ORIFICE PLATEDISCHARGE COEFFICIENT EQUATION J … · experimental data. Experiments were conducted...

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ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION

J E GallacherShell Pipe Line Corporation

Paper 5.1

NORfH SEA FLOW MEASUREMENT WORKSHOP 199023-25 October 1990

National Engmeertng LaboratoryEast Kilbride. Glasgow

, .'

THE A.G.A. REPORT NO.3ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION

AUTHORJ. E. Gallagher, P.E. - Shell Pipe Line Corporation

ABSTRACTThe API/GPA and EC Data Bases were combined by internationalmetering experts to assemble a Regression Data Set. The data setconsists of 10,346 points from ten different laboratories usingfour fluids with different sources, on twelve different meter

~tubes of differing origins, using over one-hundred orifice plates~of differing origins.

A statistical comparison of this new data set with the existingBuckingham and Stolz equations showed a significant lack of fit.As discussed later, comparison failed to substantiate theuncertainty limits previously applied to the existing equations.Regression efforts to refit the Buckingham and Stolz equationsfailed to meet the physical and statistical goals. As a result,the RG equation was developed which is statistically superior tothe currently accepted equations.The RG equation is based on our current understanding of thephysics. The equation is comprised of several terms with knownphysical significance and uses a modified Stolz linkage form. Theregression analysis confirms that the RG equation is,an excellentpredictive model for concentric, square-edged, flange-tappedorifice meters.I BACKGROUND_The orifice meter is perhaps the oldest known device for measuringor regulating the flow of fluids. Historians have credited theRomans with developing it for regulating the flow of water tohouses. The orifice meter, in essence a round hole in a flatplate mounted between two flanges, was extended to its presentstate in the early 1900s to measure natural gas flowing inpipelines. Today, the majority of all natural gas and a largeproportion of chemicals produced/transported around the world ismeasured by several hundreds of thousands of concentric,square-edged, flange-tapped, orifice meters.At the beginning of the 20th century, a significant amount ofproprietary research was conducted independently by severalmanufacturers. As a result, users of the device were forced toadopt manufacturer specific discharge coefficient tables. A largeamount of uncertainty between buyers and sellers occurred as aresult of the proprietary coefficients associated with the various

_manUfacturers' designs. This prompted the American Gas

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Association (A.G.A.), the American Society of Mechanical Engineers(ASME) and the USA National Bureau of Standards (NBS) to undertakea series of research programs.Prior to 1980, the greatest single series of experimentsconcerning the determination of orifice discharge coefficients wasconducted under the direction of Professor S. R. Beitler at OhioState Oniversity (OSO) from 1932 to 1933. The experiments wereconducted in Aater on seven pipe diameters ranging from 25 to350mm (1 to 14-inch). It is important to note that the asoexperiments preceded any metering standard. The test results arecommonly referred to as the 050 Data Base.In each of the pipe sizes, orifice plates with a wide range ofdiameters were studied. While little is now known of the detailof the pipework condition or of the plates themselves, theconsiderable care with which these tests were undertaken isnoteworthy. In fact, all flange-tapped orifice metering standardspublished today, A.G.A. Report No.3 (API/ANSI 2530), ISO 5167 andASHE 3M, are still based upon this sixty year old asu data base.The results from these experiments were used by Dr. EdgarBuckingham and Mr Howard Bean of NBS to develop a mathematicalequation to calculate the flow coefficient for orifice meters.They derived this equation by cross-plotting the data on largegraph paper to obtain the best curve fit. Bear in mind that thiseffort was performed by hand using five-place logarithmic tables,a painstakingly slow process. A tribute to the quality of thework done by Beitler, Buckingham and Bean is obvious from the factthat their results are still being applied today.In the late 1960s and early 1970s, attempts were made tomathematically rationalize the variety of discharge coefficientdata then available. Equations using a power series form evolvedwhich provided excellent fits ·to specific data bases, .but, werecomplicate(f·and ~could .not- be .u~:. 'for-~;t.p.t"oiaq,ens.:'No~e ofthe se attempts was -successfut in' l"epl'ac±ilg.-.j)1'f@'> Suckingham equationfor flange-tapped orifice meters.In the early 1970s, a joint committee of the American GasAssociation (A.G.A.), the American Petroleum Institute (API) andthe International Standards Organization (ISO) was formed toaddress perceived problems associated with the 050 Data Base. Twoindividuals ~ere selected to assess the OSU Data Base - WayneFling from the USA and Jean Stolz from France.In their assessment of the 050 Data Set, Stolz and Flingdiscovered a number of physical reasons why some of the datapoints should be questioned. It is important to note that the esuexperiments preceded all orifice metering standards. The originalobjective of Beitler's tests was to define the standard not meetthe subsequent specifications. Several installations and plateswere found to not meet the existing standard's requirements.Unfortunately, it was unknown which points were selected by

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Buckingham/Bean to generate the discharge coefficient equation.The final outcome of the Fling/Stolz analysis resulted inidentifying 303 technically defensible data points from the OSUexperiments.

In 1981, recognizing the small amount of definitive dataavailable, the API and the Gas Processors' Association (GPA)initiated a multimillion dollar project to develop a new archivaldischarge coefficient data base for concentric, square-edged,flange-tapped, orifice meters. Simultaneously, a similarexperimental program was initiated by the Commission of EuropeanCommunities (EC) in Western Europe.

II EXPERIMENTAL PATTERN

~he goa] of the these research efforts was the development of ahigh quality archival data base of orifice meter dischargecoefficients (Cd ) cov.ering the broadest possj ble range of pipeReynolds numbers (ReD).·' Th·e·exp·~riments were conducted over a tenyear period at eleven laboratories using separate test fluids -oil, water, air and natural gas.

The geometry of each set of meter tubes was identical (Figure 1)for the API/GPA program. Three sections - A, B, and C comprised asingle meter tube. A Sprenkle flow conditioner was bolted to theupstream flange of the "A" section. The orifice plates wereinstalled between the flanges joining sections "B" and "C". Thesetwo flanges are referred to as the orifice flanges.

The experiments were randomized to eliminate experimental biaswithin a laboratory. Experimental variables which were notspecifically controlled, such as mass flow rates, orifice platestesting sequences, and time-dependent variables, were also

~andomized. Randomization assured valid estimates of the~xperimental error and allowed the application of statistical

tests of significance, confidence levels and time-dependentanalyses. Replication of independent bivariate data points(Cd,ReD) was conducted to provide a measure of precision and toassess uncontrolled variables which could affect the finalresults.

Since the results of the project were to be applied in commerce,and an objective was to characterize the true nature of fluid flowthrough an orifice meter, it was decided the API/GPA experimentalpattern should encompass two sets of five nominal pipe diameters(50, 75, 100, 150 and 250 millimeters). A three-section designwas selected to facilitate inspection of internal surfaceconditions and for future installation conditions experiments.Selection of a three-section meter tube design recognized that allthe data should be taken on meter tubes with comparable roughnessvalues that are representative of commercial installations.e

T~o sets of eight nominal diameter ratios or Betas (0.050, 0.100,0.200, 0.375, 0.500, 0.575, 0.660, 0.750) were selected to producea data base amenable to statistical analysis for equationdevelopment purposes. Plates were replaced when they weredamaged, or when it was felt that the edge sharpness haddeteriorated beyond acceptable levels. The nominal Betas andnominal tube diameters for the experimental pattern are:

~ ~Qminal ~ Diameter (mm)50 75 100 150 250

0.050 X X0.100 X X X X X0.200 X X X X X0.375. X X X L~ X0.500 X X X X X

~ 0.575 X X X X X0.660 X X X X X0.750 X X X X X

For the APIjGPA experiments, to ensure uniformity of the velocityprofile at each laboratory, Sprenkle flow conditioners wereconstructed in accordance with the original Bailey Meter Companyspecifications by the NBS mechahical shop. These Sprenkle flowconditioners assured isolatiorr from laboratory induced pipingconfigurations. In essence, fully developed flow profiles weredefined and controlled mechanically through the use of Sprenkleflow conditioners and 45D of straight pipe with an internalsurface wall roughness, Ra, of approximately 3.8 micrometers (150microinches)." Additionally, velocity profile tests were taken toconfirm the presence of uniform, fully-developed, swirl-free flowprofiles.

For the EC experiments, to ensure uniformity of the velocityprofile at each laboratory, long upstream lengths of straight pipe(BOD) and flow conditioners assured isolation from laboratoryinduced piping configurations. Again, velocity profile tests weretaken to confirm the presence of uniform, fully-developed,swirl-free flow profiles.

Flow rates were selected for each pipe size and plate combinationto produce Reynolds numbers spread equally over the relevant rangeof the laboratories' capabilities. The resulting test matrixsought to correct any possible bias in the existing OSU Data Baseand minimize or eliminate all sources of bias in the newexperimental data.

Experiments were conducted on four different fluids at tenlaboratories. By using different laboratories the possibility ofany systematic bias originating from anyone laboratory would beidentified, investigated, and corrected.

The experimental design recognized the importance of the datataken on each of the four fluids. The water data were viewed as

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III EMPIRICAL DATA BASE

the keystone of the research effort. The water experimentsoccupied the intermediate Reynolds number range and hadhistorically served as the basis of the existing world-widestandards. As a result, it was deemed not necessary to have alltube/plate combinations' tested in all four fluids.

The API/GPA experiments were restricted to flange-tapped orificemeters. The fluids tested included oil, water, and natural gas.

The EC experiments covered orifice meters equipped with corner,radius, and flange tappings. The fluids tested included water,dry air, and natural gas.

The fractional factorial pattern resulted in a combination of 12meter tubes covering five nominal pipe diameters, using over 100orifice plates covering eight Betas, on four test fluids at ten

~different laboratories over a pipe Reynolds number range of 100 toW35,OOO,OOO.Control of Independent Variables

The experimental pattern was designed to vary in a controlledfashion the correlating parameters of Beta, pipe size and Reynoldsnumber for a given tapping system. In addition, the researcherswere aware of certain background variables which might affect theoutcome of the experiment. These variables were controlled at afixed level and quantified physically.

Typical background variables are the orifice plate specifications,the meter tube specifications, traceability chains, time-dependentfluid properties, individual operators, time of day, and ambienttemperature. For example, all meter tubes were quantified withrespect to circularity, diameter, steps/gaps, pipe wall roughness,etcetera. The wall roughness was quantified by the profilometer(Figure 2) and the artifact method._AS another example, all 106 orifice plates were quantified withrespect to concentricity, flatness, bore diameter, surfaceroughness, edge sharpness, and other characteristics. The edgesharpness was quantified by the accepted lead foil method (Figure3), the casting method, the beam of light method, and thefingernail method.

The empirical data associated with the API/GPA Data Base and theEC Data Base are the highest quality and largest quantityavailable today (Figure 4 & 5). The fractional factorialexperimental pattern selected by the researchers to assurecompleteness of the data over the wide range to be investigatedwhile at the same time being cost effective. The pattern variedthe significant correlating parameters for the orifice meter; pipe

_diameter, tapping type, Beta and pipe Reynolds number. The

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range of the parameters was designed to allow utilization ofReynolds La~ of Similarity to provide confidence in extrapolationto larger pipe sizes. The total cost of the combined data baseshas been estimated in excess of five million dollars.

The bivariate data, (Cd,ReD), were measured in a mannerappropriate for the test fluid and laboratory. The method ofdetermining mass flow rate, expansion factor, fluid density, andfluid viscosity varied with the laboratory apparatus and testfluid.

Copbined Data Base

The Combined Data Base contains several thousand bivariate datapoints (Cd, ReD) along with their corresponding significantindependent variables. Tests containing uncontrolled independentvariables and operator errors were excluded from the data base.Points were discarded only if a physical cause could be identifiedand both the laboratory and API/GPA or EC experts concurred on t.hp.evidence. Questionable points which were considered to bestatistical outliers Here not discarded from the data base.

Laboratory Bias

Before proceeding with equation regression, the researchersanalyzed laboratory bias within the individual data bases as wellas the combined API(GPA and EC Data Bases. Laboratory bias wouldbe evident if the discharge coefficient curve for a given Betaexhibited offsets between fluid data or between laboratories.

For the APl/GPA experiments, laboratory bias between the low· andintermediate Reynolds number laboratories does not appear to?xist ".~T~~.:.';?r1"f~G~.gj.s..rg-et:oe~ficients· curve for a given Betal.na gl.1(en:pl.pe1S a smooth, contl.nuous curve.

