EPA600/
2-84-ied
=Je
PB85-122745
Recommended Practice for the Use of
Parshall Flumes and Palmer-Bowlus
Flumes in 'Wastewater Treatment Plants
(U.S.) National Bureau of Standards (NEL)
Gaithersburg, MD
Prepared for
Municipal Environmental Research Lab.
Cincinnati, OH
Nov 84
U.S. DEPARTMENT OF COMMERCE
National Technical Information Service
NTIS
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PBB5-1227U5
EPA-600/2-84-136
November 1984
RECOMMENDED PRACTICE FOR THE USE OF
PARSHALL FLUMES AND PALMER-BOWLUS FLUMES
IN WASTEWATER TREATMENT PLANTS
by
Gershon Kulin
Fluid Engineering Division
National Bureau of Standards
Washington, D. C. 20234
EPA 78-D-X0024-1
Project Officer
Walter W. Schuk
Wastewater Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
REPRODUCED BY
NATIONAL TECHNICAL
INFORMATION SERVICE
U.S. DEPARTMEHI OF COMMERCE
SPRINGFIELD. VA. 22161
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing/
1. REPORT NO.
EPA-600/2-84-186
3. RECIPIENT'S ACCESSION NO.
PB85 12274 5
[4. TITLE AND SUBTITLE
RECOMMENDED PRACTICE FOR THE USE OF PARSHALL FLUMES
AND PALMER-BOWLUS FLUMES IN WASTEWATER TREATMENT
PLANTS
7. AUTHOR(S)
5. REPORT DATE
November 1984
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
Gershon Kulin
9. PERFORMING ORGANIZATION NAME AND ADDRESS
National Bureau of Standards
Fluid Engineering Division
Washington, DC 20234
10. PROGRAM ELEMENT NO.
B113, CAZB1B
11. CONTRACT/GRANT NO.
IAG No. EPA-78-D-X0024-1
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory--Cin. , OH
Office of Research and Development
U.S. Environmental Protection Agency
13. TYPE OF REPORT AND PERIOD COVERED
Handbook--! 0/1 /78-9/30/81
14. SPONSORING AGENCY CODE
EPA/600/14
Project Officer: Walter W. Schuk
Telephone - (513) 684-2621
16. ABSTRACT
Parshall and Palmer-Bowl us flumes are suitable for in-plant open channel
flow measurement of raw wastewater and treated effluent as well as wastewater in
intermediate stages of treatment.
Parshall flumes arc empirical devices which must be fabricated and installed
according to specific requirements in order to yield the "standard" values of
discharge. The discharge of Palmer-Bowl us flumes can be determined analytically
within specified error limits provided that described criteria for construction
and installation are met.
The accuracy of a flume-based measuring system depends upon a combination of
the accuracies of the flume itself and the secondary instrumentation. The basic
uncertainty of properly constructed and installed flumes is about ± 3 percent. If
this uncertainty is unacceptable to the user or if there are fabrication and
installation conditions, as described in the report, for which additional errors
cannot be estimated, a field calibration of the flume must be made. Suggested
methods of calibrating and monitoring the performance of the flumes and secondary
instruments are described.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
C. COSA n l-'iclil. Croup
PFLEASE TD PUBLIC
; 19. -.SECURITY CLASS .'T/n.v i
\ UNCLASSIFIED
20 jEC'wRITV CLASS ."'in .-.jkv
UNCLASSIFIED
121 NO. JF r>AilcS
64
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DISCLAIMER
Although the information described in this document has been funded
wholly or in part by the United States Environmental Protection Agency
through assistance agreement number EPA 78-D-X0024-1 to National Bureau of
Standards, it has not been subjected to the Agency's required peer and
administrative review and therefore does not necessarily reflect the views
of the Agency and no official endorsement should be inferred.
11
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FOREWORD
The U. S. Environmental Protection Agency was created because of in-
creasing public and Government concern about the dangers of pollution to the
health and welfare of the American people. Noxious air, foul water, and
spoiled land are tragic testimonies to the deterioration of our natural
environment. The complexity of that environment and the interplay of its
components require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem solu-
tion; it involves defining the problem, measuring its impact, and searching
for solutions. The Municipal Environmental Research Laboratory develops new
and improved technology and systems to prevent, treat, and manage wastewater
and solid and hazardous waste pollutant discharges from municipal and communi-
ty sources, to preserve and treat public drinking water supplies, and to mini-
mize the adverse economic, social, health, and aesthetic effects of pollution.
This publication is one of the products of that research and provides a most
vital communications link between the researcher and the user community.
Francis T. Mayo, Director
Municipal Environmental Research
Laboratory
iii
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ABSTRACT
Parshall and Palmer-Bowlus flumes are suitable for in-plant open channel
flow measurement of raw wastewater and treated effluent as well as wastewater
in intermediate stages of treatment.
Parshall flumes are empirical devices which must be fabricated and in-
stalled according to specific requirements in order to yield the "standard"
values of discharge. The discharge of Palmer-Bowlus flumes can be determined
analytically within specified error limits provided that described criteria
for construction and installation are met.
The accuracy of a flume-based measuring system depends upon a combina-
tion of the accuracies of the flume itself and the secondary instrumentation.
The basic uncertainty of properly constructed and installed flumes is about
+ 3 percent. If this uncertainty is unacceptable to the user or if there are
fabrication and installation conditions, as described in the report, for which
additional errors cannot be estimated, a field calibration of the flume must
be made. Suggested methods of calibrating and monitoring the performance of
the flumes and secondary instruments are described.
iv
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CONTENTS
Foreword
Abstract iv
1. Scope 1
2. Nomenclature and Definitions 2
2.1 Nomenclature 2
2.2 Definitions 2
3. Principles of Operation 5
3.1 Parshall Flume 5
3.2 Palmer-Bowlus Flumes 5
4. Specifications for Parshall Flumes 8
4.1 Dimensions 8
4.2 Depth Measurement 8
4.3 Depth-Discharge Relations for Free Flow 9
4.4 Limiting Conditions for Free Flow 9
4.5 Depth-Discharge Relations for Submerged Flow 9
4.6 Materials 10
5. Installation Requirements for Parshall Flumes 11
5.1 General 11
5.2 Slopes — 11
5.3 Satisfying the Requirements for Free Flow . 11
5.4 Approach Channel 12
5.5 Secondary Instruments 12
6. Specifications for Palmer-Bowlus Flumes 13
6.1 Geometry —' 13
6.2 Depth-Discharge Relations for Free Flow 13
6.3 Limiting Submergence 17
6.4 Materials 17
7. Installation Requirements for Palmer-Bowlus Flumes 18
7.1 Approach Channel 18
7.2 Slopes 18
7.3 Other Requirements 19
7.4 Secondary Instruments 19
8. Secondary Instruments 20
8.1 Components of Secondary Instrumentation 20
8.2 The Depth Measurement 20
8.3 Transmission 22
8.4 Accuracy 22
8.5 Other Requirements 22
9. Error Sources 23
9.1 Introduction 23
9.2 Parshall Flume Error Sources 23
9.3 Palmer-Bowlus Flume Error Sources 26
9.4 Error Sources in Depth Measurement 27
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10. Performance Checks and Calibrat'ions *• 30
10.1 Introduction 30
10.2 Checking the Secondary System 31
10.3 Calibrating the Primary Device (Flume) 39
11. Operation and Maintenance 45
11.1 Short Term 45
11.2 Long Term 46
12. References 47
Appendix 48
vi
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1. SCOPE
1.1 This practice describes the use of Parshall and Palmer-Bowlus flumes in
wastewater treatment plants and/or in the sewers leading to the plants.
The flumes are the primary elements of measuring systems which must also
include secondary instruments to measure depth.
1.2 This practice covers
- Specifications for the measuring system
- Recommendations for its installation
- Methods for calibrating the system
- Guidelines for its maintenance and performance monitoring.
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2. NOMENCLATURE AND DEFINITIONS
2.1 Nomenclature. Terms are defined here and where they first appear in the
text.
b = width of throat in Palmer-Bowlus flume
b = bottom width of trapezoidal throat
o
b = throat width at flow surface
c = tracer concentration, in flow measurement by dilution
f = friction factor
g = acceleration due to gravity
Ah = depth lag in stilling well, equation [8]
£ = length of stilling well pipe
m = side slope of trapezoidal throat
n = exponent in Parshall flume equation
q = tracer injection rate, in flow measurement by dilution
w = fluid weight per unit volume
y = depth of flow
A = area of flow cross section
A = area of stilling well, equation [8]
A = area of connector pipe, equation [8]
C = coefficient in Parshall flume equation
C' = coefficient in equation [8]
C = discharge coefficient
C = velocity of approach factor
D = float diameter
E. = specific energy above crest of Palmer-Bowlus flume
F = force required to move float
H = depth, for flowrate determination in Parshall flume
3.
H, = depth, for submerged flowrate in Parshall flume
H = depth, for submerged flowrate in Parshall flume
H.. = upstream depth over crest of Palmer-Bowlus flume
L = throat length, Palmer-Bowlus flume
Q = flowrate
V = velocity of flow
W = throat width, Parshall flume
A = float lag
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2.2 Definitions
2.2.1 Accuracy — The closeness of a measured result to an accepted
"true" value.
2.2.2 Boundary layer — In a flow that is otherwise essentially fric-
tiouless, a (usually relatively thin) zone of wall influence in
which the velocity decreases to zero at the boundary.
2.2.3 Critical flow — A minimum specific-energy condition for a given
open channel flowrate, wherein the average velocity is equal to
the velocity of shallow-water waves in that depth; see also
Fronde number, Subcritical flow, Supercritical flow.
2.2.4 Fluiie — In this context, a device that constricts an open chan-
nel flow in such a way that the volumetric flowrate is determin-
ablcs as a function of a measured depth or depths.
2.2.5 Free flow — In this context, a condition in which the flow depth
downstream of the flume is not high enough to affect the flow
over the flume and the flowrate can be determined from a single
upsuream depth measurement. See also Submerged flow.
2.2.6 Fronde number — A dimensionless number equal to the velocity
div:.ded by the square root of the product of the depth of flow
and the acceleration due to gravity. A Froude number of unity
corresponds to critical flow. See also Critical flow, Subcriti-
cal flow, Supercritical flow.
2.2.7 Head — In this context, a height of liquid above a specific
elevation, e.g., the flume crest.
2.2.8 Hydraulic jump — A discontinuous transition from supercritical
to iiubcritical flow usually accompanied by considerable turbu-
lenne and/or gravity waves.
2.2.9 Invert — The inside bottom of a conduit.
2.2.10 Precision — A measure of the reproducibility or repeatability of
a measurement.
2.2.11 Prinary element — The device (in this case a flume) which
creates a hydrodynamic condition that is sensed by the secondary
elenent.
2.2.12 Repeatability — See Precision.
2.2.13 Scow float — An in-stream float, usually mounted on a hinged
canl:ilever.
2.2.14 Secondary instrument — A device (in this case for depth measure-
ment:) which senses a measurable parameter characteristic of the
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flow pattern created by the primary (flume). The secondary in-
strument often converts the measured depth to a flowrate readout.
2.2.15 Specific energy — The energy of an open channel flow referenced
to the channel bottom; in a rectilinear flow, this is the sum of
the depth and velocity head.
2.2.16 Stilling well — A small reservoir connected through a constrict-
ed passage to the main channel so that the depth measurement can
be made under quiescent conditions.
2.2.17 Subcritical flow — Free surface flows with Froude number less
than 1.0; disturbances can travel upstream, so that downstream
conditions can affect upstream flows.
