1、Designation: D 5390 93 (Reapproved 2007)Standard Test Method forOpen-Channel Flow Measurement of Water with Palmer-Bowlus Flumes1This standard is issued under the fixed designation D 5390; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revi
2、sion, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers measurement of the volumetricflowrate of water and wastewater in sewers and
3、 other openchannels with Palmer-Bowlus flumes.1.2 The values stated in inch-pound units are to be regardedas the standard. The SI units given in parentheses are forinformation only.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresp
4、onsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 1129 Terminology Relating to WaterD 1941 Test Method for Open Channel Flow Measurementof
5、Water with the Parshall FlumeD 2777 Practice for Determination of Precision and Bias ofApplicable Test Methods of Committee D19 on WaterD 3858 Test Method for Open-Channel Flow Measurementof Water by Velocity-Area MethodD 5242 Test Method for Open-Channel Flow Measurementof Water with Thin-Plate Wei
6、rs2.2 ISO Standards:3ISO 4359 Liquid Flow Measurement in Open ChannelsRectangular, Trapezoidal and U-Shaped FlumesISO 555 Liquid Flow Measurements in Open ChannelsDilution Methods for Measurement of Steady FlowConstant Rate Injection Method32.3 ASME Standard:4Fluid Meters Their Theory and Applicatio
7、n3. Terminology3.1 DefinitionsFor definitions of terms used in this testmethod refer to Terminology D 1129.3.2 Definitions of Terms Specific to This Standard:3.2.1 boundary layer displacement thicknessthe boundarylayer is a layer of fluid flow adjacent to a solid surface (in thiscase, the flume thro
8、at) in which, owing to viscous friction, thevelocity increases from zero at the stationary surface to anessentially frictionless-flow value at the edge of the layer. Thedisplacement thickness is a distance normal to the solid surfacethat the surface and flow streamlines can be considered to havebeen
9、 displaced by virtue of the boundary-layer formation.3.2.2 critical flowopen channel flow in which the energyexpressed in terms of depth plus velocity head, is a minimumfor a given flowrate and channel. The Froude number is unityat critical flow.3.2.3 Froude numbera dimensionless number expressingth
10、e ratio of inertial to gravity forces in free-surface flow. It isequal to the average velocity divided by the square root of theproduct of the average depth and the acceleration due togravity.3.2.4 headthe depth of flow referenced to the floor of thethroat measured at an appropriate location upstrea
11、m of theflume; this depth plus the velocity head is often termed the totalhead or total energy head.3.2.5 hydraulic jumpan abrupt transition from supercriti-cal flow to subcritical or tranquil flow, accompanied byconsiderable turbulence or gravity waves, or both.3.2.6 long-throated flumea flume in w
12、hich the prismaticthroat is long enough relative to the head for essentially criticalflow to develop on the crest.3.2.7 primary instrumentthe device (in this case theflume) that creates a hydrodynamic condition that can besensed by the secondary instrument.1This test method is under the jurisdiction
13、 of ASTM Committee D19 on Waterand is the direct responsibility of Subcommittee D19.07 on Sediments, Geomor-phology, and Open-Channel Flow.Current edition approved June 15, 2007. Published July 2007. Originallyapproved in 1993. Last previous edition approved in 2002 as D 5390 93 (2002).2For referenc
14、ed ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd S
15、t.,4th Floor, New York, NY 10036, http:/www.ansi.org.4Available from American Society of Mechanical Engineers (ASME), ASMEInternational Headquarters, Three Park Ave., New York, NY 10016-5990, http:/www.asme.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA
16、19428-2959, United States.3.2.8 Reynolds numbera dimensionless number express-ing the ratio of inertial to viscous forces in a flow. In a flumethroat the pertinent Reynolds number is equal to the (critical)throat velocity multiplied by the throat length and divided bythe kinematic viscosity of the w
17、ater.3.2.9 scow floatan in-stream float for depth sensing,usually mounted on a hinged cantilever.3.2.10 secondary instrumentin this case, a device thatmeasures the depth of flow (referenced to the throat elevation)at an appropriate location upstream of the flume. The second-ary instrument may also c
18、onvert this measured head to anindicated flowrate, or could totalize flowrate.3.2.11 stilling wella small free-surface reservoir con-nected through a restricted passage to the approach channelupstream of the flume so that a head measurement can be madeunder quiescent conditions.3.2.12 subcritical fl