-.Again, the Combined Data Base covers eleven differentlaboratories, four fluids ~ith different sources, on twelvedifferent meter tubes of differing origins, and over one-hundredorifice plates of differing origins.

The traceability chain and method of determining mass flow,instrumentation calibration, and operating procedures were uniquefor each laboratory. Statistically, it is reasonable to assumethat laboratory bias has been randomized within the RegressionData Set. Between the API/GPA and EC Data Bases, the common pipesize and Betas was used to test this assumption.

As previously mentioned, analysis of the API/GPA Data Baseexhibited no laboratory bias between the low and intermediateBeynolds number laboratories (Figure 6). A statistical analysisby the API(GPA technical experts has confirmed the lack of bias.Graphical analysis of the EC Data Base indicates that thelaboratory biases have been randomized (Figure 7).

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Gompnring the APl/GPA and KG data graphically confirms thereasonable assumption of randomized laboratory bias be~ween datubases (Figure 8). Additionally, a statistical comparison usingany of the candidate equations confirms the extremely compatiblelevel between data bases.

~ HEGRESSION DATA SET

Rather than including possibly erroneous data for equationregression purposes, the API/GPA/A.G.A. technical expertsenvisioned two classes of data sets for orifice research -regression and comparison. At a meeting of interestedinternational orifice metering experts jn November, 1988, it wasmutually agreed that the Regression Data Set (Figure 9) be definedeas follows:

"The Regression Data Set shall consist of those data point.scontained in the API/GPA and EG discharge coefficientexperiments which were performed on orifice plates whosed i ame t.er was greater than 11.4mm (0.45 in) and if the pipeReynolds number was equal to or greater than 4,000(turbulent flow regime).

Data which does not satisfy these criteria shall be includedin the Comparison Data Set."

While it does not mean that other data is of inferior quality, itis known that insufficient information exists to determine if theindependent variables were controlled and quantified. Someexamples of comparison quality data are the OSU 303 points, the1983 NBS Boulder Experiments, the Foxboro-Columbus-Daniel 1,000point Data Base, the API/GPA Joliet Data, and the Japanese WaterData Base.

~he Regression Data Set, as defined above, consists of datagenerated on orifice meters equipped with corner, radius andflange tappings. The number of regression data points aresummarized as follows:

tapping DQ ptaflangecornerradius

5,7342,2982,160

Total Points 10,192

V INTERPRETATION OF RESEARCH DATA

Interpretation of the experiments appears to confirm several411rhYSiCaJ phenomena (Figures 10 & 11).

For high Betas, the data follows a pattern similar to the Moody'Friction Factor Diagram. The affect is greatest at a Beta of0.750 and then continuously diminishes and is imperceptible at aBeta of 0.500. It is important to note that the dischargecoefficients for a given Beta ratio collapse at the onset ofturbulent flow (ReD of 4,000).For low Betas, the data is erratic. Closer examination indicatesthat the ability to reproduce an orifice plate with a sharp edgedecreases with decreasing plate bore diameter. A reasonable lowlimit for commercial plates was thought to be 11.4mm (0.45 in)based upon lead foil and video imaging analyses.With respect to the Beta ratio conclusions, the dimensionless damheight easily summarizes the physical affect of velocity profileand the mechanical limitation of reproducing a sharp orifice edg~(Figure 12).Data associated with the 50mm (2-inch) tube exhibit an anomaly forlow to middle Betas. Further analysis indicates that thedimensionless tap hole size and dimensional location for flangetaps are the cause (Figure 13).The experiments confirmed the uncertainty guidelines practiced bythe petroleum, chemical and natural gas industries (Figure 14).Improvement in accuracy below this level under normal operatingconditions is unrealistic without in situ calibration of thedevice and secondary instrumentation.

YI BASIS FOR EQUATIONLaw of SimilarityThe empirical d~scharge coefficients determined from theexperiments are valid' if dyni'mic··Simi".l·aJ;i;.ty~~~.~s*,betweenthemetering installation and the experimental data aset >: Thisapproach is termed the Law of Similarity.Dynamic similarity is the underlying principle for present daytheoretical and experimental fluid mechanics. The principlestates that two geometrically similar meters, with identicalinitial flow directions shall display geometrically similarstreamlines.Geometric similarity requires that the experimental flow system bea scale model of the field installations. The experimentalpattern's design locates sensitive dimensional regions to explore,measure and empirically fit. A proper experimental pattern fororifice meters allows the user to extrapolate to larger meter tubediameters without increasing the uncertainty.The mechanical specificat.ions for the met.ertube, the orificeplate, the orifice flanges or fitting, the differentjal pressure

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sensing taps, the upstream and downstream piping requirements, theflow straightener (if applicable), and the thermowell must. beadhered to as stated in the standard to assure dynamic similarity,

Dynamic similarity implies a correspondence OL fluid forcesbetween the two metering systems. For the orifice meter, theinertial and viscous forces are the ones considered significantwithin the application limitations of this standard. As a result,the Reynolds number, which measures of the ratio of the inertialto viscous forces, is the term which correlates dynamic similarityin all empirical coefficient of discharge and flow coefficientequations. In fact, the Reynolds number correlation provides arational basis for extrapolation of the empirical equationprovided the physics of the fluid does not change. The physicschanges, for instance, between subsonic and sonic flow.

~he originators of the API/GPA Experiments considered fullydeveloped velocity profiles as the foundation for the experiments.This decision was discussed extensively, as were the definitionand determination of fully developed flow. Thus, the futureseries of experiments concerning field installation cond Itionswill rely solely on a technically defensible baseline.

The theoretical definition of fully developed velocity profiles isbased largely on the accumulated results of experimentalobservations of time-averaged velocity profile and, particularly,of the pressure gradient (or friction factor). It is wellestablished that both the velocity profile and the pressuregradient are sensitive to the condition of the pipe wall, whethersmooth, partially rough or fully rough, and the nature of theroughness.

Data on the pressure gradient and to a lesser extent on velocityprofiles have been accumulated since the time of Reynolds (1883).

~ome of the most noteworthy contributors of such data have been~randtl, Stanton, Nikuradse, Laufer, Hanks, and Katz. It is

important to note that even today, the microscopic flow phenomenonin a pipe is not fully understood due to the interactive nature ofthe physics.

For these reasons, fully developed flow conditions were assuredthrough the use of straight lengths of meter tube both upstreamand downstream from the orifice and the use of flow straighteners.

Form of Equation

Previous empirical discharge coefficient forms (Buckingham,Murdock, Dowdell, etc.) were mathematically derived expressionswithout any physical foundation of the flow phenomena. In 1978,Jean Stolz derived an empirical orifice equation based on thephysics of an orifice meter. Stolz postulated that discharge

~coefficients obtained with different sets of near field pressure

tappings must be related to one another based on the physics. Theexpression has been termed the Stolz linkage form.In November 1988. a joint meeting of North American and EC flowmeasurement experts unanimously accepted the equation formproposed by Reader-Harris of NEL (with two amendments byGallagher)_ The concentric, square-edged orifice platecoefficient of discharge (Cd) equation, developed byReader-Harris/Gallagher, termed the RG equation, is an evolutionof Stolz's work.The RG equation is comprised of the following terms - the infinitedischarge coefficient for corner taps, Ci(CT), a slope termconsisting of a throat Reynolds Number term and velocity profileterm, and the near field tap terms. A brief description of thephysical understanding for the equation is presented below.'Is!p TerJlLsThe near field tap terms were derived first since it was necessaryto determine them before regression of the slope and Ci(CT) terms.The best-fit terms were derived statistically using the majority·of the Combined Data Base (excluding the Joliet Data) and theGasunie 600mm flange tapping term data. The total tapping termdata set consisted of 11,346 points, nominal diameter ratios(Betas) of 0.10 to 0.75. nominal pipe diameters of 50 to 600mm,and pipe Reynolds numbers of approximately 200 to 50,000,000.Stolz's postulate states that the near field tapping terms areequal to the difference between the discharge coefficient for thecorner taps and the flange (or radius taps). The values of theterms were determined from the EC data which included all threesets of tappings_ However, the form of the tapping terms wasbased on data collected by several researchers. The value of thetapping terms in the API/GPA data could only be calculated forcomparison due to one pair of tappings (flange).The upstream term has a form which essentially is identical toStolz's ISO 5167. The downstream form is based on a suggestion byTeyssandier and Husain. Also, it was agreed that the upstream anddownstream tap terms should have a continuous first derivative.In analyzing the EC data, no effect of Reynolds on the tap termsis evident. However, for the low Reynolds Number data in theAPI(GPA experiments this is not true. The effect of low Reynoldsnumber on the upstreaa and downstream wall pressure gradient hasbeen reported by Witte, Schroeder and Johansen. One cannotproduce perfect low Reynolds number tapping terms due to the lackof data. However, it is important to produce the best onespossible.

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CiCCT) TermThe infinite discharge coefficient for corner taps, Ci(eT),increases with Beta to a maximum near Beta of 0.55 and thendecreases rapidly with increasing Beta. The form of the equation,without taking into account the tap hole diameter term, is -

Ci(CT) = AO + A1*(Beta-2) + A3*(Beta-8)The constant exponents of 2 and 8 were chosen to enable a good fitto the data while keeping the exponents reasonable.The 50mm flange tap data differed significantly from the radiustap terms by as much as 0.4 percent for small Betas. Gallagherand Teyssandier postulated this difference was a result of

_dimensional tap effects. An additional term was added to accountfor the tap hole diameter effect for 50mm tubes. While one candebate whether it should be in the tap term or Ci(CT) term,Reader-Harris proposed and it was agreed to add a tap holediameter term to the Ci(CT) term.Slope TermIntuitively, for small Betas the Cd should only depend on throatReynolds Number (Red). However, for large Betas the velocityprofile or friction factor is the correlating parameter.Several scientists have attempted to correlate Cd as a function offriction factor. While theoretically correct, the practicalapplication would be unpopular. Also, our ability to measurefriction factor is impractical in the field and difficult in thelaboratory.The slope term form should also provide for transition fromlaminar to turbulent flow because the velocity profile changes

~rapidly in the transitional flow regime. The data indicated the~slope for pipe Reynolds Number (ReD) greater than 3,500 was very

different for ReD less than 3,500.The final slope term form is as follows -

The "c" term form for ReD < 3,500 is different for ReD> 3,500 tocorrect for the velocity profile changes from laminar to turbulentflow regime.The concentric, square-edged orifice plate coefficient ofdischarge (Cd) equation, developed by Reader-Harris/Gallagher(RG), is structured into distinct linkage terms and is consideredto best represent the current regression data base. The equationis applicable to nominal pipe sizes of 2 inches (50mm) and larger,diameter ratios (Beta) of 0.10 through 0.75 provided the orifice

_late bore diameter, dr, is gr-eat.e r than 0.45 inches (11.4 mm),

and for pipe Reynolds numbers greater than or equal to 4,000. ForBetas and pipp. Reynolds numbers below the limit stated, the rp.adArshould refer to AP] HPMS Chapter 14.3 Part 1 Section 12. The RGequation is defined as follo~s:

Cd = Ci + (51*Xl) + (S2*X2)Ci = Ci(CT) + Tap TermCi(CT) = 0.5961 + 0.0291*(Beta2) - 0.2290*(Beta8)

+ 0.003*(1 - Beta)*HlTap Term = Upstrm + DnstrmUpstrm = [0.0433 + 0.0712*e(-8.5*L1) - 0.1145*e(-6.0*Ll)]

*(1 - 0.23*A)*BDnstrm = - O.0116*[M2 - O.52*(M21.3)]*(Beta1.l)*(1 - 0.14*A)(SI*XI) = 0.000511*[(IE+06*Beta)/(ReD)]0.7(S2*X2) = (0.0210 + O.0049*A)*(Beta4)*Calso -

B = (Beta4)/[1 - (Beta4)]Hl = max(2.8 - (D/N4), 0.0)H2 = [(2*L2)/(1 - Beta)]A = [(19,000*Beta)/(ReD)]0.8

for ReD greater than or equal to 3,500 -C = (lE+06/ReD)O.35

for ReD less than 3,500 -C = 30.0 - 6,500*(ReD/IE+06)

where -Beta =

Cd =

Ci =

Ci(CT) =

d =D =

Diameter ratio = diDCoefficient of discharge at a specified pipeReynolds numberCoefficient of discharge at infinite pipeReynolds numberCoefficient of discharge at infinite pipp.Reynolds number for corner-tapped orjfice meterOrifice plate bore diameter calculated at TfMeter tube internal diameter calculated at Tf

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e = Naperian constant, 2.71828L1 = 0 for corner taps

N4/D for flange taps1 for radius taps

L2 = 0 for corner tapsN4/D for flange taps0.47 for radius taps

N4 = 1.0 when D is in inches; 25.4 when D is in mmReD = pipe Reynolds number

The RG equation is based on a rational understanding of thephysics of flow through orifice meters and fits the RegressionData Set. The terms in "A" are significant only at small throatReynolds Numbers. The downstream tap term, M2, is the distancebetween the downstream face of the plate and the downstream tap

~location. The tap hole term, Ml, is significant only for nominal~meter tubes under 75mm (3 inch) equipped with 9.525mm (0.375 inch)

flange taps holes.Appendix A of this paper contains values of coefficient ofdischarge for flange-tapped orifice meters for nominal pipe sizes.

