ISO/DTR 25582

• Status: Not Published
• ICS: 17.120.10 - Flow in closed conduits
• Technical Committee: ISO/TC 30/SC 5 - Velocity and mass methods
• Current Stage: 5000 - FDIS registered for formal approval
• Start Date: 17-Jul-2026
• Completion Date: 30-Jul-2026

Overview

ISO/DTR 25582 is an ISO technical report on influences of the velocity and temperature distribution on fluid flow measurement by using Pitot static tubes. It provides practical data and references to help users better understand fluid flow measurement in closed conduits under complex industrial conditions.

This document is especially relevant where accurate Pitot static tube flow measurement depends on the quality of the flow field at the measuring cross-section. It highlights common factors that can affect measurement reliability, including upstream and downstream conduit length, velocity distribution uniformity, temperature distribution uniformity, devices for improving flow conditions, and humidity.

For engineers, metrology specialists, and industrial operators, ISO/DTR 25582 offers a useful reference for improving confidence in airflow measurement, flow profile assessment, and velocity-area method applications.

Key Topics

ISO/DTR 25582 focuses on the practical influences that shape measurement results when using Pitot static tubes:

• Length of upstream and downstream conduit
  • Guidance is provided on how conduit length can affect asymmetry, swirl, and turbulence
• Velocity distribution uniformity
  • The report discusses how non-uniform flow profiles can influence measurement accuracy
• Temperature distribution uniformity
  • It shows why temperature variations across the cross-section can matter in industrial flow measurement
• Devices for improving flow conditions
  • Examples include turning vanes, profile developers, static mixers, and multiple devices
• Humidity
  • The document also addresses humidity as a factor in flow measurement conditions

The report includes both experimental test and numerical simulation evidence, making it useful for understanding real-world measurement scenarios without relying solely on ideal conditions.

Applications

ISO/DTR 25582 is intended to support better decision-making in industrial environments where fluid flow measurement must be performed in challenging conduit layouts. Typical applications include:

• Large industrial air ducts
• Thermal power plant duct systems
• Closed conduit airflow measurement
• Flow measurement planning and assessment
• Evaluation of measurement cross-section suitability
• Use of Pitot static tubes in non-ideal flow conditions

The report is especially valuable when straight conduit lengths are limited and flow conditioning may be needed to improve measurement quality. It helps users identify when the measurement cross-section may not support stable velocity-area results and when corrective measures should be considered.

Related Standards

ISO/DTR 25582 is closely connected to several ISO standards and related references, including:

• ISO 3966 - Measurement of fluid flow in closed conduits - Velocity area method using Pitot static tubes
• ISO 7194 - Measurement of fluid flow in closed conduits - Velocity-area methods in swirling or asymmetric flow conditions
• ISO 5167-2 - Orifice plates
• ISO 5167-3 - Nozzles and Venturi nozzles
• ISO 5801 - Fans - Performance testing using standardized airways

These related standards provide the broader framework for fluid flow measurement, Pitot tube methods, and related industrial testing practices.

FINAL DRAFT
Technical
Report
ISO/TC 30/SC 5
Influences of the velocity and
Secretariat: SNV
temperature distribution on fluid
Voting begins on:
flow measurement by using Pitot
2026-10-05
static tubes
Voting terminates on:
2026-11-30
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.
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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.
Reference number
FINAL DRAFT
Technical
Report
ISO/TC 30/SC 5
Influences of the velocity and
Secretariat: SNV
temperature distribution on fluid
Voting begins on:
flow measurement by using Pitot
static tubes
Voting terminates on:
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.
© ISO 2026
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO­
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
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Published in Switzerland Reference number
ii
Contents Page
Foreword .iv
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 Symbols .1
5 Influence of length of upstream/downstream conduit .1
5.1 General .1
5.2 Circular cross-sections.2
5.2.1 Experimental test .2
5.2.2 Numerical simulation .9
5.3 Rectangular cross-sections . 12
6 Influence of velocity and temperature distribution uniformity .15
6.1 General . 15
6.2 Velocity distribution uniformity . 15
6.3 Influence of temperature distribution uniformity .18
7 Influence of devices for improving flow conditions .21
7.1 General .21
7.2 Turning vanes .21
7.3 Profile developer. 25
7.4 Static mixer . 29
7.5 Multiple devices .32
8 Influence of humidity . .40
Bibliography .42

