ISO/TR 15377:2023
(Main)Measurement of fluid flow by means of pressure-differential devices — Guidelines for the specification of orifice plates, nozzles and Venturi tubes beyond the scope of ISO 5167 series
Measurement of fluid flow by means of pressure-differential devices — Guidelines for the specification of orifice plates, nozzles and Venturi tubes beyond the scope of ISO 5167 series
This document describes the geometry and method of use for conical-entrance orifice plates, quarter-circle orifice plates, eccentric orifice plates and Venturi tubes with 10,5° convergent angles. Information is also given for square-edged orifice plates and nozzles under conditions outside the scope of ISO 5167 series. NOTE The data on which this document is based are limited in some cases.
Mesurage du débit des fluides au moyen d'appareils déprimogènes — Lignes directrices pour la spécification des diaphragmes, des tuyères et des tubes de Venturi non couverts par la série de l'ISO 5167
Le présent document décrit la géométrie et le mode d’emploi des diaphragmes à entrée conique, des diaphragmes quart de cercle, des diaphragmes excentriques et des tubes de Venturi avec un angle de convergent de 10,5°. Des informations sont également données pour les diaphragmes et tuyères à arête rectangulaire utilisés dans des conditions qui sont hors du domaine d’application de la série ISO 5167. NOTE Les données sur lesquelles est basé le présent document sont limitées dans certains cas.
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TECHNICAL ISO/TR
REPORT 15377
Fourth edition
2023-09
Measurement of fluid flow by means
of pressure-differential devices —
Guidelines for the specification of
orifice plates, nozzles and Venturi
tubes beyond the scope of ISO 5167
series
Mesurage du débit des fluides au moyen d'appareils déprimogènes —
Lignes directrices pour la spécification des diaphragmes, des tuyères
et des tubes de Venturi non couverts par la série de l'ISO 5167
Reference number
ISO/TR 15377:2023(E)
© ISO 2023
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ISO/TR 15377:2023(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023
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.
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
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ISO/TR 15377:2023(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Square-edged orifice plates and nozzles: with drain holes, in pipes below 50 mm
diameter, and as inlet and outlet devices . 3
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle . 3
5.1.1 General . 3
5.1.2 Square-edged orifice plates . 3
5.1.3 ISA 1932 nozzles . 5
5.1.4 Long radius nozzles . 5
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm . 5
5.2.1 General . 5
5.2.2 Limits of use . 5
5.2.3 Discharge coefficients and corresponding uncertainties . 6
5.3 No upstream or downstream pipeline . 6
5.3.1 General . 6
5.3.2 Flow from a large space (no upstream pipeline) into a pipeline or another
large space . 6
5.3.3 Flow into a large space (no downstream pipeline) . 8
6 Orifice plates (except square-edged) . 9
6.1 Conical entrance orifice plates . 9
6.1.1 General . 9
6.1.2 Limits of use . 9
6.1.3 Description . 10
6.1.4 Pressure tappings . 13
6.1.5 Coefficients and corresponding uncertainties .13
6.2 Quarter-circle orifice plates . 14
6.2.1 General . 14
6.2.2 Limits of use . 14
6.2.3 Description .15
6.2.4 Pressure tappings . . 18
6.2.5 Coefficients and corresponding uncertainties . 18
6.3 Eccentric orifice plates .20
6.3.1 General .20
6.3.2 Limits of use .20
6.3.3 Description .20
6.3.4 Coefficients and corresponding uncertainties .23
7 Venturi tubes with machined convergent of angle 10,5° .25
7.1 General . 25
7.2 Description . 25
7.3 Limits of use . 25
7.4 Discharge coefficient .26
7.5 Expansibility [expansion] factor . 26
7.6 Pressure loss . 26
7.7 Installation straight lengths . 26
Annex A (informative) An example of the calculations in 5.1.2 .28
Bibliography .31
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ISO/TR 15377:2023(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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use
of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
patent rights in respect thereof. As of the date of publication of this document, ISO had not received
notice of (a) patent(s) which may be required to implement this document. However, implementers are
cautioned that this may not represent the latest information, which may be obtained from the patent
database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all
such patent rights.
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 2, Pressure differential devices.
This fourth edition cancels and replaces the third edition (ISO/TR 15377:2018), which has been
technically revised.
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.
iv
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TECHNICAL REPORT ISO/TR 15377:2023(E)
Measurement of fluid flow by means of pressure-
differential devices — Guidelines for the specification of
orifice plates, nozzles and Venturi tubes beyond the scope
of ISO 5167 series
1 Scope
This document describes the geometry and method of use for conical-entrance orifice plates, quarter-
circle orifice plates, eccentric orifice plates and Venturi tubes with 10,5° convergent angles. Information
is also given for square-edged orifice plates and nozzles under conditions outside the scope of ISO 5167
series.
NOTE The data on which this document is based are limited in some cases.
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 4006, Measurement of fluid flow in closed conduits — Vocabulary and symbols
ISO 5167-1, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-
section conduits running full — Part 1: General principles and requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 4006 and ISO 5167-1 apply.
4 Symbols
For the purposes of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Dimensions
M: mass
Symbols Represented quantity SI unit
L: length
T: time
a Orifice plate pressure-tapping hole diameter L m
C Discharge coefficient dimensionless
Diameter of orifice (or throat) of primary device
d L m
a
under working conditions
d Measured drain hole diameter L m
k
a
In applications with drain holes, d is calculated from the measured values d and d [see Formulae (1) and (11)].
m k
NOTE 1 Other symbols used in this document are defined at their place of use.
NOTE 2 Subscript 1 refers to the cross-section at the plane of the upstream pressure tapping. Subscript 2 refers to the
cross-section at the plane of the downstream pressure tapping.
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ISO/TR 15377:2023(E)
TTaabblle 1 e 1 ((ccoonnttiinnueuedd))
Dimensions
M: mass
Symbols Represented quantity SI unit
L: length
T: time
Measured orifice or throat diameter (where the
d L m
m
orifice or nozzle has a drain hole)
Upstream internal pipe diameter (or upstream
D diameter of a classical Venturi tube) under working L m
conditions
d Diameter of Venturi tube pressure tappings L m
tap
e Thickness of bore L m
E, E Thickness of orifice plate L m
1
F Correction factor dimensionless
E
k Uniform equivalent roughness L m
l Pressure tapping spacing L m
L Relative pressure tapping spacing: L = l/D dimensionless
−1 −2
p Static pressure of the fluid ML T Pa
−1
q Mass flowrate MT kg/s
m
r Radius of profile L m
Arithmetical mean deviation of the (roughness)
Ra L m
profile
Re Reynolds number dimensionless
Re Pipe Reynolds number dimensionless
D
Re Throat Reynolds number dimensionless
d
Re* Throat-tapping Reynolds number (= d Re /d) dimensionless
tap d
d
β dimensionless
Diameter ratio, β =
D
−1 −2
Δp Differential pressure ML T Pa
ε Expansibility (expansion) factor dimensionless
θ Angle between the tappings used and the radius dimensionless °
from the centre of the pipe to the centre of the drain
hole
κ Isentropic exponent dimensionless
λ Friction factor dimensionless
−3 3
ρ Mass density of the fluid ML kg/m
p
2
Pressure ratio, τ =
τ dimensionless
p
1
a
In applications with drain holes, d is calculated from the measured values d and d [see Formulae (1) and (11)].
m k
NOTE 1 Other symbols used in this document are defined at their place of use.
NOTE 2 Subscript 1 refers to the cross-section at the plane of the upstream pressure tapping. Subscript 2 refers to the
cross-section at the plane of the downstream pressure tapping.
2
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ISO/TR 15377:2023(E)
5 Square-edged orifice plates and nozzles: with drain holes, in pipes below
50 mm diameter, and as inlet and outlet devices
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle
5.1.1 General
Square-edged orifice plates and nozzles with drain holes are used, installed and manufactured in
accordance with the following guidelines.
NOTE 1 The guidelines presented in this document are applicable to both drain holes for liquid in gas and vent
holes for gas in liquid.
In a horizontal pipe, a drain hole is positioned at the bottom of the pipe. In a horizontal pipe, a vent hole
is positioned at the top of the pipe.
NOTE 2 Use of drain or vent holes can help alleviate the problem of fluid hold-up, but will not resolve
measurement errors arising from the presence of two-phase flow.
5.1.2 Square-edged orifice plates
If a drain hole is drilled through the orifice plate, the coefficient values specified in ISO 5167-2 are not
used unless the following conditions are observed.
a) The diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
concentric with the orifice, of diameter (D – 0,2d). The outer edge of the drain hole is as close to the
pipe wall as practicable. It is very important that neither the upstream nor the downstream pipe
obscure the drain hole and that the hole is not so small that it blocks.
b) The drain hole is deburred and the upstream edge is sharp. Spark erosion is a good method of
producing the drain hole.
c) Single pressure tappings are orientated so that they are between 90° and 180° to the position of the
drain hole. Upstream and downstream pressure tappings are at the same orientation relative to
the drain hole.
d) The measured orifice diameter, d , is corrected to allow for the additional orifice area represented
m
by the drain hole of measured diameter d , as shown in Formula (1):
k
d
m
d = (1)
02, 5
nn
θθ*
11+−aa−−1
180 180
4 2 4
′′
1−β C +β
()
1 m
2
2
d
k
1+C
22
2
d
m
where
d
m
β = (2)
m
D
′′′
an,,θβ,CC, and are given in Formulae (3) to (8):
21
L' d
46, 2 m
a=−06,,60β exp 15 (3)
m
β d
mk
d
46,
m
n=−04,,57++30β ,117 (4)
m
d
k
3
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ISO/TR 15377:2023(E)
46,
θβ*=−92 62 (5)
m
10,/80if Ed ≤ ,5
k
C = 0,,76750+<625Ed/,if 05 Ed/,<09 (6)
2 kk
13,,30if 9≤E//d
k
2
d
k
ββ′′=+1 C (7)
m 2
2
d
m
and
′
CR(,e β )
D
C = (8)
1
′
′′
CR(,e β )
D
′
[5]
where CR(,e β *) is the discharge coefficient given by the Reader-Harris/Gallagher (1998) equation
D
′
[ISO 5167-2:2022, Formula (4)] for an orifice plate of diameter ratio β* and Reynolds number Re (L
D
1
and L’ are determined for the actual orifice plate; β* is either β or β”);
2
d
β = (9)
D
[d is given by Formula (1)]
is a fixed value of Reynolds number typical of the flow being measured. In high-
′
Re
D
6
′
pressure gas flows Re might be taken as, say, 4 × 10 (the actual Reynolds number
D
cannot be used in the calculation of d, since in that case for an orifice plate with a
drain hole d would not have a fixed value);
Ll(/= D)
is the quotient of the distance of the upstream tapping from the upstream face of the
11
plate and the pipe diameter;
Ll'(= '/D)
is the quotient of the distance of the downstream tapping from the downstream face
22
of the plate and the pipe diameter;
θ is the angle (in degrees) between the pressure tappings used and the radius from the
centre of the pipe to the centre of the drain hole (90° ≤ θ ≤ 180°);
E is the thickness of the orifice plate.
