0.225)

                                                         #19
                                                       (0.231)
                                                  #12  (0.261)

                                                           #22
                                                         (0.324)
                                                            #21
                                                         (0.362)
                                                     •
                                                     (k values
                                                     for Eq. 22)
                                     i.
_L
-i.
             0           40           80           120
                              Model Time  tf  min

                Fig. 18.  Summary of Vancouver Lake Model
                          Tests for Post-Development Study
J_
                 160
                                   34

-------
Tests Nos. 17 and 18;  Purposes:   to  evaluate  single  culvert  and  the
downstream channel.  Results;  Fig.  13  shows how inefficient  a  single
culvert is, and Fig. 14 shows how  the downstream does help  flush  the
lake, but in a cyclic  fashion as caused by  the tides.  Also,  the  lower
channel allows no opportunity for  flow  through the  lake,  only in  and
out.

Tests Nos. 19. 20 and  21;   Purpose:   to evaluate the  influence  of a
larger-than-normal  discharge from  Burnt Bridge Creek  with various con-
ditions of channel  openings.  The  tests were done to  evaluate the sug-
gestion of pos'sibly storing water  in the Burnt Bridge Creek basin and
releasing it over a short  time period in the summer.  Results;  Fig. 16
shows that the flushing efficiency of Burnt Bridge  Creek  is quite low.

Test No. 22:  Purpose: to evaluate the effect of dredging  Lake River
(near the outlet of Vancouver Lake)  on  the  flushing efficiency  with the
upstream channel open. Results:   by comparing Figs.  17 and 12, a slight
improvement  in flushing efficiency due  to widening  and deepening  of Lake
River can be observed  for  Test No. 22.

Hydraulic characteristics  in the model  were obtained  by recording
continuous stage hydrographs and by measuring  velocities  in the chan-
nels and  in Lake River near Felida.  Figure 19 shows  the  surface
velocity variations in Lake River  near  Felida  and Fig. 20 presents the
variations in  the  upstream channel velocities.
                                   35

-------
    o4
     4
                             Run
                                                          Channel*
                                                           Open
                             • 18  145000 7500  ---  Downstrea
                             o 19  145000 7500  500  Both
                             A 20  145000 7500  500  Nolther
                             a 22  145000 7500  —  Upstream
/Test Conditions:
 Vane. L. dredged, -10'mal
 Lake R. widened and dredged,
  -10'msl
 Qc-Columbia R. discharge, cfa
 Qw-Willamette R. discharge, cis
 Qg-Burnt Bridge Or. discharge, c£a
                                6        8
                              Prototype Tine, or*
                                         10       12
        14
Fig.  19.   Surface Velocity  in  Lake River  near Felida
             (near  Gage 3)     (Model measurements con-
             verted to  prototype)
                                                          Channels
                                                            Open
            h for Run 19
            h for Run 22
            Qc-Columbla R.  discharge, c "a
            Qu-Willaraette R. discharge, cfs
            QB-Burnt Bridge Cr.  discharge, cfs
            Tests with Vane. L.  dredged and Lake R.
            widened and dredged, both to -10* msl
                                                                     1.0
                                                                    0.5
                                                             0.5
                                                                51
                                                                     i.o
                                6        8
                              ProMCyp* Tim«, hn
                                          10
12
14
    Fig.  20.   Surface Velocities  and  Differences  in
                 Elevation for Upstream  Channel   (Model
                 measurements  converted  to  prototype)
                               36

-------
                 COMPUTER ANALYSIS AND  DATA  EXTENSION

Mathematical modeling was the basis  of  the hydrodynamic  computer model
used to extend  the results  of the physical hydraulic  model  study.
Details of the  hydrodynamic model are given  in Appendix  C.   Under  the
assumptions of:  a) constant lake surface area,  b)  average  evaporation
rate from the lake, c)  constant  Burnt Bridge Creek  inflow,  d) constant
seepage inflow  to and outflow from  the  lake,  and e) sinusoidal  tide
cycles in the Columbia  and  Lake  Rivers,  the  response  of  water levels
in Vancouver Lake to changes in  river and creek discharges  were ob-
tained by the water budget  concept.