2.2.18 Submerged flow — A condition in which the flow depth downstream
of the flume is high enough to affect the flow over the flume (by
partially "submerging" the overfall from the flume crest). In
this case both downstream and upstream depth measurements are
needed to determine the flowrate.
2.2.19 Supercritical flow — Free surface flows with Froude number
larger than 1.0; disturbances cannot travel upstream so down-
stream conditions do not affect the flow. For a given discharge,
supercritical flow features lower depths and higher velocities
than subcritical flow.
2.2.20 Velocity head — A measure of the kinetic energy of the flow and
equal to the square of the average velocity divided by twice the
acceleration due to gravity.
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3. PRINCIPLES OF OPERATION
3.1 Parshall Flume
3.1.1 The general shape of the flume is seen in figure 1. Upon entering
the flume the incoming flow passes through a section of lateral
convergence and, when under "free flow" conditions, passes through
a critical flow condition when it drops over the crest formed by
the steeply sloped throat.
3.1.2 Depth-Discharge Relations.
3.1.2.1 With free flow as depicted in figure 1, the flowrate is
related to the depth measured at a specified location by
an equation of the form
Q = CH" [1]
a
where Q is the flowrate, H is the depth measured as in-
dicated in paragraph 4.3.if and C and n are empirical
constants which vary with flume size and are given in
Table 1 of section 4.3.
3.1.2.2 The flume can also operate in a "submerged flow" mode,
which occurs when the downstream depth becomes so high
that the break in the floor slope of the flume can no
longer be a complete control point for the flow. In
submerged flow, two depths must be measured in order to
determine the flowrate. Therefore, it is highly desira-
ble that the installation be designed for free flow, for
which limiting submergence conditions are given in
section 4.4.2.
3.1.3 Advantages of the Parshall flume include a relatively small head
loss and a capability for self-cleansing. A disadvantage is its
empirical basis, which makes it difficult to adjust analytically
for non-standard geometries.
3.2 Palmer-Bowlus Flumes
3.2.1 The Palmer-Bowlus flume differs from the Parshall flume in that
it is a form of long-throated flume in which the channel width is
constricted and/or the floor is raised to cause critical flow in
a prismatic throat, as in figure 2. The flowrate then is a func-
tion of the upstream depth.
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A-A
Figure 2. Example of Palmer-Bowlus flume.
3.2.2 If it is assumed that an essentially rectilinear flow exists in
the throat, a one-dimensional treatment of the energy balance be-
tween an upstream section and a critical-flow section in- the throat
will yield a theoretical expression for flowrate in terms of up-
stream head. Corrections for friction effects can also be added.
3.2.3 The main advantages of Palmer-Bowlus flumes are their amenability
to theoretical analysis and their adaptability for insertion into
circular sewers at manholes.
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4. SPECIFICATIONS FOR PARSHALL FLUMES
4.1 Dimens ions
4.1.1 Parshall flumes are identified by throat width, e.g., a 1-foot
(0.305m) flume; specifying the throat size fixes all other dimen-
sions of the flume in accordance with figure 1 (reference 12.1).
4.1.2 Because exponents and coefficients for equation [1] have been ex-
perimentally determined using flumes with the dimensions in figure
1, it is imperative that installed flumes exactly match those
specified dimensions. Limited exceptions are cited in the
following.
4.1.2.1 The upstream wingwalls are sometimes eliminated, particu-
larly in sewage flows. Possible effects on accuracy are
covered in section 9.2.2.1.
4.1.2.2 If the flume operates in the free-flow mode, small devia-
tions in the dimensions of the diverging section down-
stream of the throat are unlikely to introduce errors.
4.2 Depth Measurement
4.2.1 The depth H must be measured at location "a" in figure 1. How-
ever, there are cases where measurement at the corresponding
longitudinal position along the flume centerline will not intro-
duce significant errors. See section 9.2.2.1.
4.2.2 If a second depth measurement is needed for submerged flow, it
must be made at location "b" in figure 1; but for 1, 2, and 3-inch
flumes, this measurement is made at location "c". See figure A.4
for relationship between R, and H .
4.2.3 A stilling well (not shown in figure 1) is usually desirable or
necessary to accomplish the depth measurement. Sometimes the
stilling well is furnished as a structurally integral part of a
commercial flume. In that case the stilling well must conform to
the specifications given in section 8.2.3.
4.2.4 The hole or slot in the sidewall, which connects to a stilling
well or secondary device either directly or through a short pipe,
must
- Have a projection-free and perpendicular junction with the in-
side wall, which should be smooth in the vicinity of the hole;
see also section 8.2.4.
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- Be located as low as possible along the wall consistent with the
avoidance of sediment or sludge layers, but certainly Below the
minimum anticipated surface elevation. See figure 1 for H,
hole.
4.2.5 Depth-measuring devices are covered in section 8.
4.3 Depth-Discharge Relations for Free Flow
4.3.1 Values of C and n for use in equation [1] are given Table 1, along
with the maximum flowrate for each size of flume. This table is
based on H measured in feet and Q in cubic feet per second. Depth-
discharge aata developed from Table 1 and equation [1] are given
in tabular form in Table A.I in the Appendix for flume sizes to
8 feet.
4.3.2 Values of C and n for metric units (Q in cubic meters per second)
are given in table A.2 in the Appendix. English units have been
given precedence in this report mainly 'because they are still
commonly found in field practice among Parshall flume users.
4.3.3 The estimated accuracy of the depth-discharge relations for free
flow in properly installed and operated Parshall flumes is +_ 3
percent.
4.3.4 The permissible depth range for each flume can be noted in Table
A.I in the Appendix.
4.4 Limiting Conditions for Free Flow
The limiting condition for
submergence ratio, H /H, , where H and H, are t
at points "a" and "b," respectively (figure 1).
4.4.1 The limiting condition for free flow is expressed in terms of the
the depths measured
Both are refer-
enced to the crest elevation.
4.4.2 The maximum submergence ratios for free flow are:
H /H < 0.5 for 1-in, 2-in and 3-in flumes;
b a
H./H < 0.6 for 6-in and 9-in flumes;
b a
H,/H < 0.7 for 1-ft to 8-ft flumes; and
b a
1L/H < 0.8 for 10-ft to 50-ft flumes.
b a
4.5 Depth-Discharge Relations for Submerged Flow
4.5.1 Parshall flume installations for sewage treatment plants should be
designed for free flow (section 5.3) because free-flow secondary
instrumentation is much simpler. Also, the basic accuracy of the
free-flow head-discharge relations is higher than those for sub-
merged flow. However, in the event that a flume is found to be
submerged, curves are presented in figures A.I through A.8 in the
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TABLE 1
FREE FLOW VALUES OF C AND n FOR PARSHALL FLUMES (EQUATION [1])
Throat Width
W
1 in
2 in
3 in
6 in
9 in
1 ft
1.5 ft
2 ft
3 ft
4 ft
5 ft
6 ft
7 ft
8 ft
10 ft
12 ft
15 ft
20 ft
25 ft
30 ft
40 ft
50 ft
C
0.338
0.676
0.992
2.06
3.07
4.00
6.00
8.00
12.00
16.00
20.00
24.00
28.00
32.00
39.38
46.75
57.81
76.25
94.69
113.13
150.00
186.88
n
1.55
1.55
1.55
1.58
1.53
1.522
1.538
1.550
1.566
1.578
1.587
1.595
1.601
1.607
1.6
1.6
1.6
1.6
1.6
>.6
1.6
1.6
Max.
cfs
0.2
0.5
1.1
3.9
8.9
16.1
24.6
33.1
50.4
67.9
85.6
103.5
121.4
139.5
200
350
600
1000
1200
1500
2000
3000
q
mgd
0.13
0.32
0.71
2.52
5.75
10.4
15.9
21.4
32.6
43.9
55.4
66.9
78.5
90.2
Appendix for determining flowrate based on H and a manually mea-
sured FL until repairs can be made or until submerged-flow second-
ary instrumentation can be installed. Submergence ratios higher
than 95 percent are not permitted in any case.
4.6 Materials
4.6.1 The roughness of the flume surface shall not be greater than that
corresponding to a smooth concrete finish.
4.6.2 Flume and stilling-well surfaces shall have appropriate corrosion
resistance for the flowing liquid.
10
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5. INSTALLATION REQUIREMENTS FOR PARSHALL FLUMES
5.1 General
5.1.1 The objective of the installation requirements is to insure that
the flow entering the flume is tranquil and uniformly distributed,
and simulates as closely as possible the conditions under which
the "standard" depth-discharge relations (Table 1) were originally
obtained.
5.1.2 Owing in part to the empirical nature of the flume equations, it
is often difficult to quantify the errors introduced by poor in-
stallation practices. Available information is detailed in
section 9.
5.2 Slopes
5.2.1 The flume must be constructed or installed so that the floor of
the converging section (figure 1) is level longitudinally and
laterally consistent with careful field measurement of level.
See also section 9.2.3.
5.2.2 Permissible slope upstream of the flume is governed in part by the
requirements of section 5.4.2.
5.3 Satisfying the Requirements for Free Flow
5.3.1 In cases where the downstream depth makes flume submergence a
possibility, free-flow performance can be insured at the design
stage by following a procedure that is best illustrated by using
a design example. More detailed design examples for various flume
sizes are given in reference 12.1.
5.3.1.1 Consider.a case in which the maximum anticipated flowrate
is 10 ft /s (0.283 m /s) and the maximum expected down-
stream depth is 1.80 ft (0.548 m). A 1-ft (0.305 m) flume
is the minimum size for this discharge (Table 1). From
section 4.4.1, the maximum permissible submergence is 70
percent. From Table A.I, H is 1.825 ft (0.566 m) so H
cannot exceed 0.70 x 1.825 = 1.278 ft (0.390m). At the
free-flow limit for this flume size the water surface
elevation at R. is, for practical purposes, the same as
the downstream elevation (figure 3)(12.1). Therefore, the
flume crest should be set above the bottom of the down-
stream channel by at least (1.80-1.28) = 0.52 ft (0.158 m).
11
-------
Figure 3. Setting flume elevation.
5.3.2 In principle a flume which operates submerged can be repaired by
inserting a higher floor (while retaining the overall bottom
shape), provided that upstream conditions and deposition considera-
tions permit this.
5.4 Approach Channel
5.4.1 Quantitative standards or specifications do not exist for the
length of the approach channel to the flume. It must be straight
and smooth for a long enough distance to provide a "uniform" velo-
city distribution and a tranquil water surface at the wingwall en-
trance. For this purpose,"uniform" velocity distribution is de-
fined as (at least) that associated with fully developed flow in
a long straight concrete channel of good surface quality. A later-
ally symmetrical distribution in which the maximum velocity occurs
above mid-depth at or near the vertical axis and does not exceed
about 20-25 percent of the average velocity could be considered
to satisfy this requirement.
5.4.1.1 The approach lengths cited for long-throated flumes in
section 7.1 can serve as conservative requirements for
the Parshall flume.
5.4.1.2 The adequacy of the entrance flow can also be demonstra-
ted by experimental techniques such as velocity traverses
with current meters or by other techniques provided their
adequacy for this purpose is demonstrable.
5.4.2 If the flow in the upstream channel is supercritical, a hydraulic
jump should be forced to occur at least 30 H upstream of the
flume.
5.4.3 See section 9.2.4 for effects of departures from these conditions.
5.5 Secondary Instruments
5.5.1 Requirements for secondary-instrument installation are covered in
section 8. See also section 4.2 for depth measurement locations
and stilling-well requirements.
