ISO 3966:2020
(Main)Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes
Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes
This document specifies a method for the determination in a closed conduit of the volume rate of flow of a regular flow a) of a fluid of substantially constant density or corresponding to a Mach number not exceeding 0,25, b) with substantially uniform stagnation temperature across the measuring cross-section, c) running full in the conduit, and d) under steady flow conditions. In particular, it deals with the technology and maintenance of Pitot static tubes, with the calculation of local velocities from measured differential pressures and with the computation of the flow rate by velocity integration.
Mesurage du débit des fluides dans les conduites fermées — Méthode d'exploration du champ des vitesses au moyen de tubes de Pitot doubles
Le présent document spécifie une méthode de détermination du débit-volume d'un écoulement régulier dans une conduite fermée a) d'un fluide de masse volumique sensiblement constante ou correspondant à un nombre de Mach inférieur ou égal à 0,25; b) dont la température d'arrêt est sensiblement uniforme dans toute la section de mesure; c) remplissant complètement la conduite; et d) en régime permanent. Il traite en particulier de la technologie et de l'entretien des tubes de Pitot doubles, du calcul des vitesses locales à partir des pressions différentielles mesurées et du calcul du débit par intégration de ces vitesses.
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INTERNATIONAL ISO
STANDARD 3966
Third edition
2020-07
Measurement of fluid flow in closed
conduits — Velocity area method
using Pitot static tubes
Mesurage du débit des fluides dans les conduites fermées — Méthode
d'exploration du champ des vitesses au moyen de tubes de Pitot doubles
Reference number
ISO 3966:2020(E)
©
ISO 2020
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ISO 3966:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
ii © ISO 2020 – All rights reserved
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ISO 3966:2020(E)
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols . 2
4 Principle . 3
4.1 General principle . 3
4.1.1 Graphical integration of the velocity area (see Clause 9) . 4
4.1.2 Numerical integration of the velocity area (see Clause 10) . 4
4.1.3 Arithmetical methods (see Clause 11) . 4
4.2 Measurement of the measuring cross-section . 4
4.2.1 Circular cross-sections . 4
4.2.2 Rectangular cross-sections . 4
4.3 Measurement of local velocities . 5
4.3.1 Method of exploring traverse section . 5
4.3.2 Reference measurement . 5
4.3.3 Checking of velocity distribution . 5
4.4 Location and number of measuring points in the cross-section . 6
4.4.1 General requirements . 6
4.4.2 Circular cross-sections . 6
4.4.3 Rectangular cross-sections . 6
5 Design of Pitot tubes . 7
5.1 General description . 7
5.2 Criteria to be fulfilled by the Pitot tube . 7
6 Requirements for use of Pitot tubes . 8
6.1 Selection of the measuring cross-section. 8
6.1.1 Location of the measuring cross-section (of selection) . 8
6.1.2 Avoidance of asymmetry, swirl and turbulences . 8
6.1.3 Maximum flow deviation . 8
6.1.4 Preliminary traverse tests . 9
6.2 Devices for improving flow conditions . 9
6.2.1 Anti-swirl device . 9
6.2.2 Profile developer . . . 9
6.2.3 Positioning/Location of devices . 9
6.2.4 Provisional guiding installation . 9
6.3 Limits of use . 9
6.3.1 Nature of the fluid . 9
6.3.2 Range of velocities . 9
6.3.3 Nature of the flow .10
6.3.4 Dimensional limitations .10
6.3.5 Influence of turbulence .10
6.4 Performance of measurements .10
6.4.1 Measurement of differential pressure .10
6.4.2 Differential pressure fluctuations .10
6.4.3 Determination of fluid density .11
6.5 Inspection and maintenance of the Pitot tube .11
7 Positioning of Pitot tube .11
8 Velocity computation .11
8.1 Verification of conditions for a measurement .11
8.2 Formulae for velocity computation .12
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ISO 3966:2020(E)
9 Determination of the discharge velocity by graphical integration of the velocity area .13
9.1 Circular cross-section . .14
9.2 Rectangular cross-sections .15
10 Determination of the discharge velocity by numerical integration of the velocity area .17
10.1 Circular cross-sections .17
10.2 Rectangular cross-sections .19
11 Determination of the discharge velocity by arithmetic methods .19
11.1 “Log-linear” method .20
11.1.1 Circular cross-sections .20
11.1.2 Rectangular cross-sections .20
11.2 Log-Chebyshev method .22
11.2.1 Circular cross-sections .22
11.2.2 Rectangular cross-sections .22
12 Corrections of local velocity measurements .23
12.1 Correction for stem blockage .23
12.1.1 Case where the correction can be neglected.23
12.1.2 Estimation of the correction of local velocity measurement .23
12.1.3 Estimation of the overall correction of the flow-rate value (application to
arithmetic methods) .25
12.2 Correction for transverse velocity gradient .25
12.2.1 Correction for measuring point position .26
12.2.2 Overall correction of flow rate .26
12.3 Correction for turbulence .27
12.4 Correction for head loss .28
13 Errors .28
13.1 Definition of the error .28
13.2 Errors in the estimation of the local velocity .28
13.2.1 Random errors .28
13.2.2 Systematic errors . . .29
13.3 Errors in the estimation of flow rate .30
13.3.1 Random errors .30
13.3.2 Systematic errors . . .30
13.4 Definition of the standard deviation .31
13.5 Definition of the tolerance .31
13.6 Calculation of standard deviation .32
13.6.1 Standard deviation on local velocity measurement .32
13.6.2 Standard deviation on flow-rate measurement .33
Annex A (normative) Pitot tubes .34
Annex B (normative) Correction to the measuring position of Pitot tubes used in a
transverse velocity gradient .40
Annex C (normative) Study concerning turbulence correction .42
Annex D (normative) Damping of pressure gauges .45
Annex E (normative) Measurements with a Pitot tube in a compressible fluid .47
Annex F (normative) Determination of coefficient m for extrapolation near the wall .51
Annex G (informative) Example of calculation of the uncertainty on the flow-rate
measurement by means of Pitot tubes .52
Bibliography .55
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ISO 3966:2020(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (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, governmental 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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed
conduits, Subcommittee SC 5, Velocity and mass methods.