iii
Foreword
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This document is prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed conduits,
Subcommittee SC 5, Velocity and mass methods.
Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv
FINAL DRAFT Technical Report ISO/DTR 25582:2026(en)
Influences of the velocity and temperature distribution on
fluid flow measurement by using Pitot static tubes
1 Scope
This document provides data and references to better guide measurement of fluid flow in closed conduits
with Pitot static tubes in many complex scenarios of large industrial applications.
This document illustrates influences of the following common conditions on fluid flow measurement by
using Pitot static tubes:
a) influence of length of upstream/downstream conduit;
b) influence of velocity and temperature distribution uniformity;
c) influence of devices for improving flow conditions;
d) influence of humidity.
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 3966, Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3966 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/
4 Symbols
The symbols given in ISO 3966 and the following symbols apply.
Symbol Quantity Dimensions SI unit
h relative humidity of fluid — —
r
Y the index of asymmetry of the flow — —
5 Influence of length of upstream/downstream conduit
5.1 General
ISO 3966 provides guidance on the use of Pitot tubes. According to ISO 3966,it is normally assumed that to
comply with these conditions there is a length of upstream conduit between the beginning of the working

section and any significant upstream irregularity of at least 20 diameters of a circular cross-section (or 80
times the hydraulic radius of a conduit of any cross-section shape). ISO 3966 also recommends that there be
at least 5 diameters of a circular cross-section (or 20 times the hydraulic radius of a conduit of any cross-
section shape), between the measuring cross-section and any significant downstream irregularity to avoid
asymmetry, swirl and turbulences.
5.2 Circular cross-sections
5.2.1 Experimental test
A test bench with circular conduit in laboratory is shown in Figure 1. The measuring cross-section is located
at the long horizontal circular conduit of the test bench. The cross-sectional inner dimension of the circular
conduit is 0,6 m. The lengths of the upstream and downstream straight conduit of the measuring cross-
section are 13,0 m and 6,5 m, respectively.
Dimensions in metres
a) Photograph of long horizontal conduit section with measuring cross-section
b)  Photograph of measuring cross-section and holes

c)  3D model diagram
Key
1 elbow conduit
2 comparative cross section
3 test measuring cross-section
4 straight conduit
a
Measurement hole in vertical direction.
b
Measurement hole in horizontal direction.
c
Flow direction.
Figure 1 — Test bench with circular conduit in laboratory
In this document, the influence of length of upstream/downstream circular conduit on velocity profile by
using Pitot tubes is demonstrated through the experimental test in laboratory and numerical simulation.
At the measuring cross-section of the test bench, to obtain the velocity distribution, the horizontal and
vertical directions are selected and there are 29 measuring points per direction (see Figure 2). The selection
of these measuring points is uniformly distributed along the centrelines of the measurement cross-section
and does not comply with the velocity-area method. Therefore, the obtained measurement velocity data are
only for reference in researching the flow velocity distribution.

Dimensions in millimetres
Key
X horizontal direction
Y vertical direction
Figure 2 — Measuring points at the measuring cross-section for velocity distribution
In the test, the medium is air. The relative humidity, pressure and density of the air are shown in Table 1,
which also gives the measurement data of the velocity at the measuring cross section. The fluid velocities
are measured by using Pitot tubes and calculated from the differential pressure existing between the total
and static pressures of the Pitot tube placed at these measuring points.
Table 1 — Measurement data at the measuring cross-section for velocity distribution
Horizontal direction Vertical direction
Relative humid- Relative hu-
Temperature Pressure Density Temperature Pressure Density
ity midity
3 3
°C kPa kg/m °C kPa kg/m
% %
20,5 65 101,8 1,201 18,4 65 102,0 1,213
Measuring Differential Measuring Differential
Local velocity Local velocity
points radius pressure points radius pressure
m/s m/s
mm Pa mm Pa
-280 100,279 12,92 -280 106,094 13,23
-260 124,127 14,38 -260 129,280 14,60
-240 134,535 14,97 -240 144,919 15,46
-220 143,086 15,44 -220 156,500 16,06
-200 155,236 16,08 -200 164,406 16,46