Because of the presence of C this is an iterative computation, but convergence is rapid.
1
When estimating the relative expanded uncertainty of the flow measurement the following additional
percentage uncertainty is added arithmetically to the discharge-coefficient percentage relative
expanded uncertainty given by ISO 5167-2:2022, 5.3.3.1:
d
k
2 (10)
d
m
If β ≤ 0,63, or both β ≤ 0,7 and θ = 90°, C can be set equal to 1, with no increase in uncertainty; in this
m m 1
case there will be no need to iterate.
NOTE 1 There are very limited data for D smaller than 100 mm.
NOTE 2 The formulae given here are based on work described in Reference [10].
Because the formulae in this subclause are complex, there is an example in Annex A so that a computer
program can be checked.
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ISO/TR 15377:2023(E)
5.1.3 ISA 1932 nozzles
If a drain hole is drilled through the nozzle upstream face, the coefficient values specified in ISO 5167-3
are not used unless the following conditions are observed:
a) the value of β is less than 0,625;
b) the diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
concentric with the throat, of diameter (D – 0,2d);
c) the length of the drain hole does not exceed 0,1D;
d) the drain hole is deburred and the upstream edge is sharp;
e) single pressure tappings are orientated so that they are between 90° and 180° to the position of the
drain hole;
f) the measured diameter, d , is corrected to allow for the additional throat area represented by the
m
drain hole of diameter d , as shown in Formula (11):
k
2
d
k
dd=+10,40 (11)
m
d
m
4 −0,5
NOTE Formula (11) is based on the assumption that the value for Cε(1 − β ) for flow through the drain
hole is 20 % less than the value for flow through the throat of the nozzle.
When estimating the overall uncertainty of the flow measurement, the following additional percentage
uncertainty is added arithmetically to the discharge-coefficient percentage relative expanded
uncertainty:
2
d
k
40 (12)
d
m
5.1.4 Long radius nozzles
Drain holes through these primary elements are not used.
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm
5.2.1 General
Orifice plates are installed and manufactured according to ISO 5167-2.
5.2.2 Limits of use
When square-edged orifice plates are installed in pipes of bore 25 mm to 50 mm, it is essential to
observe the following conditions:
a) The pipes have high-quality internal surfaces such as drawn copper or brass tubes, glass or plastic
pipes or drawn or fine-machined steel tubes. The steel tubes are of stainless steel for use with
corrosive fluids such as water. The roughness is according to ISO 5167-2:2022, 5.3.1.
b) Corner tappings are used, preferably of the carrier ring type detailed in ISO 5167-2:2022, Figure 4.
c) The diameter ratio, β, is within the range 0,5 ≤ β ≤ 0,7.
NOTE It is possible to have 0,23 ≤ β < 0,5, but the uncertainty increases significantly if d < 12,5 mm.
5
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ISO/TR 15377:2023(E)
5.2.3 Discharge coefficients and corresponding uncertainties
[5]
The Reader-Harris/Gallagher (1998) equation for corner tappings given in ISO 5167-2:2022, 5.3.2.1 is
used for deriving the discharge coefficients, provided the pipe Reynolds numbers are within the limits
given in ISO 5167-2:2022, 5.3.1.
An additional uncertainty of 0,5 % is added arithmetically to the relative expanded uncertainty derived
from ISO 5167-2:2022, 5.3.3.1.
5.3 No upstream or downstream pipeline
5.3.1 General
This subclause applies where there is no pipeline on either the upstream or the downstream side of the
device or on both the upstream and the downstream sides of the device, that is for flow from a large
space into a pipe or vice versa, or flow through a device installed in the partition wall between two
large spaces.
5.3.2 Flow from a large space (no upstream pipeline) into a pipeline or another large space
5.3.2.1 Upstream and downstream tappings
The space on the upstream side of the device is considered large if
a) there is no wall closer than 4d to the axis of the device or to the plane of the upstream face of the
orifice or nozzle,
b) the velocity of the fluid at any point more than 4d from the device is less than 3 % of the velocity in
the orifice or throat, and
c) the diameter of the downstream pipeline is not less than 2d.
NOTE 1 The first condition implies, for example, that an upstream pipeline of diameter greater than 8d (that is
where β < 0,125) can be regarded as a large space. The second condition, which excludes upstream disturbances
due to draughts, swirl and jet effects, implies that the fluid is to enter the space uniformly over an area of not less
than 33 times the area of the orifice or throat. For example, if the flow is provided by a fall in level of a liquid in
a tank, the area of the liquid surface needs to be not less than 33 times the area of the orifice or throat through
which the tank is discharged.
In an acceptable installation the distance of the upstream tapping (i.e. the tapping in the large space)
from the orifice or nozzle centreline is greater than 4d.
The upstream tapping is preferably located in a wall perpendicular to the plane of the orifice and within
a distance of 0,5d from that plane. The tapping does not necessarily need to be located in any wall; it
can be in the open space. If the space is very large, for example a room, the tapping is shielded from
draughts.
The downstream tapping is located as specified for corner tappings in ISO 5167-2. If the downstream
side also consists of a large space, the tapping is located as for the upstream tapping, except for Venturi
nozzles where the throat tapping is used.
NOTE 2 When the upstream and downstream tappings are at different horizontal levels, it might be necessary
to make allowance for the difference in hydrostatic head. This is usually done by reading the differential-pressure
transmitter with no fluid flow and making an appropriate correction.
5.3.2.2 Square-edged orifice plates with corner tappings
5.3.2.2.1 Square-edged orifice plates with corner tappings are manufactured according to
ISO 5167-2:2022, Clause 5.
6
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ISO/TR 15377:2023(E)
5.3.2.2.2 The limits of use for square-edged orifice plates with corner tappings where there is a flow
from a large space are as follows:
— d ≥ 12,5 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
— Re ≥ 3 500.
d
NOTE 1 It is possible to have 12,5 mm > d > 6 mm, but the uncertainty increases significantly if d < 12,5 mm.
[5]
NOTE 2 Provided that β ≤ 0,2 and d ≥ 12,5 mm, the Reader-Harris/Gallagher (1998) equation given in
ISO 5167-2:2022, 5.3.2.1 can be used in a pipeline for Re ≥ 3 500 with a relative expanded uncertainty of the
d
value of C at k = 2 (approximately 95 % confidence level) of 1 % (if Re < 5 000).
D
5.3.2.2.3 The discharge coefficient, C, is given by Formula (13):
07,
6
10
C =+0,,59610 000521 (13)
Re
d
The relative expanded uncertainty of the value of C at k = 2 (approximately 95 % confidence level) is
1 %.
5.3.2.2.4 The expansibility factor, ε, is given by Formula (14) and is only applicable if
p /p > 0,75:
2 1
1 κ
p
2
ε =−10,3511− (14)
p
1
NOTE p and Δp are usually measured: p = p – Δp.
1 2 1
When Δp/p and κ are assumed to be known without error, the relative expanded uncertainty of the
1
Δp
value of ε at k = 2 (approximately 95 % confidence level) is equal to 35, %.
κ p
1
Test results for the determination of ε are known for air, steam and natural gas only. However, there is
no known objection to using the same formula for other gases and vapours whose isentropic exponent
is known.
5.3.2.3 ISA 1932 nozzles
5.3.2.3.1 ISA 1932 nozzles are manufactured according to ISO 5167-3:2022, 5.1.
5.3.2.3.2 The limits of use for ISA 1932 nozzles where there is flow from a large space are as follows:
— d ≥ 11,5 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
— Re ≥ 100 000.
d
5.3.2.3.3 The discharge coefficient, C, is equal to 0,99. The relative expanded uncertainty of the value
of C at k = 2 (approximately 95 % confidence level) is expected to be no better than 1 %.
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ISO/TR 15377:2023(E)
5.3.2.3.4 The expansibility factor, ε, is given by Formula (15) and is only applicable if
p /p ≥ 0,75:
2 1
05,
2
()κκ−1 /
κ
κτ 1−τ
ε = (15)
κ −1 1−τ
The relative expanded uncertainty of the value of ε at k = 2 (approximately 95 % confidence level) is
equal to 2Δp/p %.
1
5.3.2.4 Venturi nozzle
5.3.2.4.1 Venturi nozzles are manufactured according to ISO 5167-3:2022, 5.4.
5.3.2.4.2 The limits of use for Venturi nozzles where there is flow from a large space are as follows:
— d ≥ 50 mm;
— downstream there is either a large space or a pipeline
...