19、owopen channel flow that is deeperand at lower velocity than critical flow for the same flowrate;sometimes called tranquil flow.3.2.13 submergencea condition where the depth of flowimmediately downstream of the flume is large enough to affectthe flow through the flume so that the flowrate can no lon
20、ger berelated to a single upstream head.3.2.14 supercritical flowopen channel flow that is shal-lower and at higher velocity than critical flow for the sameflowrate.3.2.15 tailwaterthe water elevation immediately down-stream of the flume.3.2.16 throatthe constricted portion of the flume.3.2.17 veloc
21、ity headthe square of the average velocitydivided by twice the acceleration due to gravity.4. Summary of Test Method4.1 In Palmer-Bowlus flumes, critical free-surface flow isdeveloped in a prismatic throat so that the flowrate is a uniquefunction of a single measured upstream head for a given throat
22、shape and upstream channel geometry. This function can beobtained theoretically for ideal (frictionless) flows and adjust-ments for non-ideal conditions can be obtained experimentallyor estimated from fluid-mechanics considerations.5. Significance and Use5.1 Although Palmer-Bowlus flumes can be used
23、 in manytypes of open channels, they are particularly adaptable forpermanent or temporary installation in circular sewers. Com-mercial flumes are available for use in sewers from 4 in. to 6ft (0.1 to 1.8 m) in diameter.5.2 A properly designed and operated Palmer-Bowlus iscapable of providing accurat
24、e flow measurements while intro-ducing a relatively small head loss and exhibiting goodsediment and debris-passing characteristics.6. Interferences6.1 Flumes are applicable only to open-channel flow andbecome inoperative under full-pipe flow conditions.6.2 The flume becomes inoperative if downstream
25、 condi-tions cause submergence (see 7.3.2).7. Apparatus7.1 A Palmer-Bowlus flume measuring system consists ofthe flume itself (the primary), with its immediate upstream anddownstream channels, and a depth or head measuring device(the secondary). The secondary device can range from a simplescale or g
26、age for manual readings to an instrument thatcontinuously senses the head, converts it to a flowrate, anddisplays or transmits a readout or record of the instantaneousflowrate 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
27、class of long-throatedflume in which critical flow is developed in a throat that isformed by constricted sidewalls or a bottom rise, or both.Sloped ramps form gradual transitions between the throat andthe upstream and downstream sections. See Fig. 1. The flumewas developed primarily for use in sewer
28、s5but it is adaptableto other open channels as well. There is no standardized shapefor Palmer-Bowlus flumes and, as long-throated flumes, theycan be designed to fit specific hydraulic situations using thetheory outlined in 7.2.3.7.2.1.2 Prefabricated FlumesPrefabricated flumes withtrapezoidal or rec
29、tangular throats and with circular or U-shapedoutside forms are commercially available for use in sewers.Although there is no fixed shape for Palmer-Bowlus flumes,many manufacturers of trapezoidal-throated flumes use theproportions shown in Fig. 2. These prefabricated flumes arealso available in sev
30、eral configurations depending on how theyare to be installed, for example, whether they will be placed inthe channel at the base of an existing manhole, inserted into thepipe immediately downstream of the manhole, or incorporatedinto new construction. The size of these prefabricated flumes iscustoma
31、rily referenced to the diameter of the receiving pipe5Palmer, H. K., and Bowlus, F. D., “Adaptation of Venturi Flumes to FlowMeasurements in Conduits,” Trans. ASCE, Vol 101, 1936, pp. 11951216.FIG. 1 Generalized Palmer-Bowlus (Long-Throated) Flume in aRectangular ChannelFIG. 2 Palmer-Bowlus Flume (T
32、ypical) for SewerD 5390 93 (2007)2rather than to the throat width. Refer to manufacturersliterature for flume details.7.2.1.3 Because the dimensions of prefabricated flumes maydiffer depending upon the manufacturer or the configuration, orboth, it is important that users check interior dimensionscar
33、efully before installation and insure that these dimensionsare not affected by the installation process.7.2.1.4 A Palmer-Bowlus flume can be fabricated in a pipeby raising the invert (see Fig. X3.1). Floor slabs that can begrouted into existing sewers are commercially available, as areprefabricated
34、slab-pipe combinations for insertion into largerpipes. Details may be obtained from the manufacturers litera-ture. Discharge equations for this throat shape are given inAppendix X1.7.2.2 Head Measurement LocationThe head, h, on theflume is measured at a distance upstream of the throat-approach ramp
