ASTM D5390-21

Standard Test Method for Open-Channel Flow Measurement of Water with Palmer-Bowlus Flumes

SIGNIFICANCE AND USE
5.1 Although Palmer-Bowlus flumes can be used in many types of open channels, they are particularly adaptable for permanent or temporary installation in circular sewers. Commercial flumes are available for use in sewers from 4 in. to 6 ft (0.1 to 1.8 m) in diameter.  
5.2 A properly designed and operated Palmer-Bowlus is capable of providing accurate flow measurements while introducing a relatively small head loss and exhibiting good sediment and debris-passing characteristics.
SCOPE
1.1 This test method covers measurement of the volumetric flow rate of water and wastewater in sewers and other open channels with Palmer-Bowlus flumes.  
1.2 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Oct-2021
• ICS: 17.120.20 - Flow in open channels
• Technical Committee: D19 - Water
• Drafting Committee: D19.07 - Sediments, Geomorphology, and Open-Channel Flow

Relations

• Refers: ASTM D1129-13(2020)e2 - Standard Terminology Relating to Water
• Effective Date: 01-May-2020
• Refers: ASTM D2777-12 - Standard Practice for Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
• Effective Date: 15-Jun-2012
• Refers: ASTM D1129-10 - Standard Terminology Relating to Water
• Effective Date: 01-Mar-2010
• Refers: ASTM D3858-95(2008) - Standard Test Method for Open-Channel Flow Measurement of Water by Velocity-Area Method
• Effective Date: 01-Oct-2008
• Refers: ASTM D2777-08 - Standard Practice for Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
• Effective Date: 15-Jan-2008
• Refers: ASTM D1941-91(2007) - Standard Test Method for Open Channel Flow Measurement of Water with the Parshall Flume
• Effective Date: 15-Jun-2007
• Refers: ASTM D5242-92(2007) - Standard Test Method for Open-Channel Flow Measurement of Water with Thin-Plate Weirs
• Effective Date: 15-Jun-2007
• Refers: ASTM D1129-06a - Standard Terminology Relating to Water
• Effective Date: 01-Sep-2006
• Refers: ASTM D1129-06ae1 - Standard Terminology Relating to Water
• Effective Date: 01-Sep-2006
• Refers: ASTM D2777-06 - Standard Practice for Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
• Effective Date: 15-Aug-2006
• Refers: ASTM D1129-06 - Standard Terminology Relating to Water
• Effective Date: 15-Feb-2006
• Refers: ASTM D1129-04e1 - Standard Terminology Relating to Water
• Effective Date: 01-Mar-2004
• Refers: ASTM D1129-04 - Standard Terminology Relating to Water
• Effective Date: 01-Mar-2004
• Refers: ASTM D2777-03 - Standard Practice for Determination of Precision and Bias of Applicable Methods of Committee D-19 on Water
• Effective Date: 10-Aug-2003
• Refers: ASTM D1129-03a - Standard Terminology Relating to Water
• Effective Date: 10-Aug-2003

Overview

ASTM D5390-21 is the internationally recognized standard test method for measuring open-channel flow of water and wastewater using Palmer-Bowlus flumes. Developed by ASTM International, this standard is widely used in the water industry for accurate volumetric flowrate determination in sewers and other open channels. Palmer-Bowlus flumes are particularly well-adapted for both permanent and temporary installations in circular sewer pipes, accommodating diameters from 4 inches to 6 feet (0.1 to 1.8 meters). With proper design and operation, these flumes can provide precise measurements while introducing minimal head loss and effectively passing sediment and debris.

Key Topics

• Scope of Application: Applicable to the measurement of water and wastewater flows in open channels and sewers using Palmer-Bowlus flumes. Essential for both temporary and permanent installations.
• Units of Measurement: The method uses inch-pound units as the primary standard, with SI conversions provided for informational purposes.
• Flume Design: Focuses on the selection, configuration, and installation of Palmer-Bowlus flumes based on channel or pipe size and other hydraulic conditions.
• Head and Flow Measurement: Outlines the relationship between upstream head and volumetric flowrate, ensuring reliable measurements through proper calibration and monitoring.
• Instrumentation: Discusses the use of primary instruments (the flume itself) and secondary instruments (depth/head measuring devices), including manual and automated sensors such as scow-type floats, pressure sensors, acoustic sensors, and electrical probes.
• Installation Guidelines: Emphasizes critical factors like channel approach conditions, avoidance of downstream submergence, maintaining a level installation, and effective sealing of the flume within the channel.
• Calibration and Quality Control: Recommends in-place system calibration for highest accuracy, with detailed procedures for validating both the primary flume and secondary measurement systems.
• Error Estimation: Addresses sources of error due to installation, instrumentation, and environmental variability, providing guidance to estimate and minimize measurement uncertainty.