The flow rates  in Lake  River and the upstream channel were  calculated
by using the Manning formula.  An alternative to the  upstream channel
for introducing flushing water was  a submerged culvert system as analyzed
by the Darcy-Weisbach equation  for  the  pipe  flow velocity based on the
differential head loss  between  the  Columbia  River and Vancouver Lake.

The numerical integration of a  set  of differential  equations was
achieved by explicit difference  approximation.   The  solution proceeds
in steps of time increment  of one hour  until the desired total  simula-
tion time has been reached. The validity of the hydrodynamic computer
model was verified with data from the field  and the hydraulic model.
Figure 21 gives the stage hydrograph recorded and velocities measured
in the physical hydraulic model  with the upstream channel 200 ft wide
and Vancouver Lake dredged  to  15 ft deep (bottom -10  ft  msl) .   Figure 22
presents the predicted  results  of the hydrodynamic model for the inflow-
outflow stage and discharge relations in the system at the  same condi-
tions.  The comparison  between  simulated values and those obtained from
the hydraulic model is  shown in  Table 3.


            Table 3.  Comparison of  Results between  Predicted
                Values  and Those  from the Hydraulic Model
Characteristics
Depth of Vancouver Lake
(ft)
Velocity in Lake River
(ft/sec)
Velocity in the channel
(ft/sec)
Range
max
min
max
min
max
min
Computer
Program
15.9
14.3
-3.0
-1.5
4.8
2.0
Hydraulic
Model
16.0
14.4
-3.0
-1.9
5.1
2.4
        Notes.   Conditions--channel wiatn=^uv LL.;  UULUUIU ua. a.a^
        InTThannel dredged,-10ft msl.   Negative sign means out-
        flow from the lake.   Model velocities measured with sur-
        face floats and are  therefore greater than the average
        velocity by 5% to 10%•
                                    37

-------
CO   ..
e   6
cu
oo   4
to   "*
4J
CO
                                      Conditions:
                                      Channel width, 200'
                                      Bottom of  lake and channel
           Columbia River               dredged, -10'msl

                      Vancouver Lake
                Lake River

               J_
_L
                             _L
               0.25
         1.0
        0.5       0.75

             Time,  day

(a)  Stage versus Time (recorded in

    the physical hydraulic model)


CO
O.

4J
••-1
O
0
1
1 1
cu
>




6.0
4.5
3.0

1.5


0.0

-1.5

-3.0


-
Q OQ O / — Upstream
C* U channel
0 0

O





O
_ ^^
°°oo ^ \ A^£& o °
— Lake River
' i I j i.i
              0.1
0.2      0.3      0.4

     Time,  day
               0.5
                                           0.6
                  (b) Velocity Profile (measured in

                      the physical hydraulic model)
 Fig. 21.  Prototype Inflow-Outflow Stage and Discharge Relations

           Obtained from the Physical Hydraulic Model
                              38

-------
(A

E

0>
>
o
n
o
7



6




5
O)   .
o>  4
o
                Inflow-Outflow  Stage  and Discharge Relations

                for 200-Ft Upstream Channel,  3200' Long


                                          Upstream Channel

                                          200ft wide, 15ft deep
/Columbia River
                    "Vancouver
     0
        0.2         0.4         0.6

                       Time,  day

                 (a)  Stage Versus  Time
                                                 0.8
    0
                    0.4         0.6

                       Time,  day

                 (b) Velocity Profile
1.0
                                       Lake  River
                                     (always flowing out)
      Fig.  22.  Typical Example of Upstream Channel Flow Analysis

                for One Set of Width and Depth  Conditions
                                  39

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Upon validation of the existing prototype conditions, numerous simula-
tion runs were made by the hydrodynamic model to examine the influence
of possible modifications to the system on hydraulic characteristics.

First, various widths of the upstream channel were tested to determine
the width and corresponding flow rate at which Lake River could be kept
from discharging into Vancouver Lake.  Under these conditions the tidal
flow from Lake River into Vancouver Lake would be reversed.  Flow would
always be out of Vancouver Lake via Lake River to the Columbia River
near Ridgefield.  The results for widths of 100, 150 and 200 ft are
plotted in Fig. 23.  It was found that Lake River will always flow out
of the lake if the width of the upstream channel is 150 ft or greater.

