ISO 5167-1:2003

INTERNATIONAL ISO
STANDARD 5167-1
Second edition
2003-03-01


Measurement of fluid flow by means of
pressure differential devices inserted in
circular cross-section conduits running
full —
Part 1:
General principles and requirements
Mesure 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




Reference number
ISO 5167-1:2003(E)
©
ISO 2003

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ISO 5167-1:2003(E)
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ISO 5167-1:2003(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols and subscripts. 6
4.1 Symbols . 6
4.2 Subscripts. 7
5 Principle of the method of measurement and computation. 7
5.1 Principle of the method of measurement . 7
5.2 Method of determination of the diameter ratio of the selected standard primary device . 8
5.3 Computation of flowrate. 8
5.4 Determination of density, pressure and temperature . 8
6 General requirements for the measurements . 10
6.1 Primary device. 10
6.2 Nature of the fluid . 11
6.3 Flow conditions. 11
7 Installation requirements . 11
7.1 General. 11
7.2 Minimum upstream and downstream straight lengths . 13
7.3 General requirement for flow conditions at the primary device . 13
7.4 Flow conditioners (see also Annex C). 13
8 Uncertainties on the measurement of flowrate. 16
8.1 Definition of uncertainty. 16
8.2 Practical computation of the uncertainty . 17
Annex A (informative) Iterative computations. 19
Annex B (informative) Examples of values of the pipe wall uniform equivalent roughness, k . 21
Annex C (informative) Flow conditioners and flow straighteners. 22
Bibliography . 33

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ISO 5167-1:2003(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 5167-1 was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed conduits,
Subcommittee SC 2, Pressure differential devices.
This second edition of ISO 5167-1, together with the first editions of ISO 5167-2, ISO 5167-3 and ISO 5167-4,
cancels and replaces the first edition (ISO 5167-1:1991), which has been technically revised, and
ISO 5167-1:1991/Amd.1:1998.
ISO 5167 consists of the following parts, under the general title Measurement of fluid flow by means of
pressure differential devices inserted in circular cross-section conduits running full:
— Part 1: General principles and requirements
— Part 2: Orifice plates
— Part 3: Nozzles and Venturi nozzles
— Part 4: Venturi tubes
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ISO 5167-1:2003(E)
Introduction
ISO 5167, consisting of four parts, covers the geometry and method of use (installation and operating
conditions) of orifice plates, nozzles and Venturi tubes when they are inserted in a conduit running full to
determine the flowrate of the fluid flowing in the conduit. It also gives necessary information for calculating the
flowrate and its associated uncertainty.
ISO 5167 is applicable only to pressure differential devices in which the flow remains subsonic throughout the
measuring section and where the fluid can be considered as single-phase, but is not applicable to the
measurement of pulsating flow. Furthermore, each of these devices can only be used within specified limits of
pipe size and Reynolds number.
ISO 5167 deals with devices for which direct calibration experiments have been made, sufficient in number,
spread and quality to enable coherent systems of application to be based on their results and coefficients to
be given with certain predictable limits of uncertainty.
The devices introduced into the pipe are called “primary devices”. The term primary device also includes the
pressure tappings. All other instruments or devices required for the measurement are known as “secondary
1)
devices”. ISO 5167 covers primary devices; secondary devices will be mentioned only occasionally.
ISO 5167 consists of the following four parts.
a) This part of ISO 5167 gives general terms and definitions, symbols, principles and requirements as well
as methods of measurement and uncertainty that are to be used in conjunction with Parts 2 to 4 of
ISO 5167.
b) Part 2 of ISO 5167 specifies orifice plates, which can be used with corner pressure tappings, D and D/2
2)
pressure tappings , and flange pressure tappings.
3)
c) Part 3 of ISO 5167 specifies ISA 1932 nozzles , long radius nozzles and Venturi nozzles, which differ in
shape and in the position of the pressure tappings.
4)
d) Part 4 of ISO 5167 specifies classical Venturi tubes .
Aspects of safety are not dealt with in Parts 1 to 4 of ISO 5167. It is the responsibility of the user to ensure
that the system meets applicable safety regulations.