12
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6. SPECIFICATIONS FOR PALMER-BOWLUS FLUMES
6.1 Geometry (Figure 2)
6.1.1 Throat.
6.1.1.1 The throat of the Palmer-Bowlus flume must be prismatic.
Within this constraint the throat cross-section can have
any reasonable shape, e.g., rectangular, trapezoidal,
that can be formed by a bottom rise and/or sidewall con-
striction in the channel. It must be sufficiently con-
strictive to produce critical flow.
6.1.1.2 The length, L, of the throat should preferably be about
1.5 times the maximum anticipated upstream specific
energy (referenced to the throat elevation). In sewers,
this length should be at least equal to the pipe diameter.
6.1.2 The entrance and exit transition slopes upstream and downstream of
the throat should be the same and must be no steeper than 1 on 3,
and preferably 1 on 4.
6.1.3 Depth Measurement.
6.1.3.1 The depth-measurement location shall be one to two times
the maximum depth (referenced to throat elevation) up-
stream of the flume entrance.
6.1.3.2 Other depth stations closer to the flume can be used pro-
vided that a rating equation for the selected location is
furnished with the flume or alternatively it can be shown
that there is no significant surface drawdown at that
location.
6.1.3.3 If a stilling well is used, see sections 4.2, 8.2.3 and
8.2.4.
6.2 Depth-Discharge Relations for Free Flow
6.2.1 An energy balance between the depth station (subscript 1) and the
throat (subscript 2) states that
El = y2 + V2/2g = y2 + Q2/2g A2 [2]
where E.. is the specific energy (depth plus velocity head) refer-
enced to the throat elevation and is for the moment considered con-
13
-------
stant along a frictionless flume; y~ is flow depth; g is the accel-
eration due to gravity; and V is the uniform velocity in a cross-
section of area A. The flow at section 2 is critical, so that for
minimum specific-energy
dE/dy = 1 - (Q2/gA3) dA/dy =0 [3a]
and
qV/gA3 = 1 [3b]
c c
where b is the throat width at the flow surface; and the sub-
script c denotes the critical flow condition. For a given throat
geometry, equations [2] and [3b] can be combined into an expression
for Q in terms of E.. , as given in the following examples.
6.2.1.1 For rectangular throats,
Q = Cd (2/3)3/2 b g1/2 El3/2 [4]
where b is the throat width. Here a discharge coefficient,
C , , has been applied to take into account boundary-layer
growth along the throat and other hydrodynamic effects.
6.2.1.2 For trapezoidal throats, equation [2] becomes
Q = Cd (boyc/E2 + my2/E2)(l - y^)172 (2g)1/2 E [5]
where b is the width of the throat bottom and m is the
horizontal-to-vertical sidewall slope. Equation [5] is
used in conjunction with Table 2 (reference 12.2).
6.2.1.3 Equations [4] and [5] are expressed in terms of E but
the head H. is the parameter that is actually measured
(figure 2). Therefore, these equations can be used
directly only when V /2g is negligible relative to H;
otherwise, they are modified as follows:
- For rectangular throats it is convenient to incorporate
this approach velocity effect in a coefficient C , so
that equation [4] becomes
Q = Cv Cd (2/3)372 g172 b H1372 [6]
with
o 7 1/7
Cv = (1 + QV2gA^H1)J// [ha]
and C is determinable by a trial procedure.
- For trapezoidal throats the approach-velocity effect
cannot so conveniently be lumped into a C term, but
equation [5] can be solved iteratively starting with
the measured H., in place of E.. and correcting with the
computed V /2g.
14
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TABLE 2
Y /E, AS A FUNCTION OF m AND En/b FOR TRAPEZOIDAL SECTIONS (REFERENCE 12.2)
c 1 1 o
Vbo
0
.02
.04
.06
.08
.10
.12
.14
.16
.18
.20
.22
.24
.26
.28
.30
.32
.34
.36
.38
.40
.50
.60
.70
.80
.90
1.00
1.20
1.40
1.60
1.80
2
3
4
5
10
00
Throat side slopes, horizontal
1/2:1
.667
.668
.670
.671
.672
.674
.675
.676
.678
.679
.680
.681
.683
.684
.685
.686
.687
.689
.690
.691
.692
.697
.701
.706
.709
.713
.717
.723
.729
.733
.737
.740
.753
.762
.768
.782
.800
1:1
.667
.670
.672
.675
.678
.680
.684
.686
.687
.690
.692
.694
.696
.698
.699
.701
.703
.705
.706
.708
.709
.717
.723
.728
.732
.737
.740
.747
.752
.756
.759
.762
.773
.778
.782
.791
.800
1 1/2:1
.667
.671
.675
.679
.683
.686
.690
.693
.696
.698
.701
.704
.706
.709
.711
.713
.715
.717
.719
.721
.723
.730
.737
.742
.746
.750
.754
.759
.764
.767
.770
.773
.781
.785
.788
.794
.800
2:1
.667
.672
.677
.683
.687
.692
.696
.699
.703
.706
.709
.712
.715
.718
.720
.723
.725
.727
.729
.731
.733
.740
.747
.752
.756
.759
.762
.767
.771
.774
.776
.778
.785
.788
.791
.795
.800
to vertical
3:1
.667
.675
.683
.690
.696
.701
.706
.711
.715
.719
.723
.726
.729
.732
.734
.737
.739
.741
.743
.745
.747
.7-54
.759
.764
.767
.770
.773
.776
.779
.781
.783
.785
.790
.792
.794
.797
.800
4:1
.667
.678
.687
.696
.703
.709
.715
.720
.725
.729
.733
.736
.739
.742
.744
' .747
.749
.751
.752
.754
.756
.762
.767
.771
.774
.776
.778
.782
.784
.786
.737
.788
.792
.794
.795
.798
.800
15
-------
6.2.2 It is sometimes possible to estimate C, from boundary-layer equa-
tions. However, in view of uncertainties in this computation it
is reasonable to use average values of C that have been accumu-
lated from experiments. These are shown in figure 4.
1.05
1.00
0.95
0.90
— """ *- Approximate limits of
collected data for long-
throated flumes (12.2)
0.81
0.1 0.2
0.3
0.4
0.5 0.6
E./L
0.7
08
0.9
1.0
Figure 4. C values for long-throated flumes.
6.2.3 Depth-discharge relations furnished by the manufacturer can be
used in place of the foregoing equations (see section 6.2.6).
6.2.4 Limiting Conditions.
6.2.4.1 At minimum flow H should not be less than the larger of
0.1 L or 0.2 ft (0.06m). At maximum flow H should pref-
erably not exceed about 0.6 L.
6.2.4.2 The width of a rectangular throat (or. the average width
of a trapezoidal throat) should preferably be larger
than 0.33 ft (0.10 m).
6.2.5 Accuracy.
6.2.5.1 The accuracy of these depth-discharge relations is esti-
mated to vary from + 3 percent at large H /L to + 5 to 6
percent at low H../L. The decrease in accuracy reflects
the increased importance and uncertainty of C at low
flows. d
16
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6.2.6 Ratings Furnished by Manufacturer.
6.2.6.1 The manufacturer of a prefabricated flume should provide
the user with the head-discharge relation (equation,
table or curve) for the flume even if the flume is of
standard geometry and even if the secondary instrumenta-
tion is an integral part of the flume.
6.2.6.2 If the prefabricated flume is non-standard in any way,
the manufacturer should also provide analytical or ex-
perimental information on how the head-discharge relation
was developed and an accuracy estimate.
6.3 Limiting Submergence
6.3.1 Free flow will prevail if the downstream surface elevation (ref-
erenced to the throat floor) is less than the throat critical
depth, y . This provides a conservative limit for design.
Slightly higher downstream depth limits may occur depending
on the energy-recovery of the downstream transition slopes.
6.4 Materials
6.4.1 The roughness of the flume surface shall not be greater than that
corresponding to a smooth concrete finish.
6.4.2 Flume and stilling well surfaces shall have appropriate corrosion
resistance for the flowing fluid.
17
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7. INSTALLATION REQUIREMENTS FOR PALMER-BOWLUS FLUMES
7.1 Approach Channel
7.1.1 The objective of the upstream channel requirements is to insure
that a uniformly distributed flow with a tranquil surface ap-
proaches the flume. A "uniform" distribution in this context is
described in section 5.4.1.
7.1.2 The approach channel shall be straight, free of projections and
relatively smooth for the distances given below.
7.1.2.1 If the throat width is less than half the width of the
approach channel, the straight upstream length shall be
the larger of 20 throat widths or 10 H .
7.1.2.2 If the throat width is larger than half the width of the
approach channel, the required straight approach length
is increased to 10 approach channel widths.
7.1.2.3 Specifications 7.1.2.1 and 7.1.2.2 assume that no ex-
treme conditions exist at the inlet to the specified
approach length. For example, if a small diameter pipe
discharges a high velocity flow into the channel a
longer approach would probably be needed to dissipate
the jet.
7.1.2.4 If the foregoing approach conditions are not met, the
adequacy of the entrance flow can still be demonstrated
as in section 5.4.1.2.
7.1.3 If flow in the upstream channel is supercritical, a hydraulic
jump should be forced to occur at least 30 H.. upstream of the
flume.
7.1.4 See section 9.3.2 for effects of departures from these conditions.
7.2 Slopes
7.2.1 The Palmer-Bowlus flume must be installed so that the throat, floor
is level longitudinally and transversely consistent with careful
field level measurement.
7.2.2 Maximum upstream slopes are governed in part by section 7.1.3.
18
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7.3 Other- Requirements
7.3.1 Flume inserts must be installed so that all of the flow enters
the throat, that is, there must be no leakage between the entrance
transition and the channel walls.
7.3.2 The flume must be installed so that it operates in a free flow
mode.
7.4 Secondary Instruments
7.4.1 Requirements for installation of secondary instruments are
covered in section 8.
7.4.2 See section 6.1.3 for depth-measurement locations.
19
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8. SECONDARY INSTRUMENTS
8.1 Components of the Secondary Instrumentation
8.1.1 In cases where a continuous record of flow is required, the
minimum secondary system must contain a depth measuring device
and a recorder. The user then must manually convert the depth
record to flowrates using either the equations of sections 4 and
6 or depth-discharge ratings supplied by the manufacturer.
8.1.2 Commercial secondary devices frequently incorporate internal con-
version of the measured depth to a recorded flowrate. The equa-
tion used for this conversion shall be made known to the user.
8.1.3 Transmission of the signal to a central control console or compu-
ter may be required. See section 8.3. In this case a visual
readout at the flume site shall be provided in addition.
8.2 The Depth Measurement
8.2.1 Continuous measurements of the water depth above the flume crest
can be made with several types of sensor including, but not re-
stricted to, the following:
- Floats, cylindrical and scow-type;
- Pressure sensors, e.g., bubble tubes, diaphragm gages;
- Acoustic gages;
- Electrical gages, e.g., resistance, capacitance, oscillating
probes.
8.2.2 Under emergency conditions, frequent manual readings with staff
gage or point gage can approximate a continous record. However,
for the purposes of this practice, manual readings are used only
for calibration and performance monitoring of automatic on-line
devices.
8.2.3 Stilling Wells.
8.2.3.1 A stilling well is required in cases where a wire-
supported cylindrical float is used for depth measurement
and in any situation where the water surface in the flume
is ruffled or wavy.
8.2.3.2 The stilling well must extend vertically far enough to
cover the full range of depth, without risk of a float
.resting on the bottom at low flow or protruding beyond
the top of the well at high flow.