Then, various combinations of channel length; size, number, type, and
length of the culvert; tidal fluctuation of the Columbia River; and
dredging depth of the lake were tested to determine their effects on
detention time of flow entering the lake.  As an example, the influence
of various types of culvert materials (i.e., various friction factors)
on the average flow rate (or detention time) through culverts is shown
in Fig. 24.  Finally, functional relationships were obtained for conduit
discharge as a function of each variable.  Common conditions for the
simulation runs were:  a) bottom of Vancouver Lake dredged to 10 ft
below mean sea level, b) initial lake depth of 15 ft, and c) constant
lake surface area equal to 105x10^ sq ft.

Figure 25 shows the detention time (t
-------
Fischer, Hugo B., and Holley, E. R.,  "Analysis  of  the  Use  of
Distorted Hydraulic Models  for Dispersion  Studies," Water  Resources
Research, American Geophysical Union, Vol.  7. No.  1, Feb.,  1971.

Garrison, Jack M., Granju,  Jean-Pierre  P.,  and  Price,  James T.,
"Unsteady Flow Simulation  in Rivers  and Reservoirs," Journal of  the
Hydraulics Division, American Society of Civil  Engineers,  Vol. 95,
No. HY5, Sept.,  1969, pp.  1559-1576.

Goodwin, C. R.,  Emmett, E.  W., and Glenne,  Bard,  "Tidal  Study of
Three Oregon Estuaries," Bulletin No. 45.  Engineering  Experiment
Station, Oregon  State University, Corvallis, Oregon, May,  1970.

Griffin, W. C-,  Watkins, F. A., Jr,  and Swenson, H.  A.,  "Water
Resources of the Portland,  Oregon and Vancouver, Washington,  Area,"
Geological Survey Circular  372, Washington, D.C.,  1956.

Hendricks, E. L. (prepared  under the direction  of),  "Compilation  of
Records of Surface Waters of the United States, October, 1950 to
September, 1960; Part 14. Pacific Slope Basins  in  Oregon and Lower
Columbia River Basin,"  Geological Survey Water-Supply  Paper 1738,
U.S. Geological  Survey, U.S. Government Printing,  Office, Washing-
ton, D.C., 1963.

Holley, Edward R., Harleman, Donald  R.  F.,  Fischer,  Hugo B.,  "Dis-
persion in Homogeneous  Estuary Flow," Journal of  the Hydraulics
Division, American Society  of Civil  Engineers,  Vol.  96,  No.  HY8,
Aug., 1970, pp.  1691-1709.

Lai, Chintu, "Computation of Transient  Flows in Rivers and  Estuaries
by  the Multiple-Reach Implicit Method," U.S. Geological  Survey
Prof. Paper 575-B. 1967, pp. B228-B232.

Lai, Chintu, "Computation of Transient  Flows in Rivers and  Estuaries
by  the Multiple-Reach Method of Characteristics,"  U.S. Geological
Survey Prof. Paper 575-D.  1967, pp.  D273-D280.

Lauff, George H., ed.,  Estuaries, Publication No.  83,  American
Association for  the Advancement of Science, Washington,  D.C., 1967.

Liggett, James A., "Unsteady Circulation in Shallow, Homogeneous
Lakes," Journal  of the  Hydraulics Division. American Society of
Civil Engineers, Vol. 95, No. HY4, July, 1969,  pp.  1273-1288.

Lomax, C. C., and Orsborn,  J. F., "Flushing of  Small Shallow Lakes,"
Water Pollution  Control Research Series 16010 DMG,  U.S.  Environ-
mental Protection Agency, U.S. Government  Printing Office,  Washing-
ton, D.C., Dec., 1971.

Lowe-McConnell,  R. H.,  ed., Man-Made Lakes. Proceedings  of  Royal
Geographical Society Symposium, London, England, Sept. 20-Oct. 1,
1965.

                              52

-------
Nelson, Mark L., and Rockwood,  David M.,  "Flood  Regulation  by
Columbia Treaty Projects," Journal  of  the Hydraulics  Division.
American Society of Civil Engineers, Vol.  97,  No.  HYl, Jan., 1971,
pp. 143-161.

O'Brien, Morrough P.,  "Equilibrium  Flow Areas  of Inlets  on  Sandy
Coasts," Journal of the Waterways and  Harbors  Division.  American
Society of Civil Engineers,  Vol. 95, No.  WWl,  Feb.,  1969, pp. 43-52.