This third edition cancels and replaces the second edition (ISO 3966:2008), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— All the mathematical formulae have been numbered;
— The essential Formula 4 has been corrected from Δρ/p to Δp/p;
— The related Table 2 is corrected likewise;
— The last sentence in 8.2 “for selected values of g and the Δρ/p….” was corrected accordingly;
nd
— In 11.2.2 in the 2 paragraph ef is corrected by e or f.
— Figure A.5 was changed editorially, the millimetre-grid has been removed.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
© ISO 2020 – All rights reserved v
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INTERNATIONAL STANDARD ISO 3966:2020(E)
Measurement of fluid flow in closed conduits — Velocity
area method using Pitot static tubes
1 Scope
This document specifies a method for the determination in a closed conduit of the volume rate of flow
of a regular flow
a) of a fluid of substantially constant density or corresponding to a Mach number not exceeding 0,25,
b) with substantially uniform stagnation temperature across the measuring cross-section,
c) running full in the conduit, and
d) under steady flow conditions.
In particular, it deals with the technology and maintenance of Pitot static tubes, with the calculation
of local velocities from measured differential pressures and with the computation of the flow rate by
velocity integration.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 2186, Fluid flow in closed conduits — Connections for pressure signal transmissions between primary
and secondary elements
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
Pitot static tube
"Pitot tube"
tubular device consisting of a cylindrical head attached perpendicularly to a stem allowing measurement
of a differential pressure from which the flow rate of the fluid in which it is inserted can be determined,
and which is provided with static pressure tapping holes (drilled all around the circumference of the
head at one or more cross-sections) and with a total pressure hole (facing the flow direction at the tip of
the axially symmetrical nose of the head)
3.1.2
static pressure tapping
group of holes for the measurement of fluid static pressure
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ISO 3966:2020(E)
3.1.3
total pressure tapping
hole for the measurement of fluid stagnation pressure (the pressure produced by bringing the fluid to
rest without change in entropy)
3.1.4
differential pressure
difference between the pressures at the total and static pressure taps
3.1.5
stationary rake
set of Pitot tubes, mounted on one or several fixed supports, which explore the whole diameter or
measuring section simultaneously
3.1.6
peripheral flow rate
volume flow rate in the area located between the pipe wall and the contour defined by the velocity
measuring points which are the closest to the wall
3.1.7
discharge velocity
ratio of the volume rate of flow (integral of the axial component of local velocities with respect to the
cross-sectional area) to the area of the measuring cross-section
3.1.8
relative velocity
ratio of the flow velocity at the considered point to a reference velocity measured at the same time
and being either the velocity at a particular point (e.g. the centre of a circular conduit) or the discharge
velocity in the measuring section
3.1.9
straight lenght
conduit section, the axis of which is rectilinear and the surface and cross-section of which are constant
Note 1 to entry: The shape of this section is usually circular, but it may be rectangular or annular.
3.1.10
irregularity
any element or configuration of a conduit which makes it different from a straight length
Note 1 to entry: For the purpose of this document, those irregularities which create the most significant
disturbances are bends, valves, gates and sudden widening of the section.