RAPPORT ISO/TR
TECHNIQUE 15377
Quatrième édition
2023-09
Mesurage du débit des fluides au
moyen d'appareils déprimogènes —
Lignes directrices pour la spécification
des diaphragmes, des tuyères et des
tubes de Venturi non couverts par la
série de l'ISO 5167
Measurement of fluid flow by means of pressure-differential
devices — Guidelines for the specification of orifice plates, nozzles and
Venturi tubes beyond the scope of ISO 5167 series
Numéro de référence
ISO/TR 15377:2023(F)
© ISO 2023
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ISO/TR 15377:2023(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2023
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,
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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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Web: www.iso.org
Publié en Suisse
ii
© ISO 2023 – Tous droits réservés
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ISO/TR 15377:2023(F)
Sommaire Page
Avant-propos .v
1 Domaine d’application . 1
2 Références normatives .1
3 Termes et définitions . 1
4 Symboles . 1
5 Diaphragmes et tuyères à arête rectangulaire: avec des trous de drainage, dans des
conduites d’un diamètre inférieur à 50 mm et utilisés comme appareils d’entrée et
de sortie . 3
5.1 Trous de drainage à travers la face amont du diaphragme ou de la tuyère à arête
rectangulaire . 3
5.1.1 Généralités . 3
5.1.2 Diaphragmes à arête rectangulaire . 3
5.1.3 Tuyères ISA 1932 . 5
5.1.4 Tuyères à long rayon . 5
5.2 Diaphragmes à arête rectangulaire installés dans des conduites d’un diamètre
de 25 mm ≤ D < 50 mm . 6
5.2.1 Généralités . 6
5.2.2 Limites d’utilisation . 6
5.2.3 Coefficients de décharge et incertitudes correspondantes. 6
5.3 Pas de canalisation amont ou aval . 6
5.3.1 Généralités . 6
5.3.2 Écoulement à partir d’un grand volume (pas de canalisation amont) dans
une canalisation ou dans un autre grand volume . 6
5.3.3 Écoulement dans un grand volume (pas de canalisation aval). 9
6 Diaphragmes (excepté ceux à arête rectangulaire) .10
6.1 Diaphragmes à entrée conique . . 10
6.1.1 Généralités . 10
6.1.2 Limites d’utilisation . 10
6.1.3 Description . 10
6.1.4 Prises de pression.13
6.1.5 Coefficients et incertitudes correspondantes . 14
6.2 Diaphragmes quart de cercle . 14
6.2.1 Généralités . 14
6.2.2 Limites d’utilisation . 14
6.2.3 Description .15
6.2.4 Prises de pression. 18
6.2.5 Coefficients et incertitudes correspondantes . 18
6.3 Diaphragmes excentriques . 20
6.3.1 Généralités .20
6.3.2 Limites d’utilisation . 20
6.3.3 Description .20
6.3.4 Coefficients et incertitudes correspondantes . 23
7 Tubes de Venturi à convergent usiné à un angle de 10,5° .25
7.1 Généralités . 25
7.2 Description . 25
7.3 Limites d’utilisation . 25
7.4 Coefficient de décharge . . 26
7.5 Coefficient de détente . 26
7.6 Perte de pression . 26
7.7 Longueurs droites d’installation . 26
Annexe A (informative) Exemple de calculs en 5.1.2 .28
iii
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ISO/TR 15377:2023(F)
Bibliographie .31
iv
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ISO/TR 15377:2023(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’ISO attire l’attention sur le fait que la mise en application du présent document peut entraîner
l’utilisation d’un ou de plusieurs brevets. L’ISO ne prend pas position quant à la preuve, à la validité et
à l’applicabilité de tout droit de propriété revendiqué à cet égard. À la date de publication du présent
document, l’ISO n’avait pas reçu notification qu’un ou plusieurs brevets pouvaient être nécessaires à sa
mise en application. Toutefois, il y a lieu d’avertir les responsables de la mise en application du présent
document que des informations plus récentes sont susceptibles de figurer dans la base de données de
brevets, disponible à l’adresse www.iso.org/brevets. L’ISO ne saurait être tenue pour responsable de ne
pas avoir identifié tout ou partie de tels droits de brevet.
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 2, Appareils déprimogènes.
Cette quatrième édition annule et remplace la troisième édition (ISO/TR 15377:2018), qui a fait l’objet
d’une révision technique.
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.
v
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RAPPORT TECHNIQUE ISO/TR 15377:2023(F)
Mesurage du débit des fluides au moyen d'appareils
déprimogènes — Lignes directrices pour la spécification
des diaphragmes, des tuyères et des tubes de Venturi non
couverts par la série de l'ISO 5167
1 Domaine d’application
Le présent document décrit la géométrie et le mode d’emploi des diaphragmes à entrée conique, des
diaphragmes quart de cercle, des diaphragmes excentriques et des tubes de Venturi avec un angle de
convergent de 10,5°. Des informations sont également données pour les diaphragmes et tuyères à arête
rectangulaire utilisés dans des conditions qui sont hors du domaine d’application de la série ISO 5167.
NOTE Les données sur lesquelles est basé le présent document sont limitées dans certains cas.
2 Références normatives
Les documents suivants cités dans le texte 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 4006, Mesure de débit des fluides dans les conduites fermées — Vocabulaire et symboles
ISO 5167-1, Mesurage de débit des fluides au moyen d'appareils déprimogènes insérés dans des conduites en
charge de section circulaire — Partie 1: Principes généraux et exigences générales
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions donnés dans l’ISO 4006 et l’ISO 5167-1
s’appliquent.
4 Symboles
Pour les besoins du présent document, les symboles donnés dans le Tableau 1 s’appliquent.
Tableau 1 — Symboles
Dimensions
M: masse
Symboles Grandeur représentée Unité Sl
L: longueur
T: temps
a Diamètre du trou de la prise de pression L m
C Coefficient de décharge sans dimension
a
Pour les applications avec des trous de drainage, d est calculé à partir des valeurs mesurées d et d [voir les
m k
Formules (1) et (11)].
NOTE 1 Les autres symboles utilisés dans le présent document sont définis à l’endroit où ils sont employés.
NOTE 2 L’indice 1 fait référence à la section transversale dans le plan de la prise de pression amont. L’indice 2 fait référence
à la section transversale dans le plan de la prise de pression aval.
1
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ISO/TR 15377:2023(F)
TTaabblleeaau 1 u 1 ((ssuuiitte)e)
Dimensions
M: masse
Symboles Grandeur représentée Unité Sl
L: longueur
T: temps
Diamètre de l’orifice (ou du col) de l’élément
d L m
a
primaire dans les conditions de service
d Diamètre du trou de drainage mesuré L m
k
Diamètre de l’orifice ou du col (lorsque l’orifice
d L m
m
ou la tuyère comporte un trou de drainage)
Diamètre intérieur de la conduite en amont
D (ou diamètre amont d’un tube de Venturi classique) L m
dans les conditions de service
Diamètre des prises de pression d'un tube de Ven-
d L m
tap
turi
e Épaisseur de l’orifice L m
E, E Épaisseur du diaphragme L m
1
F Facteur de correction sans dimension
E
k Rugosité uniforme équivalente L m
l Éloignement d’une prise de pression L m
L Éloignement relatif d’une prise de pression: L = l/D sans dimension
−1 −2
p Pression statique du fluide ML T Pa
−1
q Débit-masse MT kg/s
m
r Rayon du profil L m
Ra Écart moyen arithmétique du profil (de rugosité) L m
Re Nombre de Reynolds sans dimension
Re Nombre de Reynolds rapporté à la conduite sans dimension
D
Re Nombre de Reynolds au col sans dimension
d
Re* Nombre de Reynolds de la prise au col (= d Re /d) sans dimension
tap d
d
β sans dimension
Rapport des diamètres, β =
D
−1 −2
Δp Pression différentielle ML T Pa
ε Coefficient de détente sans dimension
Angle entre les prises de pression utilisées
θ et la droite passant par le centre de la conduite sans dimension °
et le centre du trou de drainage
κ Exposant isentropique sans dimension
λ Facteur de frottement sans dimension
−3 3
ρ Masse volumique du fluide ML kg/m
p
2
τ Rapport des pressions, τ = sans dimension
p
1
a
Pour les applications avec des trous de drainage, d est calculé à partir des valeurs mesurées d et d [voir les
m k
Formules (1) et (11)].
NOTE 1 Les autres symboles utilisés dans le présent document sont définis à l’endroit où ils sont employés.
NOTE 2 L’indice 1 fait référence à la section transversale dans le plan de la prise de pression amont. L’indice 2 fait référence
à la section transversale dans le plan de la prise de pression aval.
2
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ISO/TR 15377:2023(F)
5 Diaphragmes et tuyères à arête rectangulaire: avec des trous de drainage,
dans des conduites d’un diamètre inférieur à 50 mm et utilisés comme appareils
d’entrée et de sortie
5.1 Trous de drainage à travers la face amont du diaphragme ou de la tuyère à arête
rectangulaire
5.1.1 Généralités
Les diaphragmes et tuyères à arête rectangulaire avec des trous de drainage sont utilisés, installés et
fabriqués selon les lignes directrices suivantes.
NOTE 1 Les lignes directrices indiquées dans le présent document sont applicables à la fois aux trous de
drainage en cas de présence de liquide dans un écoulement gazeux et aux évents d’évacuation en cas de présence
de gaz dans un écoulement liquide.
Dans une conduite horizontale, le trou de drainage est positionné en bas de la conduite. Dans une
conduite horizontale, l’évent d’évacuation est positionné en haut de la conduite.
NOTE 2 Le fait d’utiliser des trous de drainage ou des évents d’évacuation peut contribuer à atténuer le
problème de rétention de fluide, mais ne va pas résoudre les erreurs de mesure dues à la présence d’un écoulement
diphasique.
5.1.2 Diaphragmes à arête rectangulaire
Si un trou de drainage est percé dans le diaphragme, les valeurs du coefficient spécifiées dans
l’ISO 5167-2 ne sont pas utilisées, à moins de respecter les conditions suivantes:
a) Le diamètre du trou de drainage ne dépasse pas 0,1d et aucune partie du trou n’est située dans un
cercle, concentrique avec l’orifice, de diamètre (D – 0,2d). L’arête externe du trou de drainage est
aussi proche que possible de la paroi de la conduite. Il est très important que ni la conduite amont
ni la conduite aval ne bouchent le trou de drainage et que le trou soit suffisamment grand pour ne
pas être obstrué.
b) Le trou de drainage est ébavuré et l’arête amont est vive. L’électro-érosion est une bonne méthode
pour créer un trou de drainage.
c) Les prises de pression individuelles sont orientées de manière à former un angle compris entre 90°
et 180° par rapport à la position du trou de drainage. Les prises de pression amont et aval ont la
même orientation par rapport au trou de drainage.
d) Le diamètre de l’orifice mesuré, d , est corrigé pour tenir compte de la surface supplémentaire
m
de l’orifice représentée par le trou de drainage de diamètre mesuré d , comme indiqué dans la
k
Formule (1):
d
m
d = (1)
02, 5
nn
θθ*
11+−aa−−1
180 180
4 2 4
′′
1−β C +β
()
1 m
2
2
d
k
1+C
22
2
d
m
3
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ISO/TR 15377:2023(F)
où
d
m
β = (2)
m
D
′′′
an,,θβ,CC, et sont donnés par les Formules (3) à (8):
21
L' d
46,
2 m
a=−06,,60β exp 15 (3)
m
β d
mk
d
46, m
n=−04,,57++30β ,117 (4)
m
d
k
46,
θβ*=−92 62 (5)
m
10,/80si Ed ≤ ,5
k
C = 0,,76750+<625Ed/,si 05 Ed/,<09 (6)
2 kk
13,,30si 9≤E//d
k
2
d
k
′′
ββ=+1 C (7)
m 2
2
d
m
et
′
CR(,e β )
D
C = (8)
1
′
CR(,e β′′)
D
′
[5]
où CR(,e β *) est le coefficient de décharge donné par l’équation de Reader-Harris/Gallagher (1998)
D
[ISO 5167-2:2022, Formule (4)] pour un diaphragme présentant un rapport des diamètres β* et un
′
nombre de Reynolds Re (L et L’ sont déterminées pour le diaphragme réel; β* est égal à β ou β”);
D
1 2
d
β = (9)
D
[d est donné par la Formule (1)]
est une valeur fixe du nombre de Reynolds caractéristique de l’écoulement mesuré.