Papers from the October,  1967,  Tidal Hydraulics  Symposium at the
American Society of Civil Engineers National Meeting  on  Water
Resources Engineering, New York, New York,  Journal of the Hydraulics
Division, American Society of Civil Engineers, Vol. 95,  No. HYJ.,
Jan.,  1969.

Partheniades,  Emmanuel,  "A Summary  of  the Present  Knowledge of the
Behavior of Fine Sediments in Estuaries," Tech.  Note  No. 8, Hydro-
dynamics Laboratory, Massachusetts  Institute of  Technology, Cam-
bridge, Mass., June,  1964.

Pritchard, Donald W.,  "Dispersion and  Flushing of  Pollutants in the
Estuarine Environment,"  presented at the  American  Society of Civil
Engineers National Meeting on Water Resources  Engineering, New
York,  New York, Oct.  16-20,  1967.

Pyatt, E. E.,  "On Determining Pollutant Distribution  in  Tidal
Estuaries," Geological Survey Water-Supply Paper 1586-F, U.S.
Geological Survey, U.S.  Government  Printing Office-, Washington,
D.C.,  1964.

Rantz, S. E.,  "An Empirical  Method  of  Determining  Momentary Dis-
charge of Tide-Affected  Streams," Geological Survey Water-Supply
Paper  1586-D,  U.S. Geological Survey,  U.S.  Government Printing
Office, Washington, D.C.,  1963.

Shubinski, Robert P.,  McCarty,  James C.,  and Lindorf,  Marvin R.,
"Computer Simulation  of  Estuarial Networks," Journal  of  the
Hydraulics Division. American Society  of  Civil Engineers, Vol. 91,
HY5, Sept., 1965, pp.  33-49.

Stevens, Thompson, Runyan and Ries, Inc.,  "Preliminary Report:
Vancouver Lake Alternative Land Use Development  Plans,"  June 14,
1967.

Wiegel, Robert L., Oceanographical  Engineering,  Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey, 1964.

Williams, J. R-, "Movement and Dispersion of Fluorescent Dye in the
Duwamish River Estuary,  Washington," U.S. Geological  Survey Prof.
Paper  575-B,  1967, pp. B245-B249.


                               53

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                         APPENDIX B.  NOTATION




The following symbols were used in this study:




     a    tidal half amplitudes, feet




     A    area of lake water surface; cross-sectional area;

          square feet




     C    dye concentration at any time t, second




    C0    initial dye concentration in the hydraulic model lake




     D    depth, feet




    D     nominal inside diameter of culvert, feet




    E     evaporation rate from the lake, cubic feet per second, or


          inches per year




     f    pipe  flow friction factor




     F    Froude number, F// gD


                                                      2

     g    acceleration due to gravity, feet per second




    A h    Columbia  River tidal amplitude, feet




     H    water depth of Vancouver Lake,  feet




    H,     dredged lake bottom elevation below mean sea level, feet




    IL     lake water surface elevation measured from mean sea level,


          feet




     k    dilution  rate constant




     K    minor loss coefficient




     L    characteristic length, feet




    L_    length of culvert, feet
     C



     m    subscript refers to model




     n    Manning roughness coefficient




  NclQ    number of 10-foot diameter culverts




     p    subscript refers to prototype





                                   55

-------
 P     precipitation rate onto the lake, cubic feet per second or
       inches per year

q-i     average discharge through one culvert, cubic feet per
       second

  Q    average discharge, cubic feet per second

 QB    flow rate in Burnt Bridge Creek, cubic feet per second

 Q     discharge through conduit, cubic feet per second

Q ,     discharge through man-made channel, cubic feet per second

Q      flow rate in the Columbia River, cubic feet per second

Q      flow rate through culverts, cubic feet per second

 Q.    inflow rate to the lake, cubic feet per second

QJ     local inflow rate including both surface runoff and
       ground-water contribution, cubic feet per second

 Q,    flow rate in Lake River, cubic feet per second

 Q     outflow rate from the lake, cubic feet per second

Qou    local outflow rate from the lake to ground-water storage,
       cubic feet per second