VII STATISTICAL ANALYSISSince the mid 1930's, the correlation published by Dr. E.Buckingham and Mr. Howard S. Bean has been used by A,G.A. ReportNo.3 (ANSI/API 2530). In 1980, the International StandardsOrganization (ISO) replaced the Buckingham equation with the Stolzlinkage equation in the international orifice standard (ISO 5167).Statistical analysis of the Regression Data Set and the Gasunie600mm data shows that both the Buckingham and Stolz equations donot accurately represent the data for flange-tapped orifices in

_several regions (Figure 15-16 lit 17-18). The analysis clearly .~indicates the data does not substantiate the uncertainty statement

published in both the ISO and ANSI standards.Statistical analysis of the RG equation shows an excellent fjt tothe data for flange-tapped orifice meters, The tabulation of theresiduals' performance has been organized in a manner consistentwith the experimental pattern (Figures 19-23).To test the predictive capability of the RG equation, astatistical analysis was performed on the Japanese corner tap datain water. Again, the tabulation of the residuals performanceshows an excellent extrapolation to large pipe diameters (Figure24) .Examinatjon of Residuals

The_the

residuals contain essential information on the way in whjchequation fails to properly explain the observed variation in

the dependent variable, Cd. In the previous sections, we havestated the £ollowing relationship -

Cd - £(Beta, tap location, tap hole size, andfriction factor or velocity profile)

A plot of the residuals is essential to ensure that the statisticshave not masked a correlating parameter. The principal ways toplot the residuals, e, for a given tapping system are:

* Overall histogram* Against the independent variable, X or Log(ReD)- by all Betas and Tubes combined- by Nominal Tube Diameter, D- by Nominal Diameter Ratio, Beta

*. Norma] probability plot* Against the £itted values, Cd

An equation which exhibits the best fit to the data will have anoverall histogram which exhibits a unimodal, symmetricaldistribution with a mean value o£ zero, a sharp peak in themiddle, and small frequencies on the tails. Statistically, thisis referred to as a leptokurtic distribution. It is evident thatthe RG equation exhibits this form (Figures 25-28).

Plotting the population residuals and subgroup residuals willindicate i£ the regressed equation conforms to both the physicalphenomena and regression hypotheses. Again, the RG equationresiduals exhibit an excellent per£ormance (Figures 29-35).

As previously mentioned, outliers were not rejected from theRegression Data Set. This can be seen from the overall residualplot and the plots by pipe diameter.

The volume o£ residual plots are too extensive to reproduce inthis paper. Therefore, the author has chosen to include only thecritical residual plots at this time. A complete set of plotswill be available to the public during the first quarter of 1991.

X. SUMMARY

Our time, effort and money have been directed toward a goal set in1976 - to develop an improved orifice metering standard applicableto single phase, homogeneous, Newtonian fluids associated with thepetroleum, chemical and natural gas industries. That goal shouldbe completed by year end, cumulating a ten year research effort bynumerous individuals representing three continents. Revision ofthe national and international standards is an evergreen process.We have merely reached a milestone in a much longer journey. Wehave some of the answers, but we don-t have them all.

The new equation is comprehensive in its coverage for allNewtonian fluids, its extended Stolz linkage form, its application

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to a broad range of Reynolds numbers and line sizes. and itsapplication to the various tapping arrangements used throughoutthe world. Because of the quality of the Regression Data Set. allof the candidate models produced a more accurate prediction thanthe equations currently contained in the exis~ing standards.

Issues of approach length and flow conditioning are key elementsyet to be quantified. Work will continue. but for now we havesome real answers to key problems.

IX. REFERENCES

3.

4.

6.

7.

OSU Experjmental Program

1. Bei tIer. S. R.. "The Flow of Water Through Orifices"; TheOh i.oState University. The Engineering Experiment Station.Bulletin 89 •.1935. Columbus. Ohio. USA.

2. Fling. W. A ....API Orifice Meter Program". American GasAssociation. Operating Section Proceedings. Paper 83-T-23.p. 308-311.1983.

API/GPA Experjmental Program

"Coefficients of Discharge for Concentric. Square-Edged.Flange-Tapped Orifice Meters: Equation Data Set - SupportingDocumentation for Floppy Diskettes"; American PetroleumInstitute. 1988. Washington. D. C .• USA.

Britton. C. L .• Caldwell. S., and Seidl, W., "Measurementsof Coefficients of Discharge for Concentric, Flange-Tapped.Square-Edged Orifice Meters in White Mineral Oil Over a LowReynolds Number Range"; American Petroleum Institute, 1990.Washington, D.C., USA.

Whetstone, J. R., Cleveland, W. G., Baumgarten, G. P., Woo,S., arid Croarkin, M. Carroll, "Measurements of Coefficientsof Discharge for Concentric, Flange-Tapped, Square-EdgedOrifice Meters in Water Over the Reynolds Number Range of1,000 to 2,700,000"; NIST Technical.Note 1264, June 1989,Gaithersburg, MD, USA.

Whetstone, J. R., Cleveland, W. G., Bateman, R. B., andSindt, C. F., "Measurements of Coefficients of Discharge forConcentric, Flange-Tapped, Square-Edged Orifice Meters inNatural Gas Over the Reynolds Number Range of 25,000 to16,000,000"; NIST Technical Note 1270, September 1989,Gaithersburg, MD, USA.

KC Experimental Program

Hobbs. J. M., "Experimental Data for the Determination ofBasjc 100mm Orifice Meter Discharge Coefficients";

page 15 of 17

Commission of the European Communities, Report EUR 10027,1985, Brussels, Belgium.

8. Bobbs. J. M., Sattary, J. A., and Maxwell, A. D.,"Experimental Data for the Determination of Basic 250mmOrifice Meter Discharge Coefficients"; Commission of theEuropean Communities, Report EUR 10979, 1987. Brussels,Belgium.

9. Hobbs, J. tI., "The EC Orifice Plate Project, Part I:Traceabilities of Facilities Used and Calculation MethodsEmployed"; Commission of the European Communities. ReportPR5:EUEC/17, 1987. Brussels, Belgium.

10. Hobbs, J. 1'1., "The EUEC Orifice Plate Project, Part II:Critical Evaluation of Data Obtained During EC Orifice PlateTests"; Commission of the European Communities, ReportKUEC/17, 1987, Brussels, Belgium.

11. Hobbs, J. M., "The EC Orifice Plate Project: Tables of ValidData for KC Orifice Analysis"; Commission of the EuropeanCommunities, Report EUEC/17. 1987, Brussels, Belgium.Equation Development

12. Stolz, J., "A Universal Equation for the Calculation ofDischarge Coeffcient of Orifice Plates"; Proc. Flomeko 1918- Flow Measurement of Fluids, H. H. Dijstelbergen and E. A.Spencer (Eds), North-Holland Publishing Co., Amsterdam(1918). pp 519-534.

13. Reader-Harris, M. J. and Sattary, J. A., "The Orifice PlateDischarge Coefficient Equation"; Flow Measurement &Instrumentation, vol 1. Jan. 1990, London. UK.

14. Gallagher, J. E. and Teyssandier, R. G., "Influence of TapHole Geometry on Concentric, Square-Edged Orifice Meters";Report to the Joint Experts Committee, April. 1990.

15. Private Communication ~ith J. Stolz. 1985-1990.16. Private Communication ~ith M. J. Reader-Harris. 1986-1990.

Japanese Rxperimental Program

17. ~atanabe. N., "Coefficients of Discharge for Corner-TappedOrifice Meters "; National Research Laboratory of Metrology.Private Communication, 1987. Japan.Keasurement Standards

18. API MPMS Chapter 14 Section 3 (ANSI 2530, A.G.A. Report No.3), "Orifice Metering of Natural Gas and Other Related

page 16 of 17

of 17

HYdrocarbon Fluids", American Petroleum Institute,Washington, D.C., USA, 1985.

19. International Standard ISO 5167, "Measurement of Fluid Flowby Means of Orifice Plates, Nozzles and Venturi TubesInserted in Circular Cross-Section Conduits Running Full",International Standards Organization, Geneva, Switzerland.

l:(X _ ~)2

(N 1)

GDEBAL DFORllATIOR AlIOUT THE STATIStICS

For each cell, line 1 - Mean percent· errorline 2 - Percent standard deviationline 3 - Mean absolute percent errorline 4 - Number of observationsline 5 - Percent standard deviation to model

(Ym - Yp)Percent error - --..:=--....!:--

Ym* 100

Std deviation..-.,...-

'-' .. -:.... . ·'·~-·f~.:--·':"""'·"-

Std deviationto model

Statistics for entire population in bottom right cell.* Nominal beta ratio

All data marked as restricted have that data whose pipe Reynolds number is lessthan 4000 or whose beta ratio is less than 0.19 removed from statisticalconsideration.

Nominal Pipes

50 mm 2 In75 mm 3 in100 mm 4 In150 mm 61n250 mm 10 In

Section A-ANOTES:1.) THE UPSTREAM STRAIGHT PIPE LENGTH (DIMENSIONS A + B) PROVIDED

44 PIPE DIAMETERS BETWEEN THE SPRENKLE FLOW CONDITIONER ANDTHE ORIFICE PLATE.

2.) THE DOWNSTREAM STRAIGHT PIPE LENGTH (DIMENSION C) PROVIDEDAT LEAST 14 PIPE DIAMETERS BETWEEN THE ORIFICE PLATE AND ANYCONNECTING PIPING CONFIGURATIONS.

Figure 1 Orifice meter configuration.

300 Ra - micro inches

250 . ..................

200. Plated Tubes_ Average- Global Average

150

100

50

o 2A 2B 3A 38 4A 4B 6A 58 lOA lOBPipe Designation

API ExperimentseFigure t Wall surface roughness.

'. ,

11q..r

0I111ce PIabt Edge Sharpneea

~tO~--------------~................................

--_...• , t •••••

.... DI Is: dian

_n-.--- ......--"."-.T_

OIlftce Plata Edge ShalPlIII

- .- ..

..,.... ,• , t • • 4 • •.... DIIIa Pb •

---110 _

_·A· .........-

-~- --- _--"."--- _T_.v_,,.- .

....."t •••••

.... D " " ,---OIlftce Plata legend

......D ... II1II1 ,........... Me hd..........

•71I•..II•

o.oeo0.100O.aoo0.878O.eoo0.1780.1800.780

-I E':e:';

I0.75)

O.OOJ

IO~0.5);

0.375

0.200

0.100

0.(6)

API Experirrental Pattern EEC Experirrental Pattern£':eta

.... ozo ............... ......•O.E£J..,.

!~...........•0.575.......•...•........ 05:)).......• ::::....O..llS :...•......'..... 02:)().......•..-.... 0.100................ oreo....

· _. . "':::i· .. ···3 .. ···3 .. ···3 .. .... . :::::1.. :. . ::.~g:§ •••:.~:U· .......••••.~••:.~:~J: :::::.: ••• ...J • •• I· .. :." .. .... :: :::::j :: :::=1 :: ::J ::..::::::::.. :::: : ::::@~!:::::~: ::::~>:~~l

:::::: : :::::. .... ! :!!:~ :: ...

::::::--!-ioi"+~ .

::::3 ::::3 :::• •.•• . ::J .