′
Re
D
′
Dans les écoulements de gaz à haute pression, Re peut être pris égal, par exemple,
D
6
à 4 × 10 (le nombre de Reynolds réel ne peut pas être utilisé dans le calcul de d, étant
donné que dans ce cas, pour un diaphragme avec un trou de drainage, d n’aurait pas
une valeur fixe);
Ll(/= D)
est le quotient de l’éloignement de la prise de pression amont, à partir de la face amont
11
du diaphragme et du diamètre interne de la conduite;
Ll'(= '/D)
est le quotient de l’éloignement de la prise de pression aval, à partir de la face aval du
22
diaphragme et du diamètre interne de la conduite;
θ est l’angle (en degrés) entre les prises de pression utilisées et la droite passant par le
centre de la conduite et le centre du trou de drainage (90° ≤ θ ≤ 180°);
E est l’épaisseur du diaphragme.
En raison de la présence de C , il s’agit d’un calcul par itération, mais la convergence est rapide.
1
4
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ISO/TR 15377:2023(F)
Lors de l’estimation de l’incertitude relative élargie de mesurage du débit, le pourcentage d’incertitude
supplémentaire suivant est ajouté arithmétiquement au pourcentage d’incertitude relative élargie du
coefficient de décharge donné dans l’ISO 5167-2:2022, 5.3.3.1:
d
k
2 (10)
d
m
Si β ≤ 0,63, ou si à la fois β ≤ 0,7 et θ = 90°, C peut être pris égal à 1, sans augmenter l’incertitude;
m m 1
dans ce cas, il n’y aura pas besoin d’itération.
NOTE 1 Il existe très peu de données pour un diamètre D inférieur à 100 mm.
NOTE 2 Les formules fournies ici sont basées sur les travaux décrits dans la Référence [10].
Comme les formules de ce paragraphe sont complexes, un exemple est fourni dans l’Annexe A, qui peut
servir de validation à un codage informatique de ces dernières.
5.1.3 Tuyères ISA 1932
Si un trou de drainage est percé dans la face amont de la tuyère, les valeurs du coefficient spécifiées
dans l’ISO 5167-3 ne sont pas utilisées, à moins de respecter les conditions suivantes:
a) la valeur de β est inférieure à 0,625;
b) le diamètre du trou de drainage ne dépasse pas 0,1d et aucune partie du trou n’est située dans un
cercle, concentrique avec le col, de diamètre (D – 0,2d);
c) la longueur du trou de drainage ne dépasse pas 0,1D;
d) le trou de drainage est ébavuré et l’arête amont est vive;
e) les prises de pression individuelles sont orientées de manière à former un angle compris entre 90°
et 180° par rapport à la position du trou de drainage;
f) le diamètre mesuré, d , est corrigé pour tenir compte de la surface supplémentaire du col de
m
l’orifice de la tuyère représentée par le trou de drainage de diamètre d , comme indiqué dans la
k
Formule (11):
2
d
k
dd=+10,40 (11)
m
d
m
4 −0,5
NOTE La Formule (11) repose sur l’hypothèse que la valeur de Cε(1 − β ) correspondant à l’écoulement à
travers le trou de drainage est inférieure de 20 % à la valeur de l’écoulement à travers le col de la tuyère.
Lors de l’estimation de l’incertitude globale de mesurage du débit, le pourcentage d’incertitude
supplémentaire suivant est ajouté arithmétiquement au pourcentage d’incertitude relative élargie du
coefficient de décharge:
2
d
k
40 (12)
d
m
5.1.4 Tuyères à long rayon
Ne pas utiliser de trous de drainage dans ces éléments primaires.
5
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ISO/TR 15377:2023(F)
5.2 Diaphragmes à arête rectangulaire installés dans des conduites d’un diamètre
de 25 mm ≤ D < 50 mm
5.2.1 Généralités
Les diaphragmes sont installés et fabriqués conformément à l’ISO 5167-2.
5.2.2 Limites d’utilisation
Lorsque des diaphragmes à arête rectangulaire sont installés dans des conduites d’un diamètre de
25 mm à 50 mm, il est essentiel de respecter les conditions suivantes:
a) Les conduites possèdent des surfaces internes de grande qualité, par exemple tubes en cuivre ou
laiton étiré, conduites en verre ou en plastique ou tubes en acier étiré ou finement usiné. Les tubes
en acier sont en acier inoxydable pour pouvoir être utilisés avec des fluides corrosifs tels que l’eau.
Leur rugosité est conforme à l’ISO 5167-2:2022, 5.3.1.
b) Utiliser des prises dans les angles, de préférence du type à bague porteuse détaillé dans
l’ISO 5167-2:2022, Figure 4).
c) Le rapport des diamètres, β, est compris dans la plage 0,5 ≤ β ≤ 0,7.
NOTE Il est possible d’avoir 0,23 ≤ β < 0,5, mais l’incertitude augmente de manière significative si
d < 12,5 mm.
5.2.3 Coefficients de décharge et incertitudes correspondantes
[5]
L’équation de Reader-Harris/Gallagher (1998) pour les prises dans les angles indiquée dans
l’ISO 5167-2:2022, 5.3.2.1, est utilisée pour déduire les coefficients de décharge, à condition que
les nombres de Reynolds rapportés à la conduite soient compris dans les limites indiquées dans
l’ISO 5167-2:2022, 5.3.1.
Une incertitude supplémentaire de 0,5 % est ajoutée arithmétiquement à l’incertitude relative élargie
dérivée de l’ISO 5167-2:2022, 5.3.3.1.
5.3 Pas de canalisation amont ou aval
5.3.1 Généralités
Ce paragraphe s’applique lorsqu’il n’y a pas de canalisation du côté amont ou du côté aval de l’appareil,
ou les deux, c’est-à-dire dans le cas d’un écoulement provenant d’un grand volume dans une conduite,
ou inversement, ou dans le cas d’un écoulement à travers un appareil installé dans la cloison entre deux
grands volumes.
5.3.2 Écoulement à partir d’un grand volume (pas de canalisation amont) dans une
canalisation ou dans un autre grand volume
5.3.2.1 Prises de pression amont et aval
Le volume du côté amont de l’appareil est considéré comme grand si:
a) il n’y a pas de paroi à moins de 4d de l’axe de l’appareil ou du plan de la face amont du diaphragme
ou de la tuyère;
b) la vitesse du fluide en tout point situé à plus de 4d de l’appareil est inférieure à 3 % de la vitesse
dans l’orifice ou le col; et
c) le diamètre de la canalisation aval n’est pas inférieur à 2d.
6
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ISO/TR 15377:2023(F)
NOTE 1 La première condition implique, par exemple, qu’une canalisation amont d’un diamètre supérieur à
8d (c’est-à-dire où β < 0,125) peut être considérée comme un grand volume. La seconde condition, qui exclut
les perturbations amont dues aux courants d’air, aux écoulements giratoires et aux effets de jet, implique que
le fluide entre dans le volume de manière uniforme sur une surface représentant au moins 33 fois la surface de
l’orifice ou du col. Par exemple, si l’écoulement est assuré par la chute de niveau d’un liquide dans un réservoir, la
surface du liquide ne doit pas être inférieure à 33 fois la surface de l’orifice ou du col servant à vider le réservoir.
Dans une installation acceptable, la distance entre la prise amont (c’est-à-dire la prise située dans le
grand volume) et l’axe de l’orifice ou de la tuyère est supérieure à 4d.
La prise amont est de préférence située dans une paroi perpendiculaire au plan de l’orifice et elle est
à une distance de 0,5d de ce plan. La prise n’a pas forcément besoin d’être située dans une paroi; elle
peut être située dans un espace ouvert. Si le volume est très grand, par exemple une salle, la prise est
protégée des courants d’air.
La prise aval est située comme spécifié pour les prises dans les angles dans l’ISO 5167-2. Si le côté aval
est aussi un grand volume, la prise est placée comme la prise amont, excepté pour les Venturi-tuyères
pour lesquels une prise au col est utilisée.
NOTE 2 Lorsque les prises amont et aval sont à des niveaux horizontaux différents, il peut être nécessaire
de tenir compte de la différence de charge hydrostatique. Pour cela, il suffit généralement de lire la valeur du
transmetteur de pression différentielle sans écoulement de fluide et d’effectuer la correction appropriée.
5.3.2.2 Diaphragmes à arête rectangulaire avec prises dans les angles
5.3.2.2.1 Les diaphragmes à arête rectangulaire avec prises dans les angles sont fabriqués
conformément à l’ISO 5167-2:2022, Artic
...