 0     flow rate in Willamette River, cubic feet per second

  r    subscript means prototype-to-model ratio

  R    hydraulic radius, feet

  S    slope of water surface, bed, or energy line

  t    time, second

 t^    detention time of inflow into the lake, days

  T    percent of transmittance at any time t

 TQ    percent of transmittance corresponding to GO

 T     time ratio prototype-to-model

  u    local velocity, feet per second
                               56

-------
V    average longitudinal velocity in a cross section, feet
     per second

¥    volume of lake, cubic feet

W    width of the channels and rivers, feet

Y    depth in a channel, feet

Z    depth of Lake River, feet
                              57

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                  APPENDIX C.  HYDRODYNAMIC MODEL
1.   Identify initial values of K±, Y^ and Zi; then calculate (QL).
    by Eq. (15), and (Qc)t by Eq. (16) for open channel calculation
    and Eq. (21) for pipe flow calculation.
2.  Calculate the subsequent values by using initial values.  At time
    ti+l = fci +At> use Ecls- (17) and (18> to obtain Yi+1 and Zi+1 .
    Calculate (QL)i+1 and (Qc)i+1 by using Eqs. (15), (16), or (21),
    and then obtain the change in lake depth by Eq. (8) as


        AH = [(QL),. + (Qc)t + QB + Qin + Pr - Ev - Qou] At/A  .


    Therefore, we can evaluate
                                =Hi+AH
3.  Using the results of  the previous steps as initial values, the
    procedure is repeated.


Actual tidal records were used instead of assuming the sinusoidal tidal
cycle.  Tabulated field data were used in input information and the
same procedure of calculation was followed.  The flow chart for the
Combined Hydrodynamic and DO models  is shown in Fig. 30.
                                  59

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            (Start
           Read Input
           Data
           Write Input
           Data
           Calculate
           Coefficients

4-1
« i
}•! 
m r-4

3
d o
. 0
£ •.-) -d
o -u 
-------
c
C                        a^***** *****<*******<<***
C                        *  HYCRCCYNAHC KCOCL  *
C                        * >)*** * < *** ***<•**>>**+*<<**
C
C
C
C
c     ............................. ... ........... .............................
C     . VYDROOYNAM1C  PRCGRAVM ^^ : WATER BUDGET FCR VANCOUVER  LAKE-
C     . RIV^R  SYSTCM  RV V.SING THE CONTINUITY CCNCEPT.
C     .     1.   BANNING FOPPUL/i (IN FT-SEC UNIT) — FOR UPSTREAM^CUT  CHANNEL
C     .     ?.   DARCY-VF.I SPACH EQUATION — FCR SUPMERCF.C  CULVERTS
C     . THIS PROGRAM  WAS FRIEPAREC AND REVISHC BY MARCUS  C. N.  LIN
C     . IN  MARCH,  1?71 AT hSt
C     [[[
      D1MFMSION TEMP(AOC) ,ZW(',00) ,YW(AOO) tV(AOO)
100   «[;4D(5,1 .END = 1000)  ZG, YE ,Hh .HR.F 1 , F2 ,W 1 , U2, Cl , C2. A, CCT, RNT, F2, D3,
     1RINDEX
1     FCPMAT (8F10.2)
      WRITF  (6,300) ZG.YD,HW,h?fFl ,F? , Wl ,W2 , 01 , 02, A, OCT. RNT , F3, C3,
     1R INDEX
300   FORMAT ( IHI , "HYORALUC CHCRACTFRISTICS CF LAKE RIVER SYSTEM   ',//.
     1' ZG  =',F7.2.10X, 'Y9 = ' , F8 . ? ,10X , ' HW = • , F7. 2, 10X, • HD =',F7.2,//,
     2' Fl  =«,F7.3,1CX, 'F2 =',F8.3,10X,'W1 =' , F7. 2, 10X , ' W2 =',F7.2,//,
     3' Dl  =',F10.2,7X, 'D? =',F10.2,8X,« * *• , F14.2, //• 6F20.31
      INOL X=PI NPEX
      INDLX1=3.
      C=A.*3.1A15S
      PR = C.
      COC=C.
      CIN=C.
      CB=SC.
      EV = C.
      DT=C.OC5
      CVl=(1.4«;*l"'l ) /
-------
      00 2C 1*1,201
      R1=I
           -i. )*OT
      GC TC  (CEXl
90    YWU 1 = 4. ?<3-1.25*Cr?SUHETA)
      ZUI )=«.47-0.8*CCSnHFTA)
      GO TO  S5
91    YM1 )='i. 8c-1.0*Cf SMHF.T*)
      ZWU ) = ',. <,7-0.55<-CCS(THETA)
      00 1L  s'->
9?    YMM='(.£S-
      ZW(I l='i.'.7-
      GO TC  95
93    YM j ) = 'i. e«;-o.5*CGS<
      ZW(J ) = A.'i7-
      GC TC  S5
           ) = «.£S-C.2E*CCS(TH£l/>
95    2-7.MII-ZG
      CELZh=ZV(I)-HV
      GO TC  (2CC0.3CCC) .IKCEX
2COO  IF (kl  .1C.  0.)  GC  TC 55
C
C     FLOW RATE AND VELCCITY IN THE UPSTREAM  CUT  CHANNEL
C
      Y = YMI I-YR
           = YV;U )-HVs
          ]<-mHV;-YBl 12.
          Y-H+DR1
      COO=(W1 /(l»H Y*H! )**C.6667
      IF ( 701  .IT. C.)  GC TC A
C
C     FIRST  APPROXI!"MICIv IN LPSTREAM CUT CHANEL
C
      CC=CVl*(Yt^"^**1.6667*TCl**0.5
      IF 1  .GT.  2CC.) GC  TC 12
      CC=OC*COG
      GO TC  12
11    OC=-CV1*( Y+H)**1.66/:7*<-T[ST}**0.5
      IF (Wl  .GT.   200. ) GC  TC 12
      CC=CC*COC
12    VC=OC/AC
      GC TC  5
                                     62