Applications

• Wastewater Flow Monitoring: Widely used in municipal and industrial wastewater systems to monitor and control flows in circular sewer lines.
• Regulatory Compliance: Provides standardized methods for reporting and verifying flowrates in line with regulatory requirements for discharge and treatment.
• Environmental Monitoring: Supports environmental impact assessments by allowing accurate measurement of streamflow in open channels and outfalls.
• Sewer System Management: Essential tool for ongoing maintenance, troubleshooting, and capacity planning in water infrastructure.
• Temporary Flow Measurement: Suitable for short-term flow monitoring during system modifications, construction projects, or initial plant startups.
• Research and Development: Useful in hydraulic laboratories and field studies for modeling open-channel flow behaviors.

Related Standards

The use of ASTM D5390-21 is supported by and often referenced alongside other key standards in open-channel flow measurement, including:

• ASTM D1129: Terminology Relating to Water
• ASTM D1941: Open Channel Flow Measurement of Water with the Parshall Flume
• ASTM D2777: Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
• ASTM D3858: Open-Channel Flow Measurement of Water by Velocity-Area Method
• ASTM D5242: Open-Channel Flow Measurement of Water with Thin-Plate Weirs
• ISO 4359: Liquid Flow Measurement in Open Channels-Flumes
• ISO 555: Liquid Flow Measurements in Open Channels-Dilution Methods for Measurement of Steady Flow
• ASME Fluid Meters: Their Theory and Application

Practical Value

ASTM D5390-21 delivers a proven and reliable methodology for the water sector, ensuring that Palmer-Bowlus flume installations produce consistent and accurate flow data. By following this standard, professionals in engineering, environmental monitoring, and municipal operations benefit from:

• Increased accuracy in water and wastewater monitoring
• Streamlined regulatory compliance
• Enhanced data integrity for operational and design decision-making
• Reduced maintenance and improved equipment lifespan through correct installation practices