20
-------
8.2.3.3 The diameter (or area) of the stilling well is governed
by the following requirements:
- If a float is used, there must be a clearance of at
least 0.1 ft (0.030 m) between the float and the wall
of the stilling well. This clearance should be in-
creased to 0.25 ft (0.076 m) if the well is constructed
of concrete or other rough material. The diameter of
the float itself may be governed in part by permissible
float-lag error (section 9.4.3).
- The maximum stilling well size must be selected with a
view toward possible response lag (section 9.4).
- Depth measuring devices other than the float may impose
size requirements on the stilling well. For example,
acoustic depth gages require a large enough well to
avoid interference from wall reflections. Manufacturers
shall inform the user about special stilling-well re-
quirements for their sensors.
8.2.3.4 The construction of the stilling well must be watertight
so that the only communication with the flume is through
the connecting hole or pipe.
8.2.3.5 Provision must be made for cleaning the stilling well
or flushing for removal of accumulated solids.
8.2.4 Connector Between Stilling Well and Flume.
8.2.4.1 The hole, slot or pipe connecting the stilling well to
the flume must be small enough to accomplish its basic
purpose of damping wave and surge effects. Yet it must
be large enough to stay open and also avoid introducing
a lag in the stilling well response to changing flows in
the main channel (see section 9.4.3). A hoLe or pipe
having a cross-sectional area about I/1000th of the
stilling well area or a diameter of about 1/2 in (13 mm)
is often adequate for this purpose.
8.2.4.2 When a connecting pipe is used, it is recommended that a
valve be installed in the line so that the stilling well
can be isolated for cleaning or servicing.
8.2.4.3 If the flow contains solids or other contaminants, it is
recommended that a small purge flow of tap water be added
to the stilling well to aid in keeping the connector
clean. This water should be added at a low enough rate
to cause an imperceptible depth increase in the stilling
well. For example, if the head difference due to purge
flow is not to exceed 0.001 ft (0.3 mm) and the connector
is effectively a very short 1/2-inch diameter pipe, the
flow must be less than about 0.13 gpm (0.8 cc/s).
21
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8.2.4.4 See section 4.2.4 for conditions on the flume tap.
8.3 Transmission
8.3.1 Transmission of measurements to a central location can be done
either by electrical or pneumatic means, but pneumatic trans-
mission should be limited to distances shorter than 1000 ft or
300 meters.
8.3.2 The signal shall be transmittable in computer-compatible form or
be capable of future conversion to that form.
8.4 Accuracy
8.4.1 In a system that records depth only, the accuracy of the depth
registered at the indicator/transmitter shall be within 1 percent
of the maximum depth to be measured, with repeatability within
1/2 percent.
8.4.2 In a system that records flowrate, the accuracy of the flowrate
registered at the indicator/transmitter shall be within 2 percent
at the maximum flowrate to be measured and within 3 percent at
one-half of the maximum flowrate, with repeatability within 1/2
percent.
8.4.3 The receiver/recorder accuracy, or the difference between the on-
site indicator and control-room chart, shall be within 1 percent
of the maximum reading.
8.4.4 The foregoing accuracy requirements are expressed in terms of maxi-
mum depth or flow and may have to be converted to terms of full
scale in order to conform to the accuracy statements of many com-
mercial devices. It is clearly important to avoid selecting de-
vices that will be operating at small fractions of their capacity.
8.4.5 Errors in depth measurement other than those due to internal in-
accuracies in the secondary instruments are covered in section 9.
8.5 Other Requirements
8.5.1 The stilling well and secondary equipment must be protected
against freezing where necessary.
8.5.2 Manufacturers shall furnish installation, maintenance, repair and
operation information on the secondary instruments in user manuals.
8.5.3 Manufacturers shall furnish to the users all available information
relevant to the accuracy and precision, of the instruments such as
any known temperature, pressure or humidity dependence, as well as
interferences and limitations in their use.
22
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9. ERROR SOURCES
9.1 Introduction
9.1.1 Section 9.2 describes effects of commonly found departures from
standard conditions for Parshall flumes; section 9.3 does the
same for Palmer-Bowlus flumes. Most errors in depth measurement
are common to both types of flumes and are covered in section 9.4.
9.1.2 See section 10.2 for methods of estimating total system error.
9.2 Parshall Flume Error Sources
9.2.1 Depth-Discharge Relations.
9.2.1.1 The free-flow depth-discharge data given in section 4.3
should be considered to introduce errors in discharge of
up to + 3 percent. Errors for submerged flow are larger.
9.2.1.2 Any uncorrected errors introduced by the following
sources will add to the basic 3 percent error.
9.2.2 Flume Geometry.
9.2.2.1 The curved wingwalls and entrance ramp (figure 1) are
sometimes eliminated, particularly in sewage flows where
. it is desirable to maintain upstream velocities high
enough to avoid deposition. This change has these possi-
ble effects of unknown magnitude: first, the capability
(provided by the "nozzle effect" of the wingwalls and
ramp) for flattening the incoming velocity distribution
is lost; second, the sudden change in direction of the
sidewall from the straight channel to the converging
wall of the flume causes lateral curvature in the en-
trance flow. The first effect may not have a discern-
ible effect on the performance if the approach flow is
essentially uniform to start with and if the flume is
small (see section 9.2.4.1). Any error from this source
is in the direction of underestimating the flowrate, i.e.,
the measured depth is too low for a given flowrate. The
second effect may be noticeable in large flumes, where
the abrupt change in direction could result in an in-
correct reading at the depth station.
9.2.2.2 If the throat width deviates from the prescribed width
by a small amount (a few percent), the standard discharge
23
-------
can be corrected by multiplying it by the width ratio, in
the case of 1 to 3-inch flumes (reference 12.1). In the
absence of data on larger flumes such adjustments should
probably be restricted to changes smaller than 1 percent.
9.2.3 Slope.
9.2.3.1 If the flume floor (section 5.2.1) slopes downward in the-
direction of flow, use of the measured depth in the stan-
dard rating equation will result in a computed flowrate
less than the actual. In a given flume this error in-
creases as the discharge decreases. Laboratory experi-
ments on a 3-inch flume at a 0.01 slope showed a discharge
error of 3 percent at H =0.5 ft (0.15 m) increasing to
about 10 percent at H = 0.15 ft (0.046 m).
td
9.2.3.2 It appears that if the slope does not exceed about 0.005,
an approximate correction can be made by referencing the
depth measurement to the elevation of the crest overfall.
However, this correction, which has been extrapolated
from unpublished experimental results on a 3-inch flume,
can serve for information and estimating purposes only
and cannot be employed as a standard except as agreed to
in specific cases.
9.2.3.3 No experimental information is available on the effect of
transverse slope on flow patterns in the flume. However,
to minimize the error the user should check to see that
Che depth measurement is still referenced to the crest •
centerline and correct it if necessary.
9.2.4 Approach Channel.
9.2.4.1 If the approach channel is not long, straight and smooth
enough to provide the approach flow described in section
5.4.1, the effects (if any) generally cannot be quanti-
fied. Certain qualitative judgments based on flume pro-
perties can be made as follows:
- Small flumes have (relatively) longer converging sec-
tions than the larger flumes and thus should be less
sensitive to approach conditions;
- Uneven velocity distributions (but still symmetrical in
plan view) tend to cause depth readings that err on the
low side and therefore underestimate the discharge.
9.2.4.2 When a partly full circular pipe discharges into the rec-
tangular approach channel of a Parshall flume, it is possi-
ble under certain conditions for a nominally subcritical
pipe flow to be drawn down to a supercritical condition
in the approach, particularly when the flume crest is at
the same elevation as the pipe invert. Caution must be
exercised during the design stage to avoid these situations.
24
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9.2.4.3 Certain upstream conditions cause serious surface waves
or surging which preclude good depth measurements. Apart
from the obvious case of having a hydraulic jump too close
to the flume, any full or nearly full pipe flow containing
large amounts of entrained air can feature severe surging
or instability at the outlet. Hydraulic jumps or drops in
approach pipes can create these circumstances, which can
be forestalled only by appropriate design.
9.2.5 Submergence.
9.2.5.1 Errors caused by ignoring the effect of downstream sub-
mergence can be computed from the information cited in
section 4.4. An example of these errors is shown in
figure 5 for a 1-ft flume as determined from figure A.7.
30
20
c
4>
U
« 10
\
\
•90% submergence
r70%
0.5 1.0 1.5 2jO 2.5
Head, ft
Figure 5. Errors in 1-ft Parshall flume discharge if
uncorrected for submergence.
9.2.5.2 The submergence can be checked by manually measuring the
depth at "b" and referencing it to the crest elevation.
However, the existence of a hydraulic jump downstream of
"b" can be taken as evidence of free flow.
25
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9.3 Palmer-Bowlus Flume Error Sources
9.3.1 Depth-Discharge Relations.
9.3.1.1 The flume equations developed in section 6.2 should be
considered to introduce errors in discharge of up to + 3
percent at intermediate and high values of the head-to-
throat length ratio.
9.3.1.2 Any uncorrected errors introduced by the following sources
will add to the basic 3 percent error.
9.3.2 Flume Geometry.
9.3.2.1 If the throat dimensions of the installed flume differ,
for whatever cause, from the nominal dimensions, correc-
tions can be made by the methods of section 6.2 provided
that the throat remains prismatic.
9.3.2.2 Excessive roughness of the flume surfaces will result in
C values lower than the average values given in figure
4, owing to increased energy loss and boundary-layer
thickness.
9.3.2.3 Deposits at the bottom of the approach to the flume due
to low upstream velocities effectively form a change in
geometry, for which the equations can be adjusted.
9.3.3 Slopes.
9.3.3.1 Downward slopes in the direction of flow will cause the
control (critical) point to shift from the downstream to
the upstream edge of the flume throat. This is a depar-
ture from the conditions for the derivations of equations
[5] and [6] and can cause an error of unspecifiable mag-
nitude in the discharge measurement. Small upward slopes
can be corrected for by referencing the depth measurement
to the downstream edge of the throat.
9.3.3.2 See section 9.2.3.3 for transverse slopes.
9.3.4 Approach Channel.
9.3.4.1 Approach conditions that cause non-uniform velocity dis-
tributions (but still symmetrical in plan view) will tend
to result in upstream depth readings and computed dis-
charges that are too low. The magnitude of this error
increases as the ratio of upstream velocity head to depth
increases. It is noted in this regard that excessive up-
stream roughness can increase the non-uniformity of the
upstream velocity distribution.
26
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9.3.4.2 Approach-channel Froude numbers larger than 0.6 will be
conducive to the formation of standing waves, which will
interfere with the depth measurement.
9.4 Errors Sources in Depth Measurement
9.4.1 General.
9.4.1.1 Errors described in section 9.4 must be combined with the
flume errors of sections 9.2 and 9.3 as shown in section
10.2 to obtain an estimate of the total measurement error.
9.4.1.2 It is noted from sections 4 and 6 that flume discharge
depends upon powers of measured depth of from 3/2 to 5/2,
and that the system error is therefore particularly sensi-
tive to errors in depth measurement.
9.4.1.3 Any error in referencing the zero depth to the elevation
of the flume crest will introduce an error in it that is
constant in magnitude over the flow range and therefore
relatively more important at low flows.
9.4.2 Float Gage Error.
9.4.2.1 A float-lag error is developed because a small change in
water level is necessary to develop the force needed to
overcome internal friction in the float device, i.e.,
pulley, gears, etc. The maximum lag error, A, for a
float and pulley can be shown to be, in compatible units,
A = SF/wirD2 [7]
where F is the force required to move the mechanism, D
is the cylindrical float diameter, and w is the weight
per unit volume of the flowing liquid.