TTaabblle 1 e 1 ((ccoonnttiinnueuedd))
Horizontal direction Vertical direction
Relative humid- Relative hu-
Temperature Pressure Density Temperature Pressure Density
ity midity
3 3
°C kPa kg/m °C kPa kg/m
% %
20,5 65 101,8 1,201 18,4 65 102,0 1,213
Measuring Differential Measuring Differential
Local velocity Local velocity
points radius pressure points radius pressure
m/s m/s
mm Pa mm Pa
-180 162,356 16,44 -180 171,064 16,79
-160 165,216 16,59 -160 175,698 17,02
-140 172,492 16,95 -140 177,694 17,12
-120 170,939 16,87 -120 182,499 17,35
-100 173,894 17,02 -100 180,745 17,26
-80 174,915 17,07 -80 184,611 17,45
-60 175,860 17,11 -60 184,307 17,43
-40 176,229 17,13 -40 183,821 17,41
-20 174,923 17,07 -20 184,234 17,43
0 174,796 17,06 0 186,085 17,52
20 173,684 17,01 20 184,692 17,45
40 174,463 17,04 40 185,482 17,49
60 173,712 17,01 60 184,367 17,44
80 171,655 16,91 80 181,787 17,31
100 172,366 16,94 100 182,160 17,33
120 169,259 16,79 120 180,632 17,26
140 163,205 16,49 140 175,065 16,99
160 158,207 16,23 160 168,248 16,66
180 147,744 15,69 180 165,612 16,52
200 137,603 15,14 200 154,296 15,95
220 128,610 14,63 220 142,291 15,32
240 114,932 13,83 240 134,029 14,87
260 93,164 12,46 260 115,936 13,83
280 88,966 12,17 280 104,355 13,12
Figure 3 shows the velocity distributions at horizontal and vertical diameters. Obviously, the velocity
distribution exhibits relatively good central symmetry in both horizontal and vertical directions.

a)  Horizontal direction
b)  Vertical direction
Key
r radius of the position where the measuring points are located in the horizontal direction
h
v measured velocity at the position where the measuring points are located in the horizontal direction
h
r radius of the position where the measuring points are located in the vertical direction
v
v measured velocity at the position where the measuring points are located in the vertical direction
v
Figure 3 — Measuring velocity distributions at horizontal and vertical diameters
Figure 4 gives positions of the measuring points respectively according to regulations (velocity-area
[5]
method) of ISO 3966 and EN 12599 .
a)  According to ISO 3966 b)  According to EN 12599
Key
X horizontal direction
Y vertical direction
Figure 4 — Measuring points at the measuring cross-section for velocity measurement
Table 2 shows the measuring point statistical results of the flow field at the measuring cross section
according to ISO 3966 and EN 12599. The test results indicate that, as the measuring cross-section is far
enough away from any disturbances, the relative standard deviation of the velocity distribution at the cross
section is maintained at the level which is no more than 15 %. It is normally assumed that the uniformity of
velocity distribution is acceptable with σ ≤ 15 %.
v
Table 2 — Measurement data at the measuring cross-section for velocity measurement
Measur- Local velocity Relative standard devi-
Average velocity at the
ing points ation of the velocity distri-
m/s
cross section
radius bution at the cross section
m/s
Horizontal direction Vertical direction
mm %
Refer to ISO 3966:2025
-289 11,67 12,05
-254 13,95 14,66
-207 15,74 16,32
-171 16,44 16,85
-86 16,98 17,29
15,04 13,48
86 17,00 17,41
171 16,00 16,62
207 15,05 15,89
254 13,19 14,21
289 11,34 12,07
Refer to EN 12599:2012
-285 11,98 12,44
-251 14,10 14,82
-212 15,60 16,21
-164 16,53 16,92
-95 16,96 17,26
15,11 12,63
95 16,96 17,37
164 16,15 16,73
212 14,89 15,75
251 13,33 14,35
285 11,57 12,37
Besides, two indexes are considered to characterize the symmetry of the velocity distribution:
a) According to ISO 7194, for circular ducts, the index of asymmetry of the flow (Y) is defined to evaluate
the asymmetric flow conditions and is not advisable to be greater than 0,15 to make a measurement.
The index of asymmetry of the flow (Y) can be calculated by the following Formula (1):
12/
n
 