Date: 2023-03-16 Style Definition: Heading 1: Indent: Left: 0 pt, First
line: 0 pt, Tab stops: Not at 21.6 pt
ISO/DTR 15377:2023(E)
Style Definition: Heading 2: Font: Bold, Tab stops: Not
at 18 pt
ISO/TC 30/SC 2/WG
Style Definition: Heading 3: Font: Bold
Style Definition: Heading 4: Font: Bold
Date: 2023-xx
Style Definition: Heading 5: Font: Bold
Secretariat: BSI
Style Definition: Heading 6: Font: Bold
Style Definition: ANNEX
Measurement of fluid flow by means of pressure-differential devices —
Style Definition: AMEND Terms Heading: Font: Bold
Guidelines for the specification of orifice plates, nozzles and Venturi tubes
beyond the scope of ISO 5167 series Style Definition: AMEND Heading 1 Unnumbered:
Font: Bold
Mesurage du débit des fluides au moyen d'appareils déprimogènes — Lignes directrices
Formatted: Font color: Auto
pour la spécification des diaphragmes, des tuyères et des tubes Venturi non couverts par la
série de l'ISO 5167
---------------------- Page: 1 ----------------------
ISO/DTR 15377:2023(E)
COPYRIGHT PROTECTED DOCUMENT
All rights reserved. Unless otherwise specified, 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
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
copyright@iso.org
www.iso.org
www.iso.org
ii © ISO 2023 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/DTR 15377:2023(E)
Contents Page
Foreword . 4iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Square-edged orifice plates and nozzles: With drain holes, in pipes below 50 mm
diameter, and as inlet and outlet devices . 3
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle . 3
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm . 6
5.3 No upstream or downstream pipeline . 6
6 Orifice plates (except square-edged) . 10
6.1 Conical entrance orifice plates . 10
6.2 Quarter-circle orifice plates . 14
6.3 Eccentric orifice plates . 21
7 Venturi tubes with machined convergent of angle 10,5° . 26
7.1 General . 26
7.2 Description . 26
7.3 Limits of use . 27
7.4 Discharge coefficient . 27
7.5 Expansibility [expansion] factor . 27
7.6 Pressure loss . 28
7.7 Installation straight lengths . 28
Annex A (informative) An example of the calculations in 5.1.2 . 29
Bibliography. 32
© ISO 2023 – All rights reserved iii
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ISO/DTR 15377:2023(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 documentsdocument 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).www.iso.org/directives).
Commented [eXtyles1]: The URL
www.iso.org/directives has been redirected to
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Attention is drawnISO draws attention to the possibility that some of the elementsimplementation of this
document may beinvolve the subjectuse of (a) patent(s). ISO takes no position concerning the evidence,
validity or applicability of any claimed patent rights. in respect thereof. As of the date of publication of
this document, ISO had not received notice of (a) patent(s) which may be required to implement this
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received (see www.iso.org/patents).
Commented [eXtyles2]: The URL www.iso.org/patents
has been redirected to https://www.iso.org/patents. Please
verify the URL.
Any trade name used in this document is information given for the convenience of users and does not
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www.iso.org/iso/foreword.html.), see www.iso.org/iso/foreword.html.
Commented [eXtyles3]: The URL
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This document was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed
URL.
conduits, Subcommittee SC 2, Pressure differential devices.
This fourth edition cancels and replaces the third edition (ISO/TR 15377:2018), which has been
technically revised.
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.
iv © ISO 2023 – All rights reserved
---------------------- Page: 4 ----------------------
TECHNICAL REPORT ISO/DTR 15377:2023(E)
Measurement of fluid flow by means of pressure-differential
devices — Guidelines for the specification of orifice plates, nozzles
Formatted: Pattern: Clear
and Venturi tubes beyond the scope of ISO 5167 series
Formatted: Pattern: Clear
1 Scope
This document describes the geometry and method of use for conical-entrance orifice plates, quarter-
circle orifice plates, eccentric orifice plates and Venturi tubes with 10,5° convergent angles. Information
is also given for square-edged orifice plates and nozzles under conditions outside the scope of ISO 5167
Formatted: Pattern: Clear
series.
Formatted: Pattern: Clear
NOTE The data on which this document is based are limited in some cases.
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 4006, Measurement of fluid flow in closed conduits — Vocabulary and symbols
ISO 4006, Measurement of fluid flow in closed conduits — Vocabulary and symbols
ISO 5167-1, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-
Formatted: Pattern: Clear
section conduits running full — Part 1: General principles and requirements
Formatted: Pattern: Clear
Formatted: Pattern: Clear
3 Terms and definitions
Formatted: Pattern: Clear
For the purposes of this document, the terms and definitions given in ISO 4006 and ISO 5167-1 apply.
Formatted: Pattern: Clear
Formatted: Pattern: Clear
4 Symbols
Formatted: Pattern: Clear
For the purposes of this document, the symbols given in Table 1 apply.
Formatted: Pattern: Clear
Table 1 — Symbols
Formatted: Pattern: Clear
Dimensions Formatted: Pattern: Clear
M: mass
Symbols Represented quantity SI unit
L: length
T: time
a Pressure-tapping hole diameter L m
C Discharge coefficient dimensionless
Diameter of orifice (or throat) of primary device
d L m
a
under working conditions
d Measured drain hole diameter L m
k
© ISO 2023 – All rights reserved 1
---------------------- Page: 5 ----------------------
ISO/DTR 15377:2023(E)
Measured orifice or throat diameter (where the
d L m
m
orifice or nozzle has a drain hole)
Upstream internal pipe diameter (or upstream
D diameter of a classical Venturi tube) under working L m
conditions
dtap Diameter of pressure tappings L m
e Thickness of bore L m
E, E Thickness of orifice plate L m
1
FE Correction factor dimensionless
k Uniform equivalent roughness L m
l Pressure tapping spacing L m
L Relative pressure tapping spacing: L = l/D dimensionless
−1 −2
p Static pressure of the fluid ML T Pa
−1
q Mass flowrate MT kg/s
m
Formatted: Font: Italic
r Radius of profile L m
Arithmetical mean deviation of the (roughness)
Ra L m
profile
Re Reynolds number dimensionless
Re Pipe Reynolds number dimensionless
D
Re Throat Reynolds number dimensionless
d
Re* Throat-tapping Reynolds number (= d Re /d) dimensionless
tap d
d
Diameter ratio,
β β= dimensionless
D
−1 −2
Δp Differential pressure ML T Pa
ε Expansibility (expansion) factor dimensionless
θ Angle between the tappings used and the radius dimensionless °
from the centre of the pipe to the centre of the drain
hole
κ Isentropic exponent dimensionless
λ Friction factor dimensionless
−3 3
ρ Mass density of the fluid ML kg/m
p
2
Pressure ratio,
τ=
τ dimensionless
p
1
a
In applications with drain holes, d is calculated from the measured values d and d [see Formulae (1) and (11)].
m k
Formatted: Pattern: Clear
NOTE 1 Other symbols used in this documentt are defined at their place of use.
NOTE 2 Subscript 1 refers to the cross-section at the plane of the upstream pressure tapping. Subscript 2 refers to the cross-
section at the plane of the downstream pressure tapping.
2 © ISO 2023 – All rights reserved
---------------------- Page: 6 ----------------------
ISO/DTR 15377:2023(E)
5 Square-edged orifice plates and nozzles: Withwith drain holes, in pipes below
50 mm diameter, and as inlet and outlet devices
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle
5.1.1 General
Square-edged orifice plates and nozzles with drain holes are used, installed and manufactured in
accordance with the following guidelines.
NOTE 1 The guidelines presented in this document are applicable to both drain holes for liquid in gas and vent
holes for gas in liquid.
In a horizontal pipe, a drain hole is positioned at the bottom of the pipe. In a horizontal pipe, a vent hole
is positioned at the top of the pipe.
NOTE 2 Use of drain or vent holes can help alleviate the problem of fluid hold-up, but will not resolve measurement
errors arising from the presence of two-phase flow.
5.1.2 Square-edged orifice plates
If a drain hole is drilled through the orifice plate, the coefficient values specified in ISO 5167-2 are not
used unless the following conditions are observed.
a) The diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
concentric with the orifice, of diameter (D – 0,2d). The outer edge of the drain hole is as close to the
pipe wall as practicable. It is very important that neither the upstream nor the downstream pipe
obscure the drain hole and that the hole is not so small that it blocks.
b) The drain hole is deburred and the upstream edge is sharp. Spark erosion is a good method of
producing the drain hole.
c) Single pressure tappings are orientated so that they are between 90° and 180° to the position of the
drain hole. Upstream and downstream pressure tappings are at the same orientation relative to the
drain hole.
d) The measured orifice diameter, d , is corrected to allow for the additional orifice area represented
m
by the drain hole of measured diameter d , as shown in Formula (1):
k
© ISO 2023 – All rights reserved 3
---------------------- Page: 7 ----------------------
ISO/DTR 15377:2023(E)
d
m
d=
0,25
nn
θθ *
11+ a − −−a 1
180 180
42 4
1−+ββ′′ C
( ) 1 m
2
2
d
k
1+ C
2
2
d
m
d
Field Code Changed
m
(1)
d=
0,25
nn
θθ *
11+ a − −−a 1
180 180
42 4
1−+ββ′′ C
( )
1 m
2
2
d
k
1+ C
2
2
d
m
where
d d
Formatted: Left, Adjust space between Latin and Asian
m m
β = β = (2)
m m
text, Adjust space between Asian text and numbers,
D D
Tab stops: Not at 19.85 pt + 39.7 pt + 59.55 pt +
79.4 pt + 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt
a,n,θβ′, C, an′′ d C a,n,θβ′, C, an′′ d C
are given in Formulae (3) to (8):
2 1 2 1
+ 178.6 pt + 198.45 pt
Field Code Changed
′
L d
4,6 2m
(3)
a 0,66β exp−0,15
m
Field Code Changed
β d
mk
Formatted: Pattern: Clear
d
4,6 m
n=−+0,45 7,3β + 0,117
m
d
k
(4)
4,6
θβ* 92−62
m
(5)
1,08 if Ed/ ≤ 0,5
k
C 0,7675+ 0,625Ed/ if 0,5< Ed/< 0,9
2 kk
1,33 if 0,9≤ Ed/
k
(6)
2
d
k
ββ′′ 1+ C
m2
2
d
m
(7)
and
′
′
Formatted: Adjust space between Latin and Asian text,
C(Re ,)β C(Re ,)β
D D
C = C = (8)
Adjust space between Asian text and numbers, Tab
1 1
′
′
C(Re ,)β′′
C(Re ,)β′′
D
D stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
Field Code Changed
4 © ISO 2023 – All rights reserved
=
=
=
=
---------------------- Page: 8 ----------------------
ISO/DTR 15377:2023(E)
′
C(Re ,β *)
D [5]
where is the discharge coefficient given by the Reader-Harris/Gallagher (1998) equation
(Equation (4) of [ISO 5167-2:2022), Formula (4)] for an orifice plate of diameter ratio β* and Reynolds
′
number Re (L and L’ are determined for the actual orifice plate; β* is either β or β”);
1 2
D
d d
Formatted: Adjust space between Latin and Asian text,
(9)
β= β=
Adjust space between Asian text and numbers, Tab
D D
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
[d is given by Formula (1)]
178.6 pt + 198.45 pt
is a fixed value of Reynolds number typical of the flow being measured. In high-
′
Re
Field Code Changed
D
6
′
pressure gas flows Re might be taken as, say, 4 × 10 (the actual Reynolds number
D
cannot be used in the calculation of d, since in that case for an orifice plate with a
drain hole d would not have a fixed value);
L (= lD/) is the quotient of the distance of the upstream tapping from the upstream face of the
11
plate and the pipe diameter;
L'(= lD' / ) is the quotient of the distance of the downstream tapping from the downstream face
22
of the plate and the pipe diameter;
Θ is the angle (in degrees) between the pressure tappings used and the radius from the
centre of the pipe to the centre of the drain hole (90° ≤ θ ≤ 180°);
E is the thickness of the orifice plate.
