United States
            Environmental Protection
            Agency
          Environmental Monitoring and Support
          Laboratory
          Cincinnati OH 45268
EPA-600 4-80-035
July 1980
            Research and Development
v>EPA
Calibration of a 90°
V-Notch Weir Using
Parameters Other
Than Upstream Head

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                RESEARCH REPORTING SERIES

Research reports of the Office of Research and Development. U S Environmental
Protection Agency,  have been grouped into nine series  These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental  technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields
The nine series are.

      1    Environmental Health Effects Research
      2.   Environmental Protection Technology
      3   Ecological Research
      4   Environmental Monitoring
      5.   Socioeconomic  Environmental Studies
      6   Scientific and Technical Assessment Reports (STAR)
      7   Interagency Energy-Environment Research and Development
      8   'Special" Reports
      9.  Miscellaneous Reports

 This report has been assigned to the  ENVIRONMENTAL MONITORING series.
 This series describes research conducted to develop new or improved methods
 and instrumentation for the identification and quantification of environmental
 pollutants at the lowest conceivably significant concentrations. It also includes
 studies to determine the ambient concentrations of pollutants in the environment
 and/or the variance of pollutants as a function of time or meteorological factors.
                         r                   the Natlonal Techmcal Informa-
             Springfield. Virginia 22161

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                                            EPA-600/4-80-035
                                            July 1980
          CALIBRATION OF A 90° V-NOTCH
       WEIR USING PARAMETERS OTHER  THAN
                 UPSTREAM HEAD
                      by
 Robert Eli, Harald Pedersen and Ronald Snyder
        Department of Civil Engineering
           West Virginia University
        Morgantown, West Virginia  26506
                 R805312-01-1
                Project Officer

              Edward L. Berg
        Project Management  Section
Environmental Monitoring and Support Laboratory
            Cincinnati, Ohio  45268
FNVIRONMENTAL MONITORING AND SUPPORT LABORATORY
        OFFICE OF RESEARCH AND DEVELOPMENT
    U S. ENVIRONMENTAL PROTECTION AGENCY
           CINCINNATI, OHIO  45268

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                                DISCLAIMER
     This report has been reviewed by the Environmental Monitoring ;.md
Support Laboratory-Cincinnati, U.S. Environmental Protection Agency,  m
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                                  FOREWORD
     Environmental measurements are required to determine the quality of
ambient waters and the character of waste effluents.  The Environmental
Monitoring and Support Laboratory-Cincinnati conducts research to:

     0 Develop and evaluate technique to measure the presence and concentra-
       tion of physical, chemical, and radiological pollutants in waterv
       wastewater, bottom sediments, and solid wastes.

     0 Investigate methods for the concentration, recovery, and identifica-
       tion of viruses, bacteria, and other microorganisms in water.  Conduct
       studies to determine the responses of aquatic organisms to water
       quality.

     0 Conduct an Agency-wide quality assurance program to assure standardi-
       zation and quality control of systems for monitoring water and waste-
       water.

     This publication of the Environmental Monitoring and Support Laboratory,
Cincinnati, entitled:  Calibration of a 90° V-Notch Weir Using Parameters
Other than Weir Head reports the results of a study for measuring the flow
rate using two other parameters, i.e. depth and width of water at the weir
notch.  Field Sampling personnel should find that these methods permit easier
measurement without sacrificing flow accuracy as compared to the often diffi-
cult head measurement upstream of the V-notch weir.
                                      Dwight G. Ballinger
                                      Director
                                      Environmental Monitoring and
                                         Support Laboratory
                                     ill

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                                  ABSTRACT

     Traditional calibration of 90  V-notch weirs has involved the establish-
ment of a head-discharge relationship where the head is measured well up-
stream of weir drawdown effects.  This parameter is often difficult to meas-
ure in field weir installations for checking compliance to discharge regula-
tions.  Two other parameters are proposed for use as correlation parameters
to weir discharge.  These parameters are depth and width of flow at the weir
notch.  Techniques for measuring these parameters are proposed that result
in less than 10% error in discharge at the 95% probability level in the
laboratory environment.
                                    iv

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                              CONTENTS

Disclaimer	ii
Foreword	iii
Abstract	iv
Figures	vi
Tables	viii
Acknowledgment	ix

    1.  Introduction 	   1
    2.  Conclusions  	   2
    3.  Recommendations  	   3
    4.  Literature Search  	   4
    5.  Current Practice 	   8
    6.  Experimental Apparatus 	  10
    7.  Experiment Procedures  	  33
    8.  Results	49
             Introduction  	  49
             Precision Brass Weir, Moderate to High Flows  	  49

References	63
Appendix A	65
Appendix B	78
Appendix C	93

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                                  FIGURES

Number                                                                 Page

   1    Carpenters' Square Technique Used by EPA 	    9

   2    Plan View of Testing Apparatus	^2

   3    Section A-A of Plan View Shown in Figure 2	13

   4    View of Weir Box Side Bracing	14

   5    Precision Machined Brass Weir Plate Details  	   ig

   6    Square-Cut Aluminum Field Weir Plate Details 	   17

   7    1,000 gpm Bell and Gossett Pump,  One of Two	18

   8    Line of Pumps Feeding the Weir Box	19

   9    Water Supply Lines Leading Into Turbulence Suppressor Tank .  .   20

  10    Turbulence Suppressors, Rubberized Horsehair Mounted on
          Wood Frame	21

  11    Effectiveness of Turbulence Suppression System in Producing
          a Smooth Water Surface 	   22

  12    Outlet Chute Leading From Weir Plate to Weighing Tank  ....   24

  13    Weighing Tank Diversion Box With  Cover Removed	25

  14    Storage Tank Installation for Use as a Constant  Head Water
          Supply	26

  15     Detail  of  Constant  Head Tank and  Its  Containing  Outer Overflow
          Tank	27

  16    Weighing Scale Showing  Location of Photo Transistor   	   28

  17    Light-Activated Phototransistor Relay  Circuit	29

  18    Stilling Well Installation Showing Hook Gauge and Recording
         Float Gauge	30
                                   VI

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 'figures (continued)

Number

  19    Plexiglass Stilling Wells, Hook Gauge:  Foreground, Float
          Gauge:  Rear ........................  31

  '10    Placement of  the Rule When Measuring Depth of Flow at the
          Weir Notch  .........................  34

  21    View of Small Disturbance Waves Looking Upstream .......  35

  22    View of Small Disturbance Wave When Viewed From Above the
          Weir  ............................  36

  .':'.">    Method of Reading the Rule by Extrapolation of Water Surface
          to Scale Markings  .....................  37

  2q    Use of Common Baby Powder to Produce a High Water Mark on the
          Rule  ............................  38

  25    Positioning of Calpier to Perform Measurement of Flow Width
          at Weir Crest  .......................  39
        Placement of the Caliper as Viewed From Above
                                                                        40
  27    View of a Single Caliper Tip as Properly Positioned at the
          Intersection of the Weir Crest and Water Surface  ......  41

  2 "•    Location of Caliper Tip at Intersection of the Weir Crest
          and the Flow Nappe .....................  42
  29    Aluminum Channel With Attached Meter Stick  for Measuring
          Caliper Width   .......................   44

  30    Flow Chute Leading From Weir to Weighing Tank - Trap Door
          Diversion Sealed  ......................   45

  31    Head Versus Measurement Parameters  for  Moderate  to High
          Flows, Brass Weir   .....................   -* +

  32    Installation  of  Plastic Pipe  Section  in Flow Trough to
          Facilitate  Low Flow Measurements  ..............   60
         Close-up  View of  Notch in Plastic Pipe to Contain Flow
           Nappe   ...........................   61

         Density of  Water  as a Function of Temperature  ........
                                     vii

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                                    TABLES

 Number                                                                   Page

  1   Error In Weir Discharge as a Function of Errors in the Measure-
        ment of Head (King and Brater(l))  .  .  ,	    7

  2   Weir  Calibration Data Summary, Moderate  to High Flows,  Brass
        Weir	50

  3   Blocking  Effect of  the Rule at Low Discharges  - Weir  Box  Inflow
        Held Constant	56

  4   Statistical Analysis Parameters  of Depth and Width at Weirs,
        Multiobserver Tests 	   57

  5   Expected  Error in Flow Measurement Based on Statistical Parameter
        Analysis Results  of Multiobserver  Tests  	   58

 A-l   Raw Data,  Brass Weir,  Moderate to  High Flow Calibration Runs   ...   66

 A-2   Raw Data, Multiobserver Experiment  	   75

 B-l   Raw Data, Low Flow  Calibration,  Brass  Weir	78

 B-2   Raw Data, Calibration Runs,  Aluminum Weir	82

 C-l   Regression Coefficients for  Weir Measurement Parameters Using the
        Relation Q=aH   	93

 C-2   90° V-Notch Weir Calibration Table, Machined Brass Plate   	   94

 C-3   90° V-Notch Weir Calibration Table, Machined Brass Plate   	   98

C-4  90° V-Notch Weir Calibration Table, Aluminum,  Rough Cut Plate ... 102

C-5  90° V-Notch Weir Calibration Table, Aluminum,  Rough Cut Plate ... 106
                                    viii

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                               ACKNOWLEDGMENTS

     The Department of Civil Engineering, West Virginia University, wishes
to thank Mr. Edward Berg of the Environmental Monitoring and Support Labora-
tory, Cincinnati for his interest, advice and support in connection with this
project.  Appreciation is also extended to the Environmental Protection
Agency for their monetary support of this important research.

     A special thanks is due Mr^ Gary Bryant of the Environmental Protection
Agency, Wheeling, West Virginia, office for his help in organizing the sub-
ject research investigation and providing field data, information and equip-
ment to assist the laboratory experiments.
                                    ix

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                                  SECTION 1

                                INTRODUCTION

     In general, wastewater discharge is regulated by both state and federal
organizations under criteria set forth by the Federal Water Pollution Control
Act Amendment of 1972 (FWPCA).   The purpose of the FWPCA is to "restore and
maintain the chemical, physical, and biological integrity of the nation's
waters".  Towards this end, a permit system has been established to enforce
specific effluent standards for municipal and industrial facilities.  This
system is the National Pollutant Discharge Elimination System (NPDES), so
named because a goal of the FWPCA is the elimination of pollutant discharge
into navigable waters by 1985.

     Monitoring of wastewater quality and quantity is carried on by the
NPDES permit holder and is checked by the regulatory agencies, primarily the
EPA.  Usually, wastewater characteristics are assessed at the end of the
discharge pipe.  In other words, parameters established in the NPDES permit
are usually measured immediately prior to the waste stream discharge into
the receiving body of water.  Accurate determination of flow rate is required
to compute the weight of specific pollutant discharged per unit time.  Flow
measurement devices include a broad range of classical open channel and
pressure conduit devices as well as an indescribable array of individually
designed devices and techniques.  In open channel flow, weirs or flumes are
often the most serviceable and economical measuring devices where sufficient
fall exists in the channel and flow rates are within accurate weir measure-
ment ranges.  When weirs are properly installed and maintained, flow measure-
ment can be made within ±3 to ±5%.

     The scope of this research lies exclusively within the area of the
testing of a 90° V-notch weir.   The 90° V-notch is typically used to measure
flows from 1 to 10 cubic feet per second (c.f.s.).  It should be noted that
the methods developed herein should be applicable to the whole family of
V-notch weirs.

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                                   SECTION  2

                                  CONCLUSIONS

      The  experimental  effort  involved  the  attempted  calibration of  two
 additional measurement parameters to that  of head over a  90° V-notch weir.
 The  calibration  tests,  including  a statistical  error experiment, were success-
 ful  for the  parameters;  1)  depth  of flow at the weir and  2) width of flow
 at the weir.   Based  on test statistics and experience with the measurement
 techniques,  the  depth  of flow at  the weir  notch was  the easiest to  obtain
 with the  least probability  of significant  error.  However, both techniques
 resulted  in  errors in  discharge of less  than 10% with a probability of 95%.
 This level of  accuracy is deemed  sufficient to  approve both techniques for
 field testing.

      Calibration tables  for the standard measurement  of head over the weir
 plus depth and width of  flow  at the notch  are included in the Appendix C.
 These both are for the  precision  machined  brass weir  and  the field  grade,
 straight  cut weir, for  units   in  feet  and  inches.  The tabulated values  in
 the  calibration  tables  are  based  on the equations fitted  to the experimental
 data.  The equation  giving  the discharge as a function of the flow  measure-
 ment  parameter is of the following form:

                                    Q-  aHb

 The  regression coefficients a and  b are tabulated in  the  results.

      The machined brass weir  required  two  curve fits, one for flows less
 than  0.06 cfs and one for flows greater than 0.06 cfs.  This was required
 since the weir nappe began  to cling to the weir plate at 0.06 cfs.  The
 overlap of these two fitted equations  proved to be relatively continuous
 and presented no problems in compiling the calibration tables.  The calibra-
 tion  tables are intended for use  in the field where discharges are  required
as a  function of the measurement parameters.  In view of outstanding regress-
 ion analysis curve fits, the  fitted equations are sufficient for use with
assurance of a high level of accuracy.

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                                  SECTION 3

                               RECOMMENDATIONS

     In view of the high level of success achieved in the operation of the
experimental apparatus and the calibration of new discharge measurement
parameters, it is proposed that continuing efforts be made to adapt these
new measurement techniques to other weir configurations and to field condi-
tions.  Field tests need to be carried out to determine if any unforeseen
problems exist with application of the new techniques that were not uncovered
in the laboratory.  In addition, the 90  V-notch weir and weir box system
were constructed with great care and specifications not encountered in the
field.  Weir plates for example, are often straight cut from aluminum sheet
without the knife edge and precision of machining exercised in construction
of the laboratory apparatus (similar to the weir used herein), and installed
rather haphazardly.  Therefore, it is recommended that experiments proceed
with the exsisting laboratory apparatus modified to reflect actual field
conditions.  This would include the straight cut weir already tested in
conjunction with modifications in installation and stilling basin configura-
tion.  A detail statistical study can then be conducted to determine the
expected field accuracy of actual weir installations, as opposed to carefully
tabulated laboratory developed head-discharge relationships.  This would
involve the recalibration of each of the three measurement parameters
investigated in this report.  This additional laboratory work would also
proceed with other weir configurations such as rectangular weirs.

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                                   SECTION 4

                               LITERATURE SEARCH

      In general, a weir is a precisely designed obstruction or dam erected
 across an open channel for the purpose of defining an accurate stage-discharge
 relationship.  It acts as a flow control and essentially defines flow char-
 acteristics at its point of installation.  A logical extension of flow re-
 gulation by weirs is flow measurement by weirs.  Furthermore, weirs of diff-
 erent configurations create different flow characteristics.  It was discover-
 ed that certain shaped weirs were better suited to measure specific flow
 rates.  The 90  V-notch is suitable for measuring lower flow rates, (0 to
 5 cfs) while rectangular and Cipolletti weirs are more useful at higher flow
 rates (1,2).

      Francis (3),  in 1852, derived a general formula to describe flow over
 weirs.  This formula was based upon experimental data, and related flow to
 the head of water upstream of the weir crest.  Thompson (4) presented a
 formula for flow over a 90° V-notch weir in 1858.

      Thompson Formula                 Q = 0.305 H5'2                    (4.1)

           where

                                       Q ~ flow (c.f.s.)

                                       H = upstream head (ft.)

 Barr  (4)  refined this formula in 1907 in order to achieve greater accuracy
 of flow calculations at very low (less than 0.20 ft.)  and very high heads
 (greater than 3 ft.).

      Barr Formula                      Q = 2.48 H2'1*8                    (4.2)

 Other formulas  include the following:

      University of  Michigan Formula   Q = 2.52 H2>l+7                    (4.3)


      Cone Formula                      Q = 2.49H2'1*8                    (4.4)

      These  formulas  were developed  for standard 90  V-notch weirs and  are
based  upon  experimental data.   The  Cone formula is the most common relation
used  in practice and  is regarded  as  more  accurate than the others (2).

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     The use of V-notch weirs in flow measurement has been extensively ex-
plored.  Interest was due to the simplicity of the weir, its ability to pass
corrosive or high temperature liquids without damage, and its accuracy over
a given range of flows of from .0 to approximately 5 c.f.s.  (5).  Measurement
of the upstream head could be easily and accurately accomplished.

     Standard operating criteria were established, primarily to ensure close
agreement between actual flows and derived formulas.  It was found that water
had to have a smooth surface as it crossed the weir, and that the channel
had to be of sufficient depth and width to avoid excessive approach velo-
cities (3).  Flows with heads of less than 0.20 feet tended to stick on the
weir face, causing a deviation of actual flow from discharge formulas of up
to 25% (6).  Correction coefficients were established to compensate for
conditions where the nappe did not spring free.