uv

 i
i1
 
Y  (1)
v n1
 
 
where
n is the number of radii traversed (4, 6 or 8);
u is the mean velocity calculated from the individual point velocity measurements at i radius,
i
m/s;
v is the mean axial velocity calculated from all of the individual point velocity measurements,
m/s.
b) According to EN 12599, for rectangular ducts and circular ducts, the following formula is used as a
measure of the irregularity, Irr, of the velocity profile and can be calculated by the following Formula (2).
In the case of a rectangular cross-section, the maximum and minimum values of mean velocity are
selected from the quarters of the total cross-section, of side length equal to half the duct side length. In
the case of a circular cross-section, the mean values are taken from four measurement radius at right
angles to one another. For the calculation of u the velocity in the boundary layer at the wall of the
min
duct is neglected.
uu
maxmin
Irr  (2)
2v
where
u is the maximum of the arithmetic mean of velocities in a quarter of the measuring cross-section
max
or at a radius, m/s;
u is the minimum of the arithmetic mean of velocities in a quarter of the measuring cross-section
min
or at a radius, m/s;
v is the arithmetic mean over the entire cross section, m/s.
For example, based on the data in Table 2, the index of asymmetry of the flow (Y) at the measuring cross
section is 0,026 5 which can completely meet the requirement of ISO 7194.
5.2.2 Numerical simulation
The influence of length of upstream/downstream circular conduit on velocity profile is investigated
further by numerical simulations. Figure 1 c) shows the 3D model diagram of the test bench. The length of
the upstream straight section of the comparative measuring section is 3,0 m. Figure 5 shows the velocity
distribution diagram at the comparative measuring cross-section and test measuring cross-section which
are given by numerical simulation. Figure 6 shows the velocity distribution contours at measuring cross-
sections.
Horizontal direction Vertical direction
a)  Comparative measuring cross-section
Horizontal direction Vertical direction
b)  Test measuring cross-section
Key
r radius of the position where the measuring points are located in the horizontal direction
h
v measured velocity at the position where the measuring points are located in the horizontal direction
h
r radius of the position where the measuring points are located in the vertical direction
v
v measured velocity at the position where the measuring points are located in the vertical direction
v
Figure 5 — Numerical simulation velocity distributions at horizontal and vertical directions

a)  Comparative measuring cross-section b)  Test measuring cross-section
Figure 6 — Velocity distribution contours diagram
Figure 5 shows the velocity distribution at the measuring sections of the test bench (numerical simulation
results). The numerical simulation data of the velocity distribution at the test measuring cross-section
are consistent in trend with the experimental measurement data shown in Figure 3. At the comparative
measuring cross-section, especially in horizontal direction, the symmetry of the velocity distribution is
poorly developed. Table 3 shows numerical simulation results of the points at the horizontal and vertical
directions of measuring cross section. These points refer to ISO 3966 and are the same as Figure 3 a). Results
show that
a) at the test measuring cross-section with satisfactory conditions of the upstream and downstream
conduits length, the relative standard deviation of the velocity distribution is 13,99 % and the index of
asymmetry of the flow is 0,012 4, and
b) at the comparative measuring cross-section with the length of upstream conduit between the elbow
and measuring section only 5 times the conduit diameter (not meet the requirements for use of Pitot
tubes in ISO 3966), the relative standard deviation of the velocity distribution is 19,77 % (>15 %) and
the index of asymmetry of the flow is 0,159 4 (>0,15);