3.2 Symbols
Symbol Quantity Dimensions SI unit
2 2
A cross-sectional area of the conduit L m
a, a′ distance of the extreme measuring point to the nearest wall L m
D pipe diameter L m
d head diameter L m
d′ stem diameter L m
d total pressure tapping hole diameter L m
i
H rectangular conduit height L m
h height of a particular point above the bottom L m
k blockage coefficient of a cylindrical stem — —
b
k coefficient depending on the nose shape — —
g
k coefficient of turbulence correction — —
t
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ISO 3966:2020(E)
Symbol Quantity Dimensions SI unit
L rectangular conduit width L m
l distance from a particular point to the side-wall L m
M molar mass of fluid M kg/mol
m roughness coefficient — —
Ma Mach number — —
–1 –2
p absolute static pressure of the fluid ML T Pa
3 –1 3
q volume flow rate L T m /s
V
2 –1 –1
R molar constant of gas ML T Θ J/mol⋅K
g
R pipe radius L m
r measuring circle radius L m
Re Reynolds number — —
2 2
S frontal projected area of the stem inside the conduit L m
T absolute temperature Θ K
–1
U discharge velocity LT m/s
–1
u mean velocity along a circumference or a measurement line LT m/s
–1
v local velocity of the fluid LT m/s
X pipe dimension L m
y distance of a measuring point to the wall L m
Z gas law deviation factor — —
α calibration factor of the Pitot tube — —
γ ratio of the specific heat capacities — —
–1 –2
Δp differential pressure measured by the Pitot tube ML T Pa
ε expansibility factor — —
(1 − ε) compressibility correction factor — —
λ universal coefficient for head loss — —
–1 –1
μ dynamic viscosity of the fluid ML T Pa⋅s
2 –1 2
ν kinematic viscosity of the fluid L T m /s
kv
–1 –2
ξ head loss ML T Pa
–3 3
ρ density of the fluid ML kg/m
φ Pitot tube inclination — —
4 Principle
4.1 General principle
The principle of the method consists of:
a) measuring the dimensions of the measuring section, which shall be normal to the conduit axis —
this measurement is necessary for defining the area of the cross-section (see 4.2);
b) defining the position of the measuring points in the cross-section, the number of measuring points
having to be sufficient to permit adequate determination of the velocity profile;
c) measuring the differential pressure existing between the total and static pressures of the Pitot
tube placed at these measuring points (see 4.3) and determining the density of the fluid in the test
conditions;
d) determining the local velocity of the flow, from given formulae, on the basis of previous
measurements (see Clause 8);
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ISO 3966:2020(E)
e) determining the discharge velocity from these values;
f) calculating the volume rate of flow equal to the product of the cross-sectional area and the
discharge velocity.
Errors in the techniques described in a) to f) contribute to the error in the flow-rate measurement;
other sources of error (such as the shape of the velocity distribution and the number of measuring
points) are discussed in Clause 13.
The method of measurement and the requirements defined in this document aim at reaching, at the
95 % confidence level, an uncertainty in flow rate not greater than ±2 %. To attain this result, it may
be necessary, according to measurement conditions, to take into account the corrections given in
Clause 12. If any of the requirements of this document are not fulfilled, this method may still be applied
in special cases but the uncertainty on flow rate will be larger.
This document presents three types of methods for determining the discharge velocity.
4.1.1 Graphical integration of the velocity area (see Clause 9)
This method consists in plotting the velocity profile on a graph and evaluating the area under the curve
which is bounded by the measuring points closest to the wall. To the value thus obtained is added a
calculated term which allows for the flow in the peripheral zone (the area between the wall and the
curve through the measuring positions closest to the wall) on the assumption that the velocity profile
in this zone satisfies a power law.
For this method, the measuring points may be located at whichever positions are required in order to
obtain a satisfactory knowledge of the velocity profile.
4.1.2 Numerical integration of the velocity area (see Clause 10)
The difference between this method and 4.1.1 lies in the fact that the graphical velocity profile is
replaced by an algebraic curve and the integration is carried out analytically.
4.1.3 Arithmetical methods (see Clause 11)
The arithmetical methods assume that the velocity distribution follows a particular law and the mean
velocity in the conduit is then given by a linear combination of the individual velocities measured at the
locations specified by the method.
For the arithmetical methods described in Clause 11, the assumption is made that in the peripheral
zone the velocity distribution follows a logarithmic law as a
...
NORME ISO
INTERNATIONALE 3966
Troisième édition
2020-07
Mesurage du débit des fluides dans
les conduites fermées — Méthode
d'exploration du champ des vitesses
au moyen de tubes de Pitot doubles
Measurement of fluid flow in closed conduits — Velocity area method
using Pitot static tubes
Numéro de référence
ISO 3966:2020(F)
©
ISO 2020
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ISO 3966:2020(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2020
Tous droits réservés. Sauf prescription différente ou nécessité dans le contexte de sa mise en œuvre, aucune partie de cette
publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique,
y compris la photocopie, ou la diffusion sur l’internet ou sur un intranet, sans autorisation écrite préalable. Une autorisation peut
être demandée à l’ISO à l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
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Publié en Suisse