1) See ISO 2186:1973, Fluid flow in closed conduits — Connections for pressure signal transmissions between primary
and secondary elements.
2) Orifice plates with vena contracta pressure tappings are not considered in ISO 5167.
3) ISA is the abbreviation for the International Federation of the National Standardizing Associations, which was
succeeded by ISO in 1946.
4) In the USA the classical Venturi tube is sometimes called the Herschel Venturi tube.
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INTERNATIONAL STANDARD ISO 5167-1:2003(E)

Measurement of fluid flow by means of
pressure differential devices inserted in
circular cross-section conduits running full —
Part 1:
General principles and requirements
1 Scope
This part of ISO 5167 defines terms and symbols and establishes the general principles for methods of
measurement and computation of the flowrate of fluid flowing in a conduit by means of pressure differential
devices (orifice plates, nozzles and Venturi tubes) when they are inserted into a circular cross-section conduit
running full. This part of ISO 5167 also specifies the general requirements for methods of measurement,
installation and determination of the uncertainty of the measurement of flowrate. It also defines the general
specified limits of pipe size and Reynolds number for which these pressure differential devices are to be used.
ISO 5167 (all parts) is applicable only to flow that remains subsonic throughout the measuring section and
where the fluid can be considered as single-phase. It is not applicable to the measurement of pulsating flow.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 4006:1991, Measurement of fluid flow in closed conduits — Vocabulary and symbols
ISO 5167-2:2003, Measurement of fluid flow by means of pressure differential devices inserted in circular
cross-section conduits running full — Part 2: Orifice plates
ISO 5167-3:2003, Measurement of fluid flow by means of pressure differential devices inserted in circular
cross-section conduits running full — Part 3: Nozzles and Venturi nozzles
ISO 5167-4:2003, Measurement of fluid flow by means of pressure differential devices inserted in circular
cross-section conduits running full — Part 4: Venturi tubes
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 4006 and the following apply.
NOTE The following definitions are given only for terms used in some special sense or for terms for which it seems
useful to emphasize the meaning.
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ISO 5167-1:2003(E)
3.1 Pressure measurement
3.1.1
wall pressure tapping
annular slot or circular hole drilled in the wall of a conduit in such a way that the edge of the hole is flush with
the internal surface of the conduit
NOTE The pressure tapping is usually a circular hole but in certain cases may be an annular slot.
3.1.2
static pressure of a fluid flowing through a pipeline
p
pressure which can be measured by connecting a pressure-measuring device to a wall pressure tapping
NOTE Only the value of the absolute static pressure is considered in ISO 5167 (all parts).
3.1.3
differential pressure
∆p
difference between the (static) pressures measured at the wall pressure tappings, one of which is on the
upstream side and the other of which is on the downstream side of a primary device (or in the throat for a
Venturi nozzle or a Venturi tube), inserted in a straight pipe through which flow occurs, when any difference in
height between the upstream and downstream tappings has been taken into account
NOTE In ISO 5167 (all parts) the term “differential pressure” is used only if the pressure tappings are in the positions
specified for each standard primary device.
3.1.4
pressure ratio
τ
ratio of the absolute (static) pressure at the downstream pressure tapping to the absolute (static) pressure at
the upstream pressure tapping
3.2 Primary devices
3.2.1
orifice
throat
opening of minimum cross-sectional area of a primary device
NOTE Standard primary device orifices are circular and coaxial with the pipeline.
3.2.2
orifice plate