• ••••.-1 : ::::.~--~-.-.: ::::: : :::::l : ::::: : ::::c

: ::: : ::::~. : :::. :: co::

EEC Experirrental PatternAPI Experirrental PatternTube. Tubee· ;5) :::r:: :~:~.,;..ioiii· .... ,;;..;.;.;.: .: :.~.::::.= ...;.;:.:. :.:.:. • ••••.•

151 : >:j ::: :::'= .::::=3 ::::3 : :::::~ .: ::::3 :: :::'=1 :: :::c ...

~- . . ... .. ..,. .. :::::: : ::::, ...... ..... . ....

75 :: :........::: :~ y: .....

::::: ...;5)

....::~ ...:

....151 .......

:::~ ...

100 co:::

lS ::~so : : .. ....

IFigure ~ API experimental patterns 'is EEC experimental patterns.

. .~~EXPERIMENT AL PATTERN

f-------+-/l----(,/CO '...Q)

m ///.~-y;:F. ,"'Co 5

0.64 ClJserved Cd fTl--"-- ----,~

0.63 • \•

0.64 Cllserved Cd FT1

J5:lml PipeBeLl 010.7~

0.63 troml Pipe

\ Beta 01 0.500

0.62 ~ FlJid l\'p.~. • ClI

0.51,

• WlI!t"'''' ...0.50

0.59 I I II1II ..1000 10.~ m:go 1000,000

Pille ooids er

0,62 Fluil Typeo al• WIlE,0.61

0.60

°l6.000~-'-L...'LLIOO.CQO l~~L..W.OOc,oooPpe t-e)'nolds t-runtJer

Figure,- APIJGPA experiments.

0.64 (bserved CdFl10.604 ClJs erved Cd IFl1

0.63 2l)rrn PilleBeta 01 0.630

0.62 Fluid lype

• ~Ie'0.61 rl' 0 Gao....,.-,..

.lral 70.60

O! LIIIII , ",000 ~'~ ~rrfe! 040,000,000p.,e nolds er

100rm PipeBeta 01 0575

0.63

FIu~ Type·-c Gas

0.1iZ"..::

0.61

o.m

0.591L-...................~",-"-L .........U'O ,..'-:- ........ "" ........ ,

10.000 pO,~ 1000.000 10,000,000ppe reynokis t-lJlroer

Figure', CEe experiments.

0.64 ClJserved Cd IF11OBi Cllserwd CdFT1

0.64

0.63

0.63 25I)rm P~e!lela 0I0575

0.62 Flui:l'l'jpe

• WIle,0.61

.......... 1ItNI~ Gas

0.50

°looo UL--IIIIIIIII I 111111

I~OOO l~,~O.OOO.OOOpe ~no s er

1!XmI~.Beta 01 0.650

fiJi:ll\'peo ClI·-DGos

052

0,51

0.50

FigLare ,. API and CEe experiments.

API & EEC Fegression Dat.a BaseBeta0.75l0.660

0.5750.500

0.375

0.200

0.100

0.000

L.og~D\

API s EEC Fegression Data BaseTube

100

75

Nominal Beta of 0.750 Nominal B=ta 01 0.660Ob<ClJservedCdFTl

OID , .

::':::.:'::'.:'.:~~;"::':"OBI ~.t. .

:""~."\ .

D.62f-· .. ·· .

D~1 ~ ...~.D.60f- .. · ,A.:IlI .e-.t~

Nominal E?etaof 0.575 Nominal B=ta of 0.500O~r--------------------, Ob<r-------------------,

:.:::::, .... :::::.:::.:.::::: ..::.:::::0.151 ·"'ii.i,;,·.~·""""""·

~ ..0.150 .

:••••~ ••••••••••••••••••••••••-.,.OBI .

01liiiL ,..........~'!=:-"~..-,.,,,....... ..........,.,..~....J.nllDO 1OO.1IDO LOOO.IIDO 10.000.000

Figurti ,. Nominal Bela.

Nominal E?etaof 0.375~ lliseMd CdFTl

"0..63 , .

0.f2f- "-' : .

:::::.:::.:::.::::~~~~.:

~bminal E'eta of 0.200Ob<Iliserved CdF11

'.O.E! ..•.•.•. , •.•.•.•••.•.•.•.•.•.•.•.•.••.•.•.•

::\O ~ .

I'J:)minal E?etaof 0.100 Nominal E'eta of 0.050~nr-------------------, osr-------------------,

••0,62· .. ·· · .. ·•· · .. ·

• I... '"OS) •·• .... ·.···'·"·)fi;························..,~~~~~~~~~~~IJO LOOO ID,OOO 1lO.000 LOOO.OOO

I0JI'i .

ID.64 \, .

oS! ·i I ·)I· .. ·• • •

,,- "Je, )C II0.lII r.~~ .

OBi .

w ..

Flgur. ,. Nominal Beta.

n-- .---

..... . .

• Nominal eeta0.0500.1000.2000.3750.5000.5750.6600.750

~. . .

I,L-

0.2I.!-

0.4 0.6

BetaO.B 1.00.0

-:::t- •.~ ."

Flgure.2, Damheight-concentric orifice meter.

Nominal Pipe50mm

75mm

100mm

150mm

250mm

400mm

600mm

--•

1200mm0.0 1.00.2 0.4 0.6 O.B

(Distance From Plate FacellD

Figure., Taplocation-fl."ged·tapped orifice meter.

"3.00 ...;:...---------------------,

-~.OO+-----r_----r_--_.----_r----._---,----_r----._~0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Beta Ratio

NOTES;1. Orifice plates having bore diameters less than 0.45 inch(II.4 mm),

installed according to API MPHS Chapter 14.3 Part 2, may havecoefficient of discharge{Cd) uncertainties as great as 3.0%. Thislarge uncertainty is due to problems with edge sharpness.

2. The relative uncertainty level depicted in Figure 1.6 assumes aswirl free inlet velocity profile.

Practical Uncertainty Levels

vel.profileroughnesseccentrIcity2.00

1.00

0.00 +----

~1.00

-2.00 edge sharpness

PRACTICAL UNCERTAINTY LEVELS

STATISTICS n>RAPI 2530 - FLAJlGE TAP

Tube -+ 2 in 3 in 4 in 6 in 10 ir.. 24 in Sum:naryby

Beta* ~ Beta0.100 0.000 0.000 0.000 0.883 0.569 0.000 0.654

( 0.0991 0.000 0.000 0.000 0.266 0.309 0.000 0.328to 0.000 0.000 0.000 0.883 0.569 0.000 0.654

0.1028 ) 0 0 0 29 79 0 1080.000 0.000 0.000 0.937 0.651 0.000 0.734

0.200 0.670 0.438 0.453 0.345 0.057 0.179 0.305( 0.1982 0.177 0.122 0.256 0.206 0.397 0.066 0.348

to 0.670 0.438 0.458 0.386 0.232 0.179 0.3680.2418 ) 60 57 271 83 257 70 798

0.699 0.458 0.521 0.403 0.401 0.192 0.463

0.375 0.508 0.114 0.150 0.048 -0.023 0.143 0.134( 0.3620 0.139 0.125 0.186 0.270 0.306 0.037 0.261

to 0.508 0.135 0.176 0.193 0.184 0.143 0.2100.3748 ) 104 106 287 122 202 84 905

0.529 0.169 0.239 0.274 0.307 0.148 0.294

0.500 0.220 0.204 -0.008 -0.328 0.055 -0.012 0.015( 0.4825 0.255 0.106 0.613 0.967 0.210 0.040 0.544

to 0.296 0.205 0.329 0.567 0.158 0.032 0.2850.5003 ) 113 69 164 109 164 51 670

0.338 0.231 0.613 1.021 0.217 0.042 0.544

0.575 0.050 0.248 -0.008 -0.627 0.024 -0.091 -0.053( 0.5427 0.516 0.107 0.555 1.255 0.246 0.063 0.615

to 0.342 0.248 0.274 0.749 0.176 0.093 0.2890.5770 ) 90 72 435 136 390 67 1190

0.519 0.272 0.555 1.404 0.248 0.111 0.617

0.660 0.183 0.417 0.040 -0.427 -0.003 -0.090 0.028( 0.6481 1.075 0.137 0.805 1.154 0.248 0.030 0.766

to 0.742 0.417 0.441 0.535 0.181 0.090 0.4080.6645 ) 196 64 289 92 303 58 1002

1. 090 0.442 0.806 1.231 0.248 0.096 0.767

0.750 0.484 0.891 0.588 0.222 0.025 -0.079 0.351( 0.7239 1.130 0.188 0.875 0.940 0.356 0.075 0.803

to 1.048 0.891 0.864 0.654 0.279 0.083 0.6540.7509 ) 212 101 458 130 490 34 1425

1.230 0.915 1.055 0.966 0.357 0.110 0.877

Summary 0.337 0.396 0.232 -0.102 0.045 0.027 0.150by 0.849 0.314 0.679 0.983 0.327 0.128 0.641

Tube 0.677 0.401 0.457 0.541 0.227 0.111 0.399775 469 1904 701 1885 364 6098

0.913 0.506 0.718 0.989 0.330 0.131 0.658

STATISTICS FORAPI 2530 - FLABGE TAP

ReD ... 10 4000 10000 100000 1000000 10000000 Summaryto to to to t.o to by

lleta* ~ 4000 10000 100000 1000000 10000000 100000000 Beta

0.100 0.000 0.556 0.735 0.000 0.000 0.000 0.654( 0.0991 0.000 0.342 0.295 0.000 0.0.00 0.000 0.328

t.o 0.000 0.556 0.735 0.000 0.000 0.000 0.6540.1028 ) 0 49 59 0 0 0 108

0.000 0.657 0.798 0.000 0.000 0.000 0.734

0.200 0.000 0.260 0.339 0.278 0.196 0.000 0.305( 0.1982 0.000 0.664 0.267 0.318 0.068 0.000 0.348

t.o 0.000 0.546 0.371 0.308 0.196 0.000 0.3680.2418 ) 0 108 493 119 78 0 798

0.000 0.714 0.432 0.423 0.209 0.000 0.463

0.375 0.000 -0.006 0.193 0.070 0.140 0.151 0.134( 0.3620 0.000 0.489 0.298 0.148 0.036 0.037 0.261

t.o 0.000 0.408 0.265 0.124 0.140 0.151 0.2100.3748 ) 0 46 451 324 59 25 905

0.000 0.489 0.355 0.164 0.145 0.158 0.294

0.500 0.000 -1.363 0.161 0.127 -0.019 -0.010 0.015( 0.4825 0.000 1.155 0.322 0.145 0.051 0.037 0.544

t.o 0.000 1.444 0.300 0.154 0.041 0.030 0.2850.5003 ) 0 50 201 368 12 39 670

0.000 1.798 0.360 0.192 0.054 0.038 0.544

0.575 0.000 -2.410 -0.170 0.100 0.015 -0.014 -0.053( 0.5427 0.000 1.328 0.768 0.186 0.220 0.146 0.615

to 0.000 2.411 0.473 0.160 0.173 0.115 0.2890.5770 ) 0 35 245 611 202 97 1190

0.000 2.783 0.787 0.211 0.221 0.146 0.617.. ,0·;000'. ..-3.445 ..";~:-041;"·. :O+~., ...- '-0.030 -0.121 0.0280.660 -.