ii © ISO 2020 – Tous droits réservés
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ISO 3966:2020(F)
Sommaire Page
Avant-propos .v
1 Domaine d'application . 1
2 Références normatives . 1
3 Termes et définitions . 1
3.1 Termes et définitions . 1
3.2 Symboles . 2
4 Spécifications . 3
4.1 Principe général . 3
4.1.1 Intégration graphique du champ des vitesses (voir Article 9) . 4
4.1.2 Intégration numérique du champ des vitesses (voir Article 10) . 4
4.1.3 Méthodes arithmétiques (voir Article 11) . 4
4.2 Mesurage de la section de mesure . 4
4.2.1 Sections circulaires . 4
4.2.2 Sections rectangulaires . 5
4.3 Mesurage des vitesses locales . 5
4.3.1 Méthode d’exploration de la section de mesure . 5
4.3.2 Mesurage de référence. 5
4.3.3 Contrôle de la distribution des vitesses . 6
4.4 Emplacement et nombre de points de mesure dans la section . 6
4.4.1 Exigences générales . 6
4.4.2 Sections circulaires . 6
4.4.3 Sections rectangulaires . 7
5 Conception des tubes de Pitot . 7
5.1 Description générale . 7
5.2 Critères devant être remplis par le tube de Pitot . 7
6 Exigences relatives à l’utilisation des tubes de Pitot . 8
6.1 Choix de la section de mesure . 8
6.1.1 Emplacement de la section de mesure (de sélection) . 8
6.1.2 Prévention de la dissymétrie, de la giration et de la turbulence . 8
6.1.3 Déviation maximale de l’écoulement . 9
6.1.4 Explorations préliminaires . 9
6.2 Dispositifs d’amélioration des conditions d’écoulement . 9
6.2.1 Dispositif anti-giratoire . 9
6.2.2 Égalisateur de profil . 9
6.2.3 Positionnement/Emplacement des dispositifs . 9
6.2.4 Installation provisoire de guidage .10
6.3 Limites d’utilisation .10
6.3.1 Nature du fluide .10
6.3.2 Plage de vitesses .10
6.3.3 Nature de l’écoulement .10
6.3.4 Limitations dimensionnelles .10
6.3.5 Influence de la turbulence .10
6.4 Exécution des mesurages .11
6.4.1 Mesurage de la pression différentielle .11
6.4.2 Fluctuations de la pression différentielle .11
6.4.3 Détermination de la masse volumique du fluide .11
6.5 Contrôle et entretien du tube de Pitot .11
7 Positionnement du tube de Pitot .12
8 Calcul de la vitesse .12
8.1 Vérification des conditions de mesure .12
8.2 Formules de calcul de la vitesse .13
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ISO 3966:2020(F)
9 Détermination de la vitesse débitante par intégration graphique du champ des vitesses .14
9.1 Section circulaire .14
9.2 Sections rectangulaires .16
10 Détermination de la vitesse débitante par intégration numérique du champ des
vitesses .17
10.1 Sections circulaires . .18
10.2 Sections rectangulaires .20
11 Détermination de la vitesse débitante par des méthodes arithmétiques .20
11.1 Méthode «log-linéaire» .21
11.1.1 Sections circulaires .21
11.1.2 Sections rectangulaires .21
11.2 Méthode «log-Chebyshev» .22
11.2.1 Sections circulaires .22
11.2.2 Sections rectangulaires .23
12 Corrections des mesures des vitesses locales .24
12.1 Correction de l’obstruction causée par la hampe .24
12.1.1 Cas où la correction peut être négligée .24
12.1.2 Estimation de la correction des mesures des vitesses locales .24
12.1.3 Estimation de la correction globale de la valeur du débit (applicable aux
méthodes arithmétiques) .26
12.2 Correction du gradient transversal de vitesse .26
12.2.1 Correction de la position des points de mesure .27
12.2.2 Correction globale du débit .27
12.3 Correction de la turbulence .28
12.4 Correction de la perte de charge .29
13 Erreurs .29
13.1 Définition de l’erreur .29
13.2 Erreurs sur l’estimation de la vitesse locale .29
13.2.1 Erreurs aléatoires .29
13.2.2 Erreurs systématiques .30
13.3 Erreurs sur l’estimation du débit .31
13.3.1 Erreurs aléatoires .31
13.3.2 Erreurs systématiques .31
13.4 Définition de l’écart-type .32
13.5 Définition de la tolérance .32
13.6 Calcul de l'écart-type .33
13.6.1 Écart-type sur la mesure de la vitesse locale .33
13.6.2 Écart-type sur la mesure de débit .34
Annexe A (normative) Tubes de Pitot .35
Annexe B (normative) Correction de la position de mesure de tubes de Pitot utilisés dans
un écoulement à gradient transversal de vitesse .41
Annexe C (normative) Étude concernant la correction de la turbulence .43
Annexe D (normative) Amortissement des manomètres .46
Annexe E (normative) Mesurages avec un tube de Pitot dans un fluide compressible .48
Annexe F (normative) Détermination du coefficient m pour l’extrapolation au voisinage de
la paroi .52
Annexe G (informative) Exemple de calcul de l’incertitude de mesure du débit à l’aide de
tubes de Pitot .53
Bibliographie .56
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ISO 3966:2020(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes
nationaux de normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est
en général confiée aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude
a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,
gouvernementales et non gouvernementales, en liaison avec l'ISO participent également aux travaux.
L'ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document a été
rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir www
.iso .org/ directives).
L'attention est attirée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable
de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l'élaboration du document sont indiqués dans l'Introduction et/ou dans la liste des déclarations de
brevets reçues par l'ISO (voir www .iso .org/ brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion
de l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir www .iso .org/ avant -propos.
Le présent document a été élaboré par le comité technique ISO/TC 30, Mesure de débit des fluides dans
les conduites fermées, sous-comité SC 5, Méthodes de vitesse et massiques.
Cette troisième édition annule et remplace la deuxième édition (ISO 3966:2008), qui a fait l’objet d’une
révision technique.