For anyone involved in open-channel flow measurement or sewer system management, adherence to ASTM D5390-21 is essential for operational excellence and reliability.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5390 − 21
Standard Test Method for
Open-Channel Flow Measurement of Water with Palmer-
Bowlus Flumes
This standard is issued under the fixed designation D5390; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2.2 ISO Standards:
ISO 4359 Liquid Flow Measurement in Open Channels—
1.1 This test method covers measurement of the volumetric
Rectangular, Trapezoidal and U-Shaped Flumes
flow rate of water and wastewater in sewers and other open
ISO 555 Liquid Flow Measurements in Open Channels—
channels with Palmer-Bowlus flumes.
Dilution Methods for Measurement of Steady Flow—
1.2 The values stated in inch-pound units are to be regarded
Constant Rate Injection Method
as standard. The values given in parentheses are mathematical
2.3 ASME Standard:
conversions to SI units that are provided for information only
Fluid Meters Their Theory and Application
and are not considered standard.
1.3 This standard does not purport to address all of the
3. Terminology
safety concerns, if any, associated with its use. It is the
3.1 Definitions:
responsibility of the user of this standard to establish appro-
3.1.1 For definitions of terms used in this standard, refer to
priate safety, health, and environmental practices and deter-
Terminology D1129.
mine the applicability of regulatory limitations prior to use.
3.2 Definitions of Terms Specific to This Standard:
1.4 This international standard was developed in accor-
3.2.1 boundary layer displacement thickness, n—a layer of
dance with internationally recognized principles on standard-
fluid flow adjacent to a solid surface (in this case, the flume
ization established in the Decision on Principles for the
throat) in which, owing to viscous friction, the velocity
Development of International Standards, Guides and Recom-
increases from zero at the stationary surface to an essentially
mendations issued by the World Trade Organization Technical
frictionless-flow value at the edge of the layer. The displace-
Barriers to Trade (TBT) Committee.
ment thickness is a distance normal to the solid surface that the
surface and flow streamlines can be considered to have been
2. Referenced Documents
displaced by virtue of the boundary-layer formation.
2.1 ASTM Standards:
3.2.2 critical flow, n—the energy in open channel flow
D1129 Terminology Relating to Water
expressed in terms of depth plus velocity head and is a
D1941 Test Method for Open Channel Flow Measurement
minimum for a given flow rate and channel. The Froude
of Water with the Parshall Flume
number is unity at critical flow.
D2777 Practice for Determination of Precision and Bias of
3.2.3 Froude number, n—a dimensionless number express-
Applicable Test Methods of Committee D19 on Water
ing the ratio of inertial to gravity forces in free-surface flow. It
D3858 Test Method for Open-Channel Flow Measurement
is equal to the average velocity divided by the square root of
of Water by Velocity-Area Method
the product of the average depth and the acceleration due to
D5242 Test Method for Open-Channel Flow Measurement
gravity.
of Water with Thin-Plate Weirs
3.2.4 head, n—the depth of flow referenced to the floor of
the throat measured at an appropriate location upstream of the
1 flume;thisdepthplusthevelocityheadisoftentermedthetotal
This test method is under the jurisdiction of ASTM Committee D19 on Water
and is the direct responsibility of Subcommittee D19.07 on Sediments, head or total energy head.
Geomorphology, and Open-Channel Flow.
Current edition approved Nov. 1, 2021. Published January 2022. Originally
approved in 1993. Last previous edition approved in 2013 as D5390 – 93 (2013).
DOI: 10.1520/D5390-21. Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 4th Floor, New York, NY 10036, http://www.ansi.org.
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Available from American Society of Mechanical Engineers (ASME), ASME
Standards volume information, refer to the standard’s Document Summary page on International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
the ASTM website. www.asme.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5390 − 21
3.2.5 hydraulic jump, n—an abrupt transition from super- mercial flumes are available for use in sewers from 4 in. to 6
critical flow to subcritical or tranquil flow, accompanied by ft (0.1 to 1.8 m) in diameter.
considerable turbulence or gravity waves, or both.
5.2 A properly designed and operated Palmer-Bowlus is
3.2.6 long-throated flume, n—aflumeinwhichtheprismatic
capable of providing accurate flow measurements while intro-
throat is long enough relative to the head for essentially critical ducing a relatively small head loss and exhibiting good
flow to develop on the crest.
sediment and debris-passing characteristics.
3.2.7 primary instrument, n—the device (in this case the
6. Interferences
flume) that creates a hydrodynamic condition that can be
6.1 Flumes are applicable only to open-channel flow and
sensed by the secondary instrument.
become inoperative under full-pipe flow conditions.
