1、BRITISH STANDARDBS ISO 5168:2005Measurement of fluid flow Procedures for the evaluation of uncertaintiesICS 17.120.10g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42
2、g43g55g3g47g36g58BS ISO 5168:2005This British Standard was published under the authority of the Standards Policy and Strategy Committee on 10 August 2005 BSI 10 August 2005ISBN 0 580 46279 XNational forewordThis British Standard reproduces verbatim ISO 5168:2005 and implements it as the UK national
3、standard. It supersedes BS ISO/TR 5168:1998 which is withdrawn.The UK participation in its preparation was entrusted by Technical Committee CPI/30, Measurement of fluid flow in closed conduits, to Subcommittee CPI/30/9, General topics, which has the responsibility to: A list of organizations represe
4、nted on this subcommittee can be obtained on request to its secretary.Cross-referencesThe British Standards which implement international publications referred to in this document may be found in the BSI Catalogue under the section entitled “International Standards Correspondence Index”, or by using
5、 the “Search” facility of the BSI Electronic Catalogue or of British Standards Online.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard does not of itself confer immunity from
6、 legal obligations. aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals for change, and keep UK interests informed; monitor related international and European developments and promulgate them in the UK.Su
7、mmary of pagesThis document comprises a front cover, an inside front cover, the ISO title page, pages ii to v, a blank page, pages 1 to 65 and a back cover.The BSI copyright notice displayed in this document indicates when the document was last issued.Amendments issued since publicationAmd. No. Date
8、 CommentsReference numberISO 5168:2005(E)INTERNATIONAL STANDARDISO5168Second edition2005-06-15Measurement of fluid flow Procedures for the evaluation of uncertainties Mesure de dbit des fluides Procdures pour le calcul de lincertitudeBS ISO 5168:2005iiiiiContents PageForeword ivIntroduction v1 Scope
9、 . 12 Normative references . 13 Terms and definitions. 14 Symbols and abbreviated terms . 34.1 Symbols . 34.2 Subscripts . 75 Evaluation of the uncertainty in a measurement process 86 Type A evaluations of uncertainty 96.1 General considerations 96.2 Calculation procedure 97 Type B evaluation of unc
10、ertainties . 107.1 General considerations 107.2 Calculation procedure 107.3 Rectangular probability distribution. 107.4 Normal probability distribution . 117.5 Triangular probability distribution 117.6 Bimodal probability distribution . 117.7 Assigning a probability distribution . 117.8 Asymmetric p
11、robability distributions. 118 Sensitivity coefficients. 128.1 General. 128.2 Analytical solution 128.3 Numerical solution 129 Combination of uncertainties 1310 Expression of results . 1410.1 Expanded uncertainty 1410.2 Uncertainty budget . 15Annex A (normative) Step-by-step procedure for calculating
12、 uncertainty 17Annex B (normative) Probability distributions . 20Annex C (normative) Coverage factors 22Annex D (informative) Basic statistical concepts for use in Type A assessments of uncertainty. 24Annex E (informative) Measurement uncertainty sources. 36Annex F (informative) Correlated input var
13、iables . 38Annex G (informative) Examples 40Annex H (informative) The calibration of a flow meter on a calibration rig 58Annex I (informative) Type A and Type B uncertainties in relation to contributions to uncertainty from “random” and “systematic” sources of uncertainty 61Annex J (informative) Spe
14、cial situations using two or more meters in parallel 62Annex K (informative) Alternative technique for uncertainty analysis. 64Bibliography . 65BS ISO 5168:2005BS ISO 5168:2005ivForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (
15、ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, go
16、vernmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IE
17、C Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as anInternational Standard requires approval by at least 75 % of the membe
18、r bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 5168 was prepared by Technical Committee ISO/TC 30, Measurement of fluid
19、 flow in closed conduits,Subcommittee SC 9, General topics.This second edition of ISO 5168 cancels and replaces ISO/TR 5168:1998, which has been technically revised (see Annex I). BS ISO 5168:2005vIntroduction Whenever a measurement of fluid flow (discharge) is made, the value obtained is simply the
20、 best estimate that can be obtained of the flow-rate or quantity. In practice, the flow-rate or quantity could be slightly greater or less than this value, the uncertainty characterizing the range of values within which the flow-rate or quantity is expected to lie, with a specified confidence level.