Les principales modifications par rapport à l'édition précédente sont les suivantes:
— toutes les formules mathématiques ont été numérotées;
— la Formule 4 essentielle Δρ/p a été remplacée par Δp/p;
— le Tableau 2 correspondant a été corrigé en conséquence;
— la dernière phrase en 8.2 «pour les valeurs sélectionnées de g et Δρ/p….» a été corrigée en
conséquence;
e
— en 11.2.2, dans le 2 alinéa, ef a été remplacé par e ou f.
— la Figure A.5 a fait l’objet d'une modification rédactionnelle, le quadrillage millimétré a été supprimé.
Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent
document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes
se trouve à l’adresse www .iso .org/ fr/ members .html.
© ISO 2020 – Tous droits réservés v
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NORME INTERNATIONALE ISO 3966:2020(F)
Mesurage du débit des fluides dans les conduites
fermées — Méthode d'exploration du champ des vitesses
au moyen de tubes de Pitot doubles
1 Domaine d'application
Le présent document spécifie une méthode de détermination du débit-volume d’un écoulement régulier
dans une conduite fermée
a) d’un fluide de masse volumique sensiblement constante ou correspondant à un nombre de Mach
inférieur ou égal à 0,25;
b) dont la température d’arrêt est sensiblement uniforme dans toute la section de mesure;
c) remplissant complètement la conduite; et
d) en régime permanent.
Il traite en particulier de la technologie et de l’entretien des tubes de Pitot doubles, du calcul des
vitesses locales à partir des pressions différentielles mesurées et du calcul du débit par intégration de
ces vitesses.
2 Références normatives
Les documents suivants sont cités dans le texte de sorte qu’ils constituent, pour tout ou partie de leur
contenu, des exigences du présent document. Pour les références datées, seule l'édition citée s'applique.
Pour les références non datées, la dernière édition du document de référence s'applique (y compris les
éventuels amendements).
ISO 2186, Débit des fluides dans les conduites fermées — Liaisons pour la transmission du signal de pression
entre les éléments primaires et secondaires
3 Termes et définitions
3.1 Termes et définitions
Pour les besoins du présent document, les termes et définitions suivants s’appliquent.
L'ISO et l'IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en
normalisation, consultables aux adresses suivantes:
— ISO Online browsing platform: disponible à l'adresse https:// www .iso .org/ obp
— IEC Electropedia: disponible à l'adresse http:// www .electropedia .org/
3.1.1
tube de Pitot double
«tube de Pitot»
appareil tubulaire constitué d’une antenne cylindrique fixée perpendiculairement à une hampe
permettant de mesurer une pression différentielle à partir de laquelle le débit du fluide dans lequel
il est inséré peut être déterminé, et muni d’orifices de prise de pression statique (percés toute autour
de l’antenne sur une ou plusieurs sections) et d’un orifice de prise de pression totale (situé face à la
direction d'écoulement au bout de l'étrave axi-symétrique de l’antenne)
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ISO 3966:2020(F)
3.1.2
prise de pression statique
ensemble des orifices destinés à mesurer la pression statique du fluide
3.1.3
prise de pression totale
orifice permettant de mesurer la pression d’arrêt du fluide (pression correspondant à celle obtenue en
amenant le fluide au repos sans variation d’entropie)
3.1.4
pression différentielle
différence de pression entre les prises de pression totale et statique
3.1.5
batterie fixe
ensemble de tubes de Pitot, montés sur un ou plusieurs supports fixes, qui explorent simultanément
tout le diamètre ou toute la section de mesure
3.1.6
débit pariétal
débit-volume qui s’écoule dans la zone située entre la paroi de la conduite et le contour défini par les
points de mesure de la vitesse les plus proches de la paroi
3.1.7
vitesse débitante
rapport du débit-volume (intégrale de la composante axiale des vitesses locales par rapport à l’aire de la
section transversale) à l’aire de la section de mesure
3.1.8
vitesse relative
rapport de la vitesse d'écoulement au point considéré à une vitesse de référence mesurée au même
moment, celle-ci pouvant être soit la vitesse en un point particulier (par exemple, au centre d'une
conduite circulaire) soit la vitesse débitante dans la section de mesure
3.1.9
longueur droite
tronçon de conduite dont l’axe est rectiligne et dont la surface et la section sont constantes
Note 1 à l'article: La forme de cette section est habituellement circulaire, mais peut être rectangulaire ou
annulaire.
3.1.10
singularité
tout élément ou toute configuration d'une conduite qui fait que cette conduite n’est pas une longueur droite
Note 1 à l'article: Pour les besoins du présent document, les singularités qui créent les perturbations les plus
importantes sont les coudes, les robinets, les vannes et les élargissements brusques de la section.
