ASTM D5390-93(2007)
(Test Method)Standard Test Method for Open-Channel Flow Measurement of Water with Palmer-Bowlus Flumes
Standard Test Method for Open-Channel Flow Measurement of Water with Palmer-Bowlus Flumes
SIGNIFICANCE AND USE
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.
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 flowrate 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 given in parentheses are for information only.
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 and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: D5390 − 93(Reapproved 2007)
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 2.3 ASME Standard:
Fluid Meters— Their Theory and Application
1.1 This test method covers measurement of the volumetric
flowrate of water and wastewater in sewers and other open
3. Terminology
channels with Palmer-Bowlus flumes.
3.1 Definitions—For definitions of terms used in this test
1.2 The values stated in inch-pound units are to be regarded
method refer to Terminology D1129.
as the standard. The SI units given in parentheses are for
3.2 Definitions of Terms Specific to This Standard:
information only.
3.2.1 boundary layer displacement thickness— the bound-
1.3 This standard does not purport to address all of the
ary layer is a layer of fluid flow adjacent to a solid surface (in
safety concerns, if any, associated with its use. It is the
this case, the flume throat) in which, owing to viscous friction,
responsibility of the user of this standard to establish appro-
the velocity increases from zero at the stationary surface to an
priate safety and health practices and determine the applica-
essentially frictionless-flow value at the edge of the layer. The
bility of regulatory limitations prior to use.
displacementthicknessisadistancenormaltothesolidsurface
that the surface and flow streamlines can be considered to have
2. Referenced Documents
been displaced by virtue of the boundary-layer formation.
2.1 ASTM Standards:
3.2.2 critical flow—open channel flow in which the energy
D1129 Terminology Relating to Water
expressed in terms of depth plus velocity head, is a minimum
D1941 Test Method for Open Channel Flow Measurement
for a given flowrate and channel. The Froude number is unity
of Water with the Parshall Flume
at critical flow.
D2777 Practice for Determination of Precision and Bias of
3.2.3 Froude number—a dimensionless number expressing
Applicable Test Methods of Committee D19 on Water
the ratio of inertial to gravity forces in free-surface flow. It is
D3858 Test Method for Open-Channel Flow Measurement
equal to the average velocity divided by the square root of the
of Water by Velocity-Area Method
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—the depth of flow referenced to the floor of the
2.2 ISO Standards:
throat measured at an appropriate location upstream of the
ISO 4359 Liquid Flow Measurement in Open Channels—
flume;thisdepthplusthevelocityheadisoftentermedthetotal
Rectangular, Trapezoidal and U-Shaped Flumes
head or total energy head.
ISO 555 Liquid Flow Measurements in Open Channels—
Dilution Methods for Measurement of Steady Flow—
3.2.5 hydraulic jump—an abrupt transition from supercriti-
Constant Rate Injection Method cal flow to subcritical or tranquil flow, accompanied by
considerable turbulence or gravity waves, or both.
3.2.6 long-throated flume—a flume in which the prismatic
This test method is under the jurisdiction of ASTM Committee D19 on Water
throat is long enough relative to the head for essentially critical
and is the direct responsibility of Subcommittee D19.07 on Sediments,
flow to develop on the crest.
Geomorphology, and Open-Channel Flow.
Current edition approved June 15, 2007. Published July 2007. Originally
3.2.7 primary instrument—the device (in this case the
approved in 1993. Last previous edition approved in 2002 as D5390 – 93 (2002).
flume) that creates a hydrodynamic condition that can be
DOI: 10.1520/D5390-93R07.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or sensed by the secondary instrument.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. Available from American Society of Mechanical Engineers (ASME), ASME
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St., International Headquarters, Three Park Ave., New York, NY 10016-5990, http://
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D5390 − 93 (2007)
3.2.8 Reynolds number—a dimensionless number express- 6.2 The flume becomes inoperative if downstream condi-
ing the ratio of inertial to viscous forces in a flow. In a flume tions cause submergence (see 7.3.2).
throat the pertinent Reynolds number is equal to the (critical)
7. Apparatus
throat velocity multiplied by the throat length and divided by
the kinematic viscosity of the water.
7.1 A Palmer-Bowlus flume measuring system consists of
the flume itself (the primary), with its immediate upstream and
3.2.9 scow float—an in-stream float for depth sensing,
downstream channels, and a depth or head measuring device
usually mounted on a hinged cantilever.