21、 GUM is the authoritative document on all aspects of terminology and evaluation of uncertainty and should be referred to in any situation where this International Standard does not provide enough depth or detail. Inparticular, GUM (1995), Annex F, gives guidance on evaluating uncertainty components.
22、 blank1Measurement of fluid flow Procedures for the evaluation of uncertainties 1 Scope This International Standard establishes general principles and describes procedures for evaluating the uncertainty of a fluid flow-rate or quantity. A step-by-step procedure for calculating uncertainty is given i
23、n Annex A. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 9300, Measu
24、rement of gas flow by means of critical flow Venturi nozzlesISO Guide to the expression of uncertainty in measurement (GUM), 1995 International vocabulary of basic and general terms in metrology (VIM), 1993 3 Terms and definitions For the purposes of this document, the terms and definitions given in
25、 VIM (1993), GUM (1995) and the following apply. 3.1uncertainty parameter, associated with the results of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand NOTE Uncertainties are expressed as an absolute value and do not take a positi
26、ve or negative sign. 3.2standard uncertainty u(x)uncertainty of the result of a measurement expressed as a standard deviation 3.3relative uncertainty u*(x)standard uncertainty divided by the best estimate NOTE 1 u*(x) u(x)/x.NOTE 2 u*(x) can be expressed either as a percentage or in parts per millio
27、n. NOTE 3 Relative uncertainty is sometimes referred to as dimensionless uncertainty. NOTE 4 The best estimate is in most cases the arithmetic mean of the related uncertainty interval. BS ISO 5168:200523.4combined standard uncertainty uc(y)standard uncertainty of the result of a measurement when tha
28、t result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariances of these other quantities weighted according to how the measurement result varies with changes in these quantities 3.5relative combi
29、ned uncertainty uc*(y)combined standard uncertainty divided by the best estimate NOTE 1 uc*(y) can be expressed as a percentage or parts per million. NOTE 2 uc*(y) uc(y)/y.NOTE 3 Relative combined uncertainty is sometimes referred to as dimensionless combined uncertainty. NOTE 4 The best estimate is
30、 in most cases the arithmetic mean of the related uncertainty interval. 3.6expanded uncertainty Uquantity defining an interval about the result of a measurement that can be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand NOTE
31、1 The fraction can be viewed as the coverage probability or the confidence level of the interval. NOTE 2 U kuc(y)3.7relative expanded uncertainty U*expanded uncertainty divided by the best estimate NOTE 1 U*can be expressed as a percentage or in parts per million. NOTE 2 U* kuc*(y).NOTE 3 Relative e
32、xpanded uncertainty is sometimes referred to as dimensionless expanded uncertainty. NOTE 4 The best estimate is in most cases the arithmetic mean of the related uncertainty interval. 3.8coverage factor knumerical factor used as a multiplier of the combined standard uncertainty in order to obtain an
33、expanded uncertainty NOTE A coverage factor is typically in the range 2 to 3. 3.9Type A evaluation uncertainty method of evaluation of uncertainty by the statistical analysis of a series of observations BS ISO 5168:200533.10Type B evaluation uncertainty method of evaluation of uncertainty by means o
34、ther than the statistical analysis of a series of observations 3.11sensitivity coefficient cichange in the output estimate, y, divided by the corresponding change in the input estimate, xi3.12relative sensitivity coefficient c*irelative change in the output estimate, y, divided by the corresponding
35、relative change in the input estimate, xi4 Symbols and abbreviated terms 4.1 Symbols aiestimated semi-range of a component of uncertainty associated with input estimate, xi,as defined in Annex B Atarea of the throat bibreadth associated with a vertical ibciupper bound of an asymmetric uncertainty di
36、stribution as defined in Annex B cisensitivity coefficient used to multiply the uncertainty in the input estimate, xi, to obtain the effect of a change in the input quantity on the uncertainty of the output estimate, yc*irelative sensitivity coefficient used to multiply the relative uncertainty in i