3.2 Symboles
Symbole Grandeur Dimensions Unité SI
2 2
A aire de la section transversale de la conduite L m
a, a′ distance du point de mesure extrême à la paroi la plus proche L m
D diamètre de la conduite L m
d diamètre de l’antenne L m
d′ diamètre de la hampe L m
d diamètre de l’orifice de la prise de pression totale L m
i
H hauteur de la conduite rectangulaire L m
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ISO 3966:2020(F)
Symbole Grandeur Dimensions Unité SI
h hauteur d’un point particulier à partir du bas L m
k coefficient d'obstruction d'une hampe cylindrique — —
b
k coefficient en fonction de la forme de l’étrave — —
g
k coefficient de correction de turbulence — —
t
L largeur de la conduite rectangulaire L m
l distance d’un point particulier à la paroi latérale L m
M masse molaire du fluide M kg/mol
m coefficient de rugosité — —
Ma nombre de Mach — —
–1 –2
p pression statique absolue du fluide ML T Pa
3 –1 3
q débit-volume L T m /s
V
2 –1 –1
R constante molaire du gaz ML T Θ J/mol⋅K
g
R rayon de la conduite L m
r rayon du cercle de mesure L m
Re nombre de Reynolds — —
2 2
S surface projetée frontale de la hampe à l’intérieur de la L m
conduite
T température absolue Θ K
–1
U vitesse débitante LT m/s
–1
u vitesse moyenne sur une circonférence ou sur une ligne de LT m/s
mesure
–1
v vitesse locale du fluide LT m/s
X dimensions de la conduite L m
y distance du point de mesure à la paroi L m
Z coefficient de compressibilité du gaz — —
α coefficient d'étalonnage du tube de Pitot — —
γ rapport des capacités thermiques massiques — —
–1 –2
Δp pression différentielle mesurée par le tube de Pitot ML T Pa
ε coefficient de détente — —
(1 − ε) coefficient de correction de compressibilité — —
λ coefficient universel de perte de charge — —
–1 –1
μ viscosité dynamique du fluide ML T Pa⋅s
2 –1 2
ν viscosité cinématique du fluide L T m /s
kv
–1 –2
ξ perte de charge ML T Pa
–3 3
ρ masse volumique du fluide ML kg/m
φ inclinaison du tube de Pitot — —
4 Spécifications
4.1 Principe général
Le principe de la méthode consiste:
a) à mesurer les dimensions de la section de mesure, qui doit être perpendiculaire à l’axe de la conduite
— cette mesure est nécessaire pour définir l’aire de la section (voir 4.2);
b) à définir la position des points de mesure dans la section, le nombre de points de mesure devant
être suffisant pour permettre la détermination adéquate du profil des vitesses;
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ISO 3966:2020(F)
c) à mesurer la pression différentielle entre les prises de pression totale et statique du tube de Pitot
placé en ces points de mesure (voir 4.3) et à déterminer la masse volumique du fluide dans les
conditions d’essai;
d) à déterminer la vitesse locale de l’écoulement, à partir des formules données, sur la base des
mesures précédentes (voir Article 8);
e) à déterminer la vitesse débitante d’après ces valeurs;
f) à calculer le débit-volume de l’écoulement égal au produit de l’aire de la section transversale et de la
vitesse débitante.
Les erreurs sur les méthodes décrites en a) à f) contribuent à l’erreur sur la mesure du débit; d’autres
sources d’erreur (telles que la forme de la distribution des vitesses et le nombre de points de mesure)
sont détaillées à l’Article 13.
La méthode de mesure et les exigences définies dans le présent document visent à atteindre, au niveau de
confiance de 95 %, une incertitude de mesure du débit n’excédant pas ±2 %. Pour atteindre ce résultat,
il peut être nécessaire, selon les conditions de mesure, de tenir compte des corrections indiquées à
l’Article 12. Si l’une des exigences du présent document n’est pas remplie, cette méthode peut toujours
être appliquée dans des cas particuliers, mais l’incertitude de mesure du débit sera plus élevée.
Le présent
...
FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 3966
ISO/TC 30/SC 5
Measurement of fluid flow in closed
Secretariat: SNV
conduits — Velocity area method
Voting begins on:
20200430 using Pitot static tubes
Voting terminates on:
Mesurage du débit des fluides dans les conduites fermées — Méthode
20200625
d'exploration du champ des vitesses au moyen de tubes de Pitot
doubles
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO
ISO/FDIS 3966:2020(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN
DARDS TO WHICH REFERENCE MAY BE MADE IN
©
NATIONAL REGULATIONS. ISO 2020
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ISO/FDIS 3966:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
ii © ISO 2020 – All rights reserved
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ISO/FDIS 3966:2020(E)
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols . 2
4 Principle . 3
4.1 General principle . 3
4.1.1 Graphical integration of the velocity area (see Clause 9) . 4
4.1.2 Numerical integration of the velocity area (see Clause 10) . 4
4.1.3 Arithmetical methods (see Clause 11) . 4
4.2 Measurement of the measuring crosssection . 4
4.2.1 Circular crosssections . 4
4.2.2 Rectangular crosssections . 4
4.3 Measurement of local velocities . 5
4.3.1 Method of exploring traverse section . 5
