SIST EN ISO 9300:2022

SLOVENSKI STANDARD
01-september-2022
Nadomešča:
SIST EN ISO 9300:2005
Merjenje pretoka plina na podlagi kritičnega toka v Venturijevi šobi (ISO 9300:2022)
Measurement of gas flow by means of critical flow nozzles (ISO 9300:2022)
Durchflussmessung von Gasen mit Venturidüsen bei kritischer Strömung (ISO
9300:2022)
Mesurage de débit de gaz au moyen de tuyères en régime critique (ISO 9300:2022)
Ta slovenski standard je istoveten z: EN ISO 9300:2022
ICS:
17.120.10 Pretok v zaprtih vodih Flow in closed conduits
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 9300
EUROPEAN STANDARD
NORME EUROPÉENNE
June 2022
EUROPÄISCHE NORM
ICS 17.120.10 Supersedes EN ISO 9300:2005
English Version
Measurement of gas flow by means of critical flow nozzles
(ISO 9300:2022)
Mesurage de débit de gaz au moyen de tuyères en Durchflussmessung von Gasen mit Venturidüsen bei
régime critique (ISO 9300:2022) kritischer Strömung (ISO 9300:2022)
This European Standard was approved by CEN on 17 June 2022.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

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Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 9300:2022 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 9300:2022) has been prepared by Technical Committee ISO/TC 30
"Measurement of fluid flow in closed conduits" in collaboration with CCMC.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by December 2022, and conflicting national standards
shall be withdrawn at the latest by December 2022.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 9300:2005.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 9300:2022 has been approved by CEN as EN ISO 9300:2022 without any modification.

INTERNATIONAL ISO
STANDARD 9300
Third edition
2022-06
Measurement of gas flow by means of
critical flow nozzles
Mesurage de débit de gaz au moyen de tuyères en régime critique
Reference number
ISO 9300:2022(E)
ISO 9300:2022(E)
© ISO 2022
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
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 9300:2022(E)
Contents Page
Foreword . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Pressure . 1
3.2 Temperature . 2
3.3 Nozzle . 2
3.4 Flow . 3
3.5 Flow rate . 4
3.6 Gas . 5
4 Symbols and abbreviations . 6
5 Basic equations . 9
5.1 Gas behaviour . 9
5.1.1 Isentropic process . 9
5.1.2 State equation . 9
5.2 Isentropic flow of a perfect gas . 9
5.2.1 Flowing area . 9
5.2.2 Static pressure . 9
5.2.3 Static temperature . 10
5.3 Theoretical variables at the critical point . 10
5.3.1 General . 10
5.3.2 Critical pressure . 10
5.3.3 Critical temperature . 10
5.3.4 Critical density . 10
5.3.5 Critical velocity . 10
5.4 Theoretical mass flow rates . 10
5.4.1 General . 10
5.4.2 Theoretical mass flow rate of a perfect gas . 10
5.4.3 Theoretical mass flow rate of real gas . 11
5.5 Mass flow rate . 11
6 General requirements . 11
7 Applications for which the method is suitable . 12
8 CFN . 12
8.1 General requirements for both the standard CFN types . 12
8.1.1 General . 12
8.1.2 Materials . 12
8.1.3 Contraction and throat . 13
8.1.4 Diffuser . 13
8.2 Requirements for each standard types of CFN . 14
8.2.1 Standard CFNs . Error! Bookmark not defined.
8.2.2 Toroidal-throat CFN . 15
8.2.3 Cylindrical-throat CFN . 16
9 Installation requirements . 18
9.1 General requirements for both the standard configurations . 18
9.1.1 Standard configurations . 18
9.1.2 Upstream pressure tapping . 18
9.1.3 Downstream pressure tapping . 19
ISO 9300:2022(E)
9.1.4 Temperature measurement . 19
9.1.5 Density measurement . 20
9.1.6 Drain hole . 20
9.1.7 Downstream condition . 20
9.2 Pipe configuration . 21
9.2.1 General . 21
9.2.2 Upstream pipe . 21
9.2.3 Pressure measurement . 22
9.2.4 Temperature measurement . 22
9.3 Chamber configuration . 23
9.3.1 General . 23
9.3.2 Upstream chamber . 23
9.3.3 Pressure measurement . 23
9.3.4 Temperature measurement . 23
9.3.5 Back-pressure ratio . 23
10 Calculations . 23
10.1 General . 23
10.2 Calculation of mass flow rate, q . 23
m
10.3 Calculation of discharge coefficient, C . 24
d
10.4 Calculation of critical flow function, C* or C* . 25
D
10.5 Conversion of measured pressure into stagnation pressure . 25
10.6 Conversion of measured temperature into stagnation temperature. 25
10.7 Calculation of viscosity . 25
11 Estimation of critical back-pressure ratio. 26
11.1 For a traditional diffuser at Reynolds numbers higher than 2 × 10 . 26
11.2 For any diffuser at low Reynolds numbers . 27
11.3 For CFNs without diffuser or with very short diffuser . 28
12 Uncertainties in the measurement of flow rate . 28
12.1 General . 28
12.2 Practical computation of uncertainty . 29
12.3 Correlated uncertainty components . 30
(informative) Discharge coefficient values . 32
(informative) Critical flow function . 34
(informative) Critical flow function values — Pure gases and air . 37
(informative) Computation of critical mass flux for critical flow nozzles with high
nozzle throat to upstream pipe diameter ratio, β > 0,25 . 62
(informative) Diameter correction method . 66
(informative) Adjustment of discharge coefficient curve on a data set . 71
(informative) Discharge coefficient . 79
(informative) Critical back pressure ratio . 84
(informative) Viscosity values – Pure gases and air . 92
(informative) Supplement . 108
Bibliography . 116
iv © ISO 2022 – All rights reserved