0..000 0.785 1.089 0.238 ,.....0.173 0.072 0.766( 0.6481to 0.000 3.445 0.727 0.284 0.142 0.121 0.408

0.6645 ) 0 23 197 546 138 98 10020.000 3.609 1.090 0.340 0.176 0.141 0.767

0.750 0.000 -2.205 -0.021 0.658 0.201 -0.168 0.351( 0.7239 .0.000 1.053 1.532 0.392 0.385 0.172 0.803

to 0.000 2.205 1.129 0.687 0.352 0.195 0.6540.7509 ) 0 27 174 785 328 111 1425

0.000 2.481 1.532 0.766 0.435 0.241 0.877

Summary 0.000 -0.699 0.152 0.295 0.108 -0.077 0.150by 0.000 1.530 0.726 0.359 0.295 0.155 0.641

ReD 0.000 1.184 0.473 0.336 0.238 0.134 0.3990 338 1820 2753 817 370 6098

0.000 1.683 0.742 0.465 0.314 0.173 0.658

STATISTICS FORISO 5167 - FLL&GE TAP

Tube -+ 2 in 3 in 4 in 6 in 10 in 24 in SUlOlOaryby

Beta* ~ Beta

0.100 0.000 0.000 0.000 0.742 0.398 0.000 0.490( 0.0991 0.000 0.000 0.000 0.329 0.332 0.000 0.364

to 0.000 0.000 0.000 0.742 0.434 0.000 0.5170.1028 ) 0 0 0 29 79 0 108

0.000 0.000 0.000 0.823 0.520 0.000 0.612

0.200 0.606 0.272 0.292 0.387 -0.010 -0.035 0.198( 0.1982 0.239 0.229 0.293 0.222 0.236 0.064 0.314

to 0.606 0.284 0.326 0.387 0.171 0.056 0.2770.2418 ) 60 57 271 83 257 70 798

0.656 0.358 0.414 0.448 0.236 0.073 0.371

0.375 0.450 0.019 0.ll2 0.150 -0.030 O.lll 0.ll3( 0.3620 O.lll 0.ll5 0.245 0.206 0.209 0.037 0.237

to 0.450 0.095 0.177 0.156 0.143 O.lll 0.1820.3748 ) 104 106 287 122 202 84 905

0.466 0.ll7 0.270 0.255 0.2ll 0.ll7 0.263

0.500 0.204 0.149 0.076 0.086 0.037 -0.097 0.084( 0.4825 0.229 0.064 0.233 0.166 0.166 .0.040 0.199

to 0.282 0.149 0.180. 0.154 0.135 0.098 0.1720.5003 ) ll3 69 164 109 164· 51 670

0.307 0.163 0.245 0.187 0.170 0.106 0.216

0.575 0.081 0.187 0.049 0.048 0.000 -0.222 0.028( 0.5427 0.393 0.084 0.250 0.155 0.208 0.064 0.240

to 0.330 0.187 0.193 0.130 0.160 0.222 0.1870.5770 ) 90 72 435 136 390 67 ll90

0.401 0.206 0.255 0.162 0.208 0.232 0.242

0.660 0.184 0.291 0.142 0.074 -0.046 -0.322 0.070( 0.6481 0.5ll 0.ll4 0.250 0.214 0.245 0.031 0.335

to 0.455 0.291 0.236 0.185 0.2ll 0.322 0.2750.6645 ) 196 64 289 92 303 58 1002

0.544 0.315 0.287 0.227 0.249 0.327 0.342

0.750 0.389 0.383 0.429 0.302 -0.298 -0.656 0.132( 0.7239 0.274 0.172 0.317 0.420 0.377 0.071 0.484

to 0.442 0.383 0.459 0.364 0.383 0.656 0.4210.7509 ) 212 101 458 130 490 34 1425

0.476 0.421 0.534 0.518 0.481 0.670 0.502

Summary 0.299 0.210 0.201 0.191 -0.070 -0.148 0.109by 0.375 0.189 0.309 0.303 0.317 0.226 0.343

Tube 0.422 0.229 0.279 0.244 0.235 0.204 0.271775 469 1904 701 1885 364 6098

0.480 0.283 0.369 0.359 0.324 0.270 0.360

STATISTICS FORISO 5167 - FLABGE TAP

ReD .. 10 4000 10000 100000 1000000 10000000 Summaryto to to to to to by

l!et .. * ~ 4000 10000 100000 1000000 10000000 100000000 Beta

0.100 0.000 0.687 0.327 0.000 0.000 0.000 0.490( 0.0991 0.000 0.309 0.325 0.000 0.000 0.000 0.364

to 0.000 0.687 0.376 0.000 0.000 0.000 0.5170.1028 ) 0 49 59 0 0 0 108

0.000 0.760 0.463 0.000 0.000 0.000 0.612

0.200 0.000 0.586 0.199 -0.005 -0.033 0.000 0.198( 0.1982 0.000 0.387 0.238 0.279 0.065 0.000 0.314

to 0.000 0.632 0.253 0.195 0.057 0.000 0.2770.2418 ) 0 108 493 119 78 0 798

0.000 0.705 0.310 0.279 0.073 0.000 0.371

0.375 0.000 0.555 0.147 0.005 0.107 0.120 0.113( 0.3620 0.000 0.283 0.243 0.150 0.036 0.037 0.237

to 0.000 0.555 0.208 0.112 0.107 0.120 0.1820.3748 ) 0 46 451 324 59 25 905

0.000 0.628 0.284 0.150 0.114 0.128 0.263

0.500 0.000 -0.247 0.192 0.095 -0.105 -0.095 0.084( 0.4825 0.000 0.229 0.169 0.153 0.051 0.037 0.199

to 0.000 0.274 0.222 0.142 0.109 0.095 0.1720.5003 ) 0 50 201 368 12 39 670

0.000 0.338 0.256 0.181 0.121 0.103 0.216

0.575 0.000 -0.522 0.095 0.075 -0.028 -0.124 0.028( 0.5427 0.000 0.342 0.220 0.195 0.233 0.170 0.240

to 0.000 0.522 0.209 0.158 0.186 0.192 0.1870.5770 ) 0 35 245 611 202 97 1190

0.000 0.630 0.240 0.209 0.235 0.210 0.242

0.660 0.000 -0.907 0.245 0.175 -0.1~9 -0.317 0.070( 0.6481 0.000 0.657 0.300 0.211 0.181 0.062 0.335

to 0.000 0.920 0.348 0.229 0.214 0.317 0.2750.6645 ) 0 23 197 546 138 98 1002

0.000 1.137 0.388 0.275 0.241 0.325 0.342

0.750 0.000 -0.193 0.572 0.310 -0.225 -0.679 0.132( 0.7239 .0.000 0.199 0.330 0.318 0.413 0.163 0.484

to 0.000 0.222 0.581 0.372 0.382 0.679 0.4210.7509 ) 0 27 174 785 328 111 1425

0.000 0.280 0.662 0.444 0.471 0.701 0.502

Swnmary 0.000 0.195 0.216 0.153 -0.121 -0.322 0.109by 0.000 0.634 0.281 0.260 0.31.5 0.290 0.343

ReD 0.000 0.552 0.278 0.227 0.250 0.356 0.2710 338 1820 2753 817 370 6098

0.000 0.663 0.354 0.302 0.337 0.434 0.360

-e STATISTICS FOR

READER-BARRIS/GALLAGHER - FLABGE TAP

Tube .. 2 in 3 in 4 in 6 in 10 in 24 in Summar)-by

Beta* ~ Beta0.100 0.000 0.000 0.000 0.282 0.006 0.000 0.080

( 0.0991 0.000 0.000 0.000 0.277 0.270 0.000 0.297to 0.000 0.000 0.000 0.315 0.252 0.000 0.269

0.1028 ) 0 0 0 29 79 0 1080.000 0.000 0.000 0.399 0.270 0.000 0.308

0.200 0.121 -0.019 0.056 0.109 -0.166 -0.078 -0.023( 0.1982 0.164 0.125 0.245 0.082 0.251 0.066 0.239

to 0.169 0.113 0.193 0.113 0.204 0.083 0.1710.2418 ) 60. 57 271 83 257 70 798

0.204 0.126 0.251 0.137 0.302 0.103 0.240

0.375 0.259 0.022 0.086 0.089 -0.112 0.075 0.053( 0.3620 0.094 0.101 0.238 0.196 0.217 0.038 0.218

to 0.259 0.085 0.163 0.118 0.158 0.075 0.1500.3748 ) 104 106 287 122 202 84 905

0.277 0.103 0.253 0.216 0.245 0.084 0.224

0.500 0.163 0.144 0.077 0.087 -0.086 -0.112 0.046( 0.4825 0.101 0.057 0.169 0.113 0.157 0.047 0.165

to 0.170 0.144 0.138 0.116 0.130 0.112 0.1360.5003 ) 113 69 164 109 164 51 670

0.192 0.156 0.186 0.143 0.179 0.122 0.171

0.575 0.042 0.085 -0.022 -0.046 -0.102 -0.185 -0.049( 0.5427 0.111 0.078 0.244 0.138 0.217 0.068 0.212

to 0.100 0.100 0.192 0.122 0.189 0.185 0.1700.5770 ) 90 72 435 136 390 67 1190

0.119 0.115 0.245 0.146 0.239 0.198 0.217

0.660 --0.092 0.096 -0.063 -0.180 -0.140 -0.120 -0.096( 0.6481 0.213 0.107 0.246 0.157 0.172 0.044 0.205

to 0.165 0.ll2 0.186 0.218 0.185 0.120 0.1760.6645 ) 196 64 289 92 303 58 1002

0.232 0.144 0.254 0.239 0.222 0.129 0.227

0.750 0.048 0.144 0.241 0.068 -0.142 0.022 0.053( 0.7239 0.164 O.lll 0.254 0.237 0.266 0.122 0.283

to 0.138 0.153 0.293 0.136 0.235 0.103 0.2210.7509 ) 212 101 458 130 490 34 1425

0.171 0.183 0.350 0.246 0.302 0.124 0.288

Summary 0.063 0.081 0.071 0.034 -0.122 -0.064 -0.001by 0.195 0.ll5 0.263 0.203 0.230 0.ll3 0.239

Tube 0.164 0.ll8 0.207 0.142 0.197 0.ll2 0.178775 469 1904 701 1885 364 6098

0.205 0.141 0.273 0.206 0.261 0.130 0.239

-;

STATISTICS !'OR

JUW)ER-BARRIS/GAl.l.AGBER - FLAJlGB rAl'


Beta' I 4000 10000 100000 1000000 10000000 100000000 Beta

0.100 0.000 0.122 0.045 0.000 0.000 0.000 0.080( 0.0991 0.000 0.283 0.306 0.000 0.000 0.000 0.297

to 0.000 0.256 0.280 0.000 0:000 0.000 0.2690.102B ) 0 49 59 0 0 0 108

0.000 0.309 0.309 0.000 0.000 0.000 0.308

0.200 0.000 0.026 -0.018 -0.053 -0.071 0.000 -0.023( 0.1982 0.000 0.365 0.202 0.294 0.066 0.000 0.239

to 0.000 0.227 0.162 0.220 0.079 0.000 0.1710.2U8 ) 0 108 493 119 78 0 798

0.000 0.366 0.203 0.299 0.097 0.000 0.240

0.375 0.000 0.444 0.070 -0.032 0.068 0.091 0.053( 0.3620 0.000 0.315 0.222 0.145 0.036 0.037 0.218

to 0.000 0.444 0.165 0.106 0.068 0.091 0.1500.3748 ) 0 46 451 324 59 25 905

0.000 0.548 0.233 0.148 0.078 0.100 0.224

0.500 0.000 0.136 0.132 0.009 ·0.142 -0.102 0.046( 0.4825 0.000 0.106 0.161 0.154 0.047 0.044 0.165

to 0.000 0.144 0.177 0.116 0.142 0.102 0.1360.5003 ) 0 50 201 368 12 39 670

0.000 0.174 0.20B 0.154 0.155 0.113 0.171

0.575 0.000 -0.010 -0.030 -0.060 ·0.032 -0.074 -0.049( 0.5427 0.000 0.162 0.21B 0.201 0.250 0.183 0.212

to 0.000 0.130 0.163 0.163 0.205 0.175 0.1700.5770 ) 0 35 245 611 202 97 1190

0.000 0.162 0.220 0.210 0.252 0.198 0.217

0.660 0.000 -0.243 -0.101 -0.070 -0.157 -0.109 -0.096( 0.6481 0.000 0.394 0.266 0.188 0.168 0.069 0.205

to 0.000 0.424 0.218 0.155 0.201 0.114 0.1760.6645 ) 0 23 197 546 138 98 1002

0.000 0.466 0.284 0.200 0.231 0.129 0.227

0.750 0.000 0.244 0.051 0.080 -0.006 -0.013 0.053( 0.7239 0.000 0.141 0.309 0.257 0.346 0.174 0.283

to 0.000 0.248 0.233 0.208 0.272 0.140 0.2210.7509 ) 0 27 174 785 328 111 1425

0.000 0.286 0.313 0.269 0.346 0.174 0.288

Summary 0.000 0.109 0.018 -0.009 -0.041 -0.OS7 -0.001by 0.000 0.335 0.238 0.219 0.269 0.lS0 0.239

ReD 0.000 0.253 0.181 0.164 0.209 0.135 0.1780 338 1820 2753 817 370 6098

0.000 0.352 0.239 0.219 0.272 0.160 0.239

.e STATISTICS FOR

READER-HARRIS/GALLAGHER - FLABGE TAP

Reo .. 10 4000 10000 100000 1000000 10000000 Summaryto to to to to to by

Pipe ~ 4000 10000 100000 1000000 10000000 100000000 Pipe2.000 0.000 0.071 0.050 0.080 0.000 0.000 0.063