4.3.2 Reference measurement . 5
4.3.3 Checking of velocity distribution . 5
4.4 Location and number of measuring points in the crosssection . 6
4.4.1 General requirements . 6
4.4.2 Circular crosssections . 6
4.4.3 Rectangular crosssections . 6
5 Design of Pitot tubes . 7
5.1 General description . 7
5.2 Criteria to be fulfilled by the Pitot tube . 7
6 Requirements for use of Pitot tubes . 8
6.1 Selection of the measuring crosssection. 8
6.1.1 Location of the measuring crosssection (of selection) . 8
6.1.2 Avoidance of asymmetry, swirl and turbulences . 8
6.1.3 Maximum flow deviation . 8
6.1.4 Preliminary traverse tests . 9
6.2 Devices for improving flow conditions . 9
6.2.1 Antiswirl device . 9
6.2.2 Profile developer . . . 9
6.2.3 Positioning/Location of devices . 9
6.2.4 Provisional guiding installation . 9
6.3 Limits of use . 9
6.3.1 Nature of the fluid . 9
6.3.2 Range of velocities . 9
6.3.3 Nature of the flow .10
6.3.4 Dimensional limitations .10
6.3.5 Influence of turbulence .10
6.4 Performance of measurements .10
6.4.1 Measurement of differential pressure .10
6.4.2 Differential pressure fluctuations .10
6.4.3 Determination of fluid density .11
6.5 Inspection and maintenance of the Pitot tube .11
7 Positioning of Pitot tube .11
8 Velocity computation .11
8.1 Verification of conditions for a measurement .11
8.2 Formulae for velocity computation .12
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ISO/FDIS 3966:2020(E)
9 Determination of the discharge velocity by graphical integration of the velocity area .13
9.1 Circular crosssection . .14
9.2 Rectangular crosssections .15
10 Determination of the discharge velocity by numerical integration of the velocity area .17
10.1 Circular crosssections .17
10.2 Rectangular crosssections .19
11 Determination of the discharge velocity by arithmetic methods .19
11.1 “Loglinear” method .20
11.1.1 Circular crosssections .20
11.1.2 Rectangular crosssections .20
11.2 Log-Chebyshev method .22
11.2.1 Circular crosssections .22
11.2.2 Rectangular crosssections .22
12 Corrections of local velocity measurements .23
12.1 Correction for stem blockage .23
12.1.1 Case where the correction can be neglected.23
12.1.2 Estimation of the correction of local velocity measurement .23
12.1.3 Estimation of the overall correction of the flow-rate value (application to
arithmetic methods) .25
12.2 Correction for transverse velocity gradient .25
12.2.1 Correction for measuring point position .26
12.2.2 Overall correction of flow rate .26
12.3 Correction for turbulence .27
12.4 Correction for head loss .28
13 Errors .28
13.1 Definition of the error .28
13.2 Errors in the estimation of the local velocity .28
13.2.1 Random errors .28
13.2.2 Systematic errors . . .29
13.3 Errors in the estimation of flow rate .30
13.3.1 Random errors .30
13.3.2 Systematic errors . . .30
13.4 Definition of the standard deviation .31
13.5 Definition of the tolerance .31
13.6 Calculation of standard deviation .32
13.6.1 Standard deviation on local velocity measurement .32
13.6.2 Standard deviation on flow-rate measurement .33
Annex A (normative) Pitot tubes .34
Annex B (normative) Correction to the measuring position of Pitot tubes used in a
transverse velocity gradient .40
Annex C (normative) Study concerning turbulence correction .42
Annex D (normative) Damping of pressure gauges .45
Annex E (normative) Measurements with a Pitot tube in a compressible fluid .47
Annex F (normative) Determination of coefficient m for extrapolation near the wall .51
Annex G (informative) Example of calculation of the uncertainty on the flow-rate
measurement by means of Pitot tubes .52
Bibliography .55
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ISO/FDIS 3966:2020(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (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, governmental and nongovernmental, 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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed
conduits, Subcommittee SC 5, Velocity and mass methods.
This third edition cancels and replaces the second edition (ISO 3966:2008), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— All the mathematical formulae have been numbered;
— The essential Formula 4 has been corrected from Δρ/p to Δp/p;
— The related Table 2 is corrected likewise;
— The last sentence in 8.2 “for selected values of g and the Δρ/p….” was corrected accordingly;
nd
— In 11.2.2 in the 2 paragraph ef is corrected by e or f.
— Figure A.5 was changed editorially, the millimetre-grid has been removed.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 3966:2020(E)
Measurement of fluid flow in closed conduits — Velocity
area method using Pitot static tubes
1 Scope
This document specifies a method for the determination in a closed conduit of the volume rate of flow
of a regular flow
a) of a fluid of substantially constant density or corresponding to a Mach number not exceeding 0,25,
b) with substantially uniform stagnation temperature across the measuring cross-section,
c) running full in the conduit, and
d) under steady flow conditions.