ISO 9300:2022(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organizations, governmental and non-governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
ISO 9300 was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed conduits,
Subcommittee SC 2, Pressure differential devices, in collaboration with the European Committee for
Standardization (CEN) Technical Committee CEN/SS F05, Measuring instruments, in accordance with
the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 9300:2005), which has been technically
revised.
The main changes are as follows:
— the discharge coefficient curve is given by a single equation each for the toroidal- and cylindrical-
throat critical flow nozzles (CFNs) that covers both the laminar and turbulent boundary layer
regimes;
— the discharge coefficient curve of the cylindrical-throat CFN is updated based on the recent
experimental and theoretical data;
— the quadrant CFN and detachable diffuser are introduced;
— the basic equations used to measure the discharge coefficient are listed;
— the premature unchoking phenomenon is explained to give attention to the unpredictable
unchoking at low Reynolds numbers;
— REFPROP is introduced for the calculations of critical flow function and viscosity as well as their
fitted curves are given for some pure gases and air;
ISO 9300:2022(E)
— the diameter correction method is introduced to fit the experimental discharge coefficient data to a
reference curve;
— the detailed method to match the discharge coefficient curve on an experimental data set is
described;
— the background of the specifications is given.
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.
vi © ISO 2022 – All rights reserved

INTERNATIONAL STANDARD ISO 9300:2022(E)