3.2.8 Reynolds number, n—a dimensionless number ex-
6.2 The flume becomes inoperative if downstream condi-
pressing the ratio of inertial to viscous forces in a flow. In a
tions cause submergence (see 7.3.2).
flume throat the pertinent Reynolds number is equal to the
(critical) throat velocity multiplied by the throat length and
7. Apparatus
divided by the kinematic viscosity of the water.
7.1 A Palmer-Bowlus flume measuring system consists of
3.2.9 scow float, n—an in-stream float for depth sensing,
the flume itself (the primary), with its immediate upstream and
usually mounted on a hinged cantilever.
downstream channels, and a depth or head measuring device
3.2.10 secondary instrument, n—in this case, a device that
(thesecondary).Thesecondarydevicecanrangefromasimple
measures the depth of flow (referenced to the throat elevation)
scale or gauge for manual readings to an instrument that
at an appropriate location upstream of the flume. The second-
continuously senses the head, converts it to a flow rate, and
ary instrument may also convert this measured head to an
displays or transmits a readout or record of the instantaneous
indicated flow rate, or could totalize flow rate.
flow rate or the totalized flow, or both.
3.2.11 stilling well, n—a small free-surface reservoir con-
7.2 The Palmer-Bowlus Flume:
nected through a restricted passage to the approach channel
7.2.1 General Configuration:
upstreamoftheflumesothataheadmeasurementcanbemade
7.2.1.1 The Palmer-Bowlus flume is a class of long-throated
under quiescent conditions.
flume in which critical flow is developed in a throat that is
formed by constricted sidewalls or a bottom rise, or both.
3.2.12 subcritical flow, n—open channel flow that is deeper
Sloped ramps form gradual transitions between the throat and
and at lower velocity than critical flow for the same flow rate;
the upstream and downstream sections. See Fig. 1. The flume
sometimes called tranquil flow.
was developed primarily for use in sewers but it is adaptable
3.2.13 submergence, n—aconditionwherethedepthofflow
to other open channels as well. There is no standardized shape
immediately downstream of the flume is large enough to affect
for Palmer-Bowlus flumes and, as long-throated flumes, they
the flow through the flume so that the flow rate can no longer
can be designed to fit specific hydraulic situations using the
be related to a single upstream head.
theory outlined in 7.2.3.
3.2.14 supercritical flow, n—open channel flow that is
7.2.1.2 Prefabricated Flumes—Prefabricated flumes with
shallower and at higher velocity than critical flow for the same
trapezoidalorrectangularthroatsandwithcircularorU-shaped
flow rate.
outside forms are commercially available for use in sewers.
3.2.15 tailwater, n—the water elevation immediately down- Although there is no fixed shape for Palmer-Bowlus flumes,
many manufacturers of trapezoidal-throated flumes use the
stream of the flume.
proportions shown in Fig. 2. These prefabricated flumes are
3.2.16 throat, n—the constricted portion of the flume.
also available in several configurations depending on how they
3.2.17 velocity head, n—the square of the average velocity
are to be installed, for example, whether they will be placed in
divided by twice the acceleration due to gravity.
thechannelatthebaseofanexistingmanhole,insertedintothe
pipe immediately downstream of the manhole, or incorporated
4. Summary of Test Method
into new construction.The size of these prefabricated flumes is
4.1 In Palmer-Bowlus flumes, critical free-surface flow is
developed in a prismatic throat so that the flow rate is a unique
Palmer, H. K., and Bowlus, F. D., “Adaptation of Venturi Flumes to Flow
function of a single measured upstream head for a given throat
Measurements in Conduits,” Trans. ASCE, Vol 101, 1936, pp. 1195–1216.
shape and upstream channel geometry. This function can be
obtained theoretically for ideal (frictionless) flows and adjust-
ments for non-ideal conditions can be obtained experimentally
or estimated from fluid-mechanics considerations.
5. Significance and Use
5.1 Although Palmer-Bowlus flumes can be used in many
types of open channels, they are particularly adaptable for
FIG. 1 Generalized Palmer-Bowlus (Long-Throated) Flume in a
permanent or temporary installation in circular sewers. Com- Rectangular Channel
D5390 − 21
where g is the acceleration due to gravity and C C and C
D S V
are, respectively, the discharge coefficient, throat shape
coefficient, and velocity-of-approach coefficient as defined in
the following sections. The derivation of Eq 1 is outlined in
Appendix X2.
7.2.3.2 Discharge Coeffıcient, C —Thiscoefficientapproxi-
D
mates the effect of viscous friction on the theoretical discharge
by allowing for the development of a boundary layer of
displacement thickness δ along the bottom and sides of the
*
FIG. 2 Palmer-Bowlus Flume (Typical) for Sewer
throat:
C 5 ~B /B!~1 2 δ /h! (2)
D e *
customarily referenced to the diameter of the receiving pipe
rather than to the throat width. Refer to manufacturers’
Here B is an effective throat width given by:
e
literature for flume details.
B 5 B 2 2δ @~m 11! 2 2 m# (3)
e *
7.2.1.3 Becausethedimensionsofprefabricatedflumesmay
differdependinguponthemanufacturerortheconfiguration,or