Table 3 — Numerical simulation data at the measuring cross-section for velocity measurement
Local velocity Relative standard
Measur- Average veloc-
deviation of the ve-
Index of asym-
m/s
ing points ity at the cross
locity distribution
metry of the
radius section
at the cross section
flow (Y)
Horizontal direction Vertical direction
mm m/s
%
Comparative measuring cross-section
-289 7,43 11,89
-254 9,81 15,29
-207 11,11 16,00
-171 12,42 16,40
-86 15,55 17,03
14,65 19,77 0,159 4
86 17,72 17,01
171 17,79 16,41
207 17,79 15,97
254 16,99 15,38
289 12,85 12,10
Test measuring cross-section
-289 11,35 11,60
-254 14,20 14,83
-207 15,49 16,28
-171 16,30 16,80
-86 17,27 17,56
15,12 13,99 0,014 4
86 17,46 17,37
171 16,51 16,39
207 15,96 15,70
254 14,45 14,29
289 11,35 11,21
5.3 Rectangular cross-sections
The influence of length of upstream/downstream rectangular conduit on velocity profile by using Pitot
tubes is demonstrated numerical simulation.
Figure 7 shows a 3D model of a hypothetical rectangular air duct. The cross-sectional inner dimension
of the air duct is 4,4 m × 4,0 m. The lengths of the straight sections upstream and downstream on the
hypothetical simulation cross-section are 84,0 m and 21,0 m, respectively, which meet the requirement for
use of Pitot tubes. Figure 8 shows the numerical simulation results of the velocity distribution contours
at the simulation cross section. According to log-Chebyshev method mentioned in ISO 3966, a total of 49
selected data collection grid points at the simulation cross-section are shown in Figure 9. Table 4 shows the
numerical simulation results of the velocity distribution at the cross section by using grid point statistical
method according to Log-Chebyshev method. In this simulation case, the boundary conditions of this
numerical simulation include the mass flow rate of the air which is 1 052,28 t/h (as the reference value for
comparison). The numerical simulation results indicate that
a) the velocity distribution at the simulation cross section is uniform and the relative standard deviation
of the velocity distribution is 6,7 %, and
b) for the simulation cross section, the fluid flow rate calculated from the average velocity of the cross
section is 1 061,51 t/h, with a deviation of 0,9 % from the reference value.

Dimensions in millimetres
Key
1 hypothetical simulation cross-section (4,4 m × 4,0 m)
a
Flow direction.
Figure 7 — 3D model diagram of a hypothetical rectangular air duct
Figure 8 — Velocity distribution contour at the simulation cross section

Key
X /L position of the measuring points corresponds to ratio of the abscissa X in relation to the centre of the section
i i
to the length of the section
Y /H position of the measuring points corresponds to ratio of the ordinate Y in relation to the centre of the section
i j
to the height of the section
Figure 9 — Selected grid points at the hypothetical simulation cross-section
(Log-Chebyshev method according to ISO 3966)
Table 4 — Grid points numerical simulation results of the flow field at the hypothetical cross-
section (Log-Chebyshev method)
Statistical results of local velocity at the hypothetical simulation cross-section
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 23,4 26,3 27,1 27,0 26,6 25,4 21,2
-0,297 m/s 27,6 28,7 28,6 28,3 28,0 27,4 25,5
-0,134 m/s 28,7 29,3 29,1 28,8 28,5 28,2 27,0
0 m/s 28,9 29,5 29,4 29,2 28,9 28,6 27,4
0,134 m/s 28,8 29,7 29,6 29,4 29,2 28,8 27,4
0,297 m/s 27,7 29,6 29,7 29,6 29,5 29,0 26,7
0,447 m/s 23,7 28,0 28,8 28,9 28,7 27,5 23,1
Average velocity m/s 27,9
Relative standard deviation of
% 6,7
the velocity distribution
Calculated fluid mass flow rate t/h 1 061,51