Measurement of gas flow by means of critical flow nozzles
1 Scope
This document specifies the geometry and method of use (installation in a system and operating
conditions) of critical flow nozzles (CFNs) used to determine the mass flow rate of a gas flowing through
a system basically without the need to calibrate the CFN. It also gives the information necessary for
calculating the flow rate and its associated uncertainty.
This document is applicable to nozzles in which the gas flow accelerates to the critical velocity at the
minimum flowing section, and only where there is steady flow of single-phase gas. When the critical
velocity is attained in the nozzle, the mass flow rate of the gas flowing through the nozzle is the
maximum possible for the existing inlet condition, while the CFN can only be used within specified
limits, e.g. the CFN throat to inlet diameter ratio and Reynolds number. This document deals with the
toroidal- and cylindrical-throat CFNs for which direct calibration experiments have been made in
sufficient number to enable the resulting coefficients to be used with certain predictable limits of
uncertainty.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/
3.1 Pressure
3.1.1
static pressure
pressure of the flowing gas (see Annex J)
Note 1 to entry: The static pressure is measured through a wall pressure tapping (3.1.3).
3.1.2
stagnation pressure
pressure which would exist in a flowing gas stream if the stream were brought to rest by an isentropic
process
ISO 9300:2022(E)
3.1.3
wall pressure tapping
hole drilled in the wall of a conduit to measure the static pressure (3.1.1) of the flowing gas in the
conduit
3.2 Temperature
3.2.1
static temperature
temperature of the flowing gas (see Annex J)
Note 1 to entry: The static temperature cannot be measured exactly by a temperature sensor fixed in the conduit .
3.2.2
stagnation temperature
temperature which would exist in a flowing gas stream if the stream were brought to rest by an
isentropic process (see Annex J).
3.2.3
recovery temperature (wall temperature, measured temperature)
temperature of the gas touching the wall (see Annex J)
Note 1 to entry: The temperature sensor fixed on a conduit measures the recovery temperature.
3.3 Nozzle
3.3.1
contraction
portion of the nozzle (3.3.5) upstream of the throat (3.3.2) intended to accelerate the flow and attain the
supposed flow field at the critical point (3.4.4)
3.3.2
throat
portion of the nozzle (3.3.5) where the cross section is minimum
Note 1 to entry: This document deals with nozzles with toroidal- and cylindrical-throats.
3.3.3
diffuser
divergent portion of the nozzle (3.3.5) behind the throat (3.3.2) intended to recover the pressure
3.3.4
traditional diffuser
frustum diffuser (3.3.3) machined as one piece
3.3.5
nozzle
device inserted in a system intended to use for measurement of the flow rate through system, which
consists of contraction (3.3.1) and throat (3.3.2), or contraction (3.3.1), throat (3.3.2), and diffuser
(3.3.3)
3.3.6
critical flow nozzle
CFN
nozzle (3.3.5) that attains the critical flow (3.4.2)
2 © ISO 2022 – All rights reserved

ISO 9300:2022(E)
3.3.7
normal precision nozzle
NPN
nozzle (3.3.5) machined by a lathe, with the surface polished to achieve the desired roughness
3.3.8
high precision nozzle
HPN
nozzle (3.3.5) machined by a lathe that can achieve mirror finish without polishing the surface, thus it
has the form exactly as designed
3.4 Flow
3.4.1
isentropic flow
theoretical flow along which the thermodynamic process is adiabatic and reversible (see Annex J)
3.4.2
critical flow
flow in a nozzle (3.3.5) that has attained the maximum flow rate of the nozzle (3.3.5) for a given set of
inlet conditions (see Annex J)
3.4.3
choke
attaining the critical flow (3.4.2) in a nozzle (3.3.5) (see Annex J)
3.4.4
critical point
location in the CFN (3.3.6) where the flow attains the critical velocity (3.4.11)
3.4.5
critical pressure
p *
static pressure (3.1.1) at the critical point (3.4.4) (see Annex J)
3.4.6
critical pressure of perfect gas

p *
P
theoretical static pressure (3.1.1) at the critical point (3.4.4) assuming the isentropic flow (3.4.1) of
perfect gas (3.6.1)
3.4.7
critical temperature
T *
static temperature (3.2.1) at the critical point (3.4.4)
3.4.8
critical temperature of perfect gas

T *
P
theoretical static temperature (3.2.1) at the critical point (3.4.4) assuming the isentropic flow (3.4.1) of
perfect gas (3.6.1)
ISO 9300:2022(E)
3.4.9
critical density
ρ*
density at the critical point (3.4.4)
3.4.10
critical density of perfect gas