Because of the presence of C1 this is an iterative computation, but convergence is rapid.
When estimating the relative expanded uncertainty of the flow measurement the following additional
percentage uncertainty is added arithmetically to the discharge-coefficient percentage relative expanded
uncertainty given by ISO 5167-2:2022, 5.3.3.1:
Formatted: Pattern: Clear
Formatted: Pattern: Clear
d d
k k
2 2 (10)
d d Formatted: Pattern: Clear
m m
Formatted: Pattern: Clear
If β ≤ 0,63, or both β ≤ 0,7 and θ = 90°, C can be set equal to 1, with no increase in uncertainty; in this
m m 1
Formatted: Pattern: Clear
case there will be no need to iterate.
Formatted: Adjust space between Latin and Asian text,
NOTE 1 There are very limited data for D smaller than 100 mm.
Adjust space between Asian text and numbers, Tab
stops: Not at 0 pt + 19.85 pt + 36 pt + 39.7 pt +
NOTE 2 The formulae given here are based on work described in Reference [10].
59.55 pt + 79.4 pt + 99.25 pt + 119.05 pt + 138.9 pt
+ 158.75 pt + 178.6 pt + 198.45 pt
Because the formulae in this subclause are complex, there is an example in Annex A so that a computer
Field Code Changed
program can be checked.
Formatted: Pattern: Clear
5.1.3 ISA 1932 nozzles
Formatted: Pattern: Clear
If a drain hole is drilled through the nozzle upstream face, the coefficient values specified in ISO 5167-3
Formatted: Default Paragraph Font
are not used unless the following conditions are observed.:
Formatted: Default Paragraph Font
a) Thethe value of β is less than 0,625.;
Formatted: Pattern: Clear
b) Thethe diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
Formatted: Pattern: Clear
concentric with the throat, of diameter (D – 0,2d).);
Formatted: Pattern: Clear
c) Thethe length of the drain hole does not exceed 0,1D.;
© ISO 2023 – All rights reserved 5
---------------------- Page: 9 ----------------------
ISO/DTR 15377:2023(E)
d) Thethe drain hole is deburred and the upstream edge is sharp.;
e) Singlesingle pressure tappings are orientated so that they are between 90° and 180° to the position
of the drain hole.;
f) Thethe measured diameter, d , is corrected to allow for the additional throat area represented by
m
the drain hole of diameter d , as shown in the following equation:Formula (11):
k
2 2
Formatted: Adjust space between Latin and Asian text,
d d
k k
dd 1+ 0,40 dd 1+ 0,40 (11)
Adjust space between Asian text and numbers, Tab
m m
d d
m m
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
4 −0,5
NOTE This equationFormula (11) is based on the assumption that the value for Cε(1 − β ) for flow through the
drain hole is 20 % less than the value for flow through the throat of the nozzle.
Field Code Changed
When estimating the overall uncertainty of the flow measurement, the following additional percentage
uncertainty is added arithmetically to the discharge-coefficient percentage relative expanded
uncertainty:
2 2
Formatted: Adjust space between Latin and Asian text,
d
d
k
k
(12)
40 40
Adjust space between Asian text and numbers, Tab
d d
m m
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
5.1.4 Long radius nozzles
178.6 pt + 198.45 pt
Field Code Changed
Drain holes through these primary elements are not used.
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm
5.2.1 General
Orifice plates are installed and manufactured according to ISO 5167-2.
5.2.2 Limits of use
When square-edged orifice plates are installed in pipes of bore 25 mm to 50 mm, it is essential to observe
the following conditions.:
a) The pipes have high-quality internal surfaces such as drawn copper or brass tubes, glass or plastic
pipes or drawn or fine-machined steel tubes. The steel tubes are of stainless steel for use with
corrosive fluids such as water. The roughness is according to ISO 5167-2:2022, 5.3.1.
b) Corner tappings are used, preferably of the carrier ring type detailed in ISO 5167-2:2022, Figure 4.
c) The diameter ratio, β, is within the range 0,5 ≤ β ≤ 0,7.
NOTE It is possible to have 0,23 ≤ β < 0,5, but the uncertainty increases significantly if d < 12,5 mm.
5.2.3 Discharge coefficients and corresponding uncertainties
[5]
The Reader-Harris/Gallagher (1998) equation for corner tappings given in ISO 5167-2:2022, 5.3.2.1 is
used for deriving the discharge coefficients, provided the pipe Reynolds numbers are within the limits
given in ISO 5167-2:2022, 5.3.1.
An additional uncertainty of 0,5 % is added arithmetically to the relative expanded uncertainty derived
from ISO 5167-2:2022, 5.3.3.1.
6 © ISO 2023 – All rights reserved
= =
---------------------- Page: 10 ----------------------
ISO/DTR 15377:2023(E)
5.3 No upstream or downstream pipeline
5.3.1 General
This clausesubclause applies where there is no pipeline on either the upstream or the downstream side
of the device or on both the upstream and the downstream sides of the device, that is for flow from a large
space into a pipe or vice versa, or flow through a device installed in the partition wall between two large
spaces.
5.3.2 Flow from a large space (no upstream pipeline) into a pipeline or another large space
5.3.2.1 Upstream and downstream tappings
The space on the upstream side of the device is considered large if
a) there is no wall closer than 4d to the axis of the device or to the plane of the upstream face of the
orifice or nozzle;,
b) the velocity of the fluid at any point more than 4d from the device is less than 3 % of the velocity in
the orifice or throat;, and
c) the diameter of the downstream pipeline is not less than 2d.
NOTE 1 The first condition implies, for example, that an upstream pipeline of diameter greater than 8d (that is
where β < 0,125) can be regarded as a large space. The second condition, which excludes upstream disturbances
due to draughts, swirl and jet effects, implies that the fluid is to enter the space uniformly over an area of not less
than 33 times the area of the orifice or throat. For example, if the flow is provided by a fall in level of a liquid in a
tank, the area of the liquid surface needs to be not less than 33 times the area of the orifice or throat through which
the tank is discharged.
In an acceptable installation the distance of the upstream tapping (i.e. the tapping in the large space) from
the orifice or nozzle centreline is greater than 4d.
The upstream tapping is preferably located in a wall perpendicular to the plane of the orifice and within
a distance of 0,5d from that plane. The tapping does not necessarily need to be located in any wall; it can
be in the open space. If the space is very large, for example a room, the tapping is shielded from draughts.
The downstream tapping is located as specified for corner tappings in ISO 5167-2. If the downstream side
also consists of a large space, the tapping is located as for the upstream tapping, except for Venturi nozzles
where the throat tapping is used.
NOTE 2 When the upstream and downstream tappings are at different horizontal levels, it might be necessary to
make allowance for the difference in hydrostatic head. This is usually done by reading the differential-pressure
transmitter with no fluid flow and making an appropriate correction.
5.3.2.2 Square-edged orifice plates with corner tappings
5.3.2.2.1 Square-edged orifice plates with corner tappings are manufactured according to
ISO 5167-2:2022, Clause 5.
5.3.2.2.2 The limits of use for square-edged orifice plates with corner tappings where there is a flow
from a large space are as follows:
— d ≥ 12,5 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
© ISO 2023 – All rights reserved 7
---------------------- Page: 11 ----------------------
ISO/DTR 15377:2023(E)
— Red ≥ 3 500.
NOTE 1 It is possible to have 12,5 mm > d > 6 mm, but the uncertainty increases significantly if d < 12,5 mm.
[5]
NOTE 2 Provided that β ≤ 0,2 and d ≥ 12,5 mm, the Reader-Harris/Gallagher (1998) equation given in
ISO 5167-2:2022, 5.3.2.1 can be used in a pipeline for Re ≥ 3 500 with a relative expanded uncertainty of the value
d
of C at k = 2 (approximately 95 % confidence level) of 1 % (if Re < 5 000).
D
5.3.2.2.3 The discharge coefficient, C, is given by Formula (13):
0,7 0,7
Formatted: Adjust space between Latin and Asian text,
6 6
10 10
Adjust space between Asian text and numbers, Tab
C 0,5961+ 0,000521 C 0,5961+ 0,000521 (13)
Re Re
d d stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
The relative expanded uncertainty of the value of C at k = 2 (approximately 95 % confidence level) is 1 %.
Field Code Changed
5.3.2.2.4 The expansibility factor, ε, is given by the following equationFormula (14) and is only
applicable if p /p > 0,75:
2 1
1κ 1κ
Formatted: Adjust space between Latin and Asian text,
p p
2 2
ε=1−−0,3511 ε=1−−0,3511 (14) Adjust space between Asian text and numbers, Tab
p p
1 1
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
+ 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
When Δp/p and κ are assumed to be known without error, the relative expanded uncertainty of the value
1
Field Code Changed
∆p
of ε at k = 2 (approximately 95 % confidence level) is equal to %.