thin plate in which a circular opening has been machined
NOTE Standard orifice plates are described as “thin plate” and “with sharp square edge”, because the thickness of
the plate is small compared with the diameter of the measuring section and because the upstream edge of the orifice is
sharp and square.
3.2.3
nozzle
device which consists of a convergent inlet connected to a cylindrical section generally called the “throat”
3.2.4
Venturi nozzle
device which consists of a convergent inlet which is a standardized ISA 1932 nozzle connected to a cylindrical
part called the “throat” and an expanding section called the “divergent” which is conical
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ISO 5167-1:2003(E)
3.2.5
Venturi tube
device which consists of a convergent inlet which is conical connected to a cylindrical part called the “throat”
and an expanding section called the “divergent” which is conical
3.2.6
diameter ratio
β
〈of a primary device used in a given pipe〉 ratio of the diameter of the orifice or throat of the primary device to
the internal diameter of the measuring pipe upstream of the primary device
NOTE However, when the primary device has a cylindrical section upstream, having the same diameter as that of the
pipe (as in the case of the classical Venturi tube), the diameter ratio is the ratio of the throat diameter and the diameter of
this cylindrical section at the plane of the upstream pressure tappings.
3.3 Flow
3.3.1
flowrate
rate of flow
q
mass or volume of fluid passing through the orifice (or throat) per unit time
3.3.1.1
mass flowrate
rate of mass flow
q
m
mass of fluid passing through the orifice (or throat) per unit time
3.3.1.2
volume flowrate
rate of volume flow
q
V
volume of fluid passing through the orifice (or throat) per unit time
NOTE In the case of volume flowrate, it is necessary to state the pressure and temperature at which the volume is
referenced.
3.3.2
Reynolds number
Re
dimensionless parameter expressing the ratio between the inertia and viscous forces
3.3.2.1
pipe Reynolds number
Re
D
dimensionless parameter expressing the ratio between the inertia and viscous forces in the upstream pipe
VD 4q
1 m
Re==
D
ν πµD
11
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ISO 5167-1:2003(E)
3.3.2.2
orifice or throat Reynolds number
Re
d
dimensionless parameter expressing the ratio between the inertia and viscous forces in the orifice or throat of
the primary device
Re
D
Re =
d
β
3.3.3
isentropic exponent
κ
ratio of the relative variation in pressure to the corresponding relative variation in density under elementary
reversible adiabatic (isentropic) transformation conditions
NOTE 1 The isentropic exponent κ appears in the different formulae for the expansibility [expansion] factor ε and varies
with the nature of the gas and with its temperature and pressure.
NOTE 2 There are many gases and vapours for which no values for κ have been published so far, particularly over a
wide range of pressure and temperature. In such a case, for the purposes of ISO 5167 (all parts), the ratio of the specific
heat capacity at constant pressure to the specific heat capacity at constant volume of ideal gases can be used in place of
the isentropic exponent.
3.3.4
Joule Thomson coefficient
isenthalpic temperature-pressure coefficient
µ
JT
rate of change of temperature with respect to pressure at constant enthalpy:
∂T
µ =
JT
∂p
H
or
2
RT
∂Z
u
µ =
JT
pCT∂
m,p
p
where
T is the absolute temperature;
p is the static pressure of a fluid flowing through a pipeline;
H is the enthalpy;
R is the universal gas constant;
u
C is the molar-heat capacity at constant pressure;
m,p
Z is the compressibility factor
NOTE The Joule Thomson coefficient varies with the nature of the gas and with its temperature and pressure and
can be calculated.
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ISO 5167-1:2003(E)
3.3.5
discharge coefficient
C
coefficient, defined for an incompressible fluid flow, which relates the actual flowrate to the theoretical flowrate
through a device, and is given by the formula for incompressible fluids
4
q 1− β
m