6 Influence of velocity and temperature distribution uniformity
6.1 General
Actually, in many industrial application scenarios, the measurement conditions with closed conduits cannot
meet the requirements for straight conduit lengths upstream and downstream of the measuring cross-
section as specified in 5.1. Under such conditions, special attention is paid to the influence of velocity and
temperature distribution uniformity at the measuring cross-section when using the velocity-area method
with Pitot tubes to measure airflow velocity. This clause illustrates the influence of velocity and temperature
distribution uniformity by numerical simulation research.
6.2 Velocity distribution uniformity
Figure 10 shows a 3D model of an actual air duct in a thermal power plant. There are three 90° elbows in
the entire duct, and the cross-sectional dimension of the hot secondary air duct is 4,4 m×4,0 m. The straight
conduit section is 17,0 m long. The measuring cross-section where the on-site test holes are located is 4,6 m
(approximately 4,4 times the hydraulic radius) away from the upstream elbow and 12,4 m (approximately only
11,9 times the hydraulic radius) away from the downstream elbow. The comparative cross-section I is 5,5 m
(approximately 5,3 times the hydraulic radius) away from the upstream elbow and 11,5 m (approximately
only 11,0 times the hydraulic radius) away from the downstream elbow. The comparative cross-section
II is 11,5 m (approximately 11,0 times the hydraulic radius) away from the upstream elbow and 5,5 m
(approximately only 5,3 times the hydraulic radius) away from the downstream elbow. Figure 11 shows the
numerical simulation results of the velocity distribution contours at the measuring and comparative cross-
sections. Table 5 shows the numerical simulation results of the velocity distribution at the cross-sections by
using grid points statistical method according to Log-Chebyshev method (see Figure 9). In this simulation
case, for guidance and as reference, the boundary conditions of this numerical simulation include the mass
flow rate of the hot air is 1 052,28 t/h. The numerical simulation results indicate that
a) for the cross-section where the onsite test holes are located, the relative standard deviation of the
velocity distribution is 46,3 % which is far from the standard values of a uniform flow field and the
calculated fluid mass flow rate is 1 150,72 t/h, with a significant deviation of 9,4 % from the reference
value. It can be seen that in this case the positions of the on-site measuring points are extremely
unreasonable.
b) for the comparative measuring section I, it’s close to the onsite test holes and the ratio of the upstream
and downstream straight pipe sections of the measured cross-section is about 1/2. The relative standard
deviation of the velocity distribution is 43,5 % which is far from the standard values of a uniform flow
field and the calculated fluid mass flow rate is 1 127,78 t/h, with a deviation of 7,2 % from the reference
value.
c) for the comparative measuring section II, the ratio of the upstream and downstream straight pipe
sections of the measured cross-section is about 2/1. The relative standard deviation of the velocity
distribution is 27,7 % and the calculated fluid mass flow rate is 1 108,66 t/h, with a deviation of 5,4 %
from the reference value.
For this kind measurement condition that the length of the straight conduit section cannot meet the
requirement as specified in 5.1, about the flow measurement, there are always obvious flow high-speed and
low-speed areas with a significant relative standard deviation of the velocity distribution which can lead to a
deviation between measured values and true values of fluid flow rate. Further, if the objective measurement
conditions for the straight conduit section length are indeed limited, the measuring cross-section position
is positioned at a location with flow uniformity whenever possible. If necessary, devices for improving flow
conditions (see 7.2) are employed to ensure that the velocity deviation at the measurement cross-section
remains below 15 %, because a small velocity deviation will enhance the accuracy of calculating conduit
flow rate by using velocity-area method with Pitot tubes.