     After the accuracy of V-notch weirs used as flow measurement devices
operating under standard conditions was established, (±1-2%) (7), research
began in the area of flow measurement of liquids other than water.  Since
the 90  V-notch was shown to be the most accurate triangular weir over a
wide range of discharges (7), a large portion of this work utilized 90
V-notch weirs for low flow rates.  Formulas were developed by Lenz (8) for
liquids of varying viscosities.  V-notch weirs were also calibrated for
corrosive liquids (9), and high temperature liquids (5).  As above, the
general form of these equations is:

     Q = aHb

  where

     Q = flow

     H = head upstream of the notch

 a & b = coefficients characteristic of specific liquids tested

     Techniques for precise weir measurements followed similar formats and
utilized similar testing apparatus.  The basic testing components consisted
of a weir box or flume, weir plate, weighing tank and timing mechanism, and
several methods of accurately determining the upstream head.  The particular
fluid tested was passed through the flume, across the weir, and then into
the weighing mechanism or a diversion device.  Measurements of weight per
unit time were converted to standard flow units (c.f.s.) and compared to
corresponding measurement of head.  While velocity profiles were established
for very high flow rates, the major parameter investigated was the upstream
head.  Correcting coefficients were established for variations in the weir
plate such as roughness, angle of notch, sharpness of edge, and irregularities,

     The purpose of this study centers on the exploration of weir calibration
parameters other than the upstream head.  Search of past work suggests that
the sole means of V-notch weir calibration was the upstream head.  Other work
is not reported specifically because the other measurements more than doubled
the error as compared to upstream head.

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      During the course of this investigation,  several sources were used to
 develop  the apparatus  design and testing procedures.   As an example,  Schoder  s
 paper (10)  dealt with  the testing of weirs ranging from 0.5 to 7.5 feet in
 height.   Heads  ranged  from 0.012 to  2.75 feet,  and channel widths ranged from
 0.9  to 4.2  feet.   The  major thrust of this investigation was the derivation
 of a more universal  weir discharge formula which would include corrections
 for  the  condition of the weir crest, channel characteristics, and differing
 methods  of  head measurement.

      While  the  above work dealt largely  with rectangular weirs,  several
 features of the testing apparatus and procedure were  applicable  to this pro-
 ject.  Water entered the weir box from a source of constant head,  passed
 through  a series  of  baffles,  and into a  weighing tank by way of  the weir.  A
 diversion device  was incorporated to allow the  weighing tank to  empty between
 runs.  Measurement of  the head was done  by hook or plumb-bob gauges mounted
 in the weir box or in  a stilling well.   A float gauge was often  used  to meas-
 ure  variations  in stage,  and  was located in a stilling well.   The  basic meas-
 urement  was weight per unit  time.  This  measurement was derived  from  the
 manual operation  of  a  stopwatch and  the  observation of a scale.  Weir crests
 were brass  or painted  steel,  with bevels ranging from 30° to 60  .   Water
 temperature was recorded,  along with general testing  conditions.   Zero  head
 was  established by a carefully repeated  procedure.  A hook gauge was  read
 at the weir crest with the water exactly level  with the crest or notch.  Si-
 multaneously, gauges in stilling wells were read.   The procedure was  repeated
 until  consistent  readings  were obtained.

      During a test run,  the head was  measured with the stilling  well  gauges.
 Water  was allowed to flow  across the  weir  and into the weighing  tank  until
 the  tank was  close to  full.   The flow was  then  diverted and the  weight  diff-
 erence and  time interval recorded.   The  data were  analyzed to provide com-
 parison  with  existing  formulas,  and  to derive correction coefficients for
 discharge variation  resulting  from variables such  as  crest  condition,
 channel  width,  etc.

     The general  apparatus and  method of testing used  in this study are very
 similar  to  those  described in  the  literature above.   This was done  to dup-
 licate previous data using similar methodology,  and to  derive new  data  using
 accepted methods of  research.

     Of  further interest in the  literature  is a  table  in King's Handbook (1)>
pp.  50-51, which tabulates errors  in weir discharge  resulting  from errors in
 the measurement of head.  Discharges  between 0.05 and  1.00  c.f.s. over  a
90  standard V-notch weir would  have  the percent error  shown  in Table 1.
This information is significant  in that  it  indicates  that field measurement
procedures may produce  significant errors in subsequent  flow  calculations.

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             TABLE 1.  ERROR IN WEIR DISCHARGE AS A FUNCTION OF
                       ERRORS IN THE MEASUREMENT OF HEAD (KING AND BRATER(l))
Discharge (c.f.s.)            Error in Head (ft)         Percent Error in Q
0.05


0.10


0.50



1.00



0.001
0.005
0.010
0.001
0.005
0.010
0.001
0.005
0.010
0.050
0.001
0.005
0.010
0.050
1.2
6.1
12.2
0.9
4.6
9.1
0.5
2.4
4.8
23.8
0.4
1.8
3.6
18.0

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                                  SECTION 5

                              CURRENT PRACTICE
     Difficulties have arisen in securing accurate measurements of the head
of water acting on the weir for the purpose of checking for proper installa-
tion and operation.  Weirs may be located in inaccessible places or placed
in the outfall of culverts or pipes.  Standard practice requires the measure-
ment of the upstream head at a distance of at least four times the upstream
head from the weir face.  This is to preclude faulty depth measurements which
may result from drawdown and contraction of the water surface as the flow
accelerates through the notch.  The most convenient instantaneous technique,
used by EPA to check discharge rates at the weir face (when hook or staff
gages are not installed), is the use of a carpenter's square to measure head.
The longer side of the square is inserted in the notch and projected into the
flow.  A single bubble hand held level is then used on the shorter side of
the square to plumb it in the center of flow (see Figure 1).  Depth of water
is then read from the square in inches.  This reading is converted to feet
and the appropriate discharge computed from tables.

     Several disadvantages seem to exist in using this system of measurement.
Concurrently with leaning over the nappe of the weir, the individual doing
the testing has to place the square in the notch, adjust the level bubble
so that the square is plumb, and read the water depth as accurately as
possible.  Besides from being physically difficult to accomplish, the water
depth may or may not be taken at the prescribed distance from the weir face,
since the square may not extend past the drawdown area upstream of the weir
plate.  The lack of sensitivity of a single bubble level could further com-
pound error.  Thus the error inherent in the technique might exceed 1/8 inch,
(0.010 feet).  At higher flow rates, an error of 1/2 inch, (0.42 feet), would
not be unreasonable.   Errors of this nature would create an excess of 10%
error in flow calculation.   Since pollutant discharge is directly proportion-
al to flow,  a 10% error in flow would create a 10% error in discharge pollu-
tant quantities.   Therefore, another parameter of calibration for 90  V-notch
weirs is desirable in order to attain a higher degree of accuracy in flow
measurement,  and  to facilitate the actual measurement technique.

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                                           Discharge Pipe
Nappe
                      Level
                          Carpenters' Rule
           Weir Notch
                Weir Plate
                 Figure 1.  Carpenters* Square Technique Used by EPA

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                                  SECTION 6

                           EXPERIMENTAL APPARATUS
     During the design phase of the project, it was decided that the experi-
mental apparatus should be constructed to duplicate previous laboratory weir
calibration apparatus and to satisfy installation requirements for standard
weirs as specified in design manuals (2).  These criteria include the follow-
ing items:

     (1)  The upstream face of the bulkhead should be smooth and in a vertical
          plane perpendicular to the axis of the channel.

     (2)  The upstream face of the weir plate should be smooth, straight, and
          flush with the upstream face of the bulkhead.

     (3)  The thickness of the crest, measured in the direction of flow,
          should be between 0.03 and 0.08 inch.  Tha sides of the notch
          should be inclined 45  from the vertical.

     (4)  The upstream corners of the notch must be sharp.  They should be
          machined or filed perpendicular to the upstream face, free of burrs
          or scratches, and not smoothed off with abrasive cloth or paper.
          Knife edges should be avoided because they are difficult to main-
          tain.

     (5)  The downstream edges of the notch should be relieved by chamfering
          if the plate is thicker than the prescribed crest width.  This
          chamfer should be at an angle of 45  or more to the surface of the
          crest.

     (6)  The distance of the crest from the bottom of the approach channel
          should preferably be not less than twice the depth of water above
          the crest and in no case less than one foot.

     (7)  The minimum distances of the sides of the weir from the sides of
          the channel should be at least twice the head on the weir, and
          should be measured from the intersection points of the maximum
          water surface with the edges of the weir.

     (8)  The overflow sheet (nappe)  should touch only the upstream edges of
          the crest and sides.
                                    10

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     (9)   Air should circulate freely both under and on the sides of the
          nappe.

    (10)   The measurement of head on the weir should be taken at the differ-
          ence in elevation between the notch and the water surface at a
          point upstream from the weir a distance of four times the maximum
          head on the weir face.

    (11)   The cross-sectional area of the approach channel should be at
          least 8 times that of the overflow sheet at the crest for a dis-
          tance upstream from 15 to 20 times the depth of the sheet.

Other criteria for weir box construction are in the Water Measurement Manuel
(2).  Since a typical field installation weir was also calibrated, the above
criteria for weir plate construction was not followed for tests simulating
field conditions.

     The experimental apparatus consists of three major systems, the weir
and weir box, the water supply system and recirculation system.  While these
systems are integrated into the whole calibration system, examination of
their respective design and construction will provide an adequate descrip-
tion of the entire experimental apparatus.  Flow ranges were anticipated to
range from 0.0 - 5.0 c.f.s. corresponding to a maximum average flow velocity
of approximately 0.2 ft./sec. at 5 c.f.s.  The system was designed to accomo-
date the upper range of flows, and to meet criteria previously outlined.

     The first system to be designed and constructed was the weir and weir
box system.  There were several major objectives to be met during its plan-
ning.  First, the dimensions of the weir box had to satisfy standard para-
meters of 90  V-notch weir installation for the upper range of flows.  It
also had to be large enough to include an adequate turbulence suppression
system, and small enough to fit into the lab.  The weir plate had to be of
corrosion resistant material to limit any corrosive damage to the machined
surfaces.  It also had to be large enough to contain a notch of dimensions
suitable for anticipated flows, and strong enough to resist any deflections
that might occur in the bulkhead of the weir box.

     The final weir box design was to place 3/4" thick exterior grade ply-
wood over 2" x 10" bracing.  The interior box dimensions are 20 ft. long,
7 ft. wide, and 4 ft. deep  (see Figures 2 and 3).  The floor bracing was
placed directly on the laboratory floor.  This bracing was placed 12 inches
center to center to carry the anticipated maximum load of approximately 250
pounds per square foot.  The box sides are reinforced with vertical 2" x 6"
struts (see Figure 4).

     Care was taken to ensure the watertightness of the box during construc-
tion.  Prior to assembly, all exterior and interior wood surfaces were sealed
with a wood preservative.  During assembly, all joints and seams were calked
with a butyl rubber compound.  After assembly, all interior joints and seams
were covered with fiberglass mat and resin.  The exterior edges were rein-
forced with 1-1/4" x  1-1/4" x 1/8" angle iron notched  into the bracing.  To
prevent any movement  of the structure as a whole, both ends of the box are

                                     11

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                 Scale
Stilling Wells
L.
                                     1000 gpm
                                       pump
                             1000 gpm
                               pump
                LI.
                                                                                        100 gpm
                                                                                        pump
J
                     Figure  2.  Plan  View of  Testing Apparatus

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                                6"
                                                      Discharge     Watering
                                                        /Piping.        Tank

                                                                      '



V^ 	
Staff
Discharge Gauge
Trough >.
Low Flow
Trough

\— l-~" """"""
Weighing
Tank






>
•^-^6-V-
- •*-^i--^'








28"






Recirculation



Sump
9'

— *





--
.4"

•^- 6"






10"

Gravi
ty
Turbulence SuPP^
Suppressors
V v
\
>









.










'\








**




'



V2









!"




















.1
r







I
/
j
/
(/


/






/ ^^
^^Ove
rflow
4
I
4'







Floor Slab


9'


— "





--


^ 6"










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8






Figure 3.  Section A-A of Plan View Shown in Figure 2

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Figure 4.  View of Weir Box Side Bracing




                    14

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fastened to 4" x 4" x 1/4" angle iron which is mounted to the lab floor with
anchor bolts.   When assembly was completed, the box interior was primed with
exterior primer, then painted with two coats of epoxy enamel.

     The precision machined weir plate is 1/4" thick brass measuring 30"
x 36".  The notch is 16 inches deep with an upstream crest width of 1/16"
(see Figure 5).  A machined chamfer of 30  was chosen as an appropriate
bevel.  The plate is mounted to the bulkhead of the box with woodscrews.  The
box exterior has extra bracing at the points of attachment to help insure
adequate stiffness,  After installation, a smooth bead of calking was applied
around the plate to seal the interface and to preclude turbulence formation.

     Gary Bryant of the EPA Wheeling, West Virginia field office supplied an
aluminum weir plate of the type encountered in field applications.  The
dimensions and configuration of this weir plate is shown in Figure 6.  The
weir notch was straight cut  (no bevel) from 1/8 inch thick aluminum plate.
This weir plate was also to be used in the calibration experiments.

     Water is supplied to the system from three 8,078 gallon concrete sumps
situated underneath the lab floor.  In turn, they are filled by a 2" line
carrying city water.  The sumps are connected by 8" lines.

     The four pumps were selected to provide flexibility of operation and to
cover the selected range of testing.  These pumps are mounted directly to
the lab floor and are located above the sumps.  The basic premise behind
pump operation assumed that flow could be regulated by placing a gate valve
on the discharge side to choke flow.  Two pumps are 1,000 g.p.m.  Bell and
Gossett pumps with six inch intake and six inch discharge lines  (Figure  7).
One pump  is a 500 g.p.m. Weinmar pump with six inch intake and six inch
discharge lines.  The fourth pump is a 100 g.p.m. pump with a three inch
intake and a two inch discharge line.  Intake lines are all steel with attach-
ed footvalves.  Discharge lines are schedule 40 plastic pipe with solvent
weld  fittings on the larger pumps, and steel on the small pump.  Metal to
metal joints are flange or threaded.  Plastic discharge lines are supported
overhead by hangers connected to ceiling trusses.  All the pumps are fitted
with  1/4 inch copper priming lines with air relief valves.  Figure 8 shows
the line of pumps adjacent to the stilling basin.

     Water is introduced into the weir box at the end farthest  from the weir
plate for flows in excess of 0.02 c.f.s.  Overhead lines turn downward into
a 190 gallon galvanized tank  (Figure 9).  The tank was selected  to act as a
preliminary turbulence suppressor because of its durability and  ability  to
accept surges.  The tank is open at the top and perforated on one side with
multiple 1-1/2  inch holes.  Water leaving the pipes fills the trough and
passes through  the sieve-like trough wall towards two turbulence suppressors.
These suppressors, mounted three feet apart, consist of rubberized horsehair
mounted on a wire  and wood framework  (Figure 10).  They fit  exactly into  the
cross-sectional dimensions of the weir box.  Rubberized horsehair was  select-
ed due to  its  porosity, durability, and convenience  in mounting.  This mater-
ial passes water readily enough to avoid any accumulation of head  in the  rear
of the weir box, dampens wave motion, and  effectively straightens  flow.
                                     15

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                                                                  1/16"
                                                               Hh
                                                    30° 11°
                                                               1/4"
                                                           Section A-A
   Elevation
Figure 5.  Precision Machined Brass Weir Plate Details

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                                   — 6"
                                                                  I— 1/8"-I
                                                                Section A-A
        Elevation
Figure 6.   Square-Cut Aluminum Field Weir Plate Details

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Figure 7.  1,000 gpm Bell and Cossett Pump, One of Two

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Figure 8.   Line of Pumps Feeding the Weir Box




                      19

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o
                    Figure 9.  Water Supply Lines Leading Into Turbulence Suppressor Tank

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Figure 10.  Turbulence Suppressors, Rubberized Horsehair Mounted on Wood Frame

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     Flow leaving the turbulence suppressors is smooth and glassy (Figure 11).
It passes over the weir plate, down a chute, and into the weighing tank.
Water is recirculated back into the pumps via several means.  The weighing
tank has a six inch mud valve drain and a 2 ft. x 2 ft. diversion box.  The
chute spanning the distance between weir box and weighing tank directs water
either into the weighing tank or into the diversion box when the aluminum
cover is removed (Figures 12 and 13).