-------
      OC=-CV1* (YtH)**l. 6667* (- TCI »**0.5
      IF  Ul  .GT.  20C. )  GC TC «10
      OC=CC*COC
      VCl = CC/( U*H)
      VC2 = CC/U1*Y)
      DV=( VCUVC2HI VC1-VC2J/64.4
      T£ST=-TD1*PV
      IF  [TEST  .LT.  C. )  GC TC 22
      CC=-CVl*(Y+H)**l.66(7MTEST»+*0.5
      IF  (Ul  .GT.  20C. )  GC TC 23
      QC=OC*COC
      GC  TC  23
??    CC=CV1*( Y+H)**1.6667*(-TEST)**0.5
      IF  (HI  .GT.  20C.)  GC TC 23
      cc=cc*coc
23    VC=OC/ftC
      GC  TC  5
55    CC=C.
      VC = C.
      DELYH=C.
      GO  TC  5
3000  IF  (CCT .LC. C.I  GC TC 55
C
C     FLtV. RATE  AND  VELOCITY IN CULVERTS (SUBMERGED  CONDITION  AND
C     INFLCW  TC  VAMCCtVER LAKE CNLY)
C
      OFLYH=YW(I )-Hh
      IF    GC TC 55
      CC=  AT*P.M*CV3*GELYM*0.5
C
C     FLCW  RATC  AND  VELOCITY IN LAKE RIVER
C
5     AL-W2*(H+Z)/2.
      AI=1.0*AL
      AC=1.0C*AL
      T02=Z-H*CB2
      IF  ( T02  .LT. 0. )  GC TC 6
C
C     FIRST  APPPOXI^ATICN IN THE LAKE RIVER
C
      CL=CVI*( Z+HI**1.6667*TC2*<0.5
C
C     FINAL  CALCULATICN IN Tf-E  LAKE RIVER
C
      Vl.']=Cl /( h2*Z)
      VL2=CL/< V2*H)
      OV = (VLHVL2)»(VH-VL2) /6A.4
      Tfc"ST=T02+DV
      IF  ( TEST .LT.  C. )  GC TC 4'i
      CL=C VI*< Z+HJ**1.6667«nEJU**0.5
      VL=OL/AI
      GO  TC  45
44    OL=-CVO*(/+H)**1.6667*(-TEST)**0.5
45    VL=OL/AO
                                    63

