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.

General Information

Status
Published
Publication Date
19-Jul-2020
Current Stage
6060 - International Standard published
Start Date
20-Jul-2020
Completion Date
20-Jul-2020
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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
---------------------- Page: 1 ----------------------
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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on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
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Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
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

iv © ISO 2020 – All rights reserved
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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;

— 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
H rectangular conduit height L m
h height of a particular point above the bottom L m
k blockage coefficient of a cylindrical stem — —
k coefficient depending on the nose shape — —
k coefficient of turbulence correction — —
2 © ISO 2020 – All rights reserved
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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
2 –1 –1
R molar constant of gas ML T Θ J/mol⋅K
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
U discharge velocity LT m/s
u mean velocity along a circumference or a measurement line LT m/s
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
–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);
© ISO 2020 – All rights reserved 3
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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
---------------------- Page: 1 ----------------------
ISO 3966:2020(F)
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ii © ISO 2020 – Tous droits réservés
---------------------- Page: 2 ----------------------
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

iv © ISO 2020 – Tous droits réservés
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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;
— 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
---------------------- Page: 5 ----------------------
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)
© ISO 2020 – Tous droits réservés 1
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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
H hauteur de la conduite rectangulaire L m
2 © ISO 2020 – Tous droits réservés
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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 — —
k coefficient en fonction de la forme de l’étrave — —
k coefficient de correction de turbulence — —
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
2 –1 –1
R constante molaire du gaz ML T Θ J/mol⋅K
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
U vitesse débitante LT m/s
u vitesse moyenne sur une circonférence ou sur une ligne de LT m/s
mesure
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
–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;
© ISO 2020 – Tous droits réservés 3
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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
---------------------- Page: 1 ----------------------
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

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH­1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
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

© ISO 2020 – All rights reserved iii
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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

iv © ISO 2020 – All rights reserved
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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;

— 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
---------------------- Page: 5 ----------------------
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
© ISO 2020 – All rights reserved 1
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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
H rectangular conduit height L m
h height of a particular point above the bottom L m
k blockage coefficient of a cylindrical stem — —
k coefficient depending on the nose shape — —
k coefficient of turbulence correction — —
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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
2 –1 –1
R molar constant of gas ML T Θ J/mol⋅K
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
U discharge velocity LT m/s
u mean velocity along a circumference or a measurement line LT m/s
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
–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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