0.000 0.289 0.20ii 0.099 0.000 0.000 0.1950.000 0.247 0.177 0.104 0.000 0.000 0.195

0 112 414 249 0 0 7750.000 0.298 0.212 0.128 0.000 0.000 0.205

3.000 0.000 -0.012 0.057 0.110 0.000 0.000 0.0810.000 0.138 0.116 0.103 0.000 0.000 0.1150.000 0.113 0.108 0.126 0.000 0.000 0.118

0 22 209 238 0 0 4690.000 0.138 0.129 0.151 0.000 0.000 0.141

4.000 0.000 0.193 0.031 0.058 0.217 0.000 0.0710.000 0.326 0.250 0.256 0.249 0.000 0.2630.000 0.251 0.195 0.201 0.258 0.000 0.207

0 95 622 1004 183 0 19040.000 0.379 0.251 0.262 0.331 0.000 0.273

6.000 0.000 0.251 0.105 -0.060 -0.087 0.000 0.0340.000 0.239 0.201 0.131 0.120 0.000 0.2030.000 0.261 0.153 0.111 0.117 0.000 0.142

0 68 275 328 30 0 7010.000 0.348 0.227 0.145 0.149 0.000 0.206

10.000 0.000 -0.157 -0.156 -0.117 -0.145 -0.009 -0.1220.000 0.469 0.264 0.191 0.249 0.180 0.2300.000 0.337 0.235 0.168 0.232 0.144 0.197

0 41 300 927 467 150 18850.000 0.495 0.307 0.224 0.288 0.180 0.261

24.000 0.000 0.000 0.000 -0.144 -0.020 -0.089 -0.0640.000 0.000 0.000 0.063 0.097 0.114 0.1130.000 0.000 0.000 0.144 0.082 0.129 0.112

0 0 0 7 137 220 3640.000 0.000 0.000 0.168 0.099 0.145 0.130

Summary 0.000 0.109 0.018 -0.009 -0.041 -0.057 -0.001by 0.000 0.335 0.238 0.219 0.269 0.150 0.239

ReO 0.000 0.253 0.181 0.164 0.209 0.135 0.1780 338 1820 2753 817 370 6098

0.000 0.352 0.239 0.219 0.272 .0.160 0.239

STATISTICS FOR

RUDER-BARRIS/GALLAGHER - FLAlIGE, COUER, RADIUS

Tube ... 2 in 3 in 4 in 6 in 10 in 24 in Sum"aryby

Beta* ~ Beta

0.100 0.000 0.000 0.000 0.282 0.006 0.000 0.080( 0.0991 0.000 0.000 0.000 0.277 0.270 0.000 0.297

to 0.000 0.000 0.000 0.315 0.252 0.000 0.2690.1028 ) 0 0 0 29 79 0 108

0.000 0.000 0.000 0.399 0.270 0.000 0.308

0.200 0.121 -0.019 0.102 0.109 -0.178 -0.094 -0.032( 0.1982 0.164 0.125 0.259 0.082 0.233 0.072 0.253

to 0.169 0.113 0.215 0.113 0.211 0.099 0.1870.2418 ) 60 57 632 83 625 250 1707

0.204 0.126 0.278 0.137 0.293 0.118 0.255

0.375 0.259 0.022 0.061 0.089 -0.136 0.069 0.022( 0.3620 0.094 0.101 0.211 0.196 0.213 0.050 0.206

to 0.259 0.085 0.142 0.118 0.173 0.072 0.1380.3748 ) 104 106 415 122 395 296 1438

0.277 0.103 0.219 0.216 0.253 0.085 0.208

0.500 0.163 0.144 0.125 0.087 -0.011 -0.116 0.042( 0.4825 0.101 0.057 0.191 0.113 0.174 0.069 0.177

to 0.170 0.144 0.172 0.116 0.132 0.116 0.1420.5003 ) 113 69 285 109 343 201 1120

0.192 0.156 0.229 0.143 0.175 0.135 0.182

0.575 0.042 0.085 0.064 -0.046 -0.007 -0.160 0.009( 0.5427 0.111 0.078 0.288 0.138 0.258 0.092 0.256

to 0.1.00 0.100 0.233 0.122 0.204 0.160 0.2000.5770 ) 90 72 1011 136 939 249 2497

0.119 0.115 0.295 0.146 0.258 0.185 0.256

0.660 -0.092 0.096 -0.069 -0.180 -0.023 -0.175 -0.072( 0.6481 0.213 0.107 0.251 0.157 0.210 0.104 0.216

to 0.165 0.112 0.200 0.218 0.169 0.175 0.1800.6645 ) 196 64 630 92 700 314 1996

0.232 0.144 0.260 0.239 0.211 0.204 0.228

0.750 0.048 0.144 0.142 0.068 -0.088 -0.257 0.011( 0.7239 0.164 0.111 0.329 0.237 0.310 0.209 0.320

to 0.138 0.153 0.276 0.136 0.249 0.291 0.2430.7509 ) 212 101 971 130 1222 .125 2761

0.171 0.183 0.359 0.246 0.323 0.332 0.320

Summary 0.063 0.081 0.072 0.034 -0.069 -0.107 -0.005by 0.195 0.115 0.284 0.203 0.262 0.140 0.257

Tube 0.164 0.118 0.222 0.142 0.204 0.140 0.192775 469 3944 701 4303 1435 11627

0.205 0.141 0.293 0.206 0.271 0.176 0.257

" .. , ..

STATISTICS lOR

Bl!.ADER-Ill1UlIS/GAI..L.lGHER - FLAlIGE, COlUIER, RADIUS


Beta* ~ 4000 10000 100000 1000000 10000000 100000000 Beta0.100 0.000 0.122 0.045 0.000 0.000 0.000 0.080

( 0.0991 0.000 0.283 0.306 0.000 0.000 0.000 0.297to 0.000 0.256 0.280 0.000 0.000 0.000 0.269

0.1028 ) 0 49 59 0 0 0 1080.000 0.309 0.309 0.000 0.000 0.000 0.308

0.200 0.000 -0.012 -0.025 -0.023 -0.082 0.000 -0.032( 0.1982 0.000 0.441 0.228 0.269 0.069 0.000 0.253

to 0.000 0.296 0.184 0.215 0.088 0.000 0.1870.2418 ) 0 183 922 328 274 0 1707

0.000 0.441 0.229 0.270 0.108 0.000 0.255

0.375 0.000 0.444 0.030 -0.053 0.057 0.098 0.022( 0.3620 0.000 0.315 0.238 0.145 0.048 0.042 0.206

to 0.000 0.444 0.167 0.1l5 0.062 0.098 0.1380.3748 ) 0 46 595 501 2ll 85 1438

0.000 0.548 0.240 0.155 0.075 0.107 0.208

0.500 0.000 0.136 0.1l4 0.055 -0.160 -0.100 0.042( 0.4825 0.000 0.106 0.185 0.171 0.063 0.064 0.177

to 0.000 0.144 0.181 0.135 0.161 0.100 0.1420.5003 ) 0 50 260 609 52 149 ll20

0.000 0.174 0.217 0.179 0.174 0.1l9 0.182. . ... - ~

0.575 0.000 -0.010 -0.083 0.018 0.074 -0.035 0.009( 0.5427 0.000 0.162 0.240 0.249 0.279 0.228 0.256

to 0.000 0.130 0.192 0.190 0.240 0.187 0.2000.5770 ) 0 35 364 1204 565 329 2497

0.000 0.162 0.254 0.249 0.289 0.231 0.256

0.660 0.000 -0.243 -0.149 -0.046 -0.022 -0.115 -0.072( 0.6481 0.000 0.394 0.270 0.209 0.201 0.168 0.216

to 0.000 0.424 0.247 0.165 0.166 0.171 0.i800.6645 ) 0 23 255 960 342 416 1996

0.000 0.466 0.308 0.214 0.202 0.203 0.228

0.750 0.000 0.244 0.033 0.020 -0.002 -0.024 0.01l( 0.7239 0.000 0.141 0.403 0.319 0.317 0.271 0.320

to 0.000 0.248 0.295 0.236 0.250 0.223 0.2430.7509 ) 0 27 205 1376 805 348 2761

0.000 0.286 0.405 0.320 0.317 0.272 0.320

Summary 0.000 0.077 -0.013 0.001 0.006 -0.056 -0.005by 0.000 0.383 0.261 0.251 0.256 0.212 0.257

ReD 0.000 0.279 0.198 0.185 0.195 0.176 0.1920 413 2660 4978 2249 1327 11627

0.000 0.390 0.261 0.251 0.256 0.219 0.257

STATISTICS FOR

VATAlfABE - OOJUl1!R TAP

Tube -+ 400111111 650mm 900mm 1100mm Summaryby

Beta' • Beta0.400 0.072 -0.023 0.074 -0.009 0.039

( 0.4003 0.069 0.130 0.128 0.060 0.124to 0.088 0.103 0.105 0.045 0.098

0.4090 ) 26 37 45 4 1120.101 0.132 0.148 0.061 0.130

0.500 0.015 0.044 -0.075 0.000 -0.008( 0.5005 0.132 0.113 0.100 0.000 0.125

to 0.108 0.095 0.099 0.000 0.1010.5115 ) 34 33 38 0 105

0.133 0.121 0.126 0.000 0.126

0.600 -0.093 -0.172 -0.271 0.000 -0.186( 0.6006 0.189 0.073 0.159 0.000 0.173

to 0.152 0.172 0.271 0.000 0.2060.6132 ) 41 28 49 0 118

0.211 0.189 0.317 0.000 0.254

0.700 -0.225 -0.724 0.000 0.000 -0.518( 0.7043 0.183 0.247 0.000 0.000 0.332

to 0.225 0.724 0.000 0.000 0.5180.7H2 ) 38 54 0 0 92

0.292 0.772 0.000 0.000 0.618

Summary -0.012 -0.238 -0.072 -0.075 -0.109by 0.223 0.353 0.202 0.102 0.284

Tube 0.174 0.288 0.159 0.093 0.207181 189 174 8 552

0.223 0.426 0.215 0.130 0.305

ALL eTAPS

2500r-------------------------------------------------~

II).....C:JoU

2000 ------------------------ -------------------------

1500 ----------------------

1000 ---------------------

500 --------------------

OL- ~-~,-~,Bulluwwwwmaaaal~mlmw,-~ ~-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

% Difference

2.0

Flange,

Tap1200r-----------------~-----------------------------

1000 ------------------------ - - - - - - - - - - - - - - - - - - - - - - - -

800 - - - - - - - - - - - - - - - - - - - - - - .

(I)0+-

§ 600 - - - - - - - - - - - - - - - - - - - - - -oU

- - - - - - - - - - - - - - - - - - - - - -,

400 - - - - - - - - - - - - - - - - - - - - - JIHI'II- HI - - - - - - - - - - - - - - - - - - - - -

200 -------------------- - - - - - - - - - - - - - - - - - - - -

0 -1Ill1 m ... _-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

% Difference

• eCORNER

eTAPS

1200~--------------------------------------------------~

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -,

1000 --------------------------------------------------

200 ---------------------

800

600

400

- - - - - - - - - - - - - - - - - - - - - - ..~ - - - - - - - - - - - - - - - - - - - - - - - - - - -

.,'- - - - - - - - - - - - - - - - - - - - - ~.- -

.~ !RInl ~~lYoIiIo&oI~liI.&;Il m;l",ll:l ... "-- ----'

-1.0 -0.5 0.0 0.5o-2.0 1.0 1.5 2.0-1.5

% Difference

RADIUS TAPS1200,....-------------------------_

1000 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

tlOO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

CII-+-

3 600 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -oU

400 - - - - - - - - - - - - - - - - - - - - - -

200 - - - - - - - - - - - - - - - - - - - - - ~·1flI

0 - dill Imm",,_-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

% Difference

RQ Model - Fla"8e TapAPI • ~Ee fit.., ..... lor. Doto Nt2.0

1.&

'-D

D.&~..!j D.D

.. -0.8

-1.0

-1.8

""-2.0a.o 8.0 7.0

'-(I0000)

2.00

1.eo

, .00

~ o.~o..! 0.00..~.. -0.80

-1.00

-1.80

-2.00a.o

2.0

1.8

,.D

~ D."..! D.D..J.. -0.8

-1.0

-1.8

-2.03.0

RQ Model - Corner Tap.... , .. El!e ~""'Ier. Date a.t

to.o,-(I0000)

7.0

.RQ ModelAPI 8\: eee

Radiue TapD_ ....

to.oU.O( .....c)

7.0

11 0 ------.U'C..,.