     Because of unsteady flow conditions produced when the small pump was
choked too much by the gate valve on the discharge side, low flow calibrations
could not be performed using water directly supplied by the small pump.  To
facilitate low flow calibrations a storage tank was installed above the
flume which could feed the flume by gravity flow (Figure 14).  This system
consists of two open galvanized tanks similar to the one used as a turbulence
suppressor in the flume.  These tanks are 190 gallon and 100 gallon in size.
The smaller tank is situated inside the larger tank as shown in Figure 15.
The water is supplied by an additional 2 inch discharge line from the 100
g.p.m. pump and enters the smaller inner tank.  Both discharge lines from the
100 g.p.m. pump are equipped with gate valves for flexibility of operation.
This configuration provides a constant head water supply to the flume via
the smaller tank.  Excess flow from the pump spills over the lip of the
smaller tank into the outer larger tank which acts as a catch basin to direct
the overflow back to the sumps (Figure 15).  The inner smaller tank drains
vertically through a 2 inch PVC discharge pipe down to within  18 inches of
the flume bottom, just upstream of the turbulence suppressors.

     The basic recirculation scheme is to allow the weighing tank to fill
during a test run (valve and diversion box closed).  Then, water is diverted
into the diversion box while the weighing tank is drained to allow another
run to begin.   Weir box valves are used in emergency overflow situations and
to drain the weir box when it's not in use.

     The instrumentation/flow measurement system was designed to allow flex-
ibility in parameter testing and to provide checks of the reliability of flow
measurement schemes currently practiced.  The basic apparatus consists of a
tank to collect water, a scale to weigh the water in the tank, and an elec-
tronic timer to measure weight/unit time intervals.  Weight/unit time can be
converted into volume/unit time knowing the density of water at various
temperatures.   In order to decrease the chance of human error, the electronic
timer can be triggered by the scale hand passing over a photo switching
transitor mounted in the face of the scale (Figure 16).  Figure 17 illustrates
the light-activated phototransistor relay circuit used to time 2000 Ib. in-
crements at high discharge rates.  A standard 35 mm projector is used as an
intense light source.  The incoming light strikes a phototransitor (Figure
17:  Ql) which when broken by the scale hand activates the relay, RY1, which
closes a circuit to a Heathkit digital stop watch.  Thus, for high discharges
the stop watch is activated on the first pass of the hand and deactivated
on the next pass corresponding to a 2000 Ib.  increment on the scale.  At
high discharge rates the scale hand is moving rapidly and it is impossible
to accurately start and stop the stop watch by hand.  The electronic switch-
 .ng circuit was found to eliminate this problem, giving repeatability between
 •uns within 0.04 second.

                                     22

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                                       fr


Figure 11.
Effectiveness of Turbulence Suppression System in Producing
a Smooth Water Surface
                                   23

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Figure 12.  Outlet Chute Leading From Weir Plate to Weighing Tank

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Figure 13.  Weighing Tank Diversion Box With Cover Removed




                             25

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Figure 14.  Storage Tank Installation for Use as a Constant Head Water Supply

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Figure 15.  Detail of Constant Head Tank and Its Containing Outer Overflow Tank

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Figure 16.  Weighing Scale Showing Location of Photo Transistor




                               28

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 (Unused)
           Qi       IE
        FPT 100
         Figure 17.   Light-Activated Phototransistor Relay Circuit
     Two stilling wells are mounted on the scale side of the weir box.  They
are constructed out of clear plexiglass in order to allow visual inspection
of the water level (Figures 18 and 19).  One stilling well houses a hook
gauge, calibrated in .001 foot increments.  The other contains a 12 inch
stainless steel ball which is the float for a Fisher-Porter stage recording
gauge accurate to 0.001 foot.  The float gauge is designed to provide direct
flow measurement, in million gallons per day, for 90  V-notch weirs.  Its
scale ranges from zero to four million gallons per day.

     A staff gauge is mounted in the interior of the weir box.  It provides
a visual means of estimating the upstream head.  Intervals of 0.01 feet can
be read.  The installation of a staff gauge was incorporated to check the
accuracy of measurement practices currently in use.

     Two venturi meters were installed in two separate pump discharge lines.
(The central 1,000 g.p.m. pump and the 500 g.p.m. pump).  They were included
to provide flexibility in future experimentation, and are currently not in
use.

     The overall purpose of the flow measurement system is to allow compari-
son of several established flow measurement schemes, (i.e., upstream head
on hook and staff gauge, float gauge) to actual weight per unit time measure-
ments, and to allow comparison of other flow parameters, (i.e., depth and
                                    29

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Figure 18.  Stilling Well Installation Showing Hook  Gauge and Recording
            Gauge
                                     30

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9.  Plexiglass Stilling Wells, Hook Gauge:Foreground, Float Gauge:Rear




                             31

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width of water at the weir face), with actual weight per unit time measure-
ments and existing flow measurement schemes.  The design of the measurement
systems followed standard practice.  Instruments were checked for accuracy
and recalibrated as necessary.

     In summary, the apparatus as a whole was constructed to provide leak-
free operation and durable service.  It was designed to meet standard criter-
ia and to provide flexibility in testing.
                                    32

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                                  SECTION 7

                            EXPERIMENT PROCEDURES


     The goal of this research was to establish testing parameters for 90
V-notch weir discharge that are readily measured under field conditions and
provide accurate flow calculations.  In particular, it was thought that
parameters obtainable at the weir face would be of primary interest.  Two
obvious parameters are the depth of water above the notch, and the width
of the water surface above the notch.

     Simple measuring devices were chosen to make measurements of these
parameters.  A Lufkin meter rule (part no. 1261ME), also calibrated in
inches with divisions of 1/16 inch, was selected to determine the water
depth above the notch.  The technique selected to perform this measurement
is also simple.  The rule is inserted in the notch with the zero end resting
on the bottom of the V.  The calibrated edge is pointed upstream.  A metal
bar, clamped directly to the plate above the notch, serves as a stop for
the rule when it reaches a vertical position.  The rule is kept plumb by
eye, and readings are made to the nearest 1/32 of an inch (estimated).
Figure 20 demonstrates this technique.

     As shown in Figures 21 and 22 small disturbance waves are created as a
result of the presence of the rule in the water.  These small waves are
standing waves and are positioned directly in front of rule.  At first,
there was considerable concern about reading the rule in a consistent manner,
given the presence of the waves and the curvature of the water surface.
However, after many trials with different people  (see Section 8, Results)
it was determined that the eye could easily ignore the small waves and
extrapolate back along the sides of the rule such that repeatable measure-
ments could be made to the nearest 1/32 of an inch.  This process of extra-
polating back by eye  is illustrated in Figure 23.  During the course of the
research, everyone involved with this particular measurement found it very
easy to make and repeat.

     Even though the  measurement technique outlined above was easy to master
in the laboratory it  seemed reasonable to suspect that access to a field
weir might be very limited which would cause the taking of these measure-
ments to be quite difficult.  A person measuring depth at the notch must be
able to get within an arms reach of the weir in order to measure the depth
of water at the notch.  They must  also be able to get their eyes close
enough to the weir to make the depth  reading.  After considering this pro-
blem, it was concluded that the depth of water at the notch could be taken
much more easily, and perhaps more accurately, by covering the ruler with a


                                     33

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Figure 20.  Placement of the Rule When Measuring Depth of Flow at the Weir Notch

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Figure 21. View of Small Disturbance Waves Looking Upstream

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:
                 Figure 22.   View of  Small  Disturbance  Wave When Viewed From Above the Weir

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                                       Actual Water
                                         Surface
    Line of
Extrapolation

 Figure  23.  Method of Reading the Rule by Extrapolation of Water Surface  to
            Scale Markings
powdery substance which would be washed away by the water leaving a distinct
water mark.

     Using an indicating marker, such as a powder, would eliminate the need
for getting close to the weir plate to measure the depth of water.  The field
person need only be able to reach the apex of the weir notch with a measuring
device such as the Lufkin rule utilized in this work.  Although the person
would have to be able to view the plate and be close enough to position and
steady the rule, they would not need to be close enough to read the rule in
position.  The rule could be pulled from the notch and the depth read at the
powder marker water line.

     Many various powders and dusts were considered for use as the marking
agent.  Some requirements of the material were that it be inexpensive, easily
obtainable, and hydrophobic (water repelling).  If the material were not
hydrophobic, the wetting action of the water may have made the water line
difficult to determine with accuracy.

     With the above requirements in mind, common baby powder (talc powder) was
chosen as the marking material.  The powder was sprinkled on the rule and
the excess was knocked off by tapping the rule against a solid object such as
the weir box.  A very thin layer of powder remained on the rule after tapping.
The rule was placed in the apex of the weir notch and positioned as previously
described for the optical reading.  However, in this case the rule was not
read in place, but rather it was removed as soon as it was positioned properly
and the depth of water at the notch was determined by the water line on the
rule  (Figure 24).  It was found that the waterline was sharply defined and
                                     37

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Figure 24.  Use of Common Baby Powder to Produce a High Water Mark on the
            Rule
                                    38

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U)
            Figure 25.  Positioning  of  Caliper  to  Perform Measurement  of  Flow Width  at Weir  Crest

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8

                           Figure 26.  Placement of the Caliper as Viewed From Above

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Figure 27.  View of a Single Caliper Tip as Properly Positioned at the Intersection of the Weir Crest
            and Water Surface

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 much easier to accurately read than when the rule is  in  place.

      A machinist's  caliper was selected  to  measure the width  of water above
 the notch.   Points  were attached to the  ends of  the caliper to facilitate
 measurement.   The points are approximately  1 inch long,  and are 1/8  inch
 brass rod with conical  points.  The caliper points are set at width  of water
 at  the upstream side  of the weir plate  (Figure 25).   Although the use of the
 caliper is  more difficult to accomplish  then the  depth measurement using the
 rule,  it is not as  difficult or as  inaccurate as  one  might think.  Figures
 26  and 27 show two  different views  of the placement of the caliper.  The
 technique is  to locate  the point of the  caliper  such  that it centers on the
 water crossing the  weir crest as shown in Figure  28.
               Stilling Basin
               Weir Crest
               Place Caliper Tip
               at Intersection of
               Orthogonal Dotted
               Lines
                                  Edge of Flow
                                    Nappe
Flow Direction Over Weir
  Figure 28.   Location of Caliper Tip at Intersection of  the Weir  Crest  and
              the Flow Nappe
The design of the caliper points is not critical as long as the points will
contact the weir crest as shown in Figure 28, without any other part of the
caliper coming in contact with the water surface.  The water surface is
curved at the weir plate such that a standard ruler or other direct measure-
ment device will not work without contacting the nappe and disrupting the
flow.  After the caliper is set to the width of flow at the weir plate, it is
removed and the width determined.  Measurements are taken on a Lufkin rule
identical to the one used to measure the depth of water.  However, in this
case the rule is mounted on a short piece of aluminum channel.  A small in-
dentation was drilled in the channel at exactly the zero point of the rule.
To make a measurement, one caliper point is placed in this hole and the

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caliper is rotated until the other point intersects the rule.   Measurements
are taken to the nearest 1/32 of an inch (Figure 29).

     The weir box was designed to meet standard specifications for the anti-
cipated range of flows (2).  The general scheme of testing was based upon
previous work (10,11,12).  Therefore, a secondary purpose of testing was to
check the apparatus and experimental technique against previous data and
formulas, particularly the Cone formula.

     The basic components of the testing scheme can be delineated as follows:

     1)  Water is drawn out of the sumps by a pump and introduced into the
         rear of the weir box or into the constant head tank  (Figure 4).

     2)  Water flows through the turbulence suppressors, across the weir and
         into the weighing tank or diversion chute  (Figures 12 and 13).

     3)  Measurements of weight and time are taken with the electronic timer,
         triggered manually or with the light sensitive switching circuit,
         and the scale  (Figures 16 and  17).

     4)  Measurements of head are done  with the hook  gauge mounted  in  the
         stilling well,  and read from the  staff gauge mounted on  the  interior
         weir box wall.

     5)  Parameter measurements are taken as previously described.

     After  the construction phase of the project was  completed, a general
shakedown of the various systems was done  to check  for leaks  and  operational
problems.   The initial  filling of the weir box was  done by the smallest  pump.
The weir box had no  leaks, and there was no evidence  of deflections of the
weir box structure under full load.  All pumps and  piping performed properly,
with the exception of some small leaks  that developed around  the  choke valve
packing  glands and an elbow joint.   The packing gland screws  were tightened
to correct  the valve leaks.  Silicon rubber was used  to calk  the  faulty  elbow
joint.   The mud valves  in  the weir box  and weighing tank had  to be  fitted
with rubber gaskets  to  stop minor leakage.  The entire pump/pipe  and  weir  box
leakage  was reduced  to  a few drips per  minute, and  therefore  regarded  as a
negligible  source  of experimental error.

          The turbulence suppression  system worked  extremely well.   Flow
through  the weir  box was varied  over the test  ranges, and  the water surface
approaching the weir was always  smooth  and glassy.  It was discovered that
all  the  pumps are  capable  of producing  flows well  in  excess of their  rated
capacities. This  is primarily  due  to  the  lower  than  expected discharge  head
 (probably  less  than  10  feet  of  water).   Essentially,  any  two  pumps  could
supply enough flow to  cover  the test discharge range.  This simplified
operational procedures.

          Problems developed  in  the  flow diversion and flow measurement systems,
The  original diverting trap  door had significant  leakage and  had to be sealed
so that  testing  could  be carried on  (Figure  30).   A diversion box was finally

                                      43

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                                                                        -
Figure 29.  Aluminum Channel With Attached Meter Stick for Measuring Caliper Width

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-
          Figure 30.  Flow Chute Leading From Weir to Weighing Tank — Trap Door Diversion Sealed

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 designed and incorporated into the weighing tank (Figure 13).  The diversion
 box has a removable cover which when in place allows  the weighing tank  to
 fill,  and when removed,  it diverts the flow through a hole  in  the bottom of
 the tank.  This allows  the weighing tank to be drained at higher flow rates.

     Light intensity in  the lab area was not great enough to trigger the
 light  sensitive switching circuit  for the electronic  timer.  The light
 intensity of a standard  35 mm slide projector provided sufficient light  to
 trigger the circuit,  and was  added as part of the measuring apparatus.   Card-
 board  tags were attached to the scale hand to provide a greater contrast of
 light  and dark,  thus  more clearly  defining the point  of activation for  the
 switching circuit.   With the  addition of the light source and  tags, weight
 per unit time measurements typically agree to within  ±0.03 sec. over 2000
 pound  intervals.

     The hook gauge,  float gauge,  and stilling wells  all functioned satis-
 factorily.   Laboratory physical constraints created minor difficulties  in
 installation of the float gauge, which required its placement  slightly  off
 the center of the stilling well.   However,  this slight variation did not
 affect' its  operation.

     Once the system shakedown was completed,  the point of zero head was
 established.   It was  originally intended to use the same method of zeroing
 set forth by the literature.   This method requires the utilization of two
 hook gauges;  one at the  weir  plate and another in a stilling well.  With
 the water level  in  the weir box exactly even with the  weir notch, both  gauges
 are read.   They are moved,  then readjusted for another reading.  The intent
 is  to  check the relative difference in readings for each gauge against  the
 other  in order to define any  discrepancies in gauge calibration or measure-
 ment technique.

     It  was  discovered that by carefully filling the weir box with water up
 to  the  bottom of the  notch, good calibration could be  achieved by simply
 observing the point at which  the water level exactly coincided with the
 bottom  of the notch.  Surface tension effects  did not  interfere with the
 observation  as might  be  expected.   At  this  point, the  hook gauge in the
 stilling well was read.   The  float  gauge was  set at zero  with an adjustment
 screw.   This  procedure was  repeated prior to each day's  operation.

     Testing  began  at relatively low flow rates.  Originally it was thought
 that the float gauge would  indicate variations  in flow and head fluctuations.
 However,  due  to its calibration scale  (0-4 MGD), it proved to be too insensi-
 tive to  slight variations.  Float  gauge  readings are not  included in this
 report.   Since steady flow  is  an essential  condition for  accurate discharge,
 another  indicator was required.

     The  device most sensitive to  flow variations is the  scale/weighing  tank
 system.  With the valves open  in the weighing  tank,  an equilibrium is reached
where water entering the weighing tank equals  the water leaving the tank plus
a residual pool.  At low flow  rates  the  scale clearly  indicates equilibrium,
with readings remaining constant, typically within plus or minus 2 pounds.
Since scale readings remain steady,  pump  discharge is  constant at any valve

                                     46

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setting.  This indicated that the pumps operated without significant head or
discharge fluctuations in the lower flow ranges (but greater than 0.02 c.f.s.).
At flows near zero c.f.s. (less than 0.02 c.f.s.) the constant head tank was
used in conjunction with multiple runs to assure equilibrium flow rates.  At
higher flow rates the point gage was used to assume that equilibrium flow
conditions had been reached.  While design considerations indicated that
pump flow would be constant, test verification was necessary.