3,5
κ p
1
Test results for the determination of ε are known for air, steam and natural gas only. However, there is
no known objection to using the same formula for other gases and vapours whose isentropic exponent is
known.
5.3.2.3 ISA 1932 nozzles
5.3.2.3.1 ISA 1932 nozzles are manufactured according to ISO 5167-3:2022, 5.1.
5.3.2.3.2 The limits of use for ISA 1932 nozzles where there is flow from a large space are as follows:
— d ≥ 11,5 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
— Re ≥ 100 000.
d
5.3.2.3.3 The discharge coefficient, C, is equal to 0,99. The relative expanded uncertainty of the value
of C at k = 2 (approximately 95 % confidence level) is expected to be no better than 1 %.
5.3.2.3.4 The expansibility factor, ε, is given by the following equationFormula (15) and is only
applicable if p2/p1 ≥ 0,75:
Formatted: Adjust space between Latin and Asian text,
0,5 0,5
2 2 Adjust space between Asian text and numbers, Tab
(κκ−1)/ (κκ−1)/
κ κ
κτ 1−τ κτ 1−τ
stops: Not at 19.85 pt + 39.7 pt + 59.55 pt + 79.4 pt
(15)
ε= ε=
κτ−−1 1 κτ−−1 1 + 99.25 pt + 119.05 pt + 138.9 pt + 158.75 pt +
178.6 pt + 198.45 pt
Field Code Changed
8 © ISO 2023 – All rights reserved
= =
---------------------- Page: 12 ----------------------
ISO/DTR 15377:2023(E)
The relative expanded uncertainty of the value of ε at k = 2 (approximately 95 % confidence level) is equal
to 2Δp/p %.
1
5.3.2.4 Venturi nozzle
5.3.2.4.1 Venturi nozzles are manufactured according to ISO 5167-3:2022, 5.4.
5.3.2.4.2 The limits of use for Venturi nozzles where there is flow from a large space are as follows:
— d ≥ 50 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
5 6
— 3 × 10 ≤ Re ≤ 3 × 10 .
d
5.3.2.4.3 The discharge coefficient, C, is equal to 0,985 8. The relative expanded uncertainty of the value
of C at k = 2 (approximately 95 % confidence level) is expected to be no better than 1,5 %.
5.3.2.4.4 The expansibility factor, ε, is given by the following equationFormula (16) and is only
applicable if p /p ≥ 0,75:
1
2
0,5 0,5
2 2 Formatted: Adjust space between Latin and Asian text,
(κκ−1)/ (κκ−1)/
κ κ
κτ 1−τ κτ 1−τ
Adjust space between Asian text and numbers, Tab
...
FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 15377
ISO/TC 30/SC 2
Measurement of fluid flow by means
Secretariat: BSI
of pressure-differential devices —
Voting begins on:
2023-05-09 Guidelines for the specification of
orifice plates, nozzles and Venturi
Voting terminates on:
2023-07-04
tubes beyond the scope of ISO 5167
series
Mesurage du débit des fluides au moyen d'appareils déprimogènes —
Lignes directrices pour la spécification des diaphragmes, des tuyères
et des tubes de Venturi non couverts par la série de l'ISO 5167
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/DTR 15377:2023(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 2023
---------------------- Page: 1 ----------------------
FINAL
TECHNICAL ISO/DTR
DRAFT
REPORT 15377
ISO/TC 30/SC 2
Measurement of fluid flow by means
Secretariat: BSI
of pressure-differential devices —
Voting begins on:
Guidelines for the specification of
orifice plates, nozzles and Venturi
Voting terminates on:
tubes beyond the scope of ISO 5167
series
Mesurage du débit des fluides au moyen d'appareils déprimogènes —
Lignes directrices pour la spécification des diaphragmes, des tuyères
et des tubes de Venturi non couverts par la série de l'ISO 5167
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023
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.
RECIPIENTS OF THIS DRAFT ARE INVITED TO
ISO copyright office
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
CP 401 • Ch. de Blandonnet 8
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
CH-1214 Vernier, Geneva
DOCUMENTATION.
Phone: +41 22 749 01 11
IN ADDITION TO THEIR EVALUATION AS
Reference number
Email: copyright@iso.org
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO
ISO/DTR 15377:2023(E)
Website: www.iso.org
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
Published in Switzerland
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN
DARDS TO WHICH REFERENCE MAY BE MADE IN
ii
© ISO 2023 – All rights reserved
NATIONAL REGULATIONS. © ISO 2023
---------------------- Page: 2 ----------------------
ISO/DTR 15377:2023(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Square-edged orifice plates and nozzles: with drain holes, in pipes below 50 mm
diameter, and as inlet and outlet devices . 3
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle . 3
5.1.1 General . 3
5.1.2 Square-edged orifice plates . 3
5.1.3 ISA 1932 nozzles . 5
5.1.4 Long radius nozzles . 5
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm . 5
5.2.1 General . 5
5.2.2 Limits of use . 5
5.2.3 Discharge coefficients and corresponding uncertainties . 6
5.3 No upstream or downstream pipeline . 6
5.3.1 General . 6
5.3.2 Flow from a large space (no upstream pipeline) into a pipeline or another
large space . 6
5.3.3 Flow into a large space (no downstream pipeline) . 8
6 Orifice plates (except square-edged) . 9
6.1 Conical entrance orifice plates . 9
6.1.1 General . 9
6.1.2 Limits of use . 9
6.1.3 Description . 10
6.1.4 Pressure tappings . 13
6.1.5 Coefficients and corresponding uncertainties .13
6.2 Quarter-circle orifice plates . 14
6.2.1 General . 14
6.2.2 Limits of use . 14
6.2.3 Description .15
6.2.4 Pressure tappings . . 18
6.2.5 Coefficients and corresponding uncertainties . 18
6.3 Eccentric orifice plates .20
6.3.1 General .20
6.3.2 Limits of use .20
6.3.3 Description .20
6.3.4 Coefficients and corresponding uncertainties .23
7 Venturi tubes with machined convergent of angle 10,5° .25
7.1 General . 25
7.2 Description . 25
7.3 Limits of use . 25
7.4 Discharge coefficient .26
7.5 Expansibility [expansion] factor . 26
7.6 Pressure loss . 26
7.7 Installation straight lengths . 26
Annex A (informative) An example of the calculations in 5.1.2 .28
Bibliography .31
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ISO/DTR 15377:2023(E)
Foreword
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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electrotechnical standardization.
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described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use
of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed
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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 2, Pressure differential devices.
This fourth edition cancels and replaces the third edition (ISO/TR 15377:2018), which has been
technically revised.
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.
iv
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TECHNICAL REPORT ISO/DTR 15377:2023(E)
Measurement of fluid flow by means of pressure-
differential devices — Guidelines for the specification of
orifice plates, nozzles and Venturi tubes beyond the scope
of ISO 5167 series
1 Scope
This document describes the geometry and method of use for conical-entrance orifice plates, quarter-
circle orifice plates, eccentric orifice plates and Venturi tubes with 10,5° convergent angles. Information
is also given for square-edged orifice plates and nozzles under conditions outside the scope of ISO 5167
series.
NOTE The data on which this document is based are limited in some cases.
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 4006, Measurement of fluid flow in closed conduits — Vocabulary and symbols
ISO 51671, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-
section conduits running full — Part 1: General principles and requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 4006 and ISO 5167-1 apply.
4 Symbols
For the purposes of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Dimensions
M: mass
Symbols Represented quantity SI unit
L: length
T: time
a Pressuretapping hole diameter L m
C Discharge coefficient dimensionless
Diameter of orifice (or throat) of primary device
d L m
a
under working conditions
d Measured drain hole diameter L m
k
a
In applications with drain holes, d is calculated from the measured values d and d [see Formulae (1) and (11)].
m k
NOTE 1 Other symbols used in this documentt are defined at their place of use.
NOTE 2 Subscript 1 refers to the crosssection at the plane of the upstream pressure tapping. Subscript 2 refers to the
crosssection at the plane of the downstream pressure tapping.
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ISO/DTR 15377:2023(E)
TTaabblle 1 e 1 ((ccoonnttiinnueuedd))
Dimensions
M: mass
Symbols Represented quantity SI unit
L: length
T: time
Measured orifice or throat diameter (where the
d L m
m
orifice or nozzle has a drain hole)
Upstream internal pipe diameter (or upstream
D diameter of a classical Venturi tube) under working L m
conditions
d Diameter of pressure tappings L m
tap
e Thickness of bore L m
E, E Thickness of orifice plate L m
1
F Correction factor dimensionless
E
k Uniform equivalent roughness L m
l Pressure tapping spacing L m
L Relative pressure tapping spacing: L = l/D dimensionless
−1 −2
p Static pressure of the fluid ML T Pa
−1
q Mass flowrate MT kg/s
m
r Radius of profile L m
Arithmetical mean deviation of the (roughness)
Ra L m
profile
Re Reynolds number dimensionless
Re Pipe Reynolds number dimensionless
D
Re Throat Reynolds number dimensionless
d
Re* Throat-tapping Reynolds number (= d Re /d) dimensionless
tap d
d
β dimensionless
Diameter ratio, β =
D
−1 −2
Δp Differential pressure ML T Pa
ε Expansibility (expansion) factor dimensionless
θ Angle between the tappings used and the radius dimensionless °
from the centre of the pipe to the centre of the drain
hole
κ Isentropic exponent dimensionless
λ Friction factor dimensionless
−3 3
ρ Mass density of the fluid ML kg/m
p
2
Pressure ratio, τ =
τ dimensionless
p
1
a
In applications with drain holes, d is calculated from the measured values d and d [see Formulae (1) and (11)].
m k
NOTE 1 Other symbols used in this documentt are defined at their place of use.
NOTE 2 Subscript 1 refers to the crosssection at the plane of the upstream pressure tapping. Subscript 2 refers to the
crosssection at the plane of the downstream pressure tapping.
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ISO/DTR 15377:2023(E)
5 Square-edged orifice plates and nozzles: with drain holes, in pipes below
50 mm diameter, and as inlet and outlet devices
5.1 Drain holes through the upstream face of the square-edged orifice plate or nozzle
5.1.1 General
Square-edged orifice plates and nozzles with drain holes are used, installed and manufactured in
accordance with the following guidelines.
NOTE 1 The guidelines presented in this document are applicable to both drain holes for liquid in gas and vent
holes for gas in liquid.