In particular, it deals with the technology and maintenance of Pitot static tubes, with the calculation
of local velocities from measured differential pressures and with the computation of the flow rate by
velocity integration.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 2186, Fluid flow in closed conduits — Connections for pressure signal transmissions between primary
and secondary elements
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1.1
Pitot static tube
"Pitot tube"
tubular device consisting of a cylindrical head attached perpendicularly to a stem allowing measurement
of a differential pressure from which the flow rate of the fluid in which it is inserted can be determined,
and which is provided with static pressure tapping holes (drilled all around the circumference of the
head at one or more cross-sections) and with a total pressure hole (facing the flow direction at the tip of
the axially symmetrical nose of the head)
3.1.2
static pressure tapping
group of holes for the measurement of fluid static pressure
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ISO/FDIS 3966:2020(E)
3.1.3
total pressure tapping
hole for the measurement of fluid stagnation pressure (the pressure produced by bringing the fluid to
rest without change in entropy)
3.1.4
differential pressure
difference between the pressures at the total and static pressure taps
3.1.5
stationary rake
set of Pitot tubes, mounted on one or several fixed supports, which explore the whole diameter or
measuring section simultaneously
3.1.6
peripheral flow rate
volume flow rate in the area located between the pipe wall and the contour defined by the velocity
measuring points which are the closest to the wall
3.1.7
discharge velocity
ratio of the volume rate of flow (integral of the axial component of local velocities with respect to the
crosssectional area) to the area of the measuring crosssection
3.1.8
relative velocity
ratio of the flow velocity at the considered point to a reference velocity measured at the same time
and being either the velocity at a particular point (e.g. the centre of a circular conduit) or the discharge
velocity in the measuring section
3.1.9
straight lenght
conduit section, the axis of which is rectilinear and the surface and cross-section of which are constant
Note 1 to entry: The shape of this section is usually circular, but it may be rectangular or annular.
3.1.10
irregularity
any element or configuration of a conduit which makes it different from a straight length
Note 1 to entry: For the purpose of this document, those irregularities which create the most significant
disturbances are bends, valves, gates and sudden widening of the section.
3.2 Symbols
Symbol Quantity Dimensions SI unit
2 2
A crosssectional area of the conduit L m
a, a′ distance of the extreme measuring point to the nearest wall L m
D pipe diameter L m
d head diameter L m
d′ steam diameter L m
d total pressure tapping hole diameter L m
i
H rectangular conduit height L m
h height of a particular point above the bottom L m
k blockage coefficient of a cylindrical stem — —
b
k coefficient depending on the nose shape — —
g
k coefficient of turbulence correction — —
t
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ISO/FDIS 3966:2020(E)
Symbol Quantity Dimensions SI unit
L rectangular conduit width L m
l distance from a particular point to the sidewall L m
M molar mass of fluid M kg/mol
m roughness coefficient — —
Ma Mach number — —
–1 –2
p absolute static pressure of the fluid ML T Pa
3 –1 3
q volume flow rate L T m /s
V
2 –1 –1
R molar constant of gas ML T Θ J/mol⋅K
g
R pipe radius L m
r measuring circle radius L m
Re Reynolds number — —
2 2
S frontal projected area of the stem inside the conduit L m
T absolute temperature Θ K
–1
U discharge velocity LT m/s
–1
u mean velocity along a circumference or a measurement line LT m/s
–1
v local velocity of the fluid LT m/s
X pipe dimension L m
y distance of a measuring point to the wall L m
Z gas law deviation factor — —
α calibration factor of the Pitot tube — —
γ ratio of the specific heat capacities — —
–1 –2
Δp differential pressure measured by the Pitot tube ML T Pa
ε expansibility factor — —
(1 − ε) compressibility correction factor — —
λ universal coefficient for head loss — —
–1 –1
μ dynamic viscosity of the fluid ML T Pa⋅s
2 –1 2
ν kinematic viscosity of the fluid L T m /s
kv
–1 –2
ξ head loss ML T Pa
–3 3
ρ density of the fluid ML kg/m
φ Pitot tube inclination — —
4 Principle
4.1 General principle
The principle of the method consists of:
a) measuring the dimensions of the measuring section, which shall be normal to the conduit axis —
this measurement is necessary for defining the area of the cross-section (see 4.2);
b) defining the position of the measuring points in the cross-section, the number of measuring points
having to be sufficient to permit adequate determination of the velocity profile;
c) measuring the differential pressure existing between the total and static pressures of the Pitot
tube placed at these measuring points (see 4.3) and determining the density of the fluid in the test
conditions;
d) determining the local velocity of the flow, from given formulae, on the basis of previous
measurements (see Clause 8);
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ISO/FDIS 3966:2020(E)
e) determining the discharge velocity from these values;
f) calculating the volume rate of flow equal to the product of the cross-sectional area and the
discharge velocity.
Errors in the techniques described in a) to f) contribute to the error in the flow-rate measurement;
other sources of error (such as the shape of the velocity distribution and the number of measuring
points) are discussed in Clause 13.
The method of measurement and the requirements defined in this document aim at reaching, at the
95 % confidence level, an uncertainty in flow rate not greater than ±2 %. To attain this result, it may
be necessary, according to measurement conditions, to take into account the corrections given in
Clause 12. If any of the requirements of this document are not fulfilled, this method may still be applied
in special cases but the uncertainty on flow rate will be larger.
This document presents three types of methods for determining the discharge velocity.
4.1.1 Graphical integration of the velocity area (see Clause 9)
This method consists in plotting the velocity profile on a graph and evaluating the area under the curve
which is bounded by the measuring points closest to the wall. To the value thus obtained is added a
calculated term which allows for the flow in the peripheral zone (the area between the wall and the
curve through the measuring positions closest to the wall) on the assumption that the velocity profile
in this zone satisfies a power law.
For this method, the measuring points may be located at whichever positions are required in order to
obtain a satisfactory knowledge of the velocity profile.
4.1.2 Numerical integration of the velocity
...
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