C =
π
2
dp2∆ ρ
1
4
NOTE 1 Calibration of standard primary devices by means of incompressible fluids (liquids) shows that the discharge
coefficient is dependent only on the Reynolds number for a given primary device in a given installation.
The numerical value of C is the same for different installations whenever such installations are geometrically similar and
the flows are characterized by identical Reynolds numbers.
The equations for the numerical values of C given in ISO 5167 (all parts) are based on data determined experimentally.
The uncertainty in the value of C can be reduced by flow calibration in a suitable laboratory.
4
NOTE 2 The quantity 11− β is called the “velocity of approach factor”, and the product
1
C
4
1− β
is called the “flow coefficient”.
3.3.6
expansibility [expansion] factor
ε
coefficient used to take into account the compressibility of the fluid
4
q 1− β
m
ε =
π
2
dC 2∆pρ
1
4
NOTE Calibration of a given primary device by means of a compressible fluid (gas) shows that the ratio
4
q 1− β
m

π
2
dp2∆ ρ
1
4
is dependent on the value of the Reynolds number as well as on the values of the pressure ratio and the isentropic
exponent of the gas.
The method adopted for representing these variations consists of multiplying the discharge coefficient C of the primary
device considered, as determined by direct calibration carried out with liquids for the same value of the Reynolds number,
by the expansibility [expansion] factor ε.
The expansibility factor, ε, is equal to unity when the fluid is considered incompressible (liquid) and is less than unity when
the fluid is compressible (gaseous).
This method is possible because experiments show that ε is practically independent of the Reynolds number and, for a
given diameter ratio of a given primary device, ε only depends on the pressure ratio and the isentropic exponent.
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ISO 5167-1:2003(E)
The numerical values of ε for orifice plates given in ISO 5167-2 are based on data determined experimentally. For nozzles
(see ISO 5167-3) and Venturi tubes (see ISO 5167-4) they are based on the thermodynamic general equation applied to
isentropic expansion.
3.3.7
arithmetical mean deviation of the roughness profile
Ra
arithmetical mean deviation from the mean line of the profile being measured
NOTE 1 The mean line is such that the sum of the squares of the distances between the effective surface and the
mean line is a minimum. In practice Ra can be measured with standard equipment for machined surfaces but can only be
estimated for rougher surfaces of pipes. See also ISO 4288.
NOTE 2 For pipes, the uniform equivalent roughness k may also be used. This value can be determined experimentally
(see 7.1.5) or taken from tables (see Annex B).
4 Symbols and subscripts
4.1 Symbols
Table 1 — Symbols
a
Symbol Quantity Dimension Sl unit
C Coefficient of discharge dimensionless —
2 −2 −1 −1
C Molar-heat capacity at constant pressure ML T Θ mol J/(mol⋅K)
m,p
Diameter of orifice (or throat) of primary device under working
d L m
conditions
Upstream internal pipe diameter (or upstream diameter of a
D L m
classical Venturi tube) under working conditions
2 −2 −1
H Enthalpy ML T mol J/mol
k Uniform equivalent roughness L m
Pressure loss coefficient (the ratio of the pressure loss to the
K dimensionless —
2
dynamic pressure, ρV /2)
l Pressure tapping spacing L m
L Relative pressure tapping spacing: L = l/D dimensionless —
−1 −2
p Absolute static pressure of the fluid ML T Pa
−1
q Mass flowrate MT kg/s
m
3 −1 3
q Volume flowrate L T m /s
V
R Radius L m
Ra Arithmetical mean deviation of the (roughness) profile L m
2 −2 −1 −1
R Universal gas constant ML T Θ mol J/(mol⋅K)
u
Re Reynolds number dimensionless —
Re Reynolds number referred to D dimensionless —
D
Re Reynolds number referred to d dimensionless —
d
t Temperature of the fluid Θ °C
T Absolute (thermodynamic) temperature of the fluid Θ K
U ′ Relative uncertainty dimensionless —
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ISO 5167-1:2003(E)
Table 1 (continued)
a
Symbol Quantity Dimension Sl unit
−1
V Mean axial velocity of the fluid in the pipe LT m/s
Z Compressibility factor dimensionless —
β Diameter ratio: β = d/D dimensionless —
b
γ Ratio of specific heat capacities dimensionless —
c c
δ Absolute uncertainty
−1 −2
∆p Differential pressure ML T Pa
−1 −2
∆p Pressure loss across a flow conditioner ML T Pa
c
−1 −2
∆ϖ Pressure loss across a primary device ML T Pa
ε Expansibility [expansion] factor dimensionless —
b
κ Isentropic exponent dimensionless —
λ Friction factor dimensionless —
−1 −1
µ Dynamic viscosity of the fluid ML T Pa⋅s
−1 2
µ Joule Thomson coefficient M LT Θ K/Pa

JT
2 −1 2
v Kinematic viscosity of the fluid: v = µ /ρ L T m /s
Relative pressure loss (the ratio of the pressure loss to the
ξ dimensionless —
differential pressure)
−3 3
ρ Density of the fluid ML kg/m
τ Pressure ratio: τ = p /p dimensionless —

2 1
φ Total angle of the divergent section dimensionless rad
a
M = mass, L = length, T = time, Θ = temperature
b
γ is the ratio of the specific heat capacity at constant pressure to the specific heat capacity at constant volume. For ideal gases, the
ratio of the specific heat capacities and the isentropic exponent have the same value (see 3.3.3). These values depend on the nature of
the gas.
c
The dimensions and units are those of the corresponding quantity.

