ASTM D5390-93(2002)
(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
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.
1.3 This standard does not purport to address all of the safety problems, 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:D 5390–93 (Reapproved 2002)
Standard Test Method for
Open-Channel Flow Measurement of Water with Palmer-
Bowlus Flumes
This standard is issued under the fixed designation D 5390; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This test method covers measurement of the volumetric 3.1 Definitions—For definitions of terms used in this test
flowrate of water and wastewater in sewers and other open method refer to Terminology D 1129.
channels with Palmer-Bowlus flumes. 3.2 Definitions of Terms Specific to This Standard:
1.2 The values stated in inch-pound units are to be regarded 3.2.1 boundary layer displacement thickness—theboundary
as the standard. The SI units given in parentheses are for layer is a layer of fluid flow adjacent to a solid surface (in this
information only. case, the flume throat) in which, owing to viscous friction, the
1.3 This standard does not purport to address all of the velocity increases from zero at the stationary surface to an
safety concerns, if any, associated with its use. It is the essentially frictionless-flow value at the edge of the layer. The
responsibility of the user of this standard to establish appro- displacement thickness is a distance normal to the solid surface
priate safety and health practices and determine the applica- that the surface and flow streamlines can be considered to have
bility of regulatory limitations prior to use. been displaced by virtue of the boundary-layer formation.
3.2.2 critical flow—open channel flow in which the energy
2. Referenced Documents
expressed in terms of depth plus velocity head, is a minimum
2.1 ASTM Standards:
for a given flowrate and channel. The Froude number is unity
D 1129 Terminology Relating to Water at critical flow.
D 1941 Test Method for Open Channel Flow Measurement
3.2.3 Froude number—a dimensionless number expressing
of Water with the Parshall Flume the ratio of inertial to gravity forces in free-surface flow. It is
D 2777 Practice for Determination of Precision and Bias of
equal to the average velocity divided by the square root of the
Applicable Methods of Committee D19 on Water
product of the average depth and the acceleration due to
D 3858 Test Method for Open-Channel Flow Measurement gravity.
of Water by Velocity-Area Methods
3.2.4 head—the depth of flow referenced to the floor of the
D 5242 Test Method for Open Channel Flow Measurement throat measured at an appropriate location upstream of the
of Water with Thin-Plate Weirs
flume;thisdepthplusthevelocityheadisoftentermedthetotal
2.2 ISO Standards: head or total energy head.
ISO 4359 Liquid Flow Measurement in Open Channels—
3.2.5 hydraulic jump—an abrupt transition from supercriti-
Rectangular, Trapezoidal and U-Shaped Flumes cal flow to subcritical or tranquil flow, accompanied by
ISO 555 Liquid Flow Measurements in Open Channels—
considerable turbulence or gravity waves, or both.
Dilution Methods for Measurement of Steady Flow— 3.2.6 long-throated flume—a flume in which the prismatic
Constant Rate Injection Method
throat is long enough relative to the head for essentially critical
2.3 ASME Standard: flow to develop on the crest.
Fluid Meters— Their Theory and Application
3.2.7 primary instrument—the device (in this case the
flume) that creates a hydrodynamic condition that can be
sensed by the secondary instrument.
This test method is under the jurisdiction of ASTM Committee D19 on Water
3.2.8 Reynolds number—a dimensionless number express-
and is the direct responsibility of Subcommittee D19.07 on Sediments, Geomor-
ing the ratio of inertial to viscous forces in a flow. In a flume
phology, and Open-Channel Flow.
Current edition approved April 15, 1993. Published June 1993. throat the pertinent Reynolds number is equal to the (critical)
Annual Book of ASTM Standards, Vol 11.01.
throat velocity multiplied by the throat length and divided by
Available from American National Standards Institute, 11 West 42nd Street,
the kinematic viscosity of the water.
13th Floor, New York, NY 10036.
Available fromAmerican Society of Mechanical Engineers, 345 E. 47th Street,
New York, NY 10017.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5390–93 (2002)
3.2.9 scow float—an in-stream float for depth sensing, continuously senses the head, converts it to a flowrate, and
usually mounted on a hinged cantilever. displays or transmits a readout or record of the instantaneous
3.2.10 secondary instrument—in this case, a device that flowrate or the totalized flow, or both.
measures the depth of flow (referenced to the throat elevation)
at an appropriate location upstream of the flume. The second-
ary instrument may also convert this measured head to an
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
upstream of the flume so that a head measurement can be made
under quiescent conditions.
FIG. 1 Generalized Palmer-Bowlus (Long-Throated) Flume in a
3.2.12 subcritical flow—open channel flow that is deeper
Rectangular Channel
and at lower velocity than critical flow for the same flowrate;
sometimes called tranquil flow.
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-
FIG. 2 Palmer-Bowlus Flume (Typical) for Sewer
stream of the flume.
3.2.16 throat—the constricted portion of the flume.
3.2.17 velocity head—the square of the average velocity 7.2 The Palmer-Bowlus Flume:
divided by twice the acceleration due to gravity.
7.2.1 General Configuration:
7.2.1.1 The Palmer-Bowlus flume is a class of long-throated
4. Summary of Test Method
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
customarily referenced to the diameter of the receiving pipe
6.1 Flumes are applicable only to open-channel flow and
rather than to the throat width. Refer to manufacturers’
become inoperative under full-pipe flow conditions.
literature for flume details.