ρ *
P
theoretical density at the critical point (3.4.4) assuming the isentropic flow (3.4.1) of perfect gas (3.6.1)
3.4.11
critical velocity
c*
flow velocity at the critical point (3.4.4) (see Annex J)
3.4.12
critical velocity of perfect gas

c*
P
theoretical flow velocity at the critical point (3.4.4) assuming the isentropic flow (3.4.1) of perfect gas
(3.6.1)
3.5 Flow rate
3.5.1
mass flow rate
q
m
mass of the gas passing through the CFN (3.3.6) per unit time
Note 1 to entry: In this document, the term "mass flow rate" without any adjective always refers to the true mass
flow rate through the CFN.
3.5.2
theoretical mass flow rate of perfect gas
q
th,P
theoretical mass flow rate through the CFN (3.3.6) assuming one-dimensional isentropic flow (3.4.1) of
perfect gas (3.6.1)
3.5.3
theoretical mass flow rate of real gas
q
th,R
theoretical mass flow rate through the CFN (3.3.6) assuming one-dimensional isentropic flow (3.4.1) of
real gas (3.6.1)
3.5.4
volume flow rate
q
V
volume of the gas passing through the conduit, in which the CFN (3.3.6) is installed, per unit time at a
designated location (see Annex J)
Note 1 to entry: The volume flow rate at the designated location, where the density is ρ, is given by:
q
m
q =
V
ρ
4 © ISO 2022 – All rights reserved

ISO 9300:2022(E)
3.5.5
Reynolds number
4q
m
R =
e
πdµ
dimensionless parameter calculated from the throat diameter, mass flow rate (3.5.1), and gas dynamic
viscosity at CFN (3.3.6) inlet stagnation condition (see Annex J)
3.5.6
discharge coefficient
q
m
C =
d
q
th,R
ratio of the mass flow rate (3.5.1) to theoretical one of real gas (3.6.1) at the same inlet stagnation
condition
3.5.7
critical pressure ratio
ratio of the critical pressure (3.4.5) of perfect gas (3.6.1) to the inlet stagnation pressure (3.1.2)
3.5.8
back-pressure ratio
ratio of the static pressure (3.1.1) at the diffuser exit to the inlet stagnation pressure (3.1.2)
3.5.9
local Mach number
M
a
ratio of the flow velocity to local acoustic one
3.5.10
Mach number in the upstream conduit
M
aC
ratio of the mean axial flow velocity over the cross-section of upstream conduit to the acoustic velocity
at the same location
Note to entry: It is not necessary for MaC to be accurate and it may be approximated by:
q 1
m
M =
aC
πD R
γ T
ρ
4 M
3.5.11
uncertainty
parameter, associated with the results of a measurement, that characterizes the dispersion of the values
that could reasonably be attributed to the measurand
3.6 Gas
3.6.1
perfect gas
theoretical gas whose isentropic exponent (3.6.6) equals to the specific heat that is constant at any gas
condition and also compressibility factor (3.6.3) is always unity
ISO 9300:2022(E)
3.6.2
real gas
actual gas whose isentropic exponent (3.6.6) and compressibility factor (3.6.3) depend on its pressure
and temperature
3.6.3
compressibility factor
Z
correction factor for the deviation of the real gas constant from the universal one (see Annex J)
3.6.4
critical flow function
C *
dimensionless function that relates the thermodynamic properties of the gas at the throat of CFN (3.3.6)
to its inlet stagnation condition assuming one-dimensional isentropic flow (3.4.1)
3.6.5
critical flow function for the flow rate equation using density