where m is the horizontal-to-vertical slope of the sides of the
both, it is important that users check interior dimensions
throat (zero for rectangular throats). The displacement
carefully before installation and insure that these dimensions
thickness, δ , is a function of the throat Reynolds number and
*
are not affected by the installation process.
surface roughness. However, a reasonable approximation that
7.2.1.4 A Palmer-Bowlus flume can be fabricated in a pipe
is adequate for many applications is:
by raising the invert (see Fig. X3.1). Floor slabs that can be
δ 5 0.003 L (4)
*
grouted into existing sewers are commercially available, as are
whereListhelengthofthethroat.(Betterestimatesofδ can
prefabricated slab-pipe combinations for insertion into larger
*
be obtained from boundary-layer theory, as in ISO 4359.)
pipes. Details may be obtained from the manufacturers’ litera-
7.2.3.3 Shape Coeffıcient, C (SeeAlso Appendix X2)—C is
ture. Discharge equations for this throat shape are given in
S S
given in Table 1 as a function of mH /B . H is the upstream
Appendix X1. e e e
total effective head, which is (for essentially uniform upstream
7.2.2 Head Measurement Location—The head, h, on the
velocity distribution):
flume is measured at a distance upstream of the throat-
approach ramp that is preferably equal to three times the
H 5 h1V /2g 2 δ (5)
e u *
maximum head. When the maximum head is restricted to
where V is the average velocity at the position of head
u
one-half the throat length, as is recommended in this test
measurement. For a rectangular throat, m + 0 and C is unity.
S
method, an upstream distance equal to the maximum head will
7.2.3.4 Velocity-of-Approach Coeffıcient, C —This coeffi-
V
usually be adequate to avoid the drawdown curvature of the
cientallowstheflowratetobeexpressedconvenientlyinterms
flow profile.
of the measured head, h, rather than the total head, H:
7.2.3 Discharge Relations:
3 3
7.2.3.1 The volumetric flow rate, Q, through a Palmer-
C 5 H 2 δ / h 2 δ 2 5 H /h 2 (6)
@~ ! ~ !# ~ !
V * * e e
Bowlus flume of bottom throat width, B, operating under a
C is given in Table 2 as a function of C B h /A , where A
V S e e u u
head, h, above the throat floor is:
is the cross-sectional area of the flow at the head measurement
Q 5 2/3 2g/3 1/2C C C Bh 2 (1) station. See also Appendix X3.
~ !~ !
D S V
TABLE 1 Shape Coefficient,C
S
mH /B C mH /B mC mH /B C mH /B C
e e S e e S e e S e e S
0.010 1.007 0.40 1.276 1.80 2.288 3.80 3.766
0.015 1.010 0.45 1.311 1.90 2.360 3.90 3.840
0.020 1.013 0.50 1.346 2.00 2.433 4.00 3.914
0.025 1.017 0.55 1.381 2.10 2.507 4.10 3.988
0.030 1.020 0.60 1.417 2.20 2.582 4.20 4.062
0.040 1.028 0.65 1.453 2.30 2.657 4.30 4.136
0.050 1.035 0.70 1.490 2.40 2.731 4.40 4.210
0.060 1.041 0.75 1.527 2.50 2.805 4.50 4.284
0.070 1.048 0.80 1.564 2.60 2.879 4.60 4.358
0.080 1.054 0.85 1.600 2.70 2.953 4.70 4.432
0.090 1.060 0.90 1.636 2.80 3.027 4.80 4.505
0.10 1.066 0.95 1.670 2.90 3.101 4.90 4.579
0.12 1.080 1.00 1.705 3.00 3.175 5.00 4.653
0.14 1.093 1.10 1.779 3.10 3.249 5.50 5.03
0.16 1.106 1.20 1.852 3.20 3.323 6.00 5.40
0.18 1.119 1.30 1.925 3.30 3.397 7.00 6.15
0.20 1.133 1.40 1.997 3.40 3.471 8.00 6.89
0.25 1.169 1.50 2.069 3.50 3.545 9.00 7.63
0.30 1.204 1.60 2.142 3.60 3.618 10.0 8.37
0.35 1.240 1.70 2.215 3.70 3.692 . .
D5390 − 21
TABLE 2 Velocity-of-Approach Coefficient,C
bends, junctions or other major disturbances within 25 diam-
V
C C h /A C eters upstream of the flume.
S e e u V
0.1 1.002 7.3.1.2 If the flow in the channel or sewer is supercritical,
0.2 1.009
theflumeshouldbeinstalledsothatahydraulicjumpiscaused
0.3 1.021
to form at least 25 channel widths or 30 pipe diameters
0.4 1.039
0.5 1.064 upstream.
0.6 1.098
7.3.1.3 To avoid surface disturbances at the head measure-
0.7 1.146
ment location it is recommended that the Froude number, F,of
0.8 1.218
0.9 1.340 the approach flow not exceed 0.5 for about 20 channel widths
or pipe diameters upstream, that is:
¯ 1
d
u
~ !
F 5 V / g )2# 0.5
u
7.2.3.5 Limiting Conditions—The foregoing discharge
¯
where d is the average approach depth (area divided by
equationandcoefficientsarevalidforthefollowingconditions: u
water surfaced width).
(1) 0.1 ≤ h/L ≤ 0.5, with minimum h = 0.15 ft (0.05 m),
7.3.2 Downstream Conditions—Submergence:
(2) B ≤ 0.33 ft (0.1 m),
7.3.2.1 Palmer-Bowlus flumes must be installed so as to
(3) h<6ft(2m),
avoid submergence by the tailwater. There is insufficient data
(4) The throat ramp slopes do not exceed one or three,
on flow through submerged flumes to permit flow rate adjust-
(5) Throat floor is level,
ments for this condition to be made reliably.
(6) Trapezoidalthroatsectionishighenoughtocontainthe
7.3.2.2 Submergence will be avoided if the tailwater depth
maximum flow, and
(relative to the throat floor) does not exceed the critical depth
(7) Roughness of throat surfaces does not exceed that of
in the throat. Values of the critical depth are given in Table 3.
smooth concrete.
Thisisaconservativecriterionandadherencetoitmayinsome
7.2.3.6 Calculating the Discharge for a Given Head—
cases require a steeper downstream slope or a built-in drop in
Obtaining the theoretical discharge for a given or measured