9.4.2.2 The manner in which this error is distributed during the
flow cycle depends upon whether the readout or record is
set to read correctly during the rising stage, falling
stage or midway between. For example, a 6-inch (0.15 m)
diameter float requiring 2 ounces (57 g) to move has a
maximum (or potential) float lag error of 0.021 ft (0.64
cm), which can be halved by setting the index to a cor-
rect reading between the rising and falling stages.
9.4.2.3 Equation [7] shows that float-lag error can be reduced
by minimizing the force needed to move the float and by
using a large diameter float.
9.4.2.4 Pulley-type float gages are also subject to line-shift
error because, as the float moves, a portion of the sus-
pending line moves from one side of the pulley to the
27
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other. The potential error due to line shift can be com-
puted from equation [7], in which F is now a force
obtained by multiplying the weight of the line per unit
length by the maximum float-elevation change. Unless an
unusually heavy line is used, this error should be neg-
ligible for most flume installations, the depth ranges
usually being relatively small.
9.4.2.5 It is preferable that the line-and-pulley arrangement be
such that the counterweight is not submerged at higher
stages. If submergence does occur, there is an apparent-
ly smaller pull on the float and the error again can be
estimated from equation [7] using F as the buoyancy force
on the counterweight. Particular care should be taken to
keep the descending counterweight from landing on top of
the rising float.
9.4.3 Stilling Well Lag.
9.4.3.1 For a constant rate of depth change, dH/dt, in the flume,
the depth in the stilling well will lag by an amount,
Ah = (A /A )2 (dH/dt)2 (C'/2g) [8]
w p
Here A is the sectional area of the stilling well, A is
V P
the effective area of the connecting orifice or pipe, and
C* is a head loss coefficient given below.
- If the connector hole has a thick wall that makes it
essentially a very short pipe, C* is 1.5.
- If there is a connector pipe, the additional friction
loss in the pipe is taken into account by adding to the
foregoing 1.5 the value of fi /d, where J. and d are the
length and diameter of the pipe, and f is a friction
factor that depends upon velocity through the pipe and
on pipe roughness and is likely to be in the 0.05-0.10
range. See figure A.9 in the Appendix for estimating f.
- If there is a thin wall between flume and stilling well
so that the connecting hole is effectively a sharp edged
orifice, C' = 1 and, further, A should be taken as
about 0.6 of the hole area to account for contraction.
This error is likely to be small in usual treatment plant
situations where dH/dt is small.
9.4.4 Other Errors.
9.4.4.1 Humidity effects on recorder chart paper can introduce
errors of about 1 percent.
9.4.4.2 Manufacturers must provide, as part of the requirements
of section 8.5.3, enough information for users to esti-
mate errors introduced by depth sensors and all other
components of the secondary system. However, actual
28
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system errors can be determined only by comparison of in-
place measurements with independently made measurements
of known accuracy (section 10).
9.4.4.3 Some potential error sources are associated with specific
types of secondary instruments. These errors usually can-
not be quantified and only cautionary statements can be
made. For example:
- Acoustic depth-measuring devices may incorrectly sense
foamy surfaces. See also section 8.2.3.3.
- Bubbler-tube tips placed in a flowing liquid may be
subject to errors due to dynamic pressures, unless pro-
perly shaped.
- Grease coatings may affect some types of wire probes.
29
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10. PERFORMANCE CHECKS AND CALIBRATIONS
10.1 Introduction
10.1.1 Section 10 describes two types of performance checks or calibra-
tions. The first covers only the secondary instruments, while
the second covers the entire measuring system.
10.1.1.1 Calibrating only the secondary instrument is a suffi-
cient procedure when one of the following conditions
is met:
- The primary elements (flumes) meet all specifications
and installation requirements of sections 4 and 5
(Parshall) or sections 6 and 7 (Palmer-Bowlus); and
further, the basic accuracy of the primary (section
4.3.3 or 6.2.5) is satisfactory to the user.
- The flume and its installation do not satisfy all
specifications, but the departures from standard
conditions can either be corrected for analytically
or be assigned quantitative error limits, and the
resulting estimated accuracy is satisfactory to the
user; or adequate depth-discharge data is furnished
by the manufacturer.
- The user requires only precision or repeatibility
rather than accuracy, and it can be shown that any
departures from standard conditions for the primary
will not affect the repeatibility.
10.1.1.2 A complete calibration of the entire system must be
made when the conditions described in section 10.I.L.I
do not prevail. However, a calibration of the second-
ary system is still a necessary part of the complete
calibration. In this way the performance of the pri-
mary device (flume) can be isolated and future checks
need to include only the secondary instrument so long
as flow and channel conditions remain the same.
10.1.2 The performance checks described here can be used for acceptance
testing of recently installed equipment and for future routine
performance monitoring as part of an operations and maintenance
program.
30
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10.2 Checking the Secondary System
10.2.1 Reference-Depth Measurement.
10.2.1.1 In order to check the secondary instrument it is nec-
essary to make independent depth measurements and esti-
mate their accuracy. These measurements will usually
be made using a scale (staff gage) or preferably a
point gage as described in the following sections.
10.2.1.2 Staff gage. A scale graduated at least to hundredths
of feet (or to 0.005 m) should be mounted at the proper
location along the sidewall or in a stilling well.
- This scale should be sufficiently thin and stream-
lined in section to permit an easily readable inter-
face if it is placed in the main channel.
- The effective zero reading for this scale must be
carefully determined by referencing it to the proper
crest elevation. The specific manner in which this
is done is left to the user and will depend upon such
factors as whether the flow can be diverted around
the flume, accessibility, etc. The accuracy of the
selected procedure should be estimated for use in
section 10.2.2.
10.2.1.3 Point gage. The use of a point gage instead of a
staff gage is recommended, since more accurate read-
ings are likely. The requirements for the establish-
ment of the zero reading are the same as for the staff
gage.
10.2.1.4 When the flow surface is disturbed it becomes more
difficult to make accurate reference-depth readings
with either a staff gage or point gage, although the
latter can yield acceptable results in a ruffled sur-
face if the point is carefully adjusted to be alter-
nately immersed and free of the surface for equal
amounts of time. In principle, these problems can be
avoided by making the reference measurements in the
stilling well. However, this recourse is often pre-
cluded by line-of-sight or accessibility problems,
particularly when a float is in the well, unless an
auxiliary well is used. No matter how the reference-
depth measurement is made, an estimated error for it
must be agreed upon (section 10.2.2).
10,2.1.5 It is recommended that the staff gage or point gage
be left in place after the initial calibrations so
that it can be used for future maintenance checks.
31
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10.2.2 Reference-Depth Error.
10.2.2.1 In order to compare the secondary-instrument readings
with the reference measurements in an equitable way, it
is necessary to estimate the error in the latter.
10.2.2.2 The error in the measured reference head consists of a
combination of the zero-setting error and the systema-
tic and random reading errors. The random errors asso-
ciated with an unsteady surface can be reduced by using
the average of multiple readings. A systematic error
(relative to a single observer) may result, for exam-
ple, from the interpretation of the meniscus against
the scale. As an example, suppose that it is estimated
from consideration of the leveling method that the zero
was set to within 0.003 ft (1 mm) and that the reading
error for this field situation is 0.005 ft (1.5 mm).
Then the combined error in the reference-depth measure-
ment can be estimated as
•j 71/7
[0.003) + (0.005) ]' = + 0.006 ft (1.9 mm)
10.2.3 Checking a Depth Measurement/Recording Instrument.
10.2.3.1 Section 10.2.3 pertains to instruments which record the
depth only, as distinguished from those which record
flowrate directly. If the secondary instrument is of
the latter type, see section 10.2.5.
10.2.3.2 Check the manufacturer's literature to see that the
instrument installation and operation are in accordance
with recommended usage. Also check the instrument to
see that a range has been selected to permit the largest
available chart deflection at maximum depth.
10.2.3.3 At a convenient flowrate that is steady enough to per-
mit reliable readings, observe the reference depth
(section 10.2.1) and the recorder or readout depth for
the same time and compute the difference, AH.
10.2.3.4 Repeat step 10.2.3.3 at several depths covering the
anticipated flow range, in such a way that an indica-
tion of instrument repeatability is obtained.
- As an absolute minimum, three such points should be
obtained, i.e., corresponding to a low, medium ;md
high flow; but it must be noted that this procedure
gives no indication of instrument repeatability and
is correspondingly less authoritative for instrument
evaluation.
- If the flow is cyclic, points should be obtained for
both the rising and falling stages so that errors due
to float lag or gearing backlash will be visible.
32
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10.2.3.5
- In order to accumulate numerous points in a reasonable
time, it may be necessary to create depth changes arti-
ficially; for example, by manually backing up the flow
or by changing stilling-well levels independently of
the flume. In many cases such artifices are accept-
able (always provided that reference-depth measure- •
ments and corresponding error estimates can be made),
since only the secondary instruments are being check-
ed here. In general, this method should not be
applied to in-stream sensors, whose performance may
be affected by the velocity or ruffled surface of the
unaltered flow.
Make a plot of AH versus H as shown in figure 6. In-
clude also the error bands estimated in section 10.2.2
(labeled A in figure 6). If the scatter of the AH
points is small and apparently random, draw curve C
through them as shown; but if obvious systematic dif-
ferences appear between the points for the rising and
falling stages separate curves should be drawn. Add
another line, B, representing an acceptable AH beyond
the limits of band A (section 8.4).
O.06
.04
On?
0
o.oz
0.04
-nnc
B-
A-
A_
B-
^~L~
A-'V-
V
VA--^
A V
--•A-
__
0 0.2 0.4 0.6 0.8 1.0
H
Figure 6. A method of evaluating depth-measuring instruments.
33
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10.2.3.6 If curve C.is inside of band B, and if further the
scatter of the points around C is within prescribed
limits, the instrument is operating acceptably; if not,
see section 10.2.3.8.
10.2.3.7 Even if numerous AH points were obtained for figure 6,
it should be realized that only a relatively short term
effort was involved and no indication was obtained of
errors due to long term drifts, temperature and humidity
effects, general wear and other effects. Therefore:
- It is important to establish a program for routine
and regular inspection and maintenance of the second-
ary instrument (section 11.1.2).
- This regular inspection must include check points on
the depth measurement, using the reference depth gage
left in place from the original performance check, to
see that they still fall within the performance bands
established in figure 6.
10.2.3.8 If curve C falls outside of zone B, the following should
be noted:
- A constant displacement between B and C over the range
of depths suggests the possibility of a zero-shift
error in the secondary instrument. Should this be
the case, reset the zero or otherwise adjust for the
shift and repeat the procedure of this section
(10.2.3).
- If C is a sloping straight line, there may be a need
for gain or span adjustment in the secondary instru-
ment. Repeat the procedure after adjustment.
10.2.3.9 Sections 10.2.3.5 and 10.2.3.8 provide one type of per-
formance-test procedure that takes into account the un-
certainty in the measurements that the commercial in-
strumentation is compared against. This is only a
suggested procedure; other rationally based comparisons
can be agreed upon.
10.2.4 Estimating the Error of a Discharge Obtained with a Depth
Measuring Instrument..