C **= CZ
D0
alternative critical flow function (3.6.4) to be used in the equation of mass flow rate (3.5.1) that uses
density
3.6.6
isentropic exponent
κ
ratio of the relative variation in pressure to the corresponding relative variation in density under
isentropic process
4 Symbols and abbreviations
Symbol Description Dimension SI unit
a, b, c, d, e, f, n Coefficients for Formula (17) Dimensionless —
2 2
A Flowing area L m
2 2
A* Flowing area at the critical point L m
2 2
A Cross-sectional area of nozzle exit L m
Cross-sectional area at the critical point at the operating CFN
2 2
A L m
nt
temperature
−1
-1
c Local acoustic velocity LT m·s
−1
-1
Local acoustic velocity at the critical point LT m·s
c*
−1
-1
Local acoustic velocity at the critical point of perfect gas LT m·s
c*
P
C Parameter for the equation of C* Dimensionless —
c*
C Parameter for the equation of µ Dimensionless —
μ
C Discharge coefficient Dimensionless —
d
target
C Target discharge coefficient obtained when applying the DCM Dimensionless —
d
ISO
C Discharge coefficient calculated by using Formula (17) Dimensionless —
d
Critical flow function Dimensionless —
C *
Critical flow function for the flow rate equation using density Dimensionless —
C *
D
Critical flow function of perfect gas Dimensionless —
C *
P
Critical flow function of dry air Dimensionless —
C *
DA
Critical flow function of humid air Dimensionless —
C *
HA
6 © ISO 2022 – All rights reserved

ISO 9300:2022(E)
Symbol Description Dimension SI unit
b b
Coefficient to calculate C*
C
ij,
Covariance Dimensionless —
c
v
D Diameter of the inlet conduit L m
d Throat diameter corrected by the DCM L m
DCM
d Throat diameter at the operating CFN temperature L m
nt
d Measured throat diameter (at temperature T ) L m
nt0 nt0
d Throat diameter used at the calibration for the DCM L m
ORI
d Diameter of the wall pressure tapping breakthrough into the conduit L m
p
H Relative humidity % —
R
k Coverage factor Dimensionless —
l Diffuser length L m
l1 Distance between Etoile straightener outlet and nozzle inlet plane L m
l2 Length of Etoile straightener L m
−1
M Molar mass M kg mol
M Local Mach number Dimensionless —
a
Local Mach number at the CFN exit assuming the fully subsonic flow in —
M Dimensionless
a2
the diffuser
M Local Mach number at the location of the inlet pressure tapping Dimensionless —
aC
−1 −2
p Static pressure of the gas ML T Pa
−1 −2
p Stagnation pressure of the gas at the CFN inlet ML T Pa
Static pressure of the gas measured through the upstream wall
−1 −2
p ML T Pa
pressure tapping
−1 −2
p Static pressure of the gas at the diffuser exit ML T Pa
Theoretical static pressure of the gas at the diffuser exit when the
−1 −2
p ML T Pa
2i
nozzle is choked but the flow in the diffuser is fully subsonic
−1 −2
p Static pressure in the gas at densitometer ML T Pa
den
P The Prandtl number Dimensionless —
r
−1 −2
p* Static pressure at the critical point ML T Pa
−1 −2
Theoretical static pressure at the critical point of perfect gas ML T Pa
p *
P
−1 −1
q Mass flow rate (True mass flow rate) MT kg·s
m
−1 −1
Theoretical mass flow rate of perfect gas MT kg·s
qth,P
−1 −1
Theoretical mass flow rate of real gas MT kg·s
qth,R
−1 −1
q Volume flow rate MT kg·s
V
2 −2 −1 −1 −1
R Universal gas constant (8,314 5 J/(mol·K)) M L T Θ J·mol K
R Arithmetic average roughness L m
a
Re Reynolds number Dimensionless —
ORI
Re The Reynolds number at the calibration for the DCM Dimensionless —
R Recovery factor Dimensionless —
f
r Radius of inlet contraction L m
c
r Critical back-pressure ratio Dimensionless —
CBP
r Radius in the vicinity of throat inlet in cylindrical-throat CFN L m
nt
T Static temperature of the gas Θ K
T Stagnation temperature of the gas at the CFN inlet Θ K
T Measured temperature of the gas at the CFN inlet Θ K
T Static temperature at densitometer Θ K
den
T Measured temperature Θ K
m
ISO 9300:2022(E)
Symbol Description Dimension SI unit
T Temperature when throat diameter was measured Θ K
nt0
T* Static temperature at the critical point Θ K
Theoretical static temperature at the critical point of perfect gas Θ K
T *
P
T Parameter for the equation of C* Θ K
c*
T Parameter for the equation of μ Θ K
μ
b
𝑢𝑢 Standard uncertainty (k = 1) —
b
𝑢𝑢 Combined standard uncertainty (k = 1) —
𝑐𝑐
b
U Expanded uncertainty (with specified coverage factor, k) U
b
V Coefficient to calculate viscosity U
i,j
b
U Expanded uncertainty (with specified coverage factor, k) U
xi Mole fraction of the i-th component Dimensionless —
Z Compressibility factor Dimensionless —
Ζ0 Compressibility factor at upstream stagnation condition Dimensionless —
Ζden Compressibility factor at densitometer Dimensionless —
−1 −1
α Linear expansion coefficient of the nozzle material Θ K
β Diameter ratio of the throat and conduit (dnt/D) Dimensionless —
a a
δ Absolute uncertainty
γ Heat capacity ratio Dimensionless —
κ Isentropic exponent Dimensionless —
−1 −1
µ Dynamic viscosity of the gas at the inlet stagnation conditions ML T Pa·s
−1 −1
µ Dynamic viscosity of the gas ML T Pa·s
θ Angle of the frustum diffuser wall against the nozzle AOS Dimensionless rad
-3
ρ Density of the gas ML kg
−3 −3
ρ Gas density at the inlet stagnation conditions at nozzle inlet ML kg·m
−3 −3
ρ Gas density measured by a densitometer ML kg·m
den
−3 −3
ρ∗ Theoretical density of the gas at the critical point ML kg·m
−3 −3
Theoretical density of the gas at the critical point of perfect gas ML kg·m
ρ *
P
M = mass
L = length
T = time
Θ = temperature
a
Same as the corresponding quantity.
b
Depending on each terms of the equation.