the channel immediately downstream of the flume.
head using Eq 1 is necessarily an iterative procedure; one
7.3.2.3 Less stringent criteria than that of 7.3.2.2 have been
possible
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D5390 − 93 (Reapproved 2013) D5390 − 21
Standard Test Method for
Open-Channel Flow Measurement of Water with Palmer-
Bowlus Flumes
This standard is issued under the fixed designation D5390; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This test method covers measurement of the volumetric flowrate flow rate of water and wastewater in sewers and other open
channels with Palmer-Bowlus flumes.
1.2 The values stated in inch-pound units are to be regarded as the standard. The SI units values given in parentheses are for
information only.mathematical conversions to SI units that are provided for information only and are not considered standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D1129 Terminology Relating to Water
D1941 Test Method for Open Channel Flow Measurement of Water with the Parshall Flume
D2777 Practice for Determination of Precision and Bias of Applicable Test Methods of Committee D19 on Water
D3858 Test Method for Open-Channel Flow Measurement of Water by Velocity-Area Method
D5242 Test Method for Open-Channel Flow Measurement of Water with Thin-Plate Weirs
2.2 ISO Standards:
ISO 4359 Liquid Flow Measurement in Open Channels—Rectangular, Trapezoidal and U-Shaped Flumes
ISO 555 Liquid Flow Measurements in Open Channels—Dilution Methods for Measurement of Steady Flow—Constant Rate
Injection Method
2.3 ASME Standard:
Fluid Meters Their Theory and Application
This test method is under the jurisdiction of ASTM Committee D19 on Water and is the direct responsibility of Subcommittee D19.07 on Sediments, Geomorphology,
and Open-Channel Flow.
Current edition approved Jan. 1, 2013Nov. 1, 2021. Published January 2013January 2022. Originally approved in 1993. Last previous edition approved in 20072013 as
D5390 – 93 (2007).(2013). DOI: 10.1520/D5390-93R13.10.1520/D5390-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Available from American Society of Mechanical Engineers (ASME), ASME International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
www.asme.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5390 − 21
3. Terminology
3.1 Definitions—Definitions: For definitions of terms used in this test method refer to Terminology D1129.
3.1.1 For definitions of terms used in this standard, refer to Terminology D1129.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 boundary layer displacement thickness—thickness, n—the boundary layer is a layer of fluid flow adjacent to a solid surface
(in this case, the flume throat) in which, owing to viscous friction, the velocity increases from zero at the stationary surface to an
essentially frictionless-flow value at the edge of the layer. The displacement thickness is a distance normal to the solid surface that
the surface and flow streamlines can be considered to have been displaced by virtue of the boundary-layer formation.
3.2.2 critical flow—flow, n—the energy in open channel flow in which the energy expressed in terms of depth plus velocity head,
head and is a minimum for a given flowrate flow rate and channel. The Froude number is unity at critical flow.
3.2.3 Froude number—number, n—a dimensionless number expressing the ratio of inertial to gravity forces in free-surface flow.
It is equal to the average velocity divided by the square root of the product of the average depth and the acceleration due to gravity.
3.2.4 head—head, n—the depth of flow referenced to the floor of the throat measured at an appropriate location upstream of the
flume; this depth plus the velocity head is often termed the total head or total energy head.
3.2.5 hydraulic jump—jump, n—an abrupt transition from supercritical flow to subcritical or tranquil flow, accompanied by
considerable turbulence or gravity waves, or both.
3.2.6 long-throated flume—flume, n—a flume in which the prismatic throat is long enough relative to the head for essentially
critical flow to develop on the crest.
3.2.7 primary instrument—instrument, n—the device (in this case the flume) that creates a hydrodynamic condition that can be
sensed by the secondary instrument.
3.2.8 Reynolds number—number, n—a dimensionless number expressing the ratio of inertial to viscous forces in a flow. In a flume
throat the pertinent Reynolds number is equal to the (critical) throat velocity multiplied by the throat length and divided by the
kinematic viscosity of the water.
3.2.9 scow float—float, n—an in-stream float for depth sensing, usually mounted on a hinged cantilever.
3.2.10 secondary instrument—instrument, n—in this case, a device that measures the depth of flow (referenced to the throat
elevation) at an appropriate location upstream of the flume. The secondary instrument may also convert this measured head to an
indicated flowrate, flow rate, or could totalize flowrate. flow rate.
3.2.11 stilling well—well, n—a small free-surface reservoir connected through a restricted passage to the approach channel
upstream of the flume so that a head measurement can be made under quiescent conditions.