     The constant head tank (Figures 14 and 15) was used to obtain very low
flow rates, less than 0.02 c.f.s.  The tank was maintained at overflowing to
provide the constant head.  Equipped with the 2-inch discharge line and gate
valve, the gravity tank supplied very constant low flows.  The tank was used
to obtain flows up to approximately 0.02 c.f.s.   Above this point the flow
was pumped directly to the flume from the 100 gpm pump and controlled by the
gate valve on that discharge line.

     Because of the extended time involved with obtaining a measurable
incremental weight of flow in the weighing tank, flows less than 0.01 c.f.s.
were caught in a bucket by hand and weighed on a platform scale.  This pro-
cedure was utilized for the low flows on both the machined brass and the
aluminum weir plates.  To improve accuracy, the elapsed time of catching
water with the bucket method was greater than 60 seconds.  Timing was done
with a mechanical stopwatch.  No less than 7 catches were made for each flow
rate.   Specifically, timed catches were made periodically and weighed to
determine if the flow rate was constant.

     An attempt to measure the velocity profile in the weir box was made with
a Gurley Pygmy Current Meter, Model 625.  This meter is suitable for use
between velocities of 0.05 to 3.00  feet per second.  Using the continuity
equation, Q = AV,  (Q = flow, A = cross-sectional area, V - velocity) the
mean velocity in the weir box should be near 0.12 to 0.15 feet per  second.
However, the current meter  failed  to turn,  indicating either  that  it was not
as sensitive to low velocities as  rated, or that  the velocity of flow in the
weir box was not as great as calculated.  In either case, the velocity was
too small to have any significant  impact  (velocity head was  less than 0.001
ft.), and the attempt to define a  velocity  profile was  abandoned.

     In summary, the testing procedure was  developed as  a result of a trial
and error process and designed to  be as  efficient and accurate as  conditions
would permit.  The first  step of  the procedure was  to determine  the zero
points  for the hook and  staff gauges.  This is  the  reading  on the  gauges
corresponding to the  same water  level  as  the apex of the V-notch.   This  was
accomplished by  filling  the weir box  to  the level where the  water  just  touched
the apex of  the notch.   The direct line  from the smallest  (100 gpm) pump was
used  to bring the water  level up close to  the  apex.  Then the direct line was
shut  off and  the gravity tank was  used for  fine  adjustment  of the  water level.
When  the water level  reached the same  level as the  apex,  the hook  and staff
gauges  were  read.

      The  flow  rates  of  approximately  0.02  c.f.s. and above were allowed to
flow  into  the weighing  tank to determine the weight flow rate.   The tempera-
ture  of the  water  was  taken every day  so that  a volume  flow rate could be

                                      47

-------
determined.  When using the weighing tank, the determination of constant flow
was accomplished by leaving the draining valve open and monitoring the scale
arm for equilization.  That is, when the scale arm was stationary it indicated
that the flow rate was constant.  At this point the timed weighings were
started and checked for consistency.  No less than 5 timings were made for
each flow rate up to 1.0 c.f.s.  After the timing runs were completed, the
various parameters were measured, including upstream head (hook and staff
gauges), head at the weir crest (directly by eye and powdered rule), and
width of water at the crest (caliper).

     After the flow rate passed 1.0 c.f.s., the timing was performed with
an  electronic stopwatch which was controlled by a photo switching transistor
mounted on the face of the scale.  The watch was started and stopped by the
photo transistor which was activated by the scale hand passing over it.  This
technique could only be used to time 2000 pound increments, which was equiva-
lent to one revolution of the scale hand.  When utilizing the electronic
timer, the number of timings at each flow rate was reduced to two or three.
This was done for two reasons.  First,  the electronic timer provided a higher
accuracy, never varying more than 0.04 seconds between runs.  Secondly, the
weighing tank was becoming difficult to drain between runs even when utilizing
the diversion chute.  The tank draining process often took 5 minutes.
                                     48

-------
                                   SECTION 8

                                    RESULTS
INTRODUCTION

     The results are presented in two parts consistent with the performance
of research over a period of 2.5 years.  The first 1.5 years were fully
funded by the Environmental Protection Agency and involved flow calibration
with the precision machined brass weir (Figure 5).  After the contract period
was completed (December 31, 1978), work continued using the same equipment
plus suitable modifications to permit very low flow calibrations (less than
0.06 c.f.s.) and the inclusion of a full range calibration using a typical
aluminum straight cut field weir  (Figure 6).  To maintain continuity, the
results of the original funded study are presented first, with the extended
research being presented second.

PRECISION BRASS WEIR, MODERATE TO HIGH FLOWS

     The original calibration runs on the precision brass weir covered the
range of 0.06 to 3.89 c.f.s.  Data collected during thirty-two runs is tabu-
lated in the Appendix, Table A-l, and is summarized along with selected cal-
culations in Table 2.  It was intended that flow rates covered during these
test runs, (0.06 - 3.89 c.f.s.), would prove or disprove the suitability of
the new measurement techniques.  The test parameters were measured only once
per run since no variability could be detected during a run using the new
measurement techniques.  For flow rates less' than 1 c.f.s., at least five
weight/unit time measurements were taken per run.  For discharges greater
than 1 c.f.s. only two to three measurements were made due to the difficulty
in flow diversion and weighing operations at very high flow rate.  However,
accuracy was so good using the electronic timing system that repeatability
was obtained between the two or three runs within ±0.04 seconds.  Therefore,
the automatic electronic timing system made multiple runs unnecessary at
high flow rates.

     As can be seen from Table 2, measured flow rates correspond to those
calculated by the Cone formula table values (2) within plus or minus 5%.
This essentially substantiates the basic accuracy of the experimental appara-
tus and measurement techniques since the cone formula has been considered
acceptable by most  (1,2).  Standard deviation values for individual runs
indicate that greater error in measurement is present at higher  flow rates
as would be expected with manual  timing.  Even this insignificant error is
substantially removed when the light switching circuit is used during high
flow rate runs.  Run number 20 has a standard deviation of almost 0.02 c.f.s.


                                      49

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                  TABLE 2.   WEIR CALIBRATION DATA SUMMARY, MODERATE TO HIGH FLOWS, BRASS WEIR
Ul
o

Run
No.
1
2
3
4
c
6
1
8
9
10
11
12
13
14
15
16
17
18
19
20
Measured Flow Rate
Mean Standard
Flow (cfs) Dev. (cfs)
0.060
0.076
0.090
0.103
0.117
0.140
0.178
0.219
0.262
0.324
0.355
0.446
0.480
0.525
0.629
0.698
0.770
0.853
0.921
1.029
0.0009
0.0005
0.0009
0.0007
0.0009
0.0010
0.0018
0.0015
0.0024
0.0023
0.0029
0.0039
0.0037
0.0061
0.0095
0.0102
0.0078
0.0089
0.0110
0.0195
Hook Gauge
Head (ft)
0.220
0.244
0.262
0.278
0.292
0.314
0.348
0.378
0.408
0.444
0.460
0.503
0.518
0.534
0.575
0.597
0,613
0.650
0.670
0.701
Measured Parameters
Rule Caliper
(in.) (ft.) (in.) (ft.)
2.50
2.75
2.94
3.13
3.25
3.50
3.89
4.25
4.59
4.97
5.19
5.66
5.81
5.97
6.38
6.69
6.94
7.22
7.50
7.78
0.208
0.229
0.245
0.261
0.271
0.292
0.324
0.354
0.383
0.414
0.432
0.472
0.484
0.497
0.532
0.557
0.578
0.602
0.625
0.648
5.28
5.75
6.25
6.47
6.84
7.38
7.94
8.97
9.59
10.56
11.00
11.94
12.50
12.38
13.47
14.19
14.94
15,22
15.75
16.38
0.440
0.479
0.521
0.539
0.570
0.615
0.662
0.748
0.799
0.880
0.917
0.995
1.042
1.032
1.123
1.183
1.245
1.268
1.313
1.365
Staff Gauge
Head (ft.)
0.23
0.25
0.26
0.28
0.29
0.32
0.35
0.38
0.41
0.44
0.46
0.50
0.52
0.54
0.58
0.60
0.63
0.65
0.68
0.70
Calc.
Table
Value **
(cfs)
0.058
0.075
0.090
0.104
0.118
0.141
0.182
0.223
0.270
0.332
0.363
0.453
0.487
0.525
0.631
0.699
0.740
0.856
0.922
1.032
          ** calculated from the Cone Formula
continued

-------
                                     TABLE 2 (continued)

Run
No.
21
22
23
24
25
26
27
28
29
30
31
32
Measured Flow Rate
Mean Standard Hook Gauge
Flow (cfs) Dev. (cfs) Head (ft)
1.
1.
1.
1.
1.
1.
2.
2.
2.
2.
3-
3.
094
228
463
542
872
953
195
330
428
815
324
888
0.0017 0.
* 0.
* 0.
* 0.
* 0.
* 0.
* 0.
* 0.
* 0.
* 1.
* 1.
* 1.
721
748
811
821
888
906
947
973
993
054
121
192
Measured Parameters
Rule Caliper Staff
(in.) (ft.) (in.) (ft.) Head
8.00
8.41
9.00
9.19
9.94
10.06
10.56
10.81
11.00
11.66
12.44
13.25
0.666
0.701
0.750
0.766
0.828
0.838
0.880
0.901
0.917
0.972
1.037
1.104
16.78
17-50
19.19
19.41
21.09
21.44
22.50
23.12
23.25
24.78
26.63
28.09
1.398
1.458
1.599
1.618
1.758
1.787
1.875
1.927
1.938
2.065
2.219
2.341
0

0
0
0
0
0
0
0
1
1
1
Gauge
(ft.)
.72

7ii
.83
.89
.90
.95
.98
.99
.06
.13
.20
Calc.
Table
Value *
(cfs)
1.106
1.212
1.481
1.527
1.855
1.949
2.175
2.375
2.447
2.837
3.305
3.849
*insufficient sample size to compute standard deviation

-------
The timer was operated manually during this run.  Run number 21 has a stand-
ard deviation of .002 c.f.s., which reflects the use of the light switching
circuit in obtaining time intervals at that flow rate and above.  Therefore
the light switching circuit operates very satisfactorily, and increases pre-
cision of measurement.  The net result of using electronic timing on high
flow rate runs is the maintenance of high accuracy in spite of high flow rates,

     Staff gauge readings correspond to the hook gauge readings within plus
or minus 5%.  This indicates that the staff gauge may be a reasonable indica-
tor of head in spite of poor resolution typical of these gauges.  However,
these readings were obtained at a close range of observation in good light.
Field conditions might well limit reading accuracy.

     Weir discharge was calculated as follows:

                                       Q = W x y

     where:

     W = the weight rate of flow, Ib/sec (determined experimentally)

     Y = the weight per unit volume, lb/ft3 (temperature dependent, see
         Appendix A, Figure A-l, for correction curve)

     Figure 31 shows fitted curves of head, staff, rule, and caliper readings
plotted against measured weir discharge.  By inspection, all curves have the
same general shape.  This is to be expected since the same physical phenomena
is being measured in each case.  That is, discharge over the weir is being
related to a length measurement, either a depth or a width which are both
closely related.  The cross-sectional area of flow over a 90  V-notch weir
is approximately triangular in shape.  The base width of the triangle  (corres-
ponding to the water surface) changes by an amount proportional to the alti-
tude of the triangle  (the depth over the notch).  Since there is similar be-
havior between depth over the weir notch and weir head it is not surprising
that all the measurements behave in manners described adequately by a power
curve similar to the Cone formula.

     The above argument led to the following analysis of data:  the Cone
formula Q = 2.49 H2'1*8  can be written in a generalized form:

     y = a x  where a and b are regression coefficients.  Since all the
curves appear to have the same general shape, they should all be described
by the same general equation with different coefficients.

     This shape of curve is known generally as  a power curve.   Regression
coefficients can be found as follows:
                    a = exp
                                Zln y.        T. In
                                         -  b
                                  n               n
                                      52

-------
           S(ln x±)(ln  y±) -
                               (Z In  x±)(Z  In  y±)
      b =
                                         n
                     Z(ln
                               2    (Z In  x±)'
                                         n
and
r2 =

Z(ln x±
Z(ln x±)(ln
2 (Z In x
n
'!> -
i>2 '


(Z In

Z(ln 3
x1)(Z In
n
2 (Z
^
y±)"

2
In y^2"
n
     where r is the correlation coefficient

          x. = parameter measured, run


          y  - flow, run

A regression analysis was performed on data in an attempt to describe the
curves.  The following equations were obtained:
     Hook gage:   Q = 2.49
as measured by the hook gage.
                             2-1+8
where
                                            is the actual head over the weir
     Rule:  Q = 3.01 H Z'SI where H  is the measured vertical water height
 in  the weir notch.    r            r
      Caliper:  Q = 0.46 H
                          2 .1*8
                               where H  is  the measured horizontal water
 surface width at the weir notch.

     A measure of goodness of fit is the correlation coefficient, r.   A
 perfect fit would correspond to a correlation of 1.  The curve fits resulting
 from the  above regression coefficients were extremely good as is listed in
 the  table below:

     Measurement            a           b          r
Hook gage
Rule
Caliper
2.49
3.01
0.46
2.48
2.51
2.48
0.99993
0.99992
0.99972
                                      53

-------
CO
M-l
U

-------
It is interesting to note that the regression coefficients given in the cone
formula were duplicated.  This is a good indication that the experimental
apparatus was set up and operated properly, duplicating the work of others.
Care should be taken in applying these relations in cases when the approach
velocity is not negligible.

     During test runs, caliper measurements were the most difficult to take.
The water level at the crest was very hard to see and the caliper was un-
wieldly to spread.  The brass tips had a tendency to draw the water further
up the notch by altering the surface tension effects.  Given these difficul-
ties in using the calipers, the close fit of the curve to the data points is
surprising.

     No difficulties were encountered in measuring depths at the weir notch
by use of the rule.  However, significant blockage of the flow occurs at low
flow rates due to the presence of the rule.  This effect is noticable at
flow rates, less than approximately 0.02 c.f.s. (below calibration levels
listed in Table 2).  Table 3 illustrates the effect of the rule on discharge
in the vicinity of 0.02 c.f.s.  The effect is more pronounced as discharge
drops below this level.  However, the blocking effect has no impact on the
accuracy of the flow measurement since the weight rate of flow is measured
without the rule being placed in the notch.  Thus the correlation between
depth over the notch and discharge is as accurate as before.  When the rule
is placed in the notch the discharge is momentarily reduced but the flow
rate is so low that the head over the weir will not have time to react sig-
nificantly during the reading.  The volume is so great in the stilling basin
that flows less than 0.02 c.f.s. will not produce measurable head changes
during any practical period of measurement.  For example, based on the data
in Table 3 showing an approximate 8% reduction in discharge, only 0.08 x
0.02 x 10 - 0.016 cubic feet of water would be blocked over a typical  10
second measuring period.  In a stilling basin of 7  ft. x 8  ft.  this would
correspond to a 0.003 inch increase in depth over the 10 second period.  Max-
imum measurement resolution on the rule is 0.0312 inch, a factor of    10
greater.  Therefore, even under more critical conditions  it is highly  un-
likely that this blockage effect would ever be a significant factor.

     An important consideration  in evaluating the new measurement techniques
is the repeatability of  the measurement when comparing different people  per-
forming the measurement.  An experiment was devised to determine the varia-
tion due  to different observers  performing the  same measurement.  Two  labora-
tory sections of  an  undergraduate hydraulics course were  used to provide
sample size.  An  average of 11 people made calibration measurements for  six
different discharges.   The only  guidance  provided was a  brief verbal descrip-
tion of how to  conduct  each measurement.   The discharge was then  stabilized
and  the students  made measurements of  flow depth at the  weir using  the rule,
as well as the  flow width  using  the caliper.  The  raw results,  listed  in
Table A-2 of Appendix A were  subjected  to statistical analysis.   The  statis-
tical parameters  computed  are  listed  in  Table 4.   Sample sizes  were too  small
to gain much useful  information  from  the  higher order moments.   However, the
mean and  standard deviation are  useful  parameters.   Of  interest is the error
in discharge measurements  induced by  ±  twice the standard deviation of the
new  calibration parameters.   These  calculations are summarized  in Table 5.