10.2.4.1 Estimate the error in a single depth measurement by
quadratically combining the reference-depth error and
the scatter in the measured AH for a particular value
of H. Continuing with the example of section 10.2.2,
this gives with figure 6
[(0.006)2 + (0.004)211/2 i + 0.007 ft (2 mm)
To this should be added quadratically any systematic
residual error, which is 0.005 ft (1.5 mm) in the ex-
ample of figure 6, giving an estimated depth error of
34
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0.009 ft (2.7 mm). At H = 1.0 ft (0.30 m) this is a
relative depth error of 0.9 percent. (Note: If one
is working with a depth measurement that has been
transmitted from the flume site, this additional re-
ceiving/recording error should be included; section
8.4.) The estimated error in discharge for a Par-
shall flume or Palmer-Bowlus flume with rectangular
throat would be
7 21/2-
[(3.0) + (1.5 x 0.9) \' = 3.3 percent
Here the 3.0 percent represents the estimated error
in the flume coefficient (section 9.2.1.1 or 9.3.1.1)
and the factor of 1.5 (approximate in the case of
Parshall flumes) is the relative error in Q caused by
a unit relative error in H. This factor will be
larger for trapezoidal flumes, with a limiting value
of 2.5 for triangular throats. The actual value can
be determined for specific trapezoidal geometries
from equation [5] and Table 2.
10.2.4.2 It is noted from the foregoing computation that, no
matter how accurate the depth measurement, the accu-
racy of the flowrate determination is still limited
by the 3 percent uncertainty in the flume coefficient.
Therefore, any further reduction in the total estima-
ted error will require an in-place calibration of the
primary element. See section 10.3 for flume calibra-
tions.
10.2.5 Checking a Flowrate Measurement/Recording Instrument.
10.2.5.1 Section 10.2.5 pertains to instruments that sense the
depth but internally convert it to an indicated flow-
rate. Instruments that indicate only the depth were
covered in section 10.2.3.
10.2.5.2 Check the manufacturer's literature to see that the in-
strument installation and operation are in accordance
with recommended usage. Also check the instrument to
see that a range has been selected to permit the largest
available chart or indicator deflection at maximum
flow.
10.2.5.3 Determine the reference error from the product of the
reference-depth error (section 10.2.2) and the appro-
priate exponent of the head. For example, using again
the error of 0.006 ft (1.9 mm) from section 10.2.2,
for a 1-ft (0.305 m) Parshall flume operating at a
depth of 1.2 ft (0.46 m) the reference error would be
100 x 1.5 x 0.006/1.2 = 0.75 percent
35
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3 3
The flume discharges 5.28 ft Is (0.150 m /s)^at this
depth so that the reference error is 0.04 ft /s (0.0011
m /s). This computation should be made for the antici-
pated flow range and the reference errors plotted as
shown by curves A in figure 7. It is noted that the
basic flume coefficient uncertainty of 3 percent was
not included in this reference-error computation. The
reason is that the intent of section 10.2.5 is to check
the secondary instrument only, for initial calibration
or for acceptance purposes. The response of the second-
ary instrument is not a function of uncertainty in the
primary device (flume) and its performance evaluation
need not involve that uncertainty.
0.3
0.2
O.I
o
< 0
-O.I
-0.3
A ---
A ---
4
Q
Figure 7. A method of evaluating flowrate measuring instruments.
10.2.5.4 Add to curve A (figure 7) flowrates corresponding to
the allowable error in the secondary instrument (sec-
tion 8.4), giving curve B.
10.2.5.5 At a convenient flowrate that is steady enough to per-
mit readings, observe the reference depth manually
36
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(section 10.2.1) and read the indicated flowrate at the
same time.
- Compute the discharge corresponding to the measured
reference depth using the appropriate depth-discharge
relation from section 4.3 or 6.2.
- Enter the difference between indicated and calculated
flowrate, AQ, in figure 7.
10.2.5.6 Repeat step 10.2.5.5 at several flowrates covering the
anticipated discharge range, in such a way that an in-
dication of instrument repeatability is obtained.
- As an absolute minimum, three such points should be
obtained — one each at a low, medium and high flow-
rate; but it must be noted that this procedure gives
no indication of instrument repeatability and is
correspondingly less authoritative for instrument
evaluation.
- If the flow is cyclic, points should be obtained for
both the rising and falling stages so that errors due
to float lag, gear backlash or similar effects will
be visible.
- In order to accumulate numerous points in a reason-
able time, it may be necessary to create depth changes
artificially; for example, by manually backing up the
flow or by changing stilling-well levels independent-
ly of the flume. In many cases such artifices are
acceptable (always provided that reference-depth mea-
surements and corresponding error estimates can be
made), since only the secondary Instruments are being
checked here. In general, this method should not be
applied to in-stream sensors, whose performance may
be affected by the velocity or ruffled surface of the
unaltered flow.
10.2.5.7 If the scatter of the AQ points is small and apparently
random, draw curve C through them as in the example of
figure 7; but if obvious systematic differences appear
between the points for rising and falling stages, sep-
arate curves should be drawn.
10.2.5.8 If curve C is entirely inside of band B, and if further
the scatter of the points around C is within prescribed
limits, the instrument is performing acceptably; if not,
see section 10.2.5.10.
10.2.5.9 Even if numerous AQ points were obtained for figure 7,
it should be realized that only a relatively short term
effort was involved and no indication was obtained of
errors due to long term drifts, temperature and humidity
effects, general wear and other effects. Therefore:
- It is important to establish a program for routine and_
37
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regular inspection and maintenance of the secondary
system (section 11.1.2).
- This regular inspection must include check points on
AQ, using the reference-depth gage left in place from
the original performance check, to see that they still
fall within the performance bands established in
figure 7.
10.2.5.10 If curve C falls outside of zone B, the following should
be noted:
- AQ curves shaped like those in figure 8 suggest the
possibility of a zero-shift error in the secondary.
Should this be the case, reset the zero or otherwise
adjust for the shift and repeat the procedure of this
section (10.2.5).
- If curve C is a sloping straight line passing through
zero, there may be a need for a span or gain adjust-
ment in the secondary. Repeat the procedure after
adjustment.
0.5
^j 0.4
r 0.3
o
.0.2
a
O O.I
0
l-ft Parshall: zero-
• • '
setting error = 0.05 ft
4 6
Q, cu ft/s
8
10
12
10.2.6
Figure 8. Example of zero-shift error.
10.2.5.11 Section 10.2.5 provides one type of performance-test
procedure that takes into account the uncertainty in
the measurements that the commercial instrumentation
is being compared against. This is only a suggested
procedure; other rationally based comparisons can be
agreed upon.
Estimating the Error of a Single Discharge Measurement Obtained
with a Flowrate-Measuring Instrument.
10.2.6.1 At a given flowrate, combine quadratically the percent-
age reference error (section 10.2.5.3), the percentage
38
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error represented by the scatter limits in figure 7,
any remaining systematic error indicated in figure 7,
and the basic 3 percent uncertainty in the flume co-
efficient. (Note: If one is working with a measure-
ment that has been transmitted from the flume site,
this additional recording/receiving error should be
included; section 8.4.3.)
10.2.6.2 No matter how accurate the secondary instrument is,
the accuracy of a flowrate measurement is clearly still
limited by the potential 3 percent error in the flume
coefficient. Therefore, any further reduction in the
total estimated error will require an in-place calibra-
tion of the flume. See section 10.3 for flume calibra-
tions.
10.3 Calibrating the Primary Device (Flume)
10.3.1 General.
10.3.1.1 Section 10.3 pertains to complete in-place calibration of
flume systems that do not qualify for secondary-only
calibration according to section 10.1.1.1.
> 10.3.1.2 The purpose of section 10.3 is to provide a general over-
view of methods for calibrating the flume coefficient so
that, coupled with a separate calibration of the second-
ary instruments (section 10.2), a complete calibration
•of the measuring system is accomplished. In this way,
those differences between the calibrated and recorded
flowrates that are chargeable to the primary device can
be assigned to it, and future monitoring can be re-
stricted to the secondary instrumentation.
10.3.1.3 Whatever calibration method is used, it should satisfy
the following requirements:
- The calibration tests should be performed for at least
three flowrates — low, medium and high. If possible,
the process should be repeated several times at each
flowrate.
- The reference staff gage or point gage (section 10.2.1)
should be used to measure the flume depth during these
calibrations.
- If the calibration flow measurements are made at a
location away from the immediate vicinity of the flume,
equivalence of the flowrate at the measurement location
to that through the flume must be assured.
10.3.1.4 There is no single calibration method that is applicable
to all situations. The choice may depend not only on
technical factors described in the following sections
-------
but also on such factors as the availability of man-
power, funds, and in-plant laboratory capability. These
sections point out some advantages and disadvantages of
several common calibration methods and conditions for
their use. The major methods applicable here are:
- Volumetric
- Comparison with reference meter
- Dilution
- Salt velocity
- Velocity-area traverse
10.3.2 Volumetric Calibration.
10.3.2.1 The feasibility of volumetric calibration depends upon
the availability of tank space and connecting conduits.
The potential accuracy is high, provided that:
- The tank is regular in configuration so that its
lateral dimensions can be measured within acceptable
limits of accuracy.
- The tank is large enough to permit a test run of
sufficient length for the effect of timing errors at
the start and finish to be kept within acceptable
limits.
- The change in liquid level during the run is large
enough so that the starting and finishing depths
(probably obtained by the "on-the-run" method) can
be measured within acceptable relative error limits.
- The flowrate remains relatively constant during the
, .run.
10.3.2.2 Estimate the uncertainty of the resulting Q as a com-
bination of the estimated errors of the measurements
of the lateral area, the depth change, and the elapsed
time. This uncertainty combined with the estimated
error of the simultaneously measured flume depth gives
an estimated of the error in the flume coefficient.
10.3.3 Comparison with a Reference Meter.
10.3.3.1 In this context a reference meter is a flowrate mea-
suring device whose performance can be referenced to
published standards or to recommended practices that
are acceptable to the involved parties. Examples in-
clude:
- Standard venturi tubes and venturi nozzles (references
12.3, 12.4, 12.5)
- Orifice plates (references 12.3, 12.4)
- Thin plate weirs (reference 12.6)
10.3.3.2 Meters to be used as reference devices must meet all
requirements of the accepted standards in fabrication,
installation and use, so that their coefficients and
40
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uncertainties can be used in the flume calibrations.
(It is noted in this regard that the stringent upstream
approach conditions required by published standards are
unlikely to be satisfied under most treatment-plant
conditions.)
10.3.3.3 When a differential-pressure type of meter is used as
the reference device, measure the differential pressure
with a U-tube manometer. If a commercial secondary
device is to be used in place of a manometer, it must
have had a recent calibration and complete information
on its performance must be available. Further, its
error must be included in the uncertainty of the de-
rived flume coefficient.
10.3.3.4 When a standard weir is used as the reference instru-
ment, measure its head with a point gage or equivalent
device and use the same care as described for reference-
depth measurements in section 10.2.1.
10.3.3.5 It may be acceptable to use as a reference meter an in-
strument for which there are no published standards
provided that:
- The 'device has been recently calibrated and its cur-
rent accuracy and repeatability can be satisfactorily
documented.
- The device is used under effectively the same condi-
tions for which it was calibrated.
Examples of such devices are:
- Propeller meters
- Segmental orifices
- Electromagnetic flowmeters
- Acoustic flowmeters
10.3.4 Dilution Method.
10.3.4.1 In the dilution method the flowrate is deduced from the
dilution of measurable properties (e.g., color, con-
ductivity, or fluorescence) of tracer chemicals added
to a turbulent flow in known amounts. The calibration
can be done by either the constant-rate injection
method, or the slug injection method. The constant-
rate method is recommended here because it appears more
practical for in-plant use and because documentation
on it is available in the form of published standards,
e.g., (references 12.7,12.8).