- 1\JJ0

-23 4

PERCENT

2

. ;,: \

Flange TapDM=50

j

5 6 1 8

log ReD

f3 + 0.1 X 0.2 *0.375 00.5o 0.575 ~ 0.66 0 0.75

e· Flange Ta~DM=75 .

PERCENT

3 5 7 84 6

log ReO

f3 + 0.1 X 0.2 *0.375 00.5o 0.575 ~ 0.66 8 0.75

Flange TapDM=100

PERCENT

2

."0uc..

rU1 - 1~

-23 4 5 6 7 8

log ReO

P + 0.1 X 0.2 * 0.375 0 0.5o 0.575 ~ 0.66 8 0.75

• Flange Ta~DM=150

PERCENT

2

o +-----------------~ f--------------------------------------------------

- 1

3 4 7 85 6

log ReO

(3 + 0.100.575

x 0.2 * 0.375 0 0.5/} 0_66 o 0.75

3 4 5 6 7 8

Flange TapDM-250

PERCENT

2

1

o ~.:l:••.,." ..~"J

- 1~

_2~~~X~~~~~~X~~~~~~~~~~~

log ReO

{3 + 0.1 X 0.2 *0.375 00.500.575 6 0.66 8 0.75

PERCENT

21

"T'\ 0LL'C...('

(,01- 1

\II

-2

Flange Ta~DM=600

3 7 B5 64

log ReO

(3 + 0.1 X 0.2 *0.375 00.5o 0.575 ~ 0.66 0 0.75

e TABLEB.1

Apr-90 NOHINAL2-INCH (50HH)METERR6 Equation

Flange-Tapped Discharge Coefficient - Cd(FT) D 1.939 inches49.25Iilli.eters

Pipe Reynolds NUlber (ReD):=:=:::1:::=======================================================================================================================Beh 1 4,000 10,000 50,000 100,000 500,000 1,000,000 5,000,000 10,000,000 50,000,000 100,000,000

-======1==========================================================================================================================0.02 1 0.60014 0.59940 0.59883 0.59873 0.59862 0.59860 0.59858 0.59857 G.S9857 0.598570.04 1 0.60102 0.59981 0.59890 0.59873 0.59854 0.59851 0.59847 0.59847 0.59846 0.598460.06 I 0.60178 0.60016 0.59895 0.59872 0.59848 0.59844 0.59839 0.59838 0.59837 0.598370.08 1 0.60248 0.60050 0.59901 0.59873 0.59843 0.59838 0.59832 0.59831 0.59830 0.598290.10 1 0.60315 0.60083 0.59908 0.59875 0.59840 0.59834 0.59827 0.59826 0.59824 0.59824

10.12 1 0.60381 0.60116 0.59916 0.59879 0.59839 0.59832 0.59824 0.59823 0.59821 0.598210.14 I 0.60448 0.60150 0.59927 0.59886 0.59841 0.59832 0.59B23 0.59821 0.59820 0.59819

_.161 0.60515 0.60187 0.59940 0.59894 0.59844 0.59835 0.59B25 0.59823 0.59820 0.59820.18 1 0.60586 0.60226 0.59955 0.59905 0.59850 0.59840 0.59B28 0.59826 0.59824 0.59823

0.20 1 0.60660 0.60269 0.59974 0.59919 0.59859 0.59848 0.59835 0.59832 0.59829 0.598291

0.22 1 0.60738 0.60315 0.59996 0.59936 0.59871 0.59858 0.59844 0.59841 0.59838 0.598370.24 1 0.60823 0.60367 0.60022 0.59957 0.59886 0.59872 0.59856 0.59853 0.59849 0.598480.26 1 0.60914 0.60423 0.60052 0.59982 0.59904 0.59889 0.59871 0.59867 0.59863 0.598620.28 1 0.61014 0.60487 0.60087 0.60011 0.59926 0.59909 0.59889 0.59885 0.59880 0.598780.30 1 0.61123 0.60557 0.60127 0.60045 0.59952 0.59933 0.59911 0.59906 0.59900 0.59898

10.32 1 0.61243 0.60635 0.60173 0.60084 0.59982 0.59962 0.59936 0.59931 0.59923 0.599210.34 1 0.61375 0.60722 0.60224 0.60128 0.60017 0.59994 0.59965 0.59959 0.59950 0.599480.36 1 0.61522 0.60818 0.60282 0.60178 0.60056 0.60030 0.59998 0.59990 0.59980 0.599780.38 1 0.61683 0.60926 0.60347 0.60234 0.60100 0.60071 0.60034 0.60026 0.60014 0.600110.40 1 0.61862 0.61044 0.60419 0.60296 0.60149 0.60117 0.60075 0.60065 0.60051 0.60047

10.42 1 0.62059 0.61175 0.60499 0.60365 0.60202 0.60167 0.60119 0.60108 0.60091 0.600870.44 1 0.62276 0.61319 0.60586 0.60440 0.60261 0.60221 0.60167 0.60154 0.60134 0.601290.46 1 0.62515 0.61476 0.60682 0.60522 0.60324 0.60279 0.60218 0.60203 0.60180 G.60174

•. 481 0.62777 0.61647 0.60784 0.60610 0.60391 0.60341 0.60271 0.60254 0.60228 0.60221.50 1 0.63063 0.61833 0.60895 0.60703 0.60462 0.60406 0.60327 0.60307 0.60278 0.60270

10.52 1 0.63374 . 0.62034 0.61012 0.60803 0.60536 0.60473 0.60384 0.60361 0.60327 0.603180.54 1 0.63712 0.62249 0.61136 0.60906 0.60612 0.60541 0.60441 ·0.60415 0.60376 0.603660.56 1 0.64077 0.62479 0.61265 0.61014 0.60688 0.60609 0.60497 0.60467 0.60423 0.604110.58 1 0.64470 0.62722 0.61399 0.61123 0.60763 0.60675 0.60549 0.60516 0.60465 0.604510.60 1 0.64890 0.62979 0.61535 0.61233 0.60836 0.60738 0.60596 0.60558 0.60501 0.60486

10.62 1 0.65337 0.63246 0.61671 0.61341 0.60903 0.60794 0.60636 0.60593 0.60529 0.605110.64 1 0.65811 0.63524 0.61806 0.61445 0.60963 0.60842 0.60665 0.60617 0.60545 0.605150.66 1 0.66309 0.63809 0.61937 0.61542 0.61012 0.60878 0.60681 0.60628 0.60546 0.605230.68 1 0.66829 0.64098 0.62061 0.61629 0.61047 0.60899 0.60680 0.60621 0.60529 0.605040.70 1 0.67369 0.64389 0.62174 0.61703 0.61066 0.60902 0.60660 0.60593 0.60491 0.60463

10.72 1 0.67925 0.64679 0.62274 0.61762 0.61064 0.60884 0.60615 0.60542 0.60428 0.603960.74 1 0.68494 0.64964 0.62358 0.61802 0.61040 0.60842 0.60546 0.60464 0.60339 0.60303

10.75 1 0.68781 0.65103 0.62394 0.61815 0.61019 0.60812 0.60501 0.60415 0.60282 0.60245e

TABLEB.3

Apr-90 NOMINAL4-INCH (100MM)HETERR6 Equation

'Iange-Tapp.d Oischarg. Coeffici.nt - Cd(FT) D 3.826 inch.s97.18 lilli ••t.rs

Pip. R.ynolds NUlber (R.D)c:=====.::::::::::::==========:::::::==========:====:==:==========:===c=====::::=:=:===:=:=:=:==::==========:=:=======:==:=::::===B.h. 4,000 10,000 50,000 100,000 500,000 1,000,000 5,000,000 10,000,000 50,000,000 100,000,000

a======':=:::::::=============:==========:==========:=:=:==:====:==:=======:=:=::=========:==:=:===~=:===========:===:::======:=0.02 a 0.59704 0.59689 0.59633 0.59623 0.59012 0.59610 0.59607 0.5607 0.59607 0.5%070.04 a 0.59861 0.59739 0.59648 0.59631 0.59613 0.59610 0.59606 0.59605 0.59605 0.590050.06 a 0.59945 0.59784 0.59662 0.59640 0.59616 0.59611 0.59606 0.59005 0.59605 0.5%04O.OB a 0.60024 0.59826 0.59677 0.59650 0.59620 0.59615 0.59609 0.59608 0.59606 0.590060.10 • 0.60100 0.59868 0.59693 0.59661 0.59626 0.59610 0.59613 0.59612 0.59610 0.59610

•0.12 • 0.60175 0.59910 0.59711 0.59675 0.59635 0.59627 0.59619 0.59618 0.59616 0.596160.14 I 0.60250 0.59954 0.59731 0.5%90 0.59645 0.59637 0.59628 0.59626 0.59624 0.596240.16 I 0.60320 0.60000 0.59754 0.59708 0.59658 O.596~9 0.59639 0.59637 0.5963~ 0.5963.0.18 I 0.60405 0.60048 0.59779 0.5m9 0.5967~ 0.59664 0.59652 0.59650 0.59647 0.59640.20 I 0.60498 0.60099 0.59807 O.~97~2 0.59692 0.59681 0.59668 0.59666 0.59663 0.5966

I0.22 I 0.60575 0.60155 0.59838 0.59779 0.59713 0.59701 0.59686 0.59684 0.59680 O.S96800.24 I 0.60667 0.60215 0.59873 0.59809 0.59737 0.59723 0.59708 0.59704 0.59701 0.597000.26 I 0.60767 0.60280 0.59912 0.59842 0.59765 0.59H9 0.59732 0.59728 0.59723 0.597220.28 I 0.60874 0.60352 0.59955 0.59880 0.59795 0.59779 0.59759 0.59755 0.59H9 0.597480.30 I 0.60991 0.60430 0.60004 0.59922 0.59830 0.59811 0.59789 0.59784 0.597J8 0.59776

I0.32 I 0.61118 0.60516 0.60057 0.59969 0.59868 0.59847 0.59822 0.59816 0.59809 0.598070.34 I 0.61258 0.60610 0.60116 0.60021 0.59910 l 0.59887 0.59858 0.59852 0.59843 0.598410.36 I 0.61410 0.60713 0.60181 0.60078 0.59956 0.59930 0.59898 0.59891 0.59880 0.598780.38 I 0.61578 0.60827 0.60252 0.60140 0.60006 0.59978 0.59911 0.59932 0.59920 0.599170.40 I 0.61763 0.60951 0.60330 0.60207 0.60060 0.60028 0.59987 0.59977 O.S9963 0.59959

•0.42 • 0.61965 0.61086 0.60414 0.60280 0.60118 0.60082 0.60035 0.60023 0.60007 0.600030.44 • 0.62187 0.61233 0.60504 0.60358 0.60180 0.60140 0.60086 0.60073 0.60054 0.600480.46 • 0.m29 0.61393 0.60601 0.60442 0.60245 0.60200 0.60139 0.60123 0.60101 0.600950.48 • 0.62694 0.61567 0.60705 0.60530 0.60312 0.60262 0.60192 0.60175 0.60149 0.601420.50 a 0.62983 0.61753 0.60814 0.60623 0.60381 0.60325 0.60246 0.60226 0.60197 0.6018_a0.52 • 0.63296 0.61952 0.60928 0.60719 0.60451 0.60388 0.60300 0.60277 0.60243 0.602340.54 • 0.63634 0.62164 0.61047 o .bOB17 0.60521 0.60450 0.60350 0.60324 0.60285 0.602750.56 • 0.63999 0.62389 0.61168 0.60915 0.60588 0.60509 0.60396 0.60367 0.60323 0.603100.58 I 0.64389 0.62625 0.61290 0.blO13 0.60651 0.60563 0.60436 0.60403 0.60352 0.603380.60 t 0.64806 0.62871 0.61411 0.61106 0.60707 0.60609 0.60467 0.60429 0.60372 0.60356