                                      55

-------
TABLE 3.  BLOCKING EFFECT OF THE RULE AT
          LOW DISCHARGES - WEIR BOX INFLOW
          HELD CONSTANT
Presence of Individual run
Rule in Notch times for Aw=20 Ibs, sec


Rule in Notch



No rule in notch




Rule in notch



No rule in notch


16.95
16.12
17.06
16.19
16.71
15.52
15.16
15.15
15.01
15.15
16.21
16.13
15-76
16.48
16.06
14.90
15.09
14.79
14.51
15.80
Average Mean
time, sec disch., cfs


16.61 0.0193



15.26 0.0210




16.13 0.0199



15.02 0.0214


                        56

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                TABLE 4.  STATISTICAL ANALYSIS PARAMETERS OF DEPTH AND WIDTH AT WEIRS,
                         MULTIOBSERVER TESTS.
Sec/
Run
No.
M/l
M/3
M/7
T/l
T/4
T/7
n
10
11
8
12
12
12
"Caliper" (width at weir), inches
X
6.538
9.739
12.961
6.182
9-657
12.060
Sx
0.087
0.177
0.157
0.068
0.13^
0.091
Yx
-0.650
1.008
0.889
-0.356
0.202
-0.925
kx
2.031
2.812
2.135
1.73^
2.005
2.830
vx
1.405
1.901
1.293
1.156
1.446
0.784
"Ru
y
3.063
4.546
6.086
2.896
4.586
5.716
le" (depth at weir),inches
sy
0.014
0.051
0.046
0.037
0.059
0.058
Yy
-0.068
-1.537
1.126
0.064
-1.455
-0.5H
ky
-7.615
5.610
3.272
1.333
3.927
2.154
vy
0.485
1.169
0.813
1.335
1.332
1.056

rxy
-0.164
-0.580
-0.092
0.075
0.071
0.233
n
x
S
y  =
v  =
 xy
 Sample  Size
 Mean  (Caliper)
 Standard  Deviation
 Skew  Coefficient
 Kurtosis
 Coefficient of Variation
 Mean  (Rule)
 Standard  Deviation
 Skew  Coefficient
 Kurtosis
 Coefficient of Variation
= Correlation Coefficient

-------
                   TABLE 5.  EXPECTED ERROR IN FLOW MEASUREMENT BASED ON STATISTICAL
                            PARAMETER ANALYSIS RESULTS OF MULTIOBSERVER TESTS

Sec/
Run
No.
M/l
M/3
M/7
T/l
T/4
T/7
Sample
Size,
n
10
11
8
12
12
12
"Caliper" (width at weir), inches
X
6.538
9.739
12.961
6.182
9.657
12.060
Sx
0.087
0.177
0.157
0.068
0.134
0.091
A?s
0.0034
0.0124
0.0167
0.0024
0.0092
0.0087
+
0.0067
0.0247
0.0335
0.0048
0.0185
0.0174
%*
Error
^
5^^
2^
3^
J^
2^
"Rule" (depth at weir), inches
y
3.063
4.546
6.086
2.896
4.586
|5.716
sy
0.014
0.051
0.046
0.037
0.059
0.058
±s
0.0011
0.0074
0.0104
0.0027
0.0087
0.0119
A«2S
0.0022
0.0148
0.0208
0.0054
0.0174
0.0238
%*
Error
l/^
JW^
2 ^^
^"4
^^
^<^
^^
00
   x,y    =  sample mean
   S  ,S   =  sample standard  deviation

   AQ     =  Average discharge  variation for  one  standard deviation
      S
   AQ,-.    =  Average discharge  variation for  two  standard deviations
      ds
   *% error in discharge, one standard deviation/two standard  deviation

-------
 Even  though  the measurements were made by untrained  students  in  a hurried
 atmosphere,  the error  on  all measurement parameters  was less  than 10%  at
 ±  two standard deviations.  By  the  laws of probability it  can be expected
 that  95%  of  all measurements made will fall within the two standard  devia-
 tion  range.   Therefore, the experimental evidence indicates that both  of the
 new measurement parameters, the width and depth of water at the  weir face,
 can be measured accurately using the technique described.

 Precision Brass Weir,  Low Flows

      After completion  of  the original moderate to high flow calibration runs
 using the brass weir,  additional calibration runs were conducted in  the very
 low flow  range (less than 0.06  c.f.s.).  At very low flows the nappe sticks
 to the weir  plate, effectively  changing the discharge coefficient and  necess-
 itating a separate determination of discharge coefficients by regression a-
 nalysis.   Also, in this range the blockage effect previously  discussed must
 be considered and rule measurements should be taken  as rapidly as possible
 to avoid  significant head increases (preferably in less than  10  seconds).

      Modifications to  equipment were required to avoid surging problems with
 the small 100 gpm pump at highly choked low flows.   The constant head  tank
 was installed as outlined in Section 6 and the discharge trough  was  modified
 as shown  in  Figure 32  by  installing a section of pipe to collect the flow  so
 that  a bucket could be used to  determine the weight  rate of flow for conver-
 sion  into discharge.   The pipe was notched and sealed against the weir plate
 as shown  in  Figure 33.

      The  raw data for  flow rates between 0.0009 and  0.06 c.f.s.  are  included
 in Appendix  B, Table B-l.  The regression coefficients a and  b are listed  in
 Appendix  C,  Table C-l, both in  feet and inches.

 Straight-Cut  Aluminum  Field Weir, All Flows

      The  aluminum field weir plate was attached to the back of the brass weir
 such  that  the notch was approximately one inch above  the notch in the brass
weir.   This  resulted in an approximate one inch extension  of  the aluminum
weir  crest above that  of  the brass  weir plate such that the  brass weir did
not interfere with the flow over the aluminum crest.  At very low flows the
aluminum weir flow nappe  did not cling to the weir face as had occurred with
the brass weir,   Therefore,  only one regression analysis was conducted for
each of the measurement parameters.  The powdered rule measurement was added
to  the list of measurements with the aluminum field weir since it proved to
be  easier to accomplish the reading using the meter stick  in this manner
 (Section  7).   All regression coefficients for both feet and inches are in-
cluded in Appendix C, Table C-l.

Flow Calibration Tables for Field Use

     Flow calibration tables for field use are included in Appendix  C.   Four
tables are provided for convenience.  The precision machined brass weir
 (Tables C-2 and  C-3)  will probably not often be encountered in the field due
to the expense in machining the beveled crest.   The values of discharge cover
                                      59

-------
Figure 32.  Installation of Plastic Pipe Section in Flow
            Trough to Facilitate Low Flow Measurements

                             60

-------

Figure 33.  Close-up View of Notch in Plastic Pipe to Contain Flow Nappe

-------
an approximate range from 0.001 to 4.500 c.f.s.  The discharge values were
calculated using the regression coefficients listed in Table C-l.  The brass
weir tables make use of low flow regression coefficients in the range from 0
to 0.06 c.f.s., approximately, and moderate to high flow coefficients above
0.06 c.f.s.  The aluminum field weir uses one set of coefficients for the
entire flow range.  The tables are provided in both feet and inches.   The
"rule" measurement for the aluminum weir uses the coefficients for the direct
read approach, not the "powdered" rule method.  However, if the powdered rule
method is used in the field, then the tables will still be adequate for use
since the regression coefficients are very similar and no appreciable error
will result.  Theoretically, both techniques should result in the same re-
gression coefficients.  The only explanation for variation between coefficients
is sampling error.
                                     62

-------
                               REFERENCES
1.  King, H.W. and Brater, E.F., Handbook of Hydraulics, 5th Ed., McGraw-
    Hill, New York, N.Y., 1963.

2.  Water Measurement Manual, U.S. Department of the Interior Bureau of
    Reclamation, 2nd Edition, Denver, Colorado, 1967.

3.  Nagler, F.A., "Verification of the Bazine Weir Formula by Hydro-Chemical
    Gaugings", Proceedings of the American Society of Civil Engineers,
    Vol. 44, No. 5, May  1918, p. 717.

4.  Yarnall, D.R., "The  V-Notch Weir Method of Measurement", Journal of  the
    American Society of  Mechanical Engineers, April 1913, No. 412970, p. 619.

5.  Moses,  B.D., "Tests  Made of Model Weir", Engineering Record,  Vol. 73,
    No.  15, April 8, 1916, p. 487.

6.  Blaisdell, F.W., "Discharge of V-Notch Weirs at Low Heads",  Civil
    Engineering, Vol.9,  No. 8, August 1939, pp. 495-6.

7.  O'Brien, M.P., "Least Error in V-Notch Measurements When Angle Is 90°",
    Engineering  News Record, Vol. 98, No. 25, June  23,  1927, p.  1030.

8.  Lenz,  A.T.,  "Viscosity and  Surface Tension  Effects  of V-Notch Weir
    Coefficients", Transactions of  the American Society of  Civil Engineers,
    No.  69, 1943, pp.  759-802.

 9.  Chase,  L.G., "Weir Measurements  of Liquids",  Chemical and Metallurgical
    Engineering. Vol.  23, No.  25, Dec. 22,  1920,  p.  1224.

10.  Schoder,  E.W.  and  Turner,  K.B.,  "Precise Weir Measurements", Trans-
    actions of the American  Society of Civil Engineers, No.  93,  1929,
    pp.  999-1110.

11.   Pierce, C.H.,  "Experiments on Weir Discharge",  Proceedings  of the Am-
     erican Society of  Civil  Engineers, April  1913,  No.  41650F,  p. 847.

12.   Steward,  W.G.  and  Longwell,  J.S.,  "Experiments  on Weir  Discharge",
     Proceedings of the American Society  of  Civil  Engineers, Feb. 1913,
     No.  40168F,  p.  458.

13.   Abbett, R.,  "Crest Lengths Classify  Discharge", Engineering News Record.
     Vol. 119,  No.  15,  Oct.  1937,  pp. 594-5.


                                     63

-------
14.   Pardoe, Ballester, and RehBock, "Discussion on Precise Weir Measure-
     ments", Transactions of the American Society of Civil Engineers,  No. 93
     1929, pp. 1130-1162.

15.   NPDES Compliance Sampling Manual,  U.S. Environmental Protection Agency,
     1977.
                                    64

-------
                            APPENDIX A
  62.300
   62.200
•H
CO
c


0 62.100
  62.000
   J_
                                             J.
                     15
   20          25


Temperature  (°C )
                                                         30
    Figure A-l.  Density of Water as a Function of Temperature
                                  65

-------
                 TABLE A-l.  RAW DATA, 3RASS WEIR, MODERATE  TO  HIGH FLOW CALI3RATION RUNS
ON



Run No.
1







2







3







Increment
Weight Elapsed
Water Measured Time
Temp. (Ib) (sec)
20.4°C 100 27.00
26.63
26.98
27.22
27.11
26.87
27.66
26.57
20.5°C 100 21.07
21.02
21.11
21.34
21.26
21.18
21.39
21.10
20.5°C 100 17.68
17.67
17.66
18.14
17.95
17.87
17.96
17.70

Cubic
Feet
per second
0.060
0.060
0.060
0.059
0.059
0.060
0.058
0.061
0.076
0.076
0.076
0.075
0.076
0.076
0.075
0.076
0.091
0.091
0.091
0.089
0.090
0.090
0.089
0.091

Hook
Gauge Rule Caliper
(ft) (in) (in)
1.033 2-16/32 5-9/32

Knapp sticking to

on both sides
Hook Gauge Zero =

Staff Gauge Zero =
1.057 2-24/32 5-24/32


Knapp sticking to

on both sides


1.075 2-30/32 6-8/32





Staff
(ft)
2.93

plate


0.813

2.00
2.25


plate




2.265



Knapp sticking to plate
on both sides





                                                                       continued

-------
                                                TABLE A-l (continued)
cr>



Run No.
4






5





6










Increment
Weight Elapsed
Water Measured Time
Temp. (Ib) (sec)
20.5°C 200 31.15
30.94
31.29
31.34
30.99
31.30
31.23
31.59
20. 3 t 200 27.45
27.27
27.52
27.54
27.30
27.63
27.57
27.95
20.0°C 200 22.78
22.71
22.96
22.83
22.86
23.02
23.18
23.16
23.15
22.93
23.04

Cubic
Feet
per second
0.103
0.104
0.103
0.103
0.104
0. 103
0.103
0.102
0.117
0.118
0.117
0.117
0.118
0.116
0.117
0.115
0.141
0.142
0.140
0.141
0.141
0.140
0.139
0.139
0.139
0.140
0.139

Hook
Gauge Rule Caliper
(ft) (in) (in)
1.091 3-4/32 6-15/32


Clings to bevel.
Almost springs free.


1.105 3-8/32 6-27/32

Clings to bevel.
Springs free inter-
mittently.

1.127 3-16/32




Springs free inter-
mittently.






Staff
(ft)
2.28






2.29

















-------
                                                TArsir,  A-l (continued)
CO



Run No.
7






8







9







Increment
Weight Elapsed
Water Measured Time
Temp. (Ib) (sec)
17.0°C 200 17.97
18.18
18.21
17.68
18.17
18.09
18.21
18.15
17.0°C 200 14.63
14.45
14.69
14.68
14.59
14.79
14.64
14.59
17.0°C 200 12.03
12.26
12.32
12.25
12.36
12.39
12.20
12.31

Cubic
Feet
per second
0.179
0.177
0.176
0.182
0.177
0.178
0.176
0.177
0.220
0.222
0.219
0.219
0.220
0.217
0.219
0.220
0.267
0.262
0.261
0.262
0.260
0.259
0.263
0.261

Hook
Gauge Rule Caliper
(ft) (in) (in)
1.161 3-28/32 7-30/32


Water springs free
periodically.


1.191 4-8/32 8-31/32


Water springs free.
Sticks to bevel

periodically.

1.221 4-19/32 9-19/32


Water springs free






Staff
(ft)
2.35






2.38







2.405


•




                                                                            continued

-------
TABLE A-l (continued)
Run No.
10
11
12
Increment
Weight Elapsed
Water Measured Time
Temp. (lb) (sec)
17.0°C 300 14.70
14.82
14.96
14.87
14.84
14.88
15.07
14.87
17.0°C 400 17.78
18.21
18.07
17.96
18.07
18.18
18.08
18.20
15.9°C 500 17.80
17.83
18.10
18.02
17.95
18.25
18.05
Cubic
Feet
per second
0.328
0.325
0.322
0.324
0.325
0.324
0.320
0.324
0.361
0.353
0.355
0.358
0.355
0.353
0.355
0.353
0.451
0.450
0.443
0.445
0.447
0.440
0.445
Hook
Gauge Rule Caliper Staff
(ft) (in) (in) (ft)
1.257 4-31/32 10-18/32 2.445
Water springing free.
1.273 5-6/32 11-00/32 2.46
Water springing free.
1.316 5-21/32 11-30/32 2.50
Water springing free.
                         continued

-------
TABLE A-l (continued)
Increment
Weight Elapsed
Water Measured Time
Run No. Temp. (lb) (sec)
13 15.5°C 500 16.59
16.58
16.51
16.73
16.66
16.75
16.89
16.86
14 17.2°C 500 15.25
15.48
15.37
15.17
15.37
15.38
14.94
15.44
15 17.3°C 500 12.64
12.84
12.84
12.50
12.86
12.91
12.48
12.99
Cubic
Feet
per second
0.484
0.481
0.486
0.480
0.479
0.479
0.475
0.476
0.526
0.519
0.522
0.529
0.522
0.522
0.537
0.520
0.635
0.625
0.625
0.642
0.624
0.622
0.643
0.618
	 	 	 • 	
Hook
Gauge Rule Caliper Staff
(ft) (in) (in) (ft)
1.331 5-26/32 12-16/32 2.52
Water springing free.
1.347 5-31/32 12-12/32 2.54
Water springing free.
1.388 6-12/32 13-15/32 2.575
Water springing free.
                          cont inued

-------
TA3LE A-l (continued)
Increment
Weight
Water Measured
Run No. Temp. (Ib)
16 17.3°C 600







17 17.3°C 600





18 17.3 °C 700




Elapsed
Time
(sec)
13.91
13.59
13.92
13.95
13.52
13.89
14.05
13.60
12.57
12.44
12.47
12.71
12.39
13.17
13.06
13.18
13.07
13.40
13.83
14.08

Cubic
Feet
per second
0.693
0.709
0.692
0.691
0.713
0.694
0.686
0.708
0.766
0.774
0.773
0.758
0.777
0.975
0.983
0.975
0.983
0.959
1.045
1.026
	
Hook
Gauge Rule Caliper Staff
(ft) (in) (in) (ft)
1.412 6-22/32 14-6/32 2.595



Water springing free.



1.426 6-30/32 14-30/32 2.63

Water springing free;
Tank becoming difficult
to drain between runs.

1.463 7-7/32 15-7/32 2.65

Water springing free.

                          continued

-------
TABLE A-l (continued)

Run No.
19





20



21





Increment
Weight Elapsed
Water Measured Time
Temp. (Ib) (sec)
17.3°C 800 13.77
14.09
13.83
14.14
15.80
15.09
17.5°C 1000 15.70
15.57
15.53
15.93
29.41
18 °C 2000 29.32
29.35




Cubic
Feet
per second
1.049
1.026
1.045
1.022
1.016
1.064
1.023
1.031
1.034
1.008
1.092
1.095
1.094




Hook
Gauge Rule Caliper Staff
(ft) (in) (in) (ft)
1.483 7-16/32 15-24/32 2.


Water springing free.


1.514 7-25/32 16-12/32 2.