(thesecondary).Thesecondarydevicecanrangefromasimple
3.2.10 secondary instrument—in this case, a device that
scale or gage for manual readings to an instrument that
measures the depth of flow (referenced to the throat elevation)
continuously senses the head, converts it to a flowrate, and
at an appropriate location upstream of the flume. The second-
displays or transmits a readout or record of the instantaneous
ary instrument may also convert this measured head to an
flowrate or the totalized flow, or both.
indicated flowrate, or could totalize flowrate.
3.2.11 stilling well—a small free-surface reservoir con-
nected through a restricted passage to the approach channel
upstreamoftheflumesothataheadmeasurementcanbemade
under quiescent conditions.
3.2.12 subcritical flow—open channel flow that is deeper
and at lower velocity than critical flow for the same flowrate;
sometimes called tranquil flow.
FIG. 1 Generalized Palmer-Bowlus (Long-Throated) Flume in a
Rectangular Channel
3.2.13 submergence—a condition where the depth of flow
immediately downstream of the flume is large enough to affect
theflowthroughtheflumesothattheflowratecannolongerbe
related to a single upstream head.
3.2.14 supercritical flow—open channel flow that is shal-
lower and at higher velocity than critical flow for the same
flowrate.
3.2.15 tailwater—the water elevation immediately down-
stream of the flume.
3.2.16 throat—the constricted portion of the flume.
FIG. 2 Palmer-Bowlus Flume (Typical) for Sewer
3.2.17 velocity head—the square of the average velocity
divided by twice the acceleration due to gravity.
7.2 The Palmer-Bowlus Flume:
7.2.1 General Configuration:
4. Summary of Test Method
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
4.1 In Palmer-Bowlus flumes, critical free-surface flow is
formed by constricted sidewalls or a bottom rise, or both.
developed in a prismatic throat so that the flowrate is a unique
Sloped ramps form gradual transitions between the throat and
function of a single measured upstream head for a given throat
the upstream and downstream sections. See Fig. 1. The flume
shape and upstream channel geometry. This function can be
was developed primarily for use in sewers but it is adaptable
obtained theoretically for ideal (frictionless) flows and adjust-
to other open channels as well. There is no standardized shape
ments for non-ideal conditions can be obtained experimentally
for Palmer-Bowlus flumes and, as long-throated flumes, they
or estimated from fluid-mechanics considerations.
can be designed to fit specific hydraulic situations using the
theory outlined in 7.2.3.
5. Significance and Use
7.2.1.2 Prefabricated Flumes—Prefabricated flumes with
5.1 Although Palmer-Bowlus flumes can be used in many
trapezoidalorrectangularthroatsandwithcircularorU-shaped
types of open channels, they are particularly adaptable for
outside forms are commercially available for use in sewers.
permanent or temporary installation in circular sewers. Com-
Although there is no fixed shape for Palmer-Bowlus flumes,
mercial flumes are available for use in sewers from 4 in. to 6
many manufacturers of trapezoidal-throated flumes use the
ft (0.1 to 1.8 m) in diameter.
proportions shown in Fig. 2. These prefabricated flumes are
5.2 A properly designed and operated Palmer-Bowlus is
also available in several configurations depending on how they
capable of providing accurate flow measurements while intro-
are to be installed, for example, whether they will be placed in
ducing a relatively small head loss and exhibiting good
thechannelatthebaseofanexistingmanhole,insertedintothe
sediment and debris-passing characteristics.
pipe immediately downstream of the manhole, or incorporated
into new construction.The size of these prefabricated flumes is
6. Interferences
6.1 Flumes are applicable only to open-channel flow and
Palmer, H. K., and Bowlus, F. D., “Adaptation of Venturi Flumes to Flow
become inoperative under full-pipe flow conditions. Measurements in Conduits,” Trans. ASCE, Vol 101, 1936, pp. 1195–1216.
D5390 − 93 (2007)
customarily referenced to the diameter of the receiving pipe
C 5 ~B /B!~1 2 δ /h! 2 (2)
D e *
rather than to the throat width. Refer to manufacturers’
literature for flume details.