8 © ISO 2022 – All rights reserved

ISO 9300:2022(E)
Abbreviation Description
AOS axis of symmetry
CFN critical flow nozzle
CL center line
DCM diameter correction method
HPN high precision nozzle
NPN normal precision nozzle
IP inlet plane
PUP premature unchoking phenomenon
TLS tangential line of surface
5 Basic equations
5.1 Gas behaviour
5.1.1 Isentropic process
The pressure, temperature, and density of gas in the isentropic process are related by Formulae (1) and
(2);
γ−1
p
=const. (1)
γ
T
p
= const. (2)
γ
ρ
5.1.2 State equation
The behaviour of real gas is described by Formula (3);
p RZ

= T (3)

ρ M
5.2 Isentropic flow of a perfect gas
5.2.1 Flowing area
The flowing area is related to the local Mach number by Formula (4);
11γ+
 2γ−1
1 (γ−12) M +
a
(4)
AA=

nt
M γ+ 1
a

5.2.2 Static pressure
The static pressure is related to the local Mach number by Formula (5);
γ
−
γ−1
 γ−1
(5)
p 1+ Mp

a0
2
=
ISO 9300:2022(E)
5.2.3 Static temperature
The static temperature is related to the local Mach number by Formula (6);
(6)
T= T
21+−(γ ) M
a
5.3 Theoretical variables at the critical point
5.3.1 General
The theoretical variables at the critical point are derived assuming the isentropic flow of perfect gas.
5.3.2 Critical pressure
The theoretical static pressure at the critical point is given by Formula (7);
γ
2 γ−1
(7)
pp* =
P  0
γ+ 1