10.3.4.2 In the constant rate injection method, a tracer solu-
tion of accurately known concentration is injected up-
stream at a rate which is constant and accurately mea-
surable. At a downstream distance long enough for
complete mixing, the flow is sampled and the concentra-
41
-------
tion determined after a steady state or concentration
"plateau" is attained. The flowrate, Q, is then deter-
mined from
Q = q(Cl - c2)/(c2 - CQ) [9]
where q is the rate at which the sample of concentration
c1 is injected; c_ is the measured "plateau" concentra-
tion downstream; and c (which may be close to zero) is
the background concentration of the tracer chemical ex-
isting in the flow.
10.3.4.3 This method requires accurate measurement of q and of
all concentrations; skilled personnel and specialized
equipment are needed. However, under optimum conditions
the potential accuracy is high. See references 12.7
and 12.8 for methods of estimating errors.
10.3.4.4 The tracer property must be conservative, since losses
by absorption to solids in the flow will result in an
apparent reduction in c_. The fluorescent dye Rhoda-
mine WT has been used successfully in sewage without
losses.
10.3.5 Salt-Velocity Method.
10.3.5.1 In the salt-velocity method, brine is injected sudden-
ly at an upstream station in such a way that it becomes
well distributed across the section very rapidly. The
time of passage of the salt pulse between two downstream
stations is measured by means of electrodes which detect
the increased conductivity associated with the passage
of the brine. The flowrate then can be determined pro-
vided the volume of the conduit between the electrodes
is accurately known. This method has a potential for
1 percent accuracy under optimum conditions. The accu-
racy actually obtained depends upon the tranverse mix-
ing and coherence of the injected brine slug, upon the
accuracy of determination of the centers of gravity of
the tracer-conductivity records and the time separating
them, as well as upon the accuracy of the aforementioned
volume determination.
10.3.5.2 Published standards for the salt-velocity method are
written for circular pipes flowing full (referemces 12.4,
12.9), and these or similar references must be con-
sulted for details of the method. A sufficient length
of (preferably straight) pipe upstream of the first
electrode is necessary to insure complete lateral mixing
of the salt slug when it reaches the electrode. This
length can be as short as four diameters when the in-
jection is done internally in the standard manner
42
-------
(references 12.4, 12.9). The distance between the two
sets of electrodes must be at least four diameters.
10.3.5.3 The liquid being measured must have a significantly
smaller electrical conductivity than the brine.
10.3.5.4 The brine injection must be sudden, with an injection
interval of the order of 1 second and no leakage there-
after.
10.3.5.5 The electrodes and the brine-injection devices are in-
trusive, so that the method might not be suitable for
raw sewage.
10.3.5.6 In principle, this method can be adapted to other shapes
of conduits or channels provided that the approach
length and the electrode spacing and configuration are
modified to compensate for the shape change in a manner
that is hydrodynamically sound and agreeable to the in-
volved parties.
10.3.6 Velocity-Area Method.
10.3.6.1 The velocity-area method is applied to a flow cross
section by measuring a number of velocities, each repre-
sentative of the average velocity within an incremental
area, and summing the resulting velocity-area products
over the cross section.
•
10.3.6.2 The velocities can be measured by point-velocity mea-
suring instruments such as rotating-element current
meters, electromagnetic current meters, Pitot tubes,
etc., or by acoustic velocity meters, which measure
an average velocity component along a line path. The
point-velocity instruments often tend to clog and
cannot always be used effectively in raw sewage. How-
ever, rotating and electromagnetic current meters
often can be conveniently used in open channels that
discharge treated effluent (see also section 10.3.6.4).
Pitot tubes are generally restricted to closed (full)
conduit flows where velocities are more likely to be
high enough for their use.
10.3.6.3 The accuracy of this method depends upon whether the
sampling grid is dense enough to yield the average
velocity in the section, whether each velocity is
sampled long enough to give a time—average value,
and upon the accuracy of the velocity-measuring in-
strument itself (reference 12.10). These sampling re-
quirements tend to make this a lengthy measurement, so
it can be used only where sufficiently long periods of
essentially steady flow are available.
43
-------
10.3.6.4 In cases where a point-velocity instrument is used in
an open channel, the following conditions must be ob-
served.
- The average velocity in the section preferably should
exceed 1 ft per second (0.30 m/s).
- Use only velocity-measuring instruments that have been
recently calibrated and whose present accuracy and un-
certainty can be estimated to the satisfaction of in-
volved parties.
- Consult reference (9) for distribution of velocity
sampling points in the cross section, and reference
(10) for error estimates.
44
-------
11. OPERATION AND MAINTENANCE
11.1 Short Term
11.1.1 Follow manufacturers' instructions for short-term servicing of
commercial secondary instruments, in addition to the specific
recommendations in the following.
11.1.2 After the initial tests described in section 10.2 have been com-
pleted, check at least one AH or AQ point (section 10.2.3 or
10.2.5) daily. If a point falls beyond the previously establish-
ed band, it may be necessary to obtain more points in order to
determine whether a zero or span adjustment or other repair is
necessary. Once a performance history has been established,
this check can be made less frequently if warranted, but always
at least once a week.
11.1.3 Stilling Wells.
11.1.3.1 Check the stilling-well purge flow daily.
11.1.3.2 Check the stilling well for solids accumulation and
clean as necessary. It is recommended that this check
be made daily until a sediment-accumulation history
has been established, at which time the interval can
be lengthened. As part of this procedure, also check
to see that the orifice or pipe connecting the flume
and stilling well is completely unobstructed.
11.1.4 Float Gages and Other Secondary Devices.
11.1.4.1 Floats in stilling wells should be checked for grease
or slime accumulation and wiped clean as necessary.
Make this check daily until a coating history is estab-
lished.
11.1.4.2 Scow floats used in raw sewage should be checked hourly
for fouling by debris. Regardless of where they are
used, they should be checked for grease, slime or other
accumulation as in section 11.1.4.1.
11.1.4.3 Bubbler tubes should be blown down at least weekly.
11.1.4.4 Immersed electrical sensors should be wiped clean
daily, unless it can be shown that less frequent atten-
tion is adequate.
45
-------
11.1.5 Flumes.
11.1.5.1 Flume surfaces should be wiped down weekly to free them
of slimes or other coatings. The flow need not be inter-
rupted for this type of cleaning.
11.1.5.2 Check daily for upstream bottom deposits until a deposit
history is established. Remove deposits as necessary.
11.2 Long Term
11.2.1 Follow manufacturers' instructions for long-term maintenance of
commercial secondary instruments, in addition to the following
specific recommendations.
11.2.2 Six months after the initial tests, check the longitudinal and
transverse levels of the flume for any changes due to settlement.
11.2.3 Check the zero of the reference-depth gage every three months
and adjust as necessary.
11.2.4 Check for deterioration of flume surfaces every six months,
particularly in the case of concrete flumes. Severely deterio-
rated surfaces may have to be relined to restore them to their
original roughness.
46
-------
12. REFERENCES
12.1 United States Department of the Interior, Bureau of Reclamation, "Water
Measurement Manual," Second Edition, Revised Reprint, 1967, U. S. Govt.
Printing Office.
12.2 Discharge Measurement Structures, M. G. Bos, editor, Publication No. 161,
Delft Hydraulics Laboratory, Delft, Netherlands, 1976.
12.3 International Standards Organization, "Measurement of Fluid Flow by Means
of Orifice Plates, Nozzles and Venturi Tubes Inserted in Circular Cross-
Section Conduits Running Full," ISO/DIS 5167, 1976, draft revision of
R781.
12.4 American Society of Mechanical Engineers, "Fluid Meters — Their Theory
and Application," 6th ed., 1971.
12.5 American Society for Testing and Materials, "Standard Method of Flow
Measurement of Water by the Venturi Meter Tube," ASTM D2458-69,
12.6 British Standards Institution, Standard No. 2680-4A, "Methods of Mea-
surement of Liquid Flow in Open Channels: Part 4A, Thin Plate Weirs
and Venturi Flumes," 1965.
12.7 International Standards Organization, "Measurement of Water Flow in
Closed Conduits—Tracer Methods, Part I; General," ISO No. 2975/1, 1974.
12.8 International Standards Organization, "Measurement of Water Flow in
Closed Conduits—Tracer Methods, Part II; Constant Rate Injection
Method Using Non-radioactive Tracers," ISO DIS 2975/11.
12.9 International Electrotechnical Commission, "International Code for the
Field Acceptance Tests of Hydraulic Turbines," Publication 41, 1963.
12.10 International Standards Organization, "Liquid Flow Measurement Open
Channels — Velocity-Area Methods," ISO 748, 1973.
47
-------
TABLE A.I. PARSHALL FLUME DISCHARGE
Discharge in cu ft per sec, for various throat widths
ft 1 in 2 in 3 in 6 in 9 in 1 ft 1.5 ft 2 ft 3 ft 4 ft 5 ft 6 ft 7 ft 8 ft
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
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
.0033
.0043
.0055
.0068
.0081
.0095
.0110
.0126
.0143
.0160
.0179
.0197
.0217
.0237
.0258
.0279
.032
.037
.042
.047
.052
.058
.063
.069
.075
.082
.0065
.0086
.0110
.0135
.0162
.0191
.0221
.0253
.0286
.0321
.0357
.039
.043
.047
.052
.056
.065
.074
.084
.094
.105
.116
.127
.139
.151
.163
.0280
.032
.037
.042
.047
.052
.058
.064
.070.
.076
.082
.095
.109
.123
.138
.153
.170
.187
.205
.222
.240
.054
.063
.072
.082
.092
.103
.114
.125
.137
.149
.162
.188
.216
.245
.276
.307
.34
.38
.41
.45
.48
.091
.105
.120
.135
.152
.168
.186
.204
.223
.242
.262
.30
.35
.39
.44
.49
.54
.59
.64
.70
.76
.35
.40
.46
.51
.58
.64
.71
.77
.84
.92
.99
1
1
1
1
1
.50
.58
.67
.76
.85
.94
.04
.14
.25
.35
.47
.66
.77
.88
.99
1.11
1.24
1.37
1.50
1.64
1.79
1.93
.97
1.12
1.28
1.46
1.64
1.82
2.02
2.22
2.42
2.64
2.86
1.26
1.47
1.69
1.91
2.15
2.39
2.65
2.92
3.20
3.48
3.77
2.36 2.80
2.65 3.15
2.96 3.52 4.08 4.62
3.28 3.90 4.52 5.13
3.61 4.30 4.98 5.66
3.95 4.71 5.46 6.20
4.31 5.13 5.95 6.74
4.67 5.57 6.46 7.34
(continued)
-------
TABLE A.I (continued)
.P.