-------
      cr  TC  7
      CL=-CVO*(7+H)*#1.6667*(-7C?)#*0.5
      OV=( VL H V12!*< VL1-VL2)
      'f:ST = -7D2U'V
      ir  ( TCST  . LT.  C. )  GC TC 33
      VL=OLMQ
      GC  TC  3'r
2?    Cl=C.VI*( 7*»U**1.6661«(-7EST J**0.5
3Jf PESLLTS
50    V»P,nC  <6,30)  T,CC,CFLYH,CL,CELZH,VCtVL.R<7IOtYW( I),Zi<(i >iHH
30    FORI'fiT  (r-9.3.F11.2iF10.4«F12.2tF10.A|F11.3fF11.3|FH.2«F13.4tF11.4
     1 , r i o . '1 )
      IF  (CC  .IE.  C. )  GO TC 66£
C     V/-.Trr'  LEVF-L  IN V^NCCLVEP l/'KF
666   H-fM(?H
      H'r-H »HO
?0    CCM'INUP
      CAVOOSU^/CGIMT
      HAVG-HSUW/COCNT
      OETIME-(HAVG-HB)
      *PIT[;  C6.500C)
5000  FCRKA7  ( //// ,3F?C. 3 )
      GC  1C  IOC
1000  VRITR  (6, 40)

-------
  SELECTED WATER
  RESOURCES ABSTRACTS

  INPUT TRANSACTION FORM
    ^^•^•^•^••i
    Titl8      CORRELATED STUDIES OF VANCOUVER LAKE-
              HYDRAULIC MODEL STUDY,
                                       3.  Accession No.
  7.  Authof(s)
               Orsborn, J. F.
  9.  Organization
     Washington State University,  Pullman
     Albrook Hydraulic Laboratory
     College of Engineering  Research Division
  15. Supplementary Notes   Environmental Protection Agency report
                        number EPA-R2-72-078,  October 1972.
                                                                  10,  Project No.
                                                                            16080 ERP
                                       11.  Contract/Gfant No.
  is.  Abstract  x^ effects  of possible modifications to the Vancouver Lake-Columbia River
 System on the hydraulic characteristics of that system were  tested in  a  physical hydrau-
 lic model.  A mathematical model was developed for predictive analysis and to expand the
 results of the hydraulic  model study.  Alternate methods for improving flushing action
 through Vancouver Lake by use of a conduit were investigated.
     The theories, assumptions, test procedures, data analysis and results  as  presented
 in this report are  directed towards arriving at conclusions  and  recommendations regard-
 ing proposed hydraulic engineering works and their effects on the hydraulic regime and
 water quality conditions  in Vancouver. Lake.  The tests were  conducted  to determine the
 hydraulic characteristics and the flushing efficiency of pollutants by using  a fluores-
 cent dye to simulate  the  soluble conservative pollutants in  the  prototype.  In addition,
 the hydraulic model study provided information on the dispersion, mixing,  dilution rates
 and detention times which are important factors influencing  water quality.
     This is Part 1  of a two-part study entitled "Correlated  Studies of Vancouver Lake,
 Washington."  The other part of the study is Water Quality Prediction  conducted by the
 Sanitary Engineering  Section of the College of Engineering Research Division  at Wash-
 ington State University under Project #16080 ERQ, details of which are covered in a
 separate report.
     This report was submitted in fulfillment of Project #16080 ERP under the  partial
 sponsorship of the  Environmental Protection Agency.	
   I7a. Descriptors  *Hydraulic model, *Computer model, Lakes, Tidal  effects,  Eutrophication,
                 Water resource development
  17b, Identifiers
                *Lake restoration, Enhancement, Water quantity  and quality studies
  17c. CO WRR Field & Group
  ^^HIMMH^^^MVBIMIIM^^^aHl

  18,  A vail Ability




           	
  Abstractor  John  F.  OrsboriL
02H, 04A4, 05G1, 06G
                           Send To:

                      & '•« WATER RESOURCES SCIENTIFIC INFORMATION CENTER
                        y-xj y.S-PE.PA.R!MENT_OFTHE INTERIOR
                           WASHINGTON. D. C. 2O24O
            Institution   Washington State University
WRStC 102 (REV. JUNE 197O

* V. S. GOVERNMENT PRINTING OFFICE : 1972-514-149/72

-------