4.2 Subscripts
Subscript Meaning
1 At upstream tapping plane
2 At downstream tapping plane
5 Principle of the method of measurement and computation
5.1 Principle of the method of measurement
The principle of the method of measurement is based on the installation of a primary device (such as an
orifice plate, a nozzle or a Venturi tube) into a pipeline in which a fluid is running full. The installation of the
primary device causes a static pressure difference between the upstream side and the throat or downstream
side of the device. The flowrate can be determined from the measured value of this pressure difference and
from the knowledge of the characteristics of the flowing fluid as well as the circumstances under which the
device is being used. It is assumed that the device is geometrically similar to one on which calibration has
been carried out and that the conditions of use are the same (see ISO 5167-2, ISO 5167-3 or ISO 5167-4).
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ISO 5167-1:2003(E)
The mass flowrate can be determined, since it is related to the differential pressure within the uncertainty
limits stated in ISO 5167, using Equation (1):
C π
2
qd=∆ερ2p (1)
m 1
4
4
1− β
Similarly, the value of the volume flowrate can be calculated using Equation (2):
q
m
q = (2)
V
ρ
where ρ is the fluid density at the temperature and pressure for which the volume is stated.
5.2 Method of determination of the diameter ratio of the selected standard primary device
In practice, when determining the diameter ratio of a primary element to be installed in a given pipeline, C and
ε used in Equation (1) are, in general, not known. Hence the following shall be selected a priori:
 the type of primary device to be used; and
 a flowrate and the corresponding value of the differential pressure.
The related values of q and ∆p are then inserted in Equation (1), rewritten in the form
m
2
4q
Cεβ
m
=
2
4
π∆Dp2 ρ
1− β 1
in which the diameter ratio of the selected primary device can be determined by iteration (see Annex A).
5.3 Computation of flowrate
Computation of the flowrate, which is a purely arithmetic process, is effected by replacing the different terms
on the right-hand side of Equation (1) by their numerical values.
Except for the case of Venturi tubes, C may be dependent on Re, which is itself dependent on q . In such
m
cases the final value of C, and hence of q , has to be obtained by iteration. See Annex A for guidance
m
regarding the choice of the iteration procedure and initial estimates.
The diameters d and D mentioned in the equations are the values of the diameters at the working conditions.
Measurements taken at any other conditions should be corrected for any possible expansion or contraction of
the primary device and the pipe due to the values of the temperature and pressure of the fluid during the
measurement.
It is necessary to know the density and the viscosity of the fluid at working conditions. In the case of a
compressible fluid, it is also necessary to know the isentropic exponent of the fluid at working conditions.
5.4 Determination of density, pressure and temperature
5.4.1 General
Any method of determining reliable values of the density, static pressure and temperature of the fluid is
acceptable if it does not interfere with the distribution of the flow in any way at the cross-section where
measurement is made.
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ISO 5167-1:2003(E)
5.4.2 Density
It is necessary to know the density of the fluid at the upstream pressure tapping; it can either be measured
directly or be calculated from an appropriate equation of state from a knowledge of the absolute static
pressure, absolute temperature and composition of the fluid at that location.
5.4.3 Static pressure
The static pressure of the fluid shall be measured by means of an individual pipe-wall pressure tapping, or
several such tappings interconnected, or by means of carrier ring tappings if carrier ring tappings are
permitted for the measurement of differential pressure in that tapping plane for the particular primary device.
(See 5.2 in ISO 5167-2:2003, 5.1.5, 5.2.5 or 5.3.3 in ISO 5167-3:2003 or 5.4 in ISO 5167-4:2003, as
appropriate).
Where four pressure tappings are connected together to give the pressure upstream, downstream or in the
throat of the primary device, it is best that they should be connected together in a “triple-T” arrangement as
shown in Figure 1. The “triple-T” arrangement is often used for measurement with Venturi tubes.
The static pressure tapping should be separate from the tappings provided for measuring the differential
pressure.
It is permissible to link simultaneously one pressur
...