35、that is preferably equal to three times themaximum head. When the maximum head is restricted toone-half the throat length, as is recommended in this testmethod, an upstream distance equal to the maximum head willusually be adequate to avoid the drawdown curvature of theflow profile.7.2.3 Discharge R
36、elations:7.2.3.1 The volumetric flowrate, Q, through a Palmer-Bowlus flume of bottom throat width, B, operating under ahead, h, above the throat floor is:Q 5 2/3!2g/3!1/2CDCSCVBh32 (1)where g is the acceleration due to gravity and CDCSand CVare, respectively, the discharge coefficient, throat shape
37、coef-ficient, and velocity-of-approach coefficient as defined in thefollowing sections. The derivation of Eq 1 is outlined inAppendix X2.7.2.3.2 Discharge Coeffcient, CDThis coefficient ap-proximates the effect of viscous friction on the theoreticaldischarge by allowing for the development of a boun
38、dary layerof displacement thickness d*along the bottom and sides of thethroat:CD5 Be/B!1 2d*/h!32 (2)Here Beis an effective throat width given by:Be5 B 2 2d*m21 1!12 2 m (3)where m is the horizontal-to-vertical slope of the sides of thethroat (zero for rectangular throats). The displacement thick-ne
39、ss, d*, is a function of the throat Reynolds number andsurface roughness. However, a reasonable approximation thatis adequate for many applications is:d*5 0.003 L (4)where L is the length of the throat. (Better estimates of d*can be obtained from boundary-layer theory, as in ISO 4359.)7.2.3.3 Shape
40、Coeffcient, CS(See Also Appendix X2)CSis given in Table 1 as a function of mHe/Be.Heis the upstreamtotal effective head, which is (for essentially uniform upstreamvelocity distribution):He5 h 1 Vu2/2g 2d*(5)where Vuis the average velocity at the position of headmeasurement. For a rectangular throat,
41、 m + 0 and CSis unity.7.2.3.4 Velocity-of-Approach Coeffcient, CVThis coeffi-cient allows the flowrate to be expressed conveniently in termsof the measured head, h, rather than the total head, H:CV5 H 2d*!/h 2d*!#32 5 He/he!32 (6)CVis given in Table 2 as a function of CSBehe/Au, where Auis the cross
42、-sectional area of the flow at the head measurementstation. See also Appendix X3.7.2.3.5 Limiting ConditionsThe foregoing dischargeequation and coefficients are valid for the following conditions:(a) 0.1 # h/L # 0.5, with minimum h = 0.15 ft (0.05 m),(b) B # 0.33 ft (0.1 m),(c) h 6ft(2m),TABLE 1 Sha
43、pe Coefficient, CSmHe/BeCSmHe/BemCSmHe/BeCSmHe/BeCS0.010 1.007 0.40 1.276 1.80 2.288 3.80 3.7660.015 1.010 0.45 1.311 1.90 2.360 3.90 3.8400.020 1.013 0.50 1.346 2.00 2.433 4.00 3.9140.025 1.017 0.55 1.381 2.10 2.507 4.10 3.9880.030 1.020 0.60 1.417 2.20 2.582 4.20 4.0620.040 1.028 0.65 1.453 2.30 2
44、.657 4.30 4.1360.050 1.035 0.70 1.490 2.40 2.731 4.40 4.2100.060 1.041 0.75 1.527 2.50 2.805 4.50 4.2840.070 1.048 0.80 1.564 2.60 2.879 4.60 4.3580.080 1.054 0.85 1.600 2.70 2.953 4.70 4.4320.090 1.060 0.90 1.636 2.80 3.027 4.80 4.5050.10 1.066 0.95 1.670 2.90 3.101 4.90 4.5790.12 1.080 1.00 1.705
45、3.00 3.175 5.00 4.6530.14 1.093 1.10 1.779 3.10 3.249 5.50 5.030.16 1.106 1.20 1.852 3.20 3.323 6.00 5.400.18 1.119 1.30 1.925 3.30 3.397 7.00 6.150.20 1.133 1.40 1.997 3.40 3.471 8.00 6.890.25 1.169 1.50 2.069 3.50 3.545 9.00 7.630.30 1.204 1.60 2.142 3.60 3.618 10.0 8.370.35 1.240 1.70 2.215 3.70
46、3.692 . .D 5390 93 (2007)3(d) The throat ramp slopes do not exceed one or three,(e) Throat floor is level,(f) Trapezoidal throat section is high enough to contain themaximum flow, and(g) Roughness of throat surfaces does not exceed that ofsmooth concrete.7.2.3.6 Calculating the Discharge for a Given
47、 HeadObtaining the theoretical discharge for a given or measuredhead using Eq 1 is necessarily an iterative procedure; onepossible approach is outlined in the following:(a) Calculate the estimated CDfrom Eq 2. (This coefficientremains the same during subsequent iterations.),(b) For first trial: assu
48、me H = h, compute mHe/Beandobtain CSfrom Table 1. (In most cases, use of mH/B would beadequate.),(c) Compute Q from Eq 1. (CVis 1.0 for first trial.),(d) Determine the approach velocity, Vu, for this Q and h,(e) For second trial: use H = h + Vu2/2g and correspondingsecond-trial values of CVand CS, a
49、nd(f) Compute the second-trial Q and repeat the last threesteps until convergence.7.2.3.7 Discharge Curves for Commercial FlumesWhenhead versus discharge data are provided with a commercialprefabricated flume, the manufacturer must specify the methodby which the information was obtained, that is, from laboratoryexperiments, from theory as described in this section or amodification 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 tran