6.2 The flume becomes inoperative if downstream condi-
7.2.1.3 Becausethedimensionsofprefabricatedflumesmay
tions cause submergence (see 7.3.2).
differdependinguponthemanufacturerortheconfiguration,or
both, it is important that users check interior dimensions
7. Apparatus
carefully before installation and insure that these dimensions
7.1 A Palmer-Bowlus flume measuring system consists of
are not affected by the installation process.
the flume itself (the primary), with its immediate upstream and
downstream channels, and a depth or head measuring device
(thesecondary).Thesecondarydevicecanrangefromasimple
Palmer, H. K., and Bowlus, F. D., “Adaptation of Venturi Flumes to Flow
scale or gage for manual readings to an instrument that Measurements in Conduits,” Trans. ASCE, Vol 101, 1936, pp. 1195–1216.
D 5390–93 (2002)
7.2.1.4 A Palmer-Bowlus flume can be fabricated in a pipe where m is the horizontal-to-vertical slope of the sides of the
by raising the invert (see Fig. X3.1). Floor slabs that can be throat (zero for rectangular throats). The displacement thick-
grouted into existing sewers are commercially available, as are ness, d , is a function of the throat Reynolds number and
*
prefabricated slab-pipe combinations for insertion into larger surface roughness. However, a reasonable approximation that
pipes. Details may be obtained from the manufacturers’ litera- is adequate for many applications is:
ture. Discharge equations for this throat shape are given in
d 5 0.003 L (4)
*
Appendix X1.
7.2.2 Head Measurement Location—The head, h, on the
where L is the length of the throat. (Better estimates of d
*
flume is measured at a distance upstream of the throat-
can be obtained from boundary-layer theory, as in ISO 4359.)
approach ramp that is preferably equal to three times the
7.2.3.3 Shape Coeffıcient, C (See Also Appendix X2)—C
S S
maximum head. When the maximum head is restricted to
is given in Table 1 as a function of mH /B.H is the upstream
e e e
one-half the throat length, as is recommended in this test
total effective head, which is (for essentially uniform upstream
method, an upstream distance equal to the maximum head will
velocity distribution):
usually be adequate to avoid the drawdown curvature of the
flow profile. H 5 h 1 V /2g2d (5)
e u *
7.2.3 Discharge Relations:
7.2.3.1 The volumetric flowrate, Q, through a Palmer-
where V is the average velocity at the position of head
u
Bowlus flume of bottom throat width, B, operating under a
measurement. For a rectangular throat, m + 0 and C is unity.
S
head, h, above the throat floor is:
7.2.3.4 Velocity-of-Approach Coeffıcient, C —This coeffi-
V
cient allows the flowrate to be expressed conveniently in terms
Q 5 ~2/3!~2g/3!1/2C C C Bh (1)
D S V
of the measured head, h, rather than the total head, H:
3 3
where g is the acceleration due to gravity and C C and C 2 2
C 5 [~H2d !/~h2d !# 5 ~H /h ! (6)
D S V
V * * e e
are, respectively, the discharge coefficient, throat shape coef-
ficient, and velocity-of-approach coefficient as defined in the
C is given in Table 2 as a function of C B h /A , where A
V S e e u u
following sections. The derivation of Eq 1 is outlined in
is the cross-sectional area of the flow at the head measurement
Appendix X2.
station. See also Appendix X3.
7.2.3.2 Discharge Coeffıcient, C —This coefficient ap-
D
7.2.3.5 Limiting Conditions—The foregoing discharge
proximates the effect of viscous friction on the theoretical
equationandcoefficientsarevalidforthefollowingconditions:
discharge by allowing for the development of a boundary layer
(a) 0.1# h/L# 0.5, with minimum h = 0.15 ft (0.05 m),
of displacement thickness d along the bottom and sides of the
*
(b) B# 0.33 ft (0.1 m),
throat:
(c) h<6ft(2m),
(d) The throat ramp slopes do not exceed one or three,
C 5 ~B /B!~12d /h! 2 (2)
D e *
(e) Throat floor is level,
(f) Trapezoidal throat section is high enough to contain the
Here B is an effective throat width given by:
e
maximum flow, and
(g) Roughness of throat surfaces does not exceed that of
B 5 B 2 2d @~m 1 1! 2 2 m] (3)
e *
smooth concrete.
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 . .
D 5390–93 (2002)
TABLE 2 Velocity-of-Approach Coefficient,C
7.3.2 Downstream Conditions—Submergence:
V
C C h /A C 7.3.2.1 Palmer-Bowlus flumes must be installed so as to
S e e u V
0.1 1.002
0.2 1.009
TABLE 3 Critical Depth in Throat
0.3 1.021
mH /B d /H mH /B d /H
e e e e e e e e
0.4 1.039
0.5 1.064
0.00 0.667 2.00 0.762
0.6 1.098
0.05 0.674 2.50 0.768
0.7 1.146
0.10 0.680 3.00 0.773
0.8 1.218
0.20 0.692 3.50 0.776
0.9 1.340
0.30 0.701 4.00 0.778
0.40 0.709 4.50 0.780
0.50 0.717 5.00 0.782
0.60 0.723 5.50 0.784
7.2.3.6 Calculating the Discharge for a Given Head—
0.70 0.728 6.00 0.785
Obtaining the theoretical discharge for a given or measured
0.80 0.733 8.00 0.788
head using Eq 1 is necessarily an iterative procedure; one 0.90 0.737 10.00 0.791
1.00 0.740 12.00 0.792
possible approach is outlined in the following:
1.50 0.754 20.00 0.795
(a) Calculate the estimated C from Eq 2. (This coefficient
D
remains the same during subsequent iterations.),
(b) For first trial: assume H = h, compute mH /B and
...
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