Water springing free.

1.534 8-00/32 16-25/32 2.

Light sensitive switch
activated. Trap door
activated excessive
leakage.
675





70



72





                          continued

-------
TA2LE A-l (continued)
Increment


Run No .
22

23

2k

25


26


27

28


Weight
Water Measured
Temp. (Ib)
12.5°C 2000

15°C 2000

12.5°C 2000

12.5°C 2000


13°C 2000


12.5°C 2000

13°C 2000


Elapsed Cubic
Time Feet
(sec) per second
26.13 1.228
26.12*
21.94 1.463
21.94
20.81 1.542
20.81
17.12 1.872
17.16
17.14
16.46 1.953
16.42
16.43
14.61 2.195
14.63
13.76 2.330
13.79
13.78
Hook

Gauge Rule
(ft) (in)
1.571

1.628

1.644

1.711


1.728


1.770

1.795


8-13/32

9-00/32

9-6/32

9-30/32


10-2/32


10-18/32

10-26/32



Caliper
(in)
17-16/32

19-6/32

19-13/32

21-3/32


21-4/32


22-16/32

23-4/32



Staff
(ft)


2.81

2.83

2.89


2.90


2.95

2.98


                          continued

-------
                              TABLE A-l  (continued)

Run No.
29

30

31

Increment
Weight Elapsed Cubic
Water Measured Time Feet
Temp. (lb) (sec) per second
13°C 2000 13.21 2.428
13.23
13°C 2000 11.41 2.815
11.39
13°C 2000 9.65 3.324
9.66
Hook
Gauge Rule Caliper Staff
(ft) (in) (in) (ft)
1.810 11-00/32 23-8/32 2.99

1.871 11-21/32 24-25/32 3.06

1.943 12-14/32 26-20/32 3.13

32        13°C     2000        8.27     3.888       2.014  13-8/32    28-3/32   3.20
                               8.24

-------
                              TA2.LE A-2.  RAW DATA, MULTIOBSERVER EXPERIMENT
                                                             Average       Weight
Oi
Run No .

M-l










M-3










Caliper
(in)
6 19/32
6 19/32
6 17/32
6 13/32
6 16/32
6 20/32
6 16/32
6 16/32
6 12/32
6 20/32
6 20/32
10 2/32
9 22/32
9 24/32
9 25/32
9 24/32
9 17/32
9 20/32
9 21/32
9 18/32
10 3/32
9 20/32
Meter Stick Hook Gauge Time
(in) (ft) (sec)
3 1/32 1.085 16.1*2
3 2/32
3 3/32
3 2/32
3 2/32
3 2/32
3 2/32
3 2/32
3 2/32
3 2/32
3 2/32
4 13/32 1.221 6.05
4 18/32
4 18/32
4 17/32
4 17/32
4 18/32
4 18/32
4 17/32
4 18/32
4 18/32
4 20/32
Difference Discharge
(lb) (cfs)
100 .0972










100 .2653










                                                                   continued

-------
                     TABLE A-2 (continued)
Run No. Caliper
Average Weight
Meter Stick Hook Gauge Time Difference
(in) (in) (ft) (sec) (Ib)
M-7 12
12
12
13
12
12
12
13
T-l 6
6
6
6
6
6
6
6
6
6
6
29/32
26/32
27/32
6/32
26/32
30/32
30/32
8/32
8/32
8/32
6/32
8/32
8/32
4/32
4/32
7/32
3/32
4/32
2/32
6
6
6
6
6
6
6
6
2
2
2
2
2
2
2
2
2
2
2
2/32 1.359 11.60 400
6/32
1/32
4/32
3/32
2/32
2/32
2/32
30/32 1.070 18.92 100
30/32
38/32
30/32
28/32
28/32
27/32
27/32
28/32
30/32
30/32
Discharge
(cfs)
.5535







.0848










6 8/32       2  28/32
                                               continued

-------
TABLE A-2 (continued)
Run No.
T-4
T-7
Caliper
(in)
9 14/32
9 18/32
9 22/32
9 16/32
9 24/32
9 20/32
9 24/32
9 28/32
9 28/32
9 18/32
9 18/32
9 22/32
11 30/32
12 00/32
12 04/32
11 30/32
12 04/32
11 28/32
12 04/32
12 04/32
12 04/32
12 03/32
12 04/32
12 04/32
Meter Stick Hook Gauge
(in) (ft.)
4 18/32 1.224
4 18/32
4 20/32
4 20/32
4 19/32
4 20/32
4 20/32
4 20/32
4 16/32
4 14/32
4 20/32
4 20/32
5 23/32 1.326
5 23/32
5 26/32
5 24/32
5 20/32
5 20/32
5 20/32
5 24/32
5 24/32
5 24/32
5 23/32
5 24/32
Average Weight
Time Difference Discharge
(sec) (Ib) (cfs)
17.91 300 .2689
13.50 400 .4756

-------
                             TABLE 3-1.  RAW DATA, LOW  FLOW  CALIBRATION,  BRASS WEIR
00
Water
Run Temp.
No. (°C)
1 20.0







2 20.0






3 20.0






Increment
of Weight
Ob)
6.875







17.94
17.97
17.97
18.09
18.19
18.06
18.12
18.03
80






Elapsed
Time
(sec)
120.2
120.4
120.7
120.3
120.3
120.4
120.9
120.1
60.5
60.2
60.2
60.5
60.6
60.2
60.4
60.0
120.9
121.5
119.8
120.4
118.6
120.7
120.6
120.0
Flow Hook
Rate Gauge
(cfs) (ft)
0.00092 0.041
0.00092
0.00091
0.00092
0.00092
0.00092
0.00091
0.00092
0.00476 0.078
0.00479
0.00479
0.00480
0.00482
0.00482
0.00482
0.00482
0.01062 0.112
0.01057
0.01072
0.01066
0.01082
0.01064
0.01064
0.01070
Rule Call per
(in) (in)
7/16 1



Nappe sticking to



27/32 1-13/16



Nappe sticking to


1- 1/4 2-10/16


Staff
(ft)
0.04



plate



0.08



plate


0.11


Nappe sticking, half
free on one side






                                                                                                             M
                                                                                                            JH
                                                                                                            X
                                                                         continued

-------
                                               TABLE  B-l (continued)
vo
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
4 20.0 80





5 20.0 80





6 20.0 80





Elapsed
Time
(sec)
85.8
86.3
87.7
85.0
86.0
85.7
87.5
86.4
64.9
64.6
65.1
65.3
65.1
64.8
64.2
64.8
49.5
50.5
50.1
49.5
49.8
49.5
50.0
4-9.9
Flow
Rate
(cfs)
0.0150
0.0149
0.0146
0.0151
0.0149
0.0150
0.0147
0.0149
0.0198
0.0199
0.0197
0.0197
0.0197
0.0198
0.0200
0.0198
0.0259
0.0254
0.0256
0.0259
0.0258
0.0259
0.0257
0.0257
Hook
Gauge Rule Caliper
(ft) (in) (in)
0.13 1-13/32 2-27/32


Staff
(ft)
0.13


Nappe sticking, half free
on both sides


0.141 1- 9/16 3- 6/16


Nappe sticking, half
on both sides


0.157 1-25/32 3-23/32


Nappe sticking, half
on both sides




0.145


free


0.16


free


                                                                        continued

-------
                                                TABLE B-l  (continued)
00
o
Water
Run Temp.
No. (°C)
7 20.0





8 20.0






9 20.0




Increment Elapsed
of Weight Time
Ob) (sec)
80 47.0
46.0
46.2
46.1
46.7
46.5
46.1
46.2
80 36.4
35.8
35.3
35.6
35.1
35.7
35.7
36.0
80 32.6
32.3
31.8
31.8
31.5
32.5
32.2
32.0
Flow Hook
Rate Gauge
(cfs) (ft)
0.0273 0.164
0.0279
0.0278
0.0278
0.0275
0.0276
0.0278
0.0278
0.0353 0.183
0.0359
0.0364
0.0361
0.0366
0.0360
0.0360
0.0357
.0394 0.191
.0397
.0404
.0404
.0408
.0395
.0399
.0401
Rule
(in)
1-14/16


Caliper
(in)
3- 13/16


Staff
(ft)
0.17


Nappe sticking, half free
on both sides


2- 1/16



Nappe free


2- 5/32

Water spri


3-15/16



on one side


4- 5/32

nging free


0.18






0.19


Knapp sticking on one
side



                                                                            contirr.-'.od

-------
                                               TABLE B-l  (continued)
00
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
10 20.0 80





11 20.0 80





12 20.0 100





Elapsed
Time
(sec)
30.2
29.8
29.6
29.4
29.6
29.4
30.2
29.7
25.2
25.1
25.3
25.2
25.0
25.0
25.3
25.0
30.0
29.6
29.3
29.1
29.0
29.3
29.4
29.3
Flow Hook
Rate Gauge
(cfs) (ft)
.0425 0.197
.0431
.0434
.0437
.0434
.0437
.0425
.0432
.0509 0.211
.0512
.0507
.0509
.0514
.0514
.0507
.0514
.0535 0.217
.0542
.0548
.0552
.0553
.0548
.0546
.0548
Rule Caliper
(in) (in)
2- 3/16 4- 9/32

Water springing free
both sides



2- 6/16 4- 9/16


Water springing free
both sides


2-13/32 4-27/32


Water springing free
both sides


Staff
(ft)
0.20





0.21





0.22






-------
                           TABLE  B-2.  RAW DATA, CALIBRATION RUNS, ALUMINUM WEIR
oo
ho

Run
No.
1







2






3







Water Increment
Temp. of Weight
(°C) (Ib)
19.4 10.25
10.12
10.06
10.19
10.19
10.12
10.06
10.00
19.4 80






19.4 80







Elapsed
Time
(sec)
60.3
60.2
60.3
60.3
60.4
60.3
60.2
59.9
130.0
130.0
128.0
130.9
129.2
127.0
132.0
26.0
25.6
25.5
25.6
25.2
25.6
25.8
25.7
Flow Hook
Rate Gauge
(cfs) (ft)
0.00272 0.061
0.00270
0.00268
0.00271
0.00271
0.00269
0.00268
0.00268
0.00987 0.104
0.00987
0.01003
0.00981
0.00994
0.01011
0.00972
0.0494 0.201
0.0501
0.0503
0.0501
0.0509
0.0501
0.0498
0.0499
Powdered
Rule Caliper Staff Rule
(in) (in) (ft) (in)
11/16 1- 8/16 0.07 11/16


Water springing
free with trickle
from notch.


1- 3/16 2- 2/16 0.11 1- 5/32


Water springing
free with trickle
from notch.

2- 4/16 4-11/32 0.205 2- 9/32


Water springing
free with trickle
from notch.


                                                                      continued

-------
                                               TABLE B-2 (continued)
oo
OJ
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
4 19.0 12.06
12.06
12.12
12.06
12.06
12.31
12.12
12.31
5 19.0 80







6 19.0 80







Elapsed
Time
(sec)
30.2
30.0
30.2
30.0
29.8
30.5
29.9
30.4
53.7
53.4
53.2
52.7
52.8
53.1
52.0
52.2
39.6
39.5
39.3
38.8
39.6
38.9
38.6
38.9
Flow Hook
Rate Gauge
(cfs) (ft)
0.00641 0.085
0.00645
0.00644
0.00645
0.00649
0.00648
0.00650
0.00650
0.0239 0.146
0.0240
0.0241
0.0243
0.0243
0.0242
0.0247
0.0246
0.0324 0.166
0.0325
0.0327
0.0331
0.0324
0.0330
0.0332
0.0330
Powdered
Rule Caliper Staff Rule
(in) (in) (ft) (in)
1 1-27/32 0.08 1


Water springing
free with trickle
from notch.


1-11/16 3- 2/16 0.14 1-11/16


Water springing
free with trickle
from notch.


1-29/32 3- 9/16 0.16 1-29/32


Water springing
free with trickle
from notch.


                                                                         continued

-------
                                              TABLE B-2 (continued)
00
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
7 18.0 80




8 18.0 100




9 18.0 100




Elapsed
Time
(sec)
31.9
31.3
32.0
31.2
31.9
31.7
31.9
31.3
25.9
25.8
25.8
25.5
25.6
26.1
25.6
25.4
22.8
22.9
22.7
23.2
22.7
22.9
23.0
22.8
Flow Hook
Rate Gauge
(cfs) (ft)
0.0402 0.186
0.0410
0.0401
0.0411
0.0402
0.0405
0.0402
0.0410
0.0619 0.222
0.0622
0.0622
0.0629
0.0627
0.0615
0.0627
0.0632
0.0704 0.232
0.0700
0.0707
0.0691
0.0707
0.0700
0.0697
0.0704
Rule Caliper Staff
(in) (in) (ft)
2- 1/16 3-14/16 0.185


Powdered
Rule
(in)
2- 1/16


Water springing
free with trickle
from notch.

2-15/32 4-10/16 0.215



2- 8/16


Water springing
free with trickle
from notch.

2-19/32 5- 1/16 0.225



2-10/16


Water springing
free with trickle
from notch.


                                                                        continued

-------
                                               TABLE B-2  (continued)
CO
Ul
Water Increment
Run Temp. of Weight
No. (OC) (Ib)
10 17.5 100





11 17.5 100







12 17.5 200







Elapsed
Time
(sec)
20.5
20.5
20.8
20.6
20.8
21 .0
21.0
17.6
17.4
17.6
17.6
17.7
18.0
17.8
18.4
28.5
28.8
29.2
30.3
30.0
29.6
29.0
28.7
Flow Hook
Rate Gauge
(cfs) (ft)
0.0782 0.241
0.0782
0.0771
0.0779
0.0771
0.0764
0.0764
0.0911 0.258
0.0922
0.0911
0.0911
0.0906
0.0891
0.0901
0.0872
0.113 0.280
0.111
0.110
0.106
0.107
0.108
0.111
0.112
Powdered
Rule Caliper Staff Rule
(in) (in) (ft) (in)
2-11/16 5- 5/16 0.235 2-11/16

Water springing
free with trickle
from notch.


2-14/16 5-12/16 0.255 2-14/16


Water springing
free with trickle
from notch.


3- 2/16 6- 3/16 0.275 3- 2/16


Water springing
free completely.


r- r m t f n : :r*rl

-------
                                              TABLE B-2  (continued)
00
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
13 17.5 200





14 17.5 200





15 17.5 200





Elapsed
Time
(sec)
23.7
24.1
25.0
24.7
24.3
23.8
24.0
24.3
19.2
19.3
20.0
19.5
19.1
19.0
19.2
19.7
16.3
16.4
16.9
16.6
16.3
16.2
16.3
16.6
Flow Hook
Rate Gauge
(cfs) (ft)
0.135 0.303
0.133
0.128
0.130
0.132
0.135
0.134
0.132
0.167 0.331
0.166
0.160
0.164
0.168
0.169
0.167
0.163
0.197 0.354
0.196
0.190
0.193
0.197
0.198
0.197
0.193
Rule Call per Staff
(in) (in) (ft)
3- 6/16 6-11/16 0.300


Powdered
Rule
(in)
3- 6/16


Water springing
free.


3-11/16 7- 7/16 0.325




3-11/16


Water springing
free.


3-15/16 8 0.35



3-15/16

Water springing
free.


/*• r\T~\ 1 — i n ' i a /"i




-------
                                              TABLE B-2  (continued)
oo
vj
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
16 18.0 200







17 18.0 200







18 18.0 300







Elapsed
Time
(sec)
15.1
14.7
14.5
14.5
14.7

15.3
15.3
14.9
12.5
12.3
12.0
12.0
11.9
12.2
12.5
12.2
15.4
15.2
15.3
15.8
15.6
15.2
15.2
16.0
Flow Hook
Rate Gauge
(cfs) (ft)
0.212 0.371
0.218
0.221
0.221
0.218

0.210
0.210
0.215
0.257 0.403
0.261
0.267
0.267
0.270
0.263
0.257
0.263
0.312 0.429
0.317
0.314
0.305
0.308
0.317
0.317
0.301
Powdered
Rule Caliper Staff Rule
(in) (in) (ft) (in)
4- 2/16 8-13/32 0.365 4- 2/16


Water springing
f
free .



4-15/32 9- 1/16 0.400 4-15/32


Water springing
free.



4-12/16 9-21/32 0.425 4-25/32



Water springing
free.