Here B is an effective throat width given by:
e
7.2.1.3 Becausethedimensionsofprefabricatedflumesmay
differdependinguponthemanufacturerortheconfiguration,or
B 5 B 2 2δ @~m 11! 2 2 m# (3)
e *
both, it is important that users check interior dimensions
carefully before installation and insure that these dimensions
where m is the horizontal-to-vertical slope of the sides of the
are not affected by the installation process.
throat (zero for rectangular throats). The displacement thick-
7.2.1.4 A Palmer-Bowlus flume can be fabricated in a pipe
ness, δ , is a function of the throat Reynolds number and
*
by raising the invert (see Fig. X3.1). Floor slabs that can be
surface roughness. However, a reasonable approximation that
grouted into existing sewers are commercially available, as are
is adequate for many applications is:
prefabricated slab-pipe combinations for insertion into larger
δ 5 0.003 L (4)
pipes. Details may be obtained from the manufacturers’ litera- *
ture. Discharge equations for this throat shape are given in
Appendix X1.
where L is the length of the throat. (Better estimates of δ
*
7.2.2 Head Measurement Location—The head, h, on the
can be obtained from boundary-layer theory, as in ISO 4359.)
flume is measured at a distance upstream of the throat-
7.2.3.3 Shape Coeffıcient, C (SeeAlso Appendix X2)—C is
S S
approach ramp that is preferably equal to three times the
given in Table 1 as a function of mH /B.H is the upstream
e e e
maximum head. When the maximum head is restricted to
total effective head, which is (for essentially uniform upstream
one-half the throat length, as is recommended in this test
velocity distribution):
method, an upstream distance equal to the maximum head will
H 5 h1V /2g 2 δ (5)
e u *
usually be adequate to avoid the drawdown curvature of the
flow profile.
where V is the average velocity at the position of head
7.2.3 Discharge Relations:
u
measurement. For a rectangular throat, m + 0 and C is unity.
7.2.3.1 The volumetric flowrate, Q, through a Palmer-
S
7.2.3.4 Velocity-of-Approach Coeffıcient, C —This coeffi-
Bowlus flume of bottom throat width, B , operating under a
V
cient allows the flowrate to be expressed conveniently in terms
head, h, above the throat floor is:
of the measured head, h, rather than the total head, H:
Q 5 ~2/3!~2g/3!1/2C C C Bh 2 (1)
D S V
3 3
C 5 H 2 δ / h 2 δ 2 5 H /h 2 (6)
@~ ! ~ !# ~ !
V * * e e
where g is the acceleration due to gravity and C C and C
D S V
are, respectively, the discharge coefficient, throat shape coef- C is given in Table 2 as a function of C B h /A , where A
V S e e u u
is the cross-sectional area of the flow at the head measurement
ficient, and velocity-of-approach coefficient as defined in the
following sections. The derivation of Eq 1 is outlined in station. See also Appendix X3.
Appendix X2. 7.2.3.5 Limiting Conditions—The foregoing discharge
7.2.3.2 Discharge Coeffıcient, C —Thiscoefficientapproxi- equationandcoefficientsarevalidforthefollowingconditions:
D
mates the effect of viscous friction on the theoretical discharge (a) 0.1 ≤ h/L ≤ 0.5, with minimum h = 0.15 ft (0.05 m),
by allowing for the development of a boundary layer of (b) B ≤ 0.33 ft (0.1 m),
displacement thickness δ along the bottom and sides of the (c) h<6ft(2m),
*
throat: (d) The throat ramp slopes do not exceed one or three,
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 − 93 (2007)
TABLE 2 Velocity-of-Approach Coefficient,C
the approach flow not exceed 0.5 for about 20 channel widths
V
C C h /A C or pipe diameters upstream, that is:
S e e u V
0.1 1.002
¯ 1
d
u
F 5 V /~g !)2# 0.5
0.2 1.009 u
0.3 1.021
where d¯ is the average approach depth (area divided by
0.4 1.039 u
0.5 1.064 water surfaced width).
0.6 1.098
7.3.2 Downstream Conditions—Submergence :
0.7 1.146
0.8 1.218
0.9 1.340
TABLE 3 Critical Depth in Throat
mH /B d /H mH /B d /H
e e e e e e e e
0.00 0.667 2.00 0.762
(e) Throat floor is level, 0.05 0.674 2.50 0.768
0.10 0.680 3.00 0.773
(f) Trapezoidal throat section is high enough to contain the
0.20 0.692 3.50 0.776
maximum flow, and
0.30 0.701 4.00 0.778
0.40 0.709 4.50 0.780
(g) Roughness of throat surfaces does not exceed that of
0.50 0.717 5.
...
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