I0.62 I 0.65247 0.63124 0.61528 0.61194 0.60753 0.60643 0.60484 0.60442 0.60377 0.603190.64 I 0.65713 0.63384 0.61638 0.61272 0.60795 0.60664 0.60486 0.60438 0.60365 0.603450.66 I 0.66201 0.63645 0.61737 0.61335 0.60800 0.60665 0.60467 0.60413 0.60332 0.603090.68 I 0.66708 0.63905 0.61820 0.61381 0.60792 0.60643 0.60422 0.60362 0.60271 0.602~50.70 I 0.67230 0.64160 0.61884 0.61403 0.60756 0.60591 0.60347 0.60280 0.60178 0.60149

I0.72 I 0.67764 0.64403 0.61921 0.61396 0.60686 0.60504 0.60234 0.60160 0.60046 0.600140.74 I 0.68303 0.64629 0.61926 0.61354 0.60517 0.60377 0.60078 0.59996 0.59869 0.59834

I0.75 I 0.68573 0.64733 0.bl915 0.61318 0.60505 0.60295 0.59981 0.59895 0.59762 0.59725

e

e TABLE B.6

Apr-90 NOKINAL 10-INCH (250KK) KETERRG Equation

Flange-Tapped Discharge Coefficient - Cd(FT) D 9.562 inches242.87 lilli.eters

Pipe Reynolds HUlber (ReD)======·1==:=======================================================================================:===============================BetaI 4,000 10,000 50,000 100,000 500,000 1,000,000 5,000,000 10,000,000 50,000,000 100,000,000=======,========================================:=================================================================================0.02 I 0.59767 0.59692 0.59636 0.59625 0.59614 0.59612 0.59610 0.59610 0.59609 0.596090.04 I 0.59866 M9745 0.59653 0.59637 0.59618 0.59615 0.59611 0.59611 0.59610 0.596100.06 I 0.59953 0.59792 0.59671 0.59649 0.59624 0.59620 0.59615 0.59614 0.59613 0.596130.08 I 0.60035 0.59838 0.59689 U9662 0.59632 0.59627 0.59621 0.59620 0.59618 0.596180.10 I 0.60114 0.59883 0.59709 0.59677 0.59642 0.59635 0.59628 0.59627 0.59626 0.59625

I0.12 I 0.60192 0.59928 0.59730 0.59694 0.59654 0.59646 0.59638 0.59637 0.59635 0.596350.14 I 0.60270 0.59976 0.59754 0.59713 0.59668 0.59660 0.59651 0.59649 0.59647 0.59647e16 I 0.60350 0.60025 0.m80 0.59734 0.59685 0.59676 0.59665 0.59663 0.59661 0.59661.18 I 0.60432 0.60076 0.59808 0.59158 0.59704 0.59694 0.59682 0.59680 0.m78 0.59677

0.20 I 0.60517 0.60131 0.59840 0.59785 0.59726 0.59714 0.59702 0.59699 0.59696 0.59696I

0.22 I 0.60607 0.60190 0.59874 0.59816 0.59150 0.59738 0.m24 0.59121 0.59718 0.597170.24 I 0.60702 0.60253 0.59913 0.59849 0.59778 0.59764 0.59748 0.59745 0.59741 0.597400.26 I 0.60804 0.60321 0.59955 0.59886 0.59808 0.59793 0.59775 0.59772 0.59767 0.597660.28 I 0.60914 0.60395 0.60001 0.59926 0.59842 0.59825 0.5980.5 0.59801 0.59796 0.597950.30 I 0.61032 0.60475 0.60052 0.59971 0.59879 0.59860 0.59838 0.59833 0.59827 0.59825

I0.32 I 0.61161 0.60563 0.60107 0.60019 0.59919 0.59898 0.59873 0.59867 0.59860 0.598580.34 I 0.61302 0.60658 0.60167 0.60072 0.59962 0.59939 0.59911 0.59904 0.59896 0.598930.36 I 0.61456 0.60763 0.60233 0.60130 0.60009 0.59983 0.59951 0.59944 0.59933 0.599310.38 I 0.61624 0.60876 0.60304 0.60192 0.60059 0.60030 0.59994 0.59985 0.59973 0.599700.40 I 0.61809 0.61000 0.60381 0.60259 0.60112 0.60080 0.60038 0.60028 0.60014 0.60011

I0.42 I 0.62010 0.61134 0.60463 0.60330 0.60168 0.60132 0.60085 0.60073 0.60057 0.600530.44 I 0.62231 0.61279 0.60551 ·0.60405 0.60226 0.60186 0.60132 0.60119 0.60100 0.600950.46 I 0.62473 0.61436 0.60643 0.60484 0.60286 0.60241 0.60180 0.60165 0.60143 0.60137

.48 I 0.62735 0.61605 0.60741 0.60566 0.60347 0.60297 0.60228 0.60210 0.60185 0.6017850 I 0.63021 0.61785 0.60843 0.60651 0.60409 0.60352 0.60274 0.60253 0.60224 0.60216

I0.52 I 0.63331 0.61977 0.60947 0.60737 0.60468 0.60405 0.60316 0.60293 0.60259 0.602500.54 I 0.63665 0.62181 0.61054 0.60822 0.60525 0.60454 0.60354 0.60328 0.60289 0.602780.56 I 0.64024 0.62395 0.61161 0.60906 0.60577 0.60497 0.60384 0.60355 0.60310 0.602980.58 I 0.64408 0.62618 0.61265 0.60985 0.60621 0.60532 0.60405 0.60371 0.60321 0.603070.60 I 0.64817 0.62848 0.61365 0.61057 0.60654 0.60555 0.60412 0.60374 0.60317 0.60301

I0.62 I 0.65250 0.63083 0.61457 0.61118 0.60672 0.60562 0.60402 0.60360 0.60295 0.602770.64 I 0.65706 0.63320 0.61536 0.61164 0.60672 0.60549 0.60371 0.60323 0.60250 0.602290.66 I 0.66182 0.m55 0.61599 0.61190 0.60647 0.60511 0.60312 0.60258 0.60176 0.601530.68 I 0.66675 0.63784 0.61639 0.61190 0.60592 0.60441 0.60219 0.60159 0.60067 0.600420.70 I 0.67181 0.64000 0.61650 0.61158 0.60499 0.60332 0.60086 0.60019 0.59916 0.59888

I0.72 I 0.67696 0.64198 0.61624 0.61085 0.60361 0.60176 0.59903 0.59829 0.59m 0.596830.74 I 0.68212 0.64369 0.61553 0.60963 0.60167 0.59964 0.59663 0.59580 0.59453 0.59418

I0.75 I 0.68468 0.64441 0.61497 0.60880 0.60047 0.59834 0.59517 0.59430 U9297 0.59259e

TA8LE 8.10Apr-90 NOMINAL 21-INCH (600M") KETERR6 Equa lion

Flange-Tapped Discharge Coefficient - Cd(FT) D 23.000 inch!>584.20 .illi,et"s

Pipe Reynolds Nu.be, (R,D)ca:====':=======:::=====================================================:====:::::===!:============:=======:====::::====:===:::=:=

B,ta • 1,000 10,000 50,000 100,000 500,000 1,000,000 5,000,000 10,000,000 50,000,000 100,000,000z======.:=====================================================================:=:===============::::====:=======:=:=====:=======:=0.02 • o.5m8 0.59693 0.59637 0.59627 0.59615 O. Slb13 0.59611 0.59611 0.59610 0.596100.01 • 0.59869 0.59747 0.59656 0.59639 0.59621 0.Slb18 0.59611 0.59613 0.59613 0.596130.06 • 0.59957 0.597% 0.59675 0.59653 0.59628 0.59621 0.59619 0.59618 0.59617 0.596170.08 • 0.600U 0.59843 0.59695 0.59668 0.59638 0.59632 0.59626 0.59625 0.59624 0.596240.10 • 0.60121 0.59890 0.59716 0.59684 0.59619 0.59613 0.59636 0.59635 0.59633 0.59633

•0.12 I 0.60201 0.59937 0.59739 0.59703 0.59663 0.59656 0.59618 0.59646 0.59645 0.596440.11 I 0.60280 0.59986 0.5m5 0.59724 0.59679 0.59671 0.59662 0.59660 0.59658 0.5965.0.16 I 0.60361 0.60037 0.59793 0.59747 0.59698 0.59689 0.59678 0.59676 0.59674 0.59670.18 I 0.60445 0.60090 0.59823 0.59773 0.59719 0.59709 0.59697 0.59695 0.59693 0.596920.20 I 0.60532 0.00147 0.59856 0.59802 0.59743 0.59731 0.59719 0.59716 0.59713 0.59713

I0.22 I 0.60623 0.60207 0.59893 0.59834 0.59769 0.59757 0.59742 0.59710 0.59736 0.597360.24 I 0.60720 0.60272 0.59933 0.59869 0.59798 0.59785 0.59769 0.59766 0.59762 0.597610.26 I 0.60823 0.60312 0.59977 0.59908 0.59830 0.59815 0.59798 0.59794 0.59789 0.597880.28 I 0.00934 0.60417 0.60024 0.59950 0.59866 0.59849 0.59829 0.59825 0.59820 0.598180.30 • 0.61054 0.60499 0.60076 0.59996 0.59904 0.59885 0.59863 0.59858 0.59852 0.59851

•0.32 • 0.61184 0.60587 0.60133 0.60046 0.59915 0.59925 0.59900 0.59894 0.59887 0.598850.34 • 0.61325 0.60;84 0.60195 0.60100 0.59990 0.59967 0.59938 0.59932 0.59923 0.599210.36 • 0.61480 0.60789 0.60261 0.60158 0.60037 0.60012 0.59980 0.59172 0.599;2 0.599590.38 • 0.61619 0.60903 0.60333 0.60221 0.60088 0.60059 0.60023 0.60014 0.60002 0.599990.40 • 0.61834 0.61027 0.60110 0.60288 0.60141 0.60109 0.60068 0.60058 0.60041 0.60040•0.42 I 0.62036 0.61161 0.60492 0.60358 0.60197 0.60161 0.60tH 0.60102 0.60086 0.600820.44 I 0.62257 0.61306 0.60579 0.60433 0.60255 0.60215 0.60161 0.60148 0.60129 0.601230.46 I 0.62498 0.61163 0.60671 0.60511 0.60314 0.60269 0.60208 0.60192 0.60170 0.601640.48 I 0.62761 0.61630 0.60767 0.60592 0.60373 0.60323 0.60253 0.60236 0.60210 0.6020_0.50 I 0.63046 0.61809 0.60866 0.60;74 0.60432 0.60375 0.;0297 0.60276 0.60247 0.6023

I0.52 I 0.63355 0.61999 0.60968 0.60757 0.60488 0.;0125 0.60336 0.60313 0.60279 0.602700.54 I 0.636B8 0.62200 0.61070 0.60838 0.60541 0.60470 0.60369 0.60343 0.60304 0.602940.56 I 0.6404; 0.62411 0.61172 0.60917 0.60587 0.60507 0.60394 0.60365 0.60320 0.603080.5B I 0.64129 0.62629 0.61271 0.60989 0.60624 0.60535 0.60408 0.60375 0.60324 0.601lO0.60 I 0.64836 0.62854 0.61363 0.61054 0.60649 0.60550 0.60407 0.60369 0.60312 0.60296

I0.62 I 0.65267 0.63083 0.61416 0.61105 0.60658 0.60547 0.60387 0.60345 0.60280 0.602620.64 I 0.65720 0_63313 0.6lS15 0.61140 0.60646 0.60523 0.60344 0.60296 0.60223 0.602020.66 • 0.66192 0.63539 0.61565 0.6llS3 0.60607 0.60470 0.60270 0.60216 0.60135 0.601120.68 • 0.66682 0.63757 0.61589 0.61137 0.60534 0.60383 0.60160 0.60100 0.60008 0.599830.10 • 0.67181 0.63960 0.61581 0.61084 0.60421 0.60253 0.60006 0.59939 0.59837 0.59808•0.72 • 0.67693 0.64112 0.61533 0.60987 0.60257 0.60072 0.59798 0.59724 0.59610 0.595780.14 • 0.68203 0.64293 0.61133 0.60836 0.60034 0.59829 0.59526 0.59414 0.59317 0.59281

t0.75 I 0.6B456 0.64355 0.61361 0.60736 0.59895 0.59681 0.59363 0.59276 0.59142 0.59105_

ORIFICE PLATEDISCHARGE COEFFICIENT EQUATION J … · experimental data. Experiments were conducted...

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