                                                                         continued

-------
                                              TABLE B-2  (continued)
oo
00
Water
Run Temp.
No. (°C)
19 18.0







20 18.0








21 18.0







Increment Elapsed
of Weight Time
(lb) (sec)
400 17.6
17.2
17.2
17.8
17.3
17.3
17.9
17.4
500 19.0
18.6
19.3
18.6
19.1
19.1
18.7
19.2
18.7
500 17.8
17.3
17.9
17.4
18.0
17.9
17.9
17.5
Flow Hook
Rate Gauqe
(cfs) (ft)
0.365 0.460
0.373
0.373
0.360
0.371
0.371
0.358
0.369
0.422 0.486
0.431
0.416
0.413
0.420
0.420
0.429
0.418
0.429
0.451 0.501
0.464
0.448
0.461
0.446
0.448
0.448
0.458

Rule Cali per Staff
(in) (in) (ft)
5- 3/32 10- 6/16 0.455


Powdered
Rule
(in)
5- 2/16


Water springing
free.



5-13/32 10-31/32 0.485







5-13/32



Water springing
free.



5- 9/16 11- 7/16 0.495







5-10/16



Water springing
free.





                                                                         continued

-------
                                              TABLE B-2  (continued)
oo
10
Water Increment Elapsed
Run Temp. of Weight Time
No. (°C) (Ib) (sec)
22 18.0 500 15.6
15.1
15.7
15.1
15.6
15.6
15.3
15.2
23 18.0 600 16.2
16.2
16.3
16.0
16.4
16.3
16.4
16.1
24 18.0 600 14.9
15.2
15.1
15.0
15.1
14.9
15.1
15.1
Flow Hook
Rate Gauge
(cfs) (ft)
0.514 0.529
0.531
0.511
0.531
0.514
0.514
0.524
0.528
0.594 0.559
0.594
0.590
0.602
0.587
0.590
0.587
0.598
0.646 0.573
0.633
0.637
0.642
0.637
0.646
0.637
0.637
Powdered
Rule Caliper Staff Rule
(in) (in) (ft) (in)
5-14/16 11-14/16 0.520 5-14/16

Water springing
free.
Begin operating 500
gpm pump.
6- 3/16 12-10/16 0.550 6- 7/32


Water springing
free.



6- 6/16 13- 1/16 0.565 6- 6/16


Water springing
free.



                                                                         continued

-------
TABLE B-2 (continued)
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
25 18.0 600





26 18.0 600





27 18.0 700





Elapsed
Time
(sec)
13.2
13.6
13.3
13.5
13.5
13.4
13.5
13.4
11.8
11.7
11.8
11.7
11.8
12.0
11.7
11.8
12.1
12.1
12.3
12.0
12.2
12.1
12.1
Fl ow Hook
Rate Gauge
(cfs) (ft)
0.729 0.600
0.708
0.724
0.713
0.713
0.718
0.713
0.718
0.816 0.633
0.823
0.816
0.823
0.816
0.802
0.823
0.816
0.928 0.667
0.928
0.913
0.936
0.920
0.928
0.928
Powdered
Rule Call per Staff Rule
(in) (in) (ft) (in)
6-11/16 13-13/16 0.


Water
free.


7 14-15/32 0.


Water
free.


7-13/32 15- 5/16 0.


Water
free.


600 6-11/16


springing


625 7


springing


665 7- 7/16


springing


                          continued

-------
TABLE B-2 (continued)
Water Increment
Run Temp. of Weight
No. (°C) (Ib)
28 15.0 2000




Elapsed
Time
(sec)
30.88
30.88
30.88


Fl ow Hook
Rate Gauge
(cfs) (ft)
1.038 0.701
1.038
1.038



Rule Cali per Staff
(in) (in) (ft)
7-12/16 16 0.695


Powdered
Rule
(in)
7-13/16


Water springing
free.

Begin Electronic

29 15.0 2000

30 15.0 2000


31 15.0 2000




27.46
27.49
27.46
24.16
24.15
24.16
20.63
20.61



1.168 0.735
1.167
1.168
1.333 0.775
1.328
1.333
1.554 0.826
1.556


Timing .
8- 2/16 16-12/16 0.730

8- 3/16
Water springing
free.
8- 9/16 17-12/16 0.770
8-10/16
Water springing
free.
9- 2/16 18-29/32 0.825

"ater sprii
free.

9- 3/16

i^ins

                          continued

-------
TABLE B-2 (continued)

Run
No.
32


33




34




35

Water Increment
Temp. of Weight
(°C) (Ib)
15.0 2000


15.0 2000




15.0 2000




15.0 2000

Elapsed
Time
(sec)
18.36
18.39

16.67
16.63



15.04
15.01



13.63
13.62
Flow
Rate
(cfs)
1.747
1.744

1.924
1.928



2.132
2.136



2.353
2.354
Hook
Gauge
(ft)
0.866


0.901




0.938




0.977


Rule
(in)
9-17/32


9-15/16




10-11/32




10-25/32

Powdered
Caliper Staff Rule
(in) (ft) (in)
19-14/16 0.865 9-11/16
Water springing
free.
20- 9/16 0.900 10- 1/16
Water springing
free.
Limit of 500 gpm
pump.
21- 8/16 0.940
Water springing
free.
Powdered rule too
difficult to read.
22-10/16 0.975
T»T»a t* £i T* onyirirrnTicr
                                       free.
                                       500 plus 100
                                       gpm pumps.

-------
                APPENDIX C
  TABLE C-l.  REGRESSION COEFFICIENTS FOR WEIR,
MEASUREMENT PARAMETERS USING THE RELATION Q=aH

Weir type
and conditions
bevel crest
brass, low flow
(0-0.06 c.f.s.)

bevel crest
brass, low flow
(0-0.06 c.f.s.)

bevel crest
brass, moderate
to high flows
(0.06-4.50 c.f.s.)
bevel crest
brass, moderate
to high flows
(0.06-4.50 c.f.s.)
aluminum straight
cut field weir
all flows
(0.0-4.50 c.f.s.)

aluminum straight
cut field weir,
all flows
(0.0-4.50 c.f.s.)

Measurement
type
Hook, inches
Staff, inches
Rule, inches
Caliper, inches
Hook, feet
Staff, feet
Rule, feet
Caliper, feet
Hook, inches
Staff, inches
Rule, inches
Caliper, inches
Hook, feet
Staff, feet
Rule, feet
Caliper, feet
Hook, inches
Staff, inches
Rule, inches
Powdered rule, inches
Caliper, inches
Hook, feet
Staff, feet
.Rule, feet
Powdered rule, feet
Caliper, feet
a
0.0053
0.0053
0.0066
0.0009
2.287
2.122
2.343
0.594
0.0053
0.0049
0.0059
0.0010
2.491
2.482
3.013
0.464
0.0060
0.0060
0.0070
0.0067
0.0010
2.454
2.541
3.052
2.984
0.529
r,
correlation
b coefficient
2.441
2.410
2.361
2.598
2.441
2.410
2.361
2.598
2.469
2.505
2.507
2.483
2.480
2.504
2.506
2.484
2.428
2.446
2.466
2.453
2.366
2.428
2.447
2.466
2.453
2.366
0.99964
0.99954
0.99943
0.99788
0.99967
0.99958
0.99946
0.99790
0.99991
0.99986
0.99989
0.99965
0.99993
0.99990
0.99992
0.99970
0.99992
0.99879
0.99996
0.99995
0.99897
0.99993
0.99880
0.99992
0.99997
0.99900
                        93

-------
TABLE C-2. 90  V-NOTCH WEIR CALIBRATION TABLE
             MACHINED BRASS PLATE
Head Over
Weir (Hook)
(ft)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
Discharge
(cfs)
«B^_
	
	
0.001
0.002
0.002
0.003
0.005
0.006
0.008
0.010
0.013
0.016
0.019
0.022
0.026
0.030
0.035
0.040
0.045
0.051
0.057
0.063
0.072
0.080
0.088
0.097
0.106
0.115
0.125
0.136
0.147
0.159
0.171
0.184
0.197
0.211
0.225
0.240
Water Width
at Weir
(ft)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
Discharge
(cfs)

	
	
0.001
0.001
0.002
0.004
0.005
0.007
0.009
0.012
0.015
0.018
0.022
0.026
0.031
0.036
0.037
0.042
0.048
0.054
0.060
0.067
0.075
0.083
0.091
0.100
0.110
0.120
0.130
0.142
0.153
0.165
0.178
0.191
0.205
0.220
0.235
0.250
Head at
Weir (Rule)
(ft)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0,27
0.28
0.29
0.30
0,31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
Discharge
(cfs)

- - M 	
0.001
0.001
0.002
0.003
0.004
0.006
0.008
0.010
0.013
0.016
0.019
0.023
0.027
0.031
0.036
0.041
0.046
0.052
0.059
0.068
0.076
0.084
0.093
0.103
0.113
0.124
0.135
0.147
0.160
0.173
0.187
0.202
0.217
0.233
0.249
0.267
0.285
                                 (continued)
                     94

-------
TABLE C-2 (continued)
Head Over
Weir (Hook)
(ft)
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
Discharge
(cfs)
0.255
0.271
0.288
0.305
0.323
0.341 <
0.360
0.380
0.400
0.421
0.443
0.465
0.488
0.511
0.536
0.560
0.586
0.612
0.639
0.666
0.695
0.724
0.753
0.784
0.815
0.846
0.879
0.912
0.946
0.981
1.016
1.053
1.090
1.127
1.166
1.205
1.245
1.286
1.328
Water Width
at Weir
(ft)
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
" 	 - 	
• " • —
Discharge
(cfs)
	
0.267
0.283
0.301
0.319
0.338
0.357
0.377
0.398
0.419
0.441
0.464
0.487
0.511
0.536
0.562
0.588
0.615
0.642
0.671
0.700
0.730
0.760
0.792
0.824
0.857
0.890
0.925
0.960
0.996
1.033
1.070
1.109
1.148
1.188
1.229
1.270
1.313
1.356
1.400
	 	 	 	 	 .
Head at
Weir (Rule)
(ft)

0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0,64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
•"
Discharge
(cfs)
	 _
0.303
0.323
0.343
0.363
0.385
0.407
0.430
0.454
0.479
0.504
0.530
0.557
0.585
0.614
0.643
0.674
0.705
0.737
0.769
0.803
0.838
0.873
0,909
0.947
0.985
1.024
1.064
1.104
1.146
1.189
1.233
1.277
1.323
1.369
1.417
1.465
1.515
1.565
1.617
                    (continued)



          95

-------
TABLE  C-2  (continued)

Head Over
Weir (Hook)
(ft)
Discharge
(cfs)
Water Width
at Weir
(ft)
Discharge
(cfs)
Head at
Weir (Rule)
(ft)
Discharge
(cfs)

0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.370
1.413
1.457
1.502
1.548
1.594
1.642
1.690
1.739
1.788
1.839
1.890
1.943
1.996
2.050
2.105
2.160
2.217
2.274
2.333
2.392
2.452
2.513
2.575
2.638
2.701
2.766
2.831
2.898
2.965
3.033
3.102
3.173
3.244
3.316
3.389
3.462
3.537
3.613
1.58
1.60
1.62
1.64
1.66
1.68
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
2.00
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.28
2.30
2.32
2.34
1.445
1.491
1.538
1.586
1.634
1.683
1.734
1.785
1.837
1.890
1.943
1.998
2.054
2.110
2.168
2.226
2.285
2.345
2.407
2.469
2.532
2.596
2.661
2.727
2.794
2.861
2.930
3.000
3.071
3.143
3.215
3.289
3.364
3.440
3.516
3.594
3.673
3.753
3.834
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.669
1.722
1.777
1.832
1.889
1.946
2.005
2.065
2.125
2.187
2.250
2.314
2.379
2.445
2.512
2.580
2.650
2.720
2.792
2.864
2.938
3.013
3.089
3.166
3.245
3.324
3.405
3.487
3.570
3.654
3.739
3.826
3.914
4.002
4.093
4.184
4.277
4.370
4.465 .
                    (continued)
         96

-------
TABLE  C-2  (continued)
Head Over
Weir (Hook)
(ft)

Discharge
(cfs)
Water Width
at Weir
(ft)

Discharge
(cfs)
Head at
Weir (Rule)
(ft)

Discharge
(cfs)

1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
3.690
3.767
3.846
3.926
4.006
4.088
4.170
4.254
2.36
2.38
2.40
2.42
2.44
2.46
2.48
2.50
3.916
3.999
4.083
4.168
4.254
4.341
4.429
4.518
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
4.562
4.659
4.758
4.858
4.959
5.062
5.165
5.270
          97

-------
TABLE C-3. 90° V-NOTCH WEIR CALIBRATION TABLE
            MACHINED BRASS PLATE
Head Over
Weir (Hook)
(in)
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
Discharge
(cfs)
___
	
	
0.001
0.001
0.002
0.002
0.003
0.004
0.005
0.007
0.008
0.010
0.012
0.014
0.017
0.019
0.022
0.025
0.029
0.032
0.036
0.040
0.045
0.050
0.055
0.060
0.067
0.073
0.080
0.087
0.094
0.101
0.109
0.117
0.125
0.134
0.143
0.153
0.162
Water Width
at Weir
(in)
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
3.80
4.00
4.20
4.40
4.60
4.80
5.00
5.20
5.40
5.60
5.80
6.00
6.20
6.40
6.60
6.80
7.00
7.20
7.40
7.60
7.80
8.00
Discharge
(cfs)
^•^
	
	
0.001
0.001
0.001
0.002
0.003
0.004
0.005
0.007
0.009
0.011
0.013
0.016
0.018
0.022
0.025
0.029
0.033
0.037
0.042
0.047
0.053
0.059
0.060
0.066
0.072
0.079
0.086
0.093
0.100
0.108
0.117
0.125
0.135
0.144
0.154
0.164
0.175
Head at
Weir (Rule)
(in)
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
Discharge
(cfs)
	 • —
	
	
0.001
0.001
0.002
0.003
0.004
0.005
0.007
0.008
0.010
0.012
0.015
0.017
0.020
0.023
0.026
0.030
0.034
0.038
0.042
0.047
0.052
0.057
0.063
0.071
0.078
0.085
0.093
0.101
0.109
0.118
0.127
0.136
0.146
0.157
0.168
0.179
0.191
                    98
                              (continued)

-------
Table  C-3  (continued)

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
8.00
8.10
0.173
0.183
0.194
0.206
0.217
0.229
0.242
0.255
0.268
0.282
0.296
0.311
0.325
0.341
0.357
0.373
0.390
0.407
0.424
0.442
0.461
0.479
0.499
0.518
0.539
0.559
0.581
0.602
0.624
0.647
0.670
0.693
0.717
0.742
0.767
0.792
0.818
0.845
0.872
0.899
0.928
8.20
8.40
8.60
8.80
9.00
9.20
9.40
9.60
9.80
10.00
10.20
10.40
10.60
10.80
11.00
11.20
11.40
11.60
11.80
12.00
12.20
12.40
12.60
12.80
13.00
13.20
13.40
13.60
13.80
14.00
14.20
14.40
14.60
14.80
15.00
15.20
15.40
15.60
15.80
16.00
16.20
0.186
0.197
0.209
0.221
0.234
0.247
0.261
0.275
0.289
0.304
0.319
0.335
0.351
0.368
0.385
0.403
0.421
0.440
0.459
0.478
0.498
0.519
0.540
0.561
0.583
0.606
0.629
0.652
0.677
0.701
0.726
0.752
0.778
0.805
0.832
0.860
0.888
0.917
0.947
0.977
1.007
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
8.00
8.10
0.203
0.215
0.229
0.242
0.256
0.271
0.286
0.301
0.317
0.334
0.351
0.368
0.386
0.405
0.424
0.443
0.463
0.484
0.505
0.527
0.549
0.572
0.595
0.619
0.644
0.669
0.695
0.721
0.748
0.775
0.803
0.832
0.861
0.891
0.922
0.953
0.985
1.017
1.050
1.084
1.118
                    (continued)



          99

-------
TABLE  C-3 (continued)

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
10.00
10.10
10.20
10.30
10.40
10.50
10.60
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
11.50
11.60
11.70
11.80
11.90
12.00
12.10
12.20
0.956
0.985
1.015
1.045
1.075
1.106
1.138
1.170
1.203
1.236
1.270
1.305
1.339
1.375
1.411
1.447
1.485
1.522
1.561
1.599
1.639
1.679
1.719
1.760
1.802
1.844
1.887
1.931
1.975
2.019
2.064
2.110
2.157
2.204
2.251
2.299
2.348
2.398
2.448
2.498
2.550
16.40
16.60
16.80
17.00
17.20
17.40
17.60
17.80
18.00
18.20
18.40
18.60
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
21.00
21.20
21.40
21.60
21.80
22.00
22.20
22.40
22.60
22.80
23.00
23.20
23.40
23.60
23.80
24.00
24.20
24.40
1.039
1.070
1.103
1.136
1.169
1.203
1.238
1.273
1.309
1.345
1.382
1.420
1.458
1.497
1.536
1.576
1.617
1.658
1.700
1.743
1.786
1.829
1.874
1.919
1.965
2.011
2.058
2.106
2.154
2.203
2.252
2.303
2.354
2.405
2.458
2.510
2.564
2.618
2.673
2.729
2.785
8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
10.00
10.10
10.20
10.30
10.40
10.50
10.60
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
11.50
11.60
11.70
11.80
11.90
12.00
12.10
12.20
1.153
1.188
1.225
1.262
1.299
1.337
1.376
1.416
1.456
1.497
1.538
1.581
1.624
1.667
1.712
1.757
1.802
1.849
1.896
1.944
1.993
2.042
2.092
2.143
2.194
2.247
2.300
2.353
2.408
2.463
2.519
2.576
2.633
2.692
2.751
2.811
2.871
1.933
2.995
3.058
3.121
                   (continued)