5.3.3 Critical temperature
The theoretical static temperature at the critical point is given by Formula (8);
(8)
TT* =
P0
γ+1
5.3.4 Critical density
The theoretical density at the critical point is given by Formula (9);
γ−1
(9)
ρρ* =
P0
γ+ 1

5.3.5 Critical velocity
The theoretical flow velocity at the critical point is given by Formula (10);
R
(10)
cT**= γ
P P
M
5.4 Theoretical mass flow rates
5.4.1 General
The theoretical mass flow rates are derived assuming one-dimensional isentropic flow of perfect or real
gas.
5.4.2 Theoretical mass flow rate of a perfect gas
The theoretical mass flow rate of a perfect gas is defined by the product of flowing area, local acoustic
velocity, and density at the critical point assuming one-dimensional isentropic flow of a perfect gas, i.e.
Z = 1 and k = γ, which is given by Formula (11);
10 © ISO 2022 – All rights reserved

ISO 9300:2022(E)
p
(11)
q ≡=A **c ρ * A *C *
th,P P P P
R

T

M

5.4.3 Theoretical mass flow rate of real gas
The theoretical mass flow rate of real gas is defined by the product of flowing area, local acoustic
velocity, and density at the critical point assuming one-dimensional isentropic flow of real gas, which is
given by Formula (12);
p
(12)
q ≡=A **c ρ * A *C *
th,R
R

T

M
5.5 Mass flow rate
The mass flow rate of CFN is given by Formulae (13) or (14);
(13)
q = C q
m d th,R
or
(14)
q = C A **C p ρ
( )
m d D 0 0
6 General requirements
a) The flow shall be steady-state and single-phase with no condensation to the critical point (throat).
b) A sufficiently low back-pressure ratio shall be applied on the CFN to maintain the critical flow.
NOTE The typical pressure ratio required to operate the CFN with a sufficiently long diffuser can be about 0,8 at high
5 3
Reynolds numbers, e.g., greater than 2×10 (corresponding to ca. 50 m /h CFN at the atmospheric pressure); however, it
is often necessary to keep the ratio lower than 0,5 at low Reynolds numbers or sometimes 0,25 at very low Reynolds
numbers (see Clause 11 and Annex H).
c) The thermodynamic properties of the gas, C * and M (or and ρ when a densitometer is used),
C *
D
are required at low uncertainties (see 10.4).
NOTE For a gas mixture, accurate gas composition is required to calculate C * at sufficiently low uncertainty.
If the following requirements cannot be achieved, the CFN will have to be flow calibrated at the same
condition as in its application.
d) The gas should have no significant relaxation effect (see B.5).
e) The temperatures of the gas and CFN should be stable (see Annex J).
f) The form and surface in the contraction and throat should be accurately machined as specified in
Clause 8 (see Annex G).
g) The form of the CFN will be verified periodically, especially in the contraction and throat (see
Annex G).
NOTE The contraction and throat can be deformed over time by the impact of any solids contained in the gas.
ISO 9300:2022(E)
The contraction and throat shall retain their cleanliness and hence surface finish. If this cannot be
guaranteed, the measurement shall not be claimed to conform to this document, and flow calibration is
recommended.
7 Applications for which the method is suitable
Each application should be evaluated to determine whether a CFN or some other device is the most
suitable.
The most common applications for CFNs are to act as working or reference standards to calibrate other
flowmeters, as check or transfer standards to verify or compare calibration facilities, as controllers of
flow rates, and so on.
Important considerations are:
a) The mass and volume flow rates through the CFN are independent of the downstream condition.
b) The volume flow rate through the conduit where the CFN is installed is almost constant at any
upstream pressure if the temperature is stable.
NOTE Multiple CFNs installed in parallel (e.g. the chamber configuration) are required to vary the volume flow rate
through the CFN system for a fixed upstream pressure (see 9.3 and Annex J).
Some other considerations are:
c) Accurate measurements of the pressure and temperature (or density when using a densitometer)
are required only at the upstream location of the
...