37、nput estimate, xi,to obtain the effect of a relative change in the input quantity on the relative uncertainty of the output estimate, yCccalibration coefficient C discharge coefficient CVcoefficient of variationdidepth associated with a vertical idoorifice diameter do,0orifice diameter measured at t
38、emperature T0,xdppipe diameter dp,0pipe diameter measured at temperature T0,xE mean meter error, expressed as a fractionBS ISO 5168:20054jE jth meter error, expressed as a fraction f functional relationship between estimates of the measurand, y, and the input estimates, xi, on which y depends ifxwwp
39、artial derivative with respect to input quantity, xi, of the functional relationship, f,between the measurand and the input quantities F flow factor, equal to rqpFexpflow factor for a new design FRedp 0,8dp19 000 ReEFrefreference flow factorFsfactor, assumed to be unity, that relates the discrete su
40、m over the finite number of verticals to the integral of the continuous function over the cross-section k coverage factor used to calculate the expanded uncertainty, Uktcoverage factor derived from a table; see D.12 K meter factorK mean meter factor jK jth K-factor; lblength of crest lhgauged head l
41、1distance from the upstream tapping to the upstream face L1l1divided by the pipe diameter, dp2lc distance from the downstream tapping to the downstream face 2Lc2lc divided by the pipe diameter, dpm particular item in a set of data mc number of data sets to be pooled ms number of verticals 2Mc 221L E
42、c n number of repeat readings or observations nc exponent of lh, usually 1,5 for a rectangular weir and 2,5 for a V-notch BS ISO 5168:20055ncc number of depths in a vertical at which velocity measurements are made N number of input estimates, xi, on which the measurand depends p0upstream pressure pm
43、tpressure difference across the orifice meter prpressure difference across the radiator P(ai) probability that an input estimate, xi, has a value of aiq volume flow-rateqmamass flow; Q flow, expressed in cubic metres per second, at flowing conditions R specific gas constant RedpReynolds number relat
44、ed to dpby the expression VdpU/Psmt,popooled experimental standard deviation of the orifice plate readingsspestandard deviation of a larger set of data used with a smaller data set spostandard deviation pooled from several sets of datasr,popooled experimental standard deviation for the radiator read
45、ings s(x) experimental standard deviation of a random variable, x, determined from n repeated observations s x experimental standard deviation of the arithmetic mean, xt Students statistic T0upstream absolute temperature T0,xtemperature at which measurement x is madeTopoperating temperature uc,corr(
46、y) combined uncertainty for those components for multiple meters that are correlated uc,uncorr(y) combined uncertainty for those components for multiple meters that are uncorrelated u*calinstrument calibration uncertainty from all sources, formerly called systematic errors or biases u*crirelative un
47、certainty in point velocity at a particular depth in vertical i due to the variable responsiveness of the current meter u*drelative standard uncertainty in the coefficient of discharge BS ISO 5168:20056u*eirelative uncertainty in point velocity at a particular depth in vertical i due to velocity flu
48、ctuations (pulsations) in the stream u*lbrelative standard uncertainty in the measurement of the crest length u*lhrelative standard uncertainty in the measurement of the gauged head u*msrelative uncertainty due to the limited number of verticals u*pirelative uncertainty in mean velocity, Vi, due to
49、the limited number of depths at which velocity measurements are made at vertical, iu*(Q) combined relative standard uncertainty in the discharge; usmstandard uncertainty of a single value based on past experienceu(xi,corr) correlated components of uncertainty in a single meter u(xi,uncorr) uncorrelated components of uncertainty in a single meter u*(xi) standard uncertainty associated with the input estimate, xi*c()uy combined standard uncertainty associated with the output estimate, yu*(xi) relative standard uncertainty asso