UD
H
a
ft
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
0.80
0.82
0.84
0.86
0.88
0.90
Discharge in cu ft per sec, for various throat widths
1 in
.088
.095
.101
.108
.115
.123
.130
.138
.145
.153
.161
.169
.178
.186
2 in
.176
.189
.203
.217
.231
.245
.260
.275
.291
.306
.322
.338
.355
.372
.389
.406
.424
.442
.460
3 in
.259
.278
.298
.318
.339
.360
.382
.404
.426
.449
.473
.497
.521
.546
.571
.60
.62
.65
.67
.70
.73
.76
.79
.81
.84
6 in
.52
.56
.60
.65
.69
.73
.78
.82
.87
.92
.97
1.02
1.07
1.12
1.17
1.23
1.28
1.34
1.39
1.45
1.50
1.56
1.62
1.68
1.74
9 in
.81
.87
.94
1.00
1.06
1.13
1.20
1.26
1.33
1.41
1.48
1..55
1.63
1.70
1.78
1.86
1.94
2.02
2.10
2.18
2.27
2.35
2.44
2.52
2.61
1 ft
1.07
1.15
1.23
1.31
1.39
1.48
1.57
1.66
1.75
1.84
1.93
2.03
2.13
2.23
2.33
2.43
2.53
2.63
2.74
2.85
2.96
3.07
3.18
3.29
3.41
1.5 ft
1.58
1.70
1.82
1.94
2.07
2.19
2.33
2.46
2.60
2.73
2.88
3.02
3.17
3.32
3.47
3.62
3.78
3.93
4.09
4.26
4.42
4.59
4.76
4.93
5.10
2 ft
2.09
2.24
2.40
2.56
2.73
2.90
3.08
3.26
3.44
3.62
3.81
4.01
4.20
4.40
4.60
4.81
5.02
5.23
5.44
5.66
5.88
6.11
6.33
6.56
6.79
3 ft
3.08
3.32
3.56
3.80
4.05
4.31
4.57
4.84
5.11
5.39
5.68
5.97
6.26
6.56
6.86
7.17
7.49
7.81
8.13
8.46
8.79
9.13
9.48
9.82
10.17
4 ft
4.07
4.38
4.70
5.03
5.36
5.70
6.05
6.41
6.77
7.15
7.53
7.91
8.31
8.71
9.11
9.53
9.95
10.38
10.81
11.25
11.70
12.15
12.61
13.07
13.55
5 ft
5.05
5.43
5.83
6.24
6.66
7.09
7.52
7.97
8.43
8.89
9.37
9.85
10.34
10.85
11.36
11.88
12.40
12.94
13.48
14.04
14.60
15.17
15.75
16.33
16.92
6 ft
6.02
6.48
6.96
7.45
7.94
8.46
8.98
9.52
10.07
10.63
11.20
11.78
12.38
12.98
13.59
14.22
14.85
15.49
16.15
16.81
17.49
18.17
18.87
19.57
20.29
7 ft
6.98
7.52
8.08
8.65
9.23
9.83
10.45
11.07
11.71
12.36
13.02
13.70
14.40
15.10
15.82
16.55
17.29
18.04
18.81
19.59
20.39
21.18
21.99
22.82
23.66
8 ft
7.94
8.55
9.19
9.84
10.51
11.19
11.89
12.60
13.33
14.08
14.84
15.62
16.41
17.22
18.04
18.87
19.71
20.57
21.46
22.36
23.26
24.18
25.11
26.06
27.02
(continued)
-------
TABLE A.I (continued)
tn
O
H
a
ft 1 in
0.92
0.94
0.96
0.98
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
Discharge in
2 in 3 in 6 in
.87 1.81
.90 1.87
.93 1.93
.96 2.00
.99 2.06
1.07 2.23
2.39
2.57
2.75
2.93
3.12
3.31
3.51
3.71
3.91
9 in
2.70
2.79
2.88
2.98
3.07
3.31
3.55
3.80
4.06
4.32
4.59
4.86
5.14
5.42
5.71
6.00
6.30
6.61
6.91
7.23
7.55
7.87
8.20
8.53
8.87
cu ft per sec,
1 ft
3.52
3.64
3.76
3.88
4.00
4.31
4.62
4.95
5.28
5.62
5.96
6.32
6.68
7.04
7.41
7.79
8.18
8.57
8.97
9.38
9.79
10.20
10.62
11.06
11.49
1.5 ft
5.28
5.46
5.63
5.82
6.00
6.47
6.95
7.44
7.94
8.46
8.98
9.52
10.07
10.63
11.19
11.77
12.36
12.96
13.57
14.19
14.82
15.45
16.10
16.76
17.42
for various throat widths
2 ft
7.03
7.27
7.51
7.75
8.00
8.63
9.27
9.94
10.61
11.31
12.01
12.74
13.48
14.23
15.00
15.78
16.58
17.38
18.21
19.04
19.90
20.76
21.63
22.53
23.43
3 ft
10.53
10.89
11.26
11.63
12.00
12.96
13.93
14.94
15.96
17.02
18.10
19.20
20.32
21.47
22.64
23.84
25.05
26.29
27.55
28.82
30.13
31.45
32.79
34.14
35.53
4 ft
14.03
14.51
15.00
15.50
16.00
17.28
18.60
19.94
21.33
22.75
24.21
25.69
27.21
28.76
30.34
31.95
33.59
35.26
36.96
38.69
40.45
42.24
44.05
45.90
47.77
5 ft
17.52
18.13
18.75
19.37
20.00
21.61
23.26
24.96
26.71
28.50
30.33
32.20
34.11
36.06
38.06
40.09
42.17
44.28
46.43
48.61
50.83
53.09
55.39
57.72
60.08
6 ft
21.01
21.75
22.49
23.24
24.00
25.94
27.94
30.00
32.10
34.26
36.47
38.74
41.05
43.42!
45.82
48.28
50.79
53.34
55.95
58.60
61.29
64.01
66.81
69.63
72.50
7 ft
24.50
25.36
26.22
27.10
28.00
30.28
32.62
35.02
37.50
40.02
42.62
45.26
47.99
50.76
53.59
56.48
59.42
62.42
65.48
68.59
71.75
74.98
78.24
81.57
84.94
8 ft
27.99
28.97
29.97
30.98
32.00
34.61
37.30
40.06
42.89
45.80
48.78
51.84
54.95
58.14
61.38
64.71
68.10
71.56
75.07
78.66
82.29
86.00
89.76
93.59
97.48
(continued)
-------
TABLE A.I (continued)
H
a
ft 1 in 2 in 3
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
Discharge in cu ft per sec,
in 6 in 9 in 1
11.
12.
12.
13.
13.
14.
14.
15.
15.
16.
ft
93
37
82
28
74
21
68
16
64
13
1.5 ft
18.10
18.78
19.47
20.17
20.88
21.60
22.33
23.06
23.81
24.56
for various throat widths
2 ft
24.34
25.27
26.20
27.15
28.12
29.09
30.08
31.08
32.08
33.11
3 ft
36.94
38.35
39.79
41.25
42.73
44.22
45.74
47.27
48.82
50.39
4 ft
49.67
51.59
53.54
55.52
57.52
59.56
61.61
63.69
65.80
67.93
5
62
64
67
69
72
75
77
80
82
85
ft
.48
.92
.39
.90
.43
.01
.61
.25
.92
.62
6 ft
75.42
78.37
81.36
84.41
87.49
90.61
93.77
96.97
100.2
103.5
7 ft
88.37
91.84
95.37
98.94
102.6
106.2
110.0
113.7
117.5
121.4
8 ft
101.4
105.4
109.5
113.6
117.8
122.0
126.3
130.7
135.1
139.5
-------
TABLE A.2. METRIC COEFFICIENTS FOR PARSHALL FLUMES
(use H in meters in eq.[l] and obtain Q in m /s)
1
2
3
6
9
1
1
2
3
4
5
6
7
8
Throat
in
in
in
in
in
ft
1/2 ft
ft
ft
ft
ft
ft
ft
ft
Width
2.
5.
7.
0.
0.
0.
0.
0.
0.
1.
1.
1.
2.
2.
5 cm
1 cm
6 cm
152 m
229 m
305 m
457 m
610 m
914 m
219 m
524 m
829 m
134 m
438 m
0.
0.
0.
0.
0.
0.
1.
1.
2.
2.
3.
4.
5.
6.
C
060
121
177
381
535
691
056
429
184
954
732
518
313
115
n
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
55
55
55
58
53
522
538
550
566
578
587
595
601
607
52
-------
0.02
0.03
100 90
Percent submergence
Figure A.I. ' Rate of submerged flow through
a 1-inch Parshall flume (Ref. 12.1).
TJ
O
0>
E
o
Ift
Q.
ID
2.00
100 90 80 70 60 50
Percent submergence
Figure A.2. Rate of submerged flow through
a 2-inch Parshall flume (Ref.12.1).
-------
010
O20
500
10
100 90 80 70 60 50 40
Percent submergence
10
Figure A.3. Rate of submerged flow through
a 3-inch Parshall flume (Ref. 12.1).
Figure A.4. Relationship of HC and ^ gages for
1-.2-, and 3-inch Parshall flumes for submergences
greater than 50 percent (Ref. 12.1).
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h.
u
E
_Q
3
C
0)
u
w
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Q.
c
u
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c
41
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1
1
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I
/
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1
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t
1
1
(
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/
1
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/
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l.C
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5
1
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1
1
f
f
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f
1
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f
1
1
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1
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1
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/
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0
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i
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A
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i
f
t
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i/
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i
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s
1
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;
5
/
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4
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f
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1
j
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1
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3
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f
/
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^
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/
J
f
f
r
/
/
Hn
V
3
/
J
Ft
5
I
t
j
f
4
Discharge, cu.ft./sec
Figure A.5. Diagram for determining rate of submerged flow for a
6-inch Parshall flume (Ref. 12.1).
60
70
BO
90
96
1 L ' ' L
.1 .3 .4 .3 .6 .7 .» .9 1.0 1.1 1.2 1.3 1.4 1.3 Ha / ft
7
0.0 0.3 1.0 1.3 20 2.3 3.0 3.J 40 4.5 50 5.5 47
Discharge, cu. ft./sec
Figure A.6. Diagram for determining rate of submerged flow for a
9-inch Parshall flume (Ref. 12.1).
55
-------
Percent submergence
70
90
2.0
1.3
~ 1.0
O
I
/
//
I/I
/
/
/
/
/
/
/
/
/
j
f
f
/
/
/
//
7
'
x1
X
x
/
/;
/
{
0 72
<""
X
x
^
/
/
/
x
s
' ^
'/
x
^
x
7
•
/
xi
x
,/
X
^
^s
4 7
X"
x
x
X1
x"*,
/x-
x
^
jX
7
X""
x
x
x
x
x
X
^
;
d
^
8 80
s^
S
^
/
X
x
x
^
'
,
^
x
*
X
X
,x
^
x
x
^
^X'
12 84
jX
.
f
S
X
x
x^
x
x
x
x
x
:*:
-*
jzd
86
*
X
x
X
x
x
x*
^
x*
1
X"
x
x
x
a
X
^
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90
^,
S
X
x
5=
7""
^X"
9
'
X
X
^
^
!
x^
x
p
^
9
^
j
^
±5
£;
^ vT"
90
^.
E^2 H-
W, ft M
1 1 0
1.3 1.4
2 1.8
3 2.4
4 3.1
3 37
6 43
7 49
8 3.4
Note-Correction used directly for
1-ft flumes. For larger sizes multioly
chart correction by factor M.
ill 1 I 1 I i I 1 1 i I i
.10
.20
.30
10
2.0
3.0
10 0
Correction, co. ff./sec
Figure A.7. Diagram for determining correction to be subtracted
from free-discharge flow to obtain rate of submerged flow through
Parshall flumes 1 to 8 feet wide (Ref. 12.1).
Percent
submergence -,80
i.o
10
Note-Correction is used directly
for 10 ft. flumes. For
larger sizes the correction
equals the chart value x M.,
30 100 200 300
Correction, cu. ft./sec
Figure A.8. Diagram for determining correction to be subtracted
from free-discharge flow to obtain rate of submerged flow through
Parshall flumes 10 to 50 feet wide (Ref. 12.1).
56
-------
lOOf
Typ. k =.001 ft, case iron —
.005 ft, concrete
10
10-
10
Velocity x diam. / kinematic viscosity
Figure A. 9. Friction-factor curves for stilling-well connector.
57
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