3.2.12 subcritical flow—flow, n—open channel flow that is deeper and at lower velocity than critical flow for the same flowrate;
flow rate; sometimes called tranquil flow.
3.2.13 submergence—submergence, n—a condition where the depth of flow immediately downstream of the flume is large enough
to affect the flow through the flume so that the flowrate flow rate can no longer be related to a single upstream head.
3.2.14 supercritical flow—flow, n—open channel flow that is shallower and at higher velocity than critical flow for the same
flowrate. flow rate.
3.2.15 tailwater—tailwater, n—the water elevation immediately downstream of the flume.
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3.2.16 throat—throat, n—the constricted portion of the flume.
3.2.17 velocity head—head, n—the square of the average velocity divided by twice the acceleration due to gravity.
4. Summary of Test Method
4.1 In Palmer-Bowlus flumes, critical free-surface flow is developed in a prismatic throat so that the flowrate flow rate is a unique
function of a single measured upstream head for a given throat shape and upstream channel geometry. This function can be
obtained theoretically for ideal (frictionless) flows and adjustments for non-ideal conditions can be obtained experimentally or
estimated from fluid-mechanics considerations.
5. Significance and Use
5.1 Although Palmer-Bowlus flumes can be used in many types of open channels, they are particularly adaptable for permanent
or temporary installation in circular sewers. Commercial flumes are available for use in sewers from 4 in. to 6 ft (0.1 to 1.8 m)
in diameter.
5.2 A properly designed and operated Palmer-Bowlus is capable of providing accurate flow measurements while introducing a
relatively small head loss and exhibiting good sediment and debris-passing characteristics.
6. Interferences
6.1 Flumes are applicable only to open-channel flow and become inoperative under full-pipe flow conditions.
6.2 The flume becomes inoperative if downstream conditions cause submergence (see 7.3.2).
7. Apparatus
7.1 A Palmer-Bowlus flume measuring system consists of the flume itself (the primary), with its immediate upstream and
downstream channels, and a depth or head measuring device (the secondary). The secondary device can range from a simple scale
or gagegauge for manual readings to an instrument that continuously senses the head, converts it to a flowrate, flow rate, and
displays or transmits a readout or record of the instantaneous flowrate flow rate or the totalized flow, or both.
7.2 The Palmer-Bowlus Flume:
7.2.1 General Configuration:
7.2.1.1 The Palmer-Bowlus flume is a class of long-throated flume in which critical flow is developed in a throat that is formed
by constricted sidewalls or a bottom rise, or both. Sloped ramps form gradual transitions between the throat and the upstream and
downstream sections. See Fig. 1. The flume was developed primarily for use in sewers but it is adaptable to other open channels
as well. There is no standardized shape for Palmer-Bowlus flumes and, as long-throated flumes, they can be designed to fit specific
hydraulic situations using the theory outlined in 7.2.3.
7.2.1.2 Prefabricated Flumes—Prefabricated flumes with trapezoidal or rectangular throats and with circular or U-shaped outside
forms are commercially available for use in sewers. Although there is no fixed shape for Palmer-Bowlus flumes, many
FIG. 1 Generalized Palmer-Bowlus (Long-Throated) Flume in a Rectangular Channel
Palmer, H. K., and Bowlus, F. D., “Adaptation of Venturi Flumes to Flow Measurements in Conduits,” Trans. ASCE, Vol 101, 1936, pp. 1195–1216.
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FIG. 2 Palmer-Bowlus Flume (Typical) for Sewer
manufacturers of trapezoidal-throated flumes use the proportions shown in Fig. 2. These prefabricated flumes are also available
in several configurations depending on how they are to be installed, for example, whether they will be placed in the channel at
the base of an existing manhole, inserted into the pipe immediately downstream of the manhole, or incorporated into new
construction. The size of these prefabricated flumes is customarily referenced to the diameter of the receiving pipe rather than to
the throat width. Refer to manufacturers’ literature for flume details.
7.2.1.3 Because the dimensions of prefabricated flumes may differ depending upon the manufacturer or the configuration, or both,
it is important that users check interior dimensions carefully before installation and insure that these dimensions are not affected
by the installation process.
7.2.1.4 A Palmer-Bowlus flume can be fabricated in a pipe by raising the invert (see Fig. X3.1). Floor slabs that can be grouted
into existing sewers are commercially available, as are prefabricated slab-pipe combinations for insertion into larger pipes. Details
may be obtained from the manufacturers’ literature. Discharge equations for this throat shape are given in Appendix X1.
7.2.2 Head Measurement Location—The head, h, on the flume is measured at a distance upstream of the throat-approach ramp that
is preferably equal to three times the maximum head. When the maximum head is restricted to one-half the throat length, as is