         100

-------
TABLE  C-3  (continued)

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.60
13.70
13.80
13.90
14.00
14.10
14.20
14.30
14.40
14.50
14.60
14.70
14.80
14.90
15.00
2.602
2.654
2.707
2.761
2.816
2.871
2.926
2.983
3.040
3.097
3.155
3.214
3.274
3.334
3.395
3.456
3.519
3.581
3.645
3.709
3.774
3.839
3.906
3.972
4.040
4.108
4.177
4.247
24.60
24.80
25.00
25.20
25.40
25.60
25.80
26.00
26.20
26.40
26.60
26.80
27.00
27.20
27.40
27.60
27.80
28.00
28.20
28.40
28.60
28.80
29.00
29.20
29.40
29.60
29.80
30.00
2.842
2.900
2.959
3.018
3.077
3.138
3.199
3.261
3.324
3.387
3.451
3.516
3.582
3.648
3.715
3.782
3.851
3.920
3.990
4.061
4.132
4.204
4.277
4.350
4.425
4.500
4.576
4.652
12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.60
13.70
13.80
13.90
14.00
14.10
14.20
14.30
14.40
14.50
14.60
14.70
14.80
14.90
15.00
3.186
3.251
3.317
3.384
3.452
3.521
3.590
3.660
3.731
3.803
3.876
3.949
4.023
4.099
4.174
4.251
4.329
4.407
4.487
4.567
4.648
4.730
4.813
4.896
4.981
5.066
5.153
5.240
         101

-------
TABLE  C-4. 90
V-NOTCH WEIR CALIBRATION TABLE
  ALUMINUM, ROUGH CUT PLATE

Head Over
Weir (Hook)
(ft)
Discharge
(cfs)
Water Width
at Weir
(ft)
Discharge
(cfs)
Head at
Weir (Rule)
(ft)
Discharge
(cfs)

0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
___
	
	
0.001
0.002
0.003
0.004
0.005
0.007
0.009
0.012
0.014
0.017
0.021
0.025
0.029
0.033
0.038
0.044
0.049
0.055
0.062
0.069
0.077
0.085
0.093
0.102
0.112
0.121
0.132
0.143
0.154
0.166
0.179
0.192
0.205
0.220
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
___
	
0.001
0.001
0.002
0.004
0.005
0.007
0.009
0.012
0.015
0.018
0.022
0.026
0.031
0.036
0.041
0.047
0.054
0.061
0.068
0.076
0.084
0.093
0.103
0.113
0.123
0.134
0.146
0.158
0.171
0.184
0.198
0.212
0.227
0.243
0.259
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
___
	
0.001
0.001
0.002
0.003
0.004
0.006
0.008
0.010
0.013
0.016
0.020
0.024
0.028
0.033
0.039
0.044
0.051
0.058
0.065
0.073
0.081
0.090
0.100
0.110
0.121
0.132
0.144
0.157
0.170
0.184
0.198
0.213
0.229
0.246
0.263 '
                      102
                                 (continued)

-------
TABLE C-4  (continued)

Head Over
Weir (Hook)
(ft)
Discharge
(cfs)
Water Width
at Weir
(ft)
Discharge
(cfs)
Head at
Weir (Rule)
(ft)
Discharge
(cfs)

0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.234
0.249
0.265
0.282
0.299
0.316
0.334
0.353
0.372
0.392
0.413
0.434
0.456
0.478
0.502
0.525
0.550
0.575
0.600
0.627
0.654
0.682
0.710
0.739
0.769
0.799
0.830
0.862
0.895
0.928
0.962
0.997
1.032
1.068
1.105
1.143
1.181
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
.1 . 20
1.22
1.24
1.26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
1.42
1.44
1.46
1.48
0.276
0.294
0.312
0.331
0.350
0.370
0.391
0.412
0.434
0.457
0.480
0.504
0.529
0.554
0.580
0.607
0.635
0.663
0.692
0.721
0.752
0.783
0.814
0.847
0.880
0.914
0.949
0.984
1.020
1.057
1.095
1.133
1.173
1.213
1.254
1.295
1.337
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.281
0.299
0.319
0.339
0.359
0.381
0.403
0.426
0.450
0.474
0.499
0.526
0.552
0.580
0.608
0.638
0.668
0.699
0.730
0.763
0.797
0.831
0.866
0.902
0.939
0.977
1.015
1.055
1.095
1.137
1.179
1.222
1.266
1.312
1.358
1.405
1.452
                       (continued)





          103

-------
TABLE  C-4  (continued)

Head Over
Weir (Hook)
(ft)
Discharge
(cfs)
Water Width
at Weir
(ft)
Discharge
(cfs)
Head at
Weir (Rule)
(ft)
Discharge
(cfs)

0.75
0.76
0.77
0.78
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.220
1.260
1.301
1.342
1.385
1.427
1.471
1.516
1.561
1.607
1.654
1.702
1.750
1.799
1.849
1.900
1.952
2.004
2.058
2.112
2.167
2.222
2.279
2.337
2.395
2.454
2.514
2.575
2.637
2.699
2.763
2.827
2.892
2.958
3.025
3.093
3.162
1.50
1.52
1.54
1.56
1.58
1.60
1.62
1.64
1.66
1.68
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
2.00
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
1.381
1.425
1.469
1.515
1.561
1.608
1.656
1.705
1.755
1.805
1.856
1.909
1.961
2.015
2.070
2.125
2.182
2.239
2.297
2.356
2.415
2.476
2,537
2.600
2.663
2.727
2.792
2.858
2.925
2.992
3.061
3.130
3.200
3.272
3.344
3.417
3.491
0.75
0.76
0.77
0.78
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.501
1.551
1.602
1.654
1.707
1.760
1.815
1.871
1.928
1.985
2.044
2.104
2.165
2.227
2.290
2.354
2.419
2.485
2.552
2.620
2.689
2.760
2.831
2.904
2.977
3.052
3.128
3.205
3.283
3.362
3.442
3.524
3.606
3.690
3.775
3.861
3.948
                      (continued)
         104

-------
TABLE  C-4  (continued)

Head Over
Weir (Hook)
(ft)

Discharge
(cfs)
Water Width
at Weir
(ft)

Discharge
(cfs)
Head at
Weir (Rule)
(ft)

Discharge
(cfs)

1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
3.231
3.302
3.373
3.445
3.519
3.593
3.668
3.744
3.820
3.898
3.977
4.056
4.137
4.218
2.24
2.26
2.28
2.30
2.32
2.34
2.36
2.38
2.40
2.42
2.44
2.46
2.48
2.50
3.566
3.641
3.718
3.796
3.874
3.954
4.034
4.115
4.198
4.281
4.365
4.450
4.536
4.623
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
4.036
4.125
4.216
4.308
4.401
4.495
4.590
4.687
4.784
4.883
4.983
5.085
5.187
5.291
         105

-------
T/BLE  C-5. 90° V-NOTCH WEIR CALIBRATION TABLE
           ALUMINUM, ROUGH CUT PLATE

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80

	
	
0.001
0.001
0.002
0.003
0.003
0.005
0.006
0.008
0.009
0.011
0.014
0.016
0.019
0.022
0.025
0.029
0.032
0.036
0.041
0.045
0.050
0.056
0.061
0.067
0.073
0.080
0.086
0.094
0.101
0.109
0.117
0.126
0.135
0.144
0.153
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
3.80
4.00
4.20
4.40
4.60
4.80
5.00
5.20
5.40
5.60
5.80
6.00
6.20
6.40
6.60
6.80
7.00
7.20
7.40
7.60
___
	
	
0.001
0.001
0.002
0.002
0.003
0.004
0.005
0.006
0.008
0.010
0.011
0.013
0.016
0.018
0.021
0.024
0.027
0.030
0.033
0.037
0.041
0.045
0.049
0.054
0.059
0.064
0.069
0.075
0.081
0.087
0.093
0.100
0.107
0.114
0.121
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80

	
	
0.001
0.001
0.002
0.003
0.004
0.005
0.007
0.009
0.011
0.013
0.016
0.019
0.022
0.026
0.030
0.034
0.039
0.044
0.049
0.055
0.061
0.067
0.074
0.081
0.089
0.097
0.105
0.114
0.123
0.133
0.143
0.154
0.165
0.176
0.188
                                  (continued)
                      106

-------
TABLE  C-5  (continued)

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
0.163
0.174
0.184
0.196
0.207
0.219
0.231
0.244
0.257
0.271
0.284
0.299
0.313
0.329
0.344
0.360
0.376
0.393
0.411
0.428
0.446
0.465
0.484
0.504
0.524
0.544
0.565
0.586
0.608
0.630
0.653
0.676
0.700
0.724
0.749
0.774
0.799
0.826
0.852
7.80
8.00
8.20
8.40
8.60
8.80
9.00
9.20
9.40
9.60
9.80
10.00
10.20
10.40
10.60
10.80
11.00
11.20
11.40
11.60
11.80
12.00
12.20
12.40
12.60
12.80
13.00
13.20
13.40
13.60
13.80
14.00
14.20
14.40
14.60
14.80
15.00
15.20
15.40
0.129
0.137
0.145
0.154
0.163
0.172
0.181
0.191
0.201
0.211
0.221
0.232
0.243
0.255
0.267
0.279
0.291
0.304
0.317
0.330
0.344
0.358
0.372
0.386
0.401
0.417
0.432
0.448
0.464
0.481
0.498
0.515
0.532
0.550
0.569
0.587
0.606
0.626
0.645
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
0.201
0.214
0.227
0.241
0.255
0.270
0.286
0.302
0.318
0.335
0.352
0.370
0.389
0.408
0.428
0.448
0.469
0.490
0.512
0.534
0.557
0.581
0.605
0.630
0.655
0.681
0.708
0.735
0.762
0.791
0.820
0.849
0.880
0.910
0.942
0.974
1.007
1.040
1.074
                        (continued)
            107

-------
TABLE  C-5  (continued)

Head Over
Weir (Hook)
(in)
Discharge
(cfs)
Water Width
at Weir
(in)
Discharge
(cfs)
Head at
Weir (Rule)
(in)
Discharge
(cfs)

7.80
7.90
8.00
8.10
8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
10.00
10.10
10.20
10.30
10. 40
10.50
10.60
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
11.50
11.60
0.879
0.907
0.935
0.964
0.993
1.023
1.053
1.083
1.115
1.146
1.179
1.211
1.245
1.278
1.313
1.348
1.383
1.419
1.456
1.493
1.531
1.569
1.607
1.647
1.687
1.727
1.768
1.810
1.852
1.894
1.938
1.982
2.026
2.071
2.117
2.163
2.210
2.257
2.305
15.60
15.80
16.00
16.20
16.40
16.60
16.80
17.00
17.20
17.40
17.60
17.80
18.00
18.20
18.40
18.60
18.80
19.00
19.20
19.40
19.60
19.80
20.00
20.20
20.40
20.60
20.80
21.00
21.20
21.40
21.60
21.80
22.00
22.20
22.40
22.60
22.80
23.00
23.20
0.665
0.686
0.706
0.727
0.749
0.771
0.793
0.815
0.838
0.861
0.885
0.909
0.933
0.958
0.983
1.008
1.034
1.061
1.087
1.114
1.141
1.169
1.197
1.226
1.255
1.284
1.314
1.344
1.374
1.405
1.437
1.468
1.500
1.533
1.566
1.599
1.633
1.667
1.701
7.80
7.90
8.00
8.10
8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
10.00
10.10
10.20
10.30
10.40
10.50
10.60
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
11.50
11.60
1.109
1.145
1.181
1.217
1.255
1.293
1.332
1.371
1.411
1.452
1.493
1.536
1.579
1.622
1.666
1.711
1.757
1.804
1.851
1.899
1.947
1.997
2.047
2.098
2.149
2.202
2.255
2.309
2.363
2.419
2.475
2.532
2.589
2.648
2.707
2.767
2.828
2.889
2.952
                      (continued)
         108

-------
TABLE C-5  (continued)

Head Over
Weir (Hook)
(in)

11.70
11.80
11.90
12.00
12.10
12.20
12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.60
13.70
13.80
13.90
14.00
14.10
14.20
14.30
14.40
14.50
14.60
14.70
14.80
14.90
15.00

Discharge
(cfs)
2.353
2.403
2.452
2.503
2.554
2.605
2.657
2.710
2.763
2.817
2.872
2.927
2.983
3.039
3.097
3.154
3.213
3.272
3.331
3.391
3.452
3.514
3.576
3.639
3.702
3.766
3.831
3.896
3.962
4.029
4.096
4.164
4.233
4.302
Water Width
at Weir
(in)
23.40
23.60
23.80
24.00
24.20
24.40
24.60
24.80
25.00
25.20
25.40
25.60
25.80
26.00
26.20
26.40
26.60
26.80
27.00
27.20
27.40
27.60
27.80
28.00
28.20
28.40
28.60
28.80
29.00
29.20
29.40
29.60
29.80
30.00
Discharge
(cfs)
1.736
1.771
1.807
1.843
1.880
1.917
1.954
1.992
2.030
2.069
2.108
2.147
2.187
2.228
2.268
2.309
2.351
2.393
2.436
2.478
2.522
2.566
2.610
2.654
2.699
2.745
2.791
2.837
2.884
2.931
2.979
3.027
3.076
3.125
Head at
Weir (Rule)
(in)
11.70
11.80
11.90
12.00
12.10
12.20
12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.60
13.70
13.80
13.90
14.00
14.10
14.20
14.30
14.40
14.50
14.60
14.70
14.80
14.90
15.00
Discharge
(cfs)
3.015
3.079
3.143
3.209
3.275
3.342
3.410
3.479
3.549
3.619
3.690
3.762
3.835
3.909
3.984
4.059
4.135
4.212
4.290
4.369
4.449
4.529
4.611
4.693
4.776
4.860
4.945
5.031
5.117
5.205
5.293
5.382
5.472
S.SfiT
         109

-------
                                    TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing/
1. REPORT NO.
   EPA-600/4-80-Q35
4. TITLE AND SUBTITLE
  Calibration  of a 90° V-Notch  Weir Using Parameters
  Other than Upstream Mead
             5. REPORT DATE
                 JULY  1980 ISSUING  DATE.
             6. PERFORMING ORGANIZATION CODE
                                                             I. RECIPIENT'S ACCESSION-NO.
7. AUTHOR(S)
  Robert  Eli,  Harald Pederson,  and Ronald Snyder
                                                            8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
  Dept. of  Civil  Engineering
  West Virginia University
  Morgantown,  WV   26506
              10. PROGRAM ELEMENT NO.
                C39B10
             11. CONTRACT/GRANT NO.
                                                              R805312-01-1
12. SPONSORING AGENCY NAME AND ADDRESS
  Environmental  Monitoring and  Support Laboratory
  Office of  Research and Development
  U.S.  Environmental Protection Agency
  Cincinnati, Ohio 45268
              13. TYPE OF REPORT AND PERIOD COVERED
               July,  1977-April,  1980
              14. SPONSORING AGENCY CODE
                    EPA/600/03
15. SUPPLEMENTARY NOTES
16. ABSTRACT
  Traditional  calibration of 90   V-Notch Weirs  has  involved the  establishment of  a
  head-discharge  relationship where the head is measured upstream  of weir drawdown
  effects.  This  parameter is often difficult to  measure in field  weir installations.
  Two other parameters are proposed for use as  correlation parameters to weir
  discharge.   These parameters are  depth and width  of flow at the  weir notch.
  Techniques for  measuring these  parameters are proposed that result in less than
  10% error in discharge at the 95% probability level in the laboratory environment.
17.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                               b.IDENTIFIERS/OPEN ENDED TERMS
                           c.  COSATI 1 ield/Group
  Water Flow Measurement
  Weir
  Quality Control
                               13B
13. DISTRIBUTION STATEMENT
  Release to public
                                               19. SECURITY CLASS (This Report)
                                                 Unclassified	
                            21. NO. OF PAGES

                                  120
20. SECURITY CLASS (This page)
  Unclassified
                                                                          22. PRICE
EPA Form 2220-1 (9-73)
                                            110
                                                            U.S. GOVERNMENT PRINTING OFFICE:  1980--657-165/0052

-------