In a horizontal pipe, a drain hole is positioned at the bottom of the pipe. In a horizontal pipe, a vent hole
is positioned at the top of the pipe.
NOTE 2 Use of drain or vent holes can help alleviate the problem of fluid hold-up, but will not resolve
measurement errors arising from the presence of two-phase flow.
5.1.2 Square-edged orifice plates
If a drain hole is drilled through the orifice plate, the coefficient values specified in ISO 5167-2 are not
used unless the following conditions are observed.
a) The diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
concentric with the orifice, of diameter (D – 0,2d). The outer edge of the drain hole is as close to the
pipe wall as practicable. It is very important that neither the upstream nor the downstream pipe
obscure the drain hole and that the hole is not so small that it blocks.
b) The drain hole is deburred and the upstream edge is sharp. Spark erosion is a good method of
producing the drain hole.
c) Single pressure tappings are orientated so that they are between 90° and 180° to the position of the
drain hole. Upstream and downstream pressure tappings are at the same orientation relative to
the drain hole.
d) The measured orifice diameter, d , is corrected to allow for the additional orifice area represented
m
by the drain hole of measured diameter d , as shown in Formula (1):
k
d
m
d = (1)
02, 5
nn
θθ*
11+−aa−−1
180 180
4 2 4
′′
1−β C +β
()
1 m
2
2
d
k
1+C
22
2
d
m
where
d
m
β = (2)
m
D
′′′
an,,θβ,CC, and are given in Formulae (3) to (8):
21
′
Ld
46, 2 m
a=−06,,60β exp 15 (3)
m
β d
mk
3
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ISO/DTR 15377:2023(E)
d
46, m
n=−04,,57++30β ,117 (4)
m
d
k
46,
θβ*=−92 62 (5)
m
10,/80if Ed ≤ ,5
k
C = 0,,76750+<625Ed/,if 05 Ed/,<09 (6)
2 kk
13,,30if 9≤E//d
k
2
d
k
′′
ββ=+1 C (7)
m 2
2
d
m
and
′
CR(,e β )
D
C = (8)
1
′
′′
CR(,e β )
D
′
[5]
where CR(,e β *) is the discharge coefficient given by the Reader-Harris/Gallagher (1998) equation
D
′
[ISO 5167-2:2022, Formula (4)] for an orifice plate of diameter ratio β* and Reynolds number Re (L
D 1
and L’ are determined for the actual orifice plate; β* is either β or β”);
2
d
β = (9)
D
[d is given by Formula (1)]
is a fixed value of Reynolds number typical of the flow being measured. In high-
′
Re
D
6
′
pressure gas flows Re might be taken as, say, 4 × 10 (the actual Reynolds number
D
cannot be used in the calculation of d, since in that case for an orifice plate with a
drain hole d would not have a fixed value);
Ll(/= D)
is the quotient of the distance of the upstream tapping from the upstream face of the
11
plate and the pipe diameter;
Ll'(= '/D)
is the quotient of the distance of the downstream tapping from the downstream face
22
of the plate and the pipe diameter;
Θ is the angle (in degrees) between the pressure tappings used and the radius from the
centre of the pipe to the centre of the drain hole (90° ≤ θ ≤ 180°);
E is the thickness of the orifice plate.
Because of the presence of C this is an iterative computation, but convergence is rapid.
1
When estimating the relative expanded uncertainty of the flow measurement the following additional
percentage uncertainty is added arithmetically to the discharge-coefficient percentage relative
expanded uncertainty given by ISO 5167-2:2022, 5.3.3.1:
d
k
2 (10)
d
m
If β ≤ 0,63, or both β ≤ 0,7 and θ = 90°, C can be set equal to 1, with no increase in uncertainty; in this
m m 1
case there will be no need to iterate.
NOTE 1 There are very limited data for D smaller than 100 mm.
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ISO/DTR 15377:2023(E)
NOTE 2 The formulae given here are based on work described in Reference [10].
Because the formulae in this subclause are complex, there is an example in Annex A so that a computer
program can be checked.
5.1.3 ISA 1932 nozzles
If a drain hole is drilled through the nozzle upstream face, the coefficient values specified in ISO 5167-3
are not used unless the following conditions are observed:
a) the value of β is less than 0,625;
b) the diameter of the drain hole does not exceed 0,1d and no part of the hole lies within a circle,
concentric with the throat, of diameter (D – 0,2d);
c) the length of the drain hole does not exceed 0,1D;
d) the drain hole is deburred and the upstream edge is sharp;
e) single pressure tappings are orientated so that they are between 90° and 180° to the position of the
drain hole;
f) the measured diameter, d , is corrected to allow for the additional throat area represented by the
m
drain hole of diameter d , as shown in the following Formula (11):
k
2
d
k
dd=+10,40 (11)
m
d
m
4 −0,5
NOTE Formula (11) is based on the assumption that the value for Cε(1 − β ) for flow through the drain
hole is 20 % less than the value for flow through the throat of the nozzle.
When estimating the overall uncertainty of the flow measurement, the following additional percentage
uncertainty is added arithmetically to the discharge-coefficient percentage relative expanded
uncertainty:
2
d
k
40 (12)
d
m
5.1.4 Long radius nozzles
Drain holes through these primary elements are not used.
5.2 Square-edged orifice plates installed in pipes of diameter 25 mm ≤ D < 50 mm
5.2.1 General
Orifice plates are installed and manufactured according to ISO 5167-2.
5.2.2 Limits of use
When square-edged orifice plates are installed in pipes of bore 25 mm to 50 mm, it is essential to
observe the following conditions:
a) The pipes have high-quality internal surfaces such as drawn copper or brass tubes, glass or plastic
pipes or drawn or fine-machined steel tubes. The steel tubes are of stainless steel for use with
corrosive fluids such as water. The roughness is according to ISO 5167-2:2022, 5.3.1.
b) Corner tappings are used, preferably of the carrier ring type detailed in ISO 5167-2:2022, Figure 4.
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ISO/DTR 15377:2023(E)
c) The diameter ratio, β, is within the range 0,5 ≤ β ≤ 0,7.
NOTE It is possible to have 0,23 ≤ β < 0,5, but the uncertainty increases significantly if d < 12,5 mm.
5.2.3 Discharge coefficients and corresponding uncertainties
[5]
The Reader-Harris/Gallagher (1998) equation for corner tappings given in ISO 51672:2022, 5.3.2.1 is
used for deriving the discharge coefficients, provided the pipe Reynolds numbers are within the limits
given in ISO 51672:2022, 5.3.1.
An additional uncertainty of 0,5 % is added arithmetically to the relative expanded uncertainty derived
from ISO 51672:2022, 5.3.3.1.
5.3 No upstream or downstream pipeline
5.3.1 General
This subclause applies where there is no pipeline on either the upstream or the downstream side of the
device or on both the upstream and the downstream sides of the device, that is for flow from a large
space into a pipe or vice versa, or flow through a device installed in the partition wall between two
large spaces.
5.3.2 Flow from a large space (no upstream pipeline) into a pipeline or another large space
5.3.2.1 Upstream and downstream tappings
The space on the upstream side of the device is considered large if
a) there is no wall closer than 4d to the axis of the device or to the plane of the upstream face of the
orifice or nozzle,
b) the velocity of the fluid at any point more than 4d from the device is less than 3 % of the velocity in
the orifice or throat, and
c) the diameter of the downstream pipeline is not less than 2d.
NOTE 1 The first condition implies, for example, that an upstream pipeline of diameter greater than 8d (that is
where β < 0,125) can be regarded as a large space. The second condition, which excludes upstream disturbances
due to draughts, swirl and jet effects, implies that the fluid is to enter the space uniformly over an area of not less
than 33 times the area of the orifice or throat. For example, if the flow is provided by a fall in level of a liquid in
a tank, the area of the liquid surface needs to be not less than 33 times the area of the orifice or throat through
which the tank is discharged.
In an acceptable installation the distance of the upstream tapping (i.e. the tapping in the large space)
from the orifice or nozzle centreline is greater than 4d.
The upstream tapping is preferably located in a wall perpendicular to the plane of the orifice and within
a distance of 0,5d from that plane. The tapping does not necessarily need to be located in any wall; it
can be in the open space. If the space is very large, for example a room, the tapping is shielded from
draughts.
The downstream tapping is located as specified for corner tappings in ISO 5167-2. If the downstream
side also consists of a large space, the tapping is located as for the upstream tapping, except for Venturi
nozzles where the throat tapping is used.
NOTE 2 When the upstream and downstream tappings are at different horizontal levels, it might be necessary
to make allowance for the difference in hydrostatic head. This is usually done by reading the differential-pressure
transmitter with no fluid flow and making an appropriate correction.
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ISO/DTR 15377:2023(E)
5.3.2.2 Square-edged orifice plates with corner tappings
5.3.2.2.1 Square-edged orifice plates with corner tappings are manufactured according to
ISO 51672:2022, Clause 5.
5.3.2.2.2 The limits of use for square-edged orifice plates with corner tappings where there is a flow
from a large space are as follows:
— d ≥ 12,5 mm;
— downstream there is either a large space or a pipeline whose diameter is not less than 2d;
— Re ≥ 3 500.
d
NOTE 1 It is possible to have 12,5 mm > d > 6 mm, but the uncertainty increases significantly if d < 12,5 mm.
[5]
NOTE 2 Provided that β ≤ 0,2 and d ≥ 12,5 mm, the Reader-Harris/Gallagher (1998) equation given in
ISO 51672:2022, 5.3.2.1 can be used in a pipeline for Re ≥ 3 500 with a relative expanded uncertainty of the
d
value of C at k = 2 (approximately 95 % confidence level) of 1 % (if Re < 5 000).
D
5.3.2.2.3 The discharge coefficient, C, is given by Formula (13):
07,
6
10
C =+0,,59610 000521 (13)
Re
d
The relative expanded uncertainty of the value of C at k = 2 (approximately 95 % confidence level) is
1 %.
5.3.2.2.4 The expansibility factor, ε, is given by the following Formula (14) and is only applicable if p /
2
p > 0,75:
1
1 κ
p
2
ε =−10,3511− (14)
p
1
When Δp/p and κ are assumed to be known without error, the relative expanded uncert
...
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