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
-------
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"
<
r
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
-------
1/16"
Hh
30° 11°
1/4"
Section A-A
Elevation
Figure 5. Precision Machined Brass Weir Plate Details
-------
— 6"
I— 1/8"-I
Section A-A
Elevation
Figure 6. Square-Cut Aluminum Field Weir Plate Details
-------
Figure 7. 1,000 gpm Bell and Cossett Pump, One of Two
-------
Figure 8. Line of Pumps Feeding the Weir Box
19
-------
o
Figure 9. Water Supply Lines Leading Into Turbulence Suppressor Tank
-------
Figure 10. Turbulence Suppressors, Rubberized Horsehair Mounted on Wood Frame
-------
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
-------
fr
Figure 11.
Effectiveness of Turbulence Suppression System in Producing
a Smooth Water Surface
23
-------
Figure 12. Outlet Chute Leading From Weir Plate to Weighing Tank
-------
Figure 13. Weighing Tank Diversion Box With Cover Removed
25
-------
Figure 14. Storage Tank Installation for Use as a Constant Head Water Supply
-------
Figure 15. Detail of Constant Head Tank and Its Containing Outer Overflow Tank
-------
Figure 16. Weighing Scale Showing Location of Photo Transistor
28
-------
(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
-------
Figure 18. Stilling Well Installation Showing Hook Gauge and Recording
Gauge
30
-------
9. Plexiglass Stilling Wells, Hook Gauge:Foreground, Float Gauge:Rear
31
-------
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
-------
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
-------
Figure 20. Placement of the Rule When Measuring Depth of Flow at the Weir Notch
-------
Figure 21. View of Small Disturbance Waves Looking Upstream
-------
:
Figure 22. View of Small Disturbance Wave When Viewed From Above the Weir
-------
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
-------
Figure 24. Use of Common Baby Powder to Produce a High Water Mark on the
Rule
38
-------
U)
Figure 25. Positioning of Caliper to Perform Measurement of Flow Width at Weir Crest
-------
8
Figure 26. Placement of the Caliper as Viewed From Above
-------
Figure 27. View of a Single Caliper Tip as Properly Positioned at the Intersection of the Weir Crest
and Water Surface
-------
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
-------
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
-------
-
Figure 29. Aluminum Channel With Attached Meter Stick for Measuring Caliper Width
-------
-
Figure 30. Flow Chute Leading From Weir to Weighing Tank — Trap Door Diversion Sealed
-------
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
-------
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
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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
-------
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
-------
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
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