recommended in this test method, an upstream distance equal to the maximum head will usually be adequate to avoid the
drawdown curvature of the flow profile.
7.2.3 Discharge Relations:
7.2.3.1 The volumetric flowrate, flow rate, Q, through a Palmer-Bowlus flume of bottom throat width, B, operating under a head,
h, above the throat floor is:
Q 5 ~2/3!~2g/3!1/2C C C Bh 2 (1)
D S V
where g is the acceleration due to gravity and C C and C are, respectively, the discharge coefficient, throat shape coefficient,
D S V
and velocity-of-approach coefficient as defined in the following sections. The derivation of Eq 1 is outlined in Appendix X2.
7.2.3.2 Discharge Coeffıcient, C —This coefficient approximates the effect of viscous friction on the theoretical discharge by
D
allowing for the development of a boundary layer of displacement thickness δ along the bottom and sides of the throat:
*
C 5 B /B 12 δ /h 2 (2)
~ !~ !
D e *
Here B is an effective throat width given by:
e
B 5 B 2 2δ @ m 11 2 2 m# (3)
~ !
e *
where m is the horizontal-to-vertical slope of the sides of the throat (zero for rectangular throats). The displacement thickness,
δ , is a function of the throat Reynolds number and surface roughness. However, a reasonable approximation that is adequate for
*
many applications is:
δ 5 0.003 L (4)
*
where L is the length of the throat. (Better estimates of δ can be obtained from boundary-layer theory, as in ISO 4359.)
*
7.2.3.3 Shape Coeffıcient, C (See Also Appendix X2)—C is given in Table 1 as a function of mH /B/B .H is the upstream total
S S e e e
effective head, which is (for essentially uniform upstream velocity distribution):
H 5 h1V /2g 2 δ (5)
e u *
where V is the average velocity at the position of head measurement. For a rectangular throat, m + 0 and C is unity.
u S
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TABLE 1 Shape Coefficient, C
S
mH /B C mH /B mC mH /B C mH /B C
e e S e e S e e S e e S
0.010 1.007 0.40 1.276 1.80 2.288 3.80 3.766
0.015 1.010 0.45 1.311 1.90 2.360 3.90 3.840
0.020 1.013 0.50 1.346 2.00 2.433 4.00 3.914
0.025 1.017 0.55 1.381 2.10 2.507 4.10 3.988
0.030 1.020 0.60 1.417 2.20 2.582 4.20 4.062
0.040 1.028 0.65 1.453 2.30 2.657 4.30 4.136
0.050 1.035 0.70 1.490 2.40 2.731 4.40 4.210
0.060 1.041 0.75 1.527 2.50 2.805 4.50 4.284
0.070 1.048 0.80 1.564 2.60 2.879 4.60 4.358
0.080 1.054 0.85 1.600 2.70 2.953 4.70 4.432
0.090 1.060 0.90 1.636 2.80 3.027 4.80 4.505
0.10 1.066 0.95 1.670 2.90 3.101 4.90 4.579
0.12 1.080 1.00 1.705 3.00 3.175 5.00 4.653
0.14 1.093 1.10 1.779 3.10 3.249 5.50 5.03
0.16 1.106 1.20 1.852 3.20 3.323 6.00 5.40
0.18 1.119 1.30 1.925 3.30 3.397 7.00 6.15
0.20 1.133 1.40 1.997 3.40 3.471 8.00 6.89
0.25 1.169 1.50 2.069 3.50 3.545 9.00 7.63
0.30 1.204 1.60 2.142 3.60 3.618 10.0 8.37
0.35 1.240 1.70 2.215 3.70 3.692 . .
7.2.3.4 Velocity-of-Approach Coeffıcient, C —This coefficient allows the flowrate flow rate to be expressed conveniently in terms
V
of the measured head, h, rather than the total head, H:
3 3
C 5 @~H 2 δ !/~h 2 δ !#2 5 ~H /h ! 2 (6)
V * * e e
C is given in Table 2 as a function of C B h /A , where A is the cross-sectional area of the flow at the head measurement
V S e e u u
station. See also Appendix X3.
7.2.3.5 Limiting Conditions—The foregoing discharge equation and coefficients are valid for the following conditions:
(1) 0.1 ≤ h/L ≤ 0.5, with minimum h = 0.15 ft (0.05 m),
(2) B ≤ 0.33 ft (0.1 m),
(3) h < 6 ft (2 m),
(4) The throat ramp slopes do not exceed one or three,
(5) Throat floor is level,
(6) Trapezoidal throat section is high enough to contain the maximum flow, and
(7) Roughness of throat surfaces does not exceed that of smooth concrete.
7.2.3.6 Calculating the Discharge for a Given Head—Obtaining the theoretical discharge for a given or measured head using Eq
1 is necessarily an iterative procedure; one possible approach is outlined in the following:
(1) Calculate the estimated C from Eq 2Eq 2. . (This coefficient remains the same during subsequent iterations.),
D
(2) For first trial: assume H = h, compute mH /B and obtain C from Table 1. (In most cases, use of mH/B would be
e e S
adequate.),
(3) Compute Q from Eq 1. (C is 1.0 for first trial.),
V
(4) Determine the approach velocity, V , for this Q and h,
u
(5) For second trial: use H = h + V /2g and corresponding second-trial values of C and C , and
u V S
(6) Compute the second-trial Q and repeat the last three steps until convergence.
TABLE 2 Velocity-of-Approach Coefficient, C
V
C C h /A C
S e e u V
0.1 1.002
0.2 1.009
0.3 1.021
0.4 1.039
0.5 1.064
0.6 1.098
0.7 1.146
0.8 1.218
0.9 1.340
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7.2.3.7 Discharge Curves for Commercial Flumes—When head versus discharge data are provided with a commercial
prefabricated flume, the manufacturer must specify the method by which the information was obtained, that is, from laboratory
experiments, from theory as described in this section or a modification thereof. An accuracy estimate should be included.
7.3 Installation Conditions:
7.3.1 Approach Conditions:
7.3.1.1 The flow approaching the flume should be tranquil and uniformly distributed across the channel in order to conform to the
conditions assumed in the derivation of Eq 1. For this purp
...