Dimensions in metres
Key
1 comparative cross-section II
2 comparative cross-section I
3 cross-section where the on-site test holes are located
a
Air inlet.
b
Flow direction.
c
Air outlet.
Figure 10 — 3D model of an actual air duct in a thermal power plant

a)  On-site measuring cross-section
b)  Comparative measuring cross-section I c)  Comparative measuring cross-section II
Figure 11 — Velocity distribution contours at the onsite measuring and comparative
cross-sections
Table 5 — Grid points numerical simulation results of the flow field at cross-sections
Cross section where the onsite test holes are located
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 34,5 40,0 43,1 44,3 44,7 44,5 43,1
-0,297 m/s 36,1 36,0 36,5 38,0 40,7 43,7 44,6
-0,134 m/s 35,2 29,6 25,0 25,3 31,0 41,7 45,4
0 m/s 32,5 23,2 15,4 16,1 26,0 41,3 45,6
0,134 m/s 27,9 16,1 7,1 9,9 25,7 42,4 45,7
0,297 m/s 18,3 8,4 2,0 4,0 23,7 43,8 45,7
0,447 m/s 7,9 9,7 9,1 6,6 27,2 44,2 44,6
Average velocity m/s 30,1
Relative standard deviation of
% 46,3
the velocity distribution
Calculated fluid mass flow rate t/h 1 150,72
Comparative measuring cross-section I

TTaabblle 5 e 5 ((ccoonnttiinnueuedd))
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 34,2 38,7 41,5 42,9 43,7 43,9 42,5
-0,297 m/s 35,6 34,9 34,7 35,9 38,9 42,6 43,9
-0,134 m/s 35,0 29,1 23,5 22,8 27,9 39,7 44,4
0 m/s 33,2 24,4 15,8 14,7 22,7 38,9 44,6
0,134 m/s 30,0 19,5 9,5 9,2 20,6 39,7 44,6
0,297 m/s 22,3 13,7 5,7 3,9 17,3 41,1 44,7
0,447 m/s 13,2 13,4 11,6 7,2 19,2 42,9 43,5
Average velocity m/s 29,5
Relative standard deviation of
% 43,5
the velocity distribution
Calculated fluid mass flow rate t/h 1 127,78
Comparative measuring cross-section II
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 33,9 35,5 36,9 38,3 39,7 40,7 38,8
-0,297 m/s 34,4 32,3 30,9 31,4 33,7 37,8 40,0
-0,134 m/s 33,6 28,2 23,2 21,8 24,4 32,6 39,8
0 m/s 32,4 26,0 19,5 17,0 19,3 29,6 39,5
0,134 m/s 30,9 24,7 18,1 14,9 16,1 27,5 39,3
0,297 m/s 27,7 24,0 19,9 17,0 15,7 28,4 40,0
0,447 m/s 24,2 24,2 23,0 20,5 17,1 34,8 39,6
Average velocity m/s 29,0
Relative standard deviation of
% 27,7
the velocity distribution
Calculated fluid mass flow rate t/h 1 108,66
6.3 Influence of temperature distribution uniformity
Figure 12 a) shows a 3D model of an actual mixed air duct for hot and cold air. The dimension of the hot
air duct is 2,0 m × 1,2 m and the dimension of the cold air duct is 0,8 m × 0,6 m. The cold primary air duct
is connected to the side of the hot air duct (see Figure 12 b)), and the straight section where the flow
measurement section is located is 3,7 m long. The simulation measuring cross-section (2,0 m × 1,2 m) is
2,6 m far away from the upstream elbow.

Dimensions in metres
a)  3D model b)  Field photo
Key
1 measuring cross section
2 elbow
a
Cold air inlet.
b
Hot air inlet.
c
Mixed air outlet.
Figure 12 — Actual mixed air duct for hot and cold air
To illustrate the influence of temperature distribution uniformity, two simulation cases are done. In this first
simulation case, the boundary conditions of this numerical simulation include the mass flow rate of the hot
air is 65,57 t/h with a temperature of 573 K, the mass flow rate of the cold air is 26,47 t/h with a temperature
of 313 K. In this second simulation case, the mass flow rate of the hot air is 120,05 t/h with a temperature
of 313 K, the mass flow rate of the cold air is 26,47 t/h with a temperature of 313 K. By comparing these
two simulation cases, it can be seen that the inlet air velocities of hot and cold air are deliberately kept
consistent. Besides, about the second simulation case, since the temperatures of the hot air and the cold air
are the same, so there is no temperature deviation in the flow field in the air duct.
Figure 13 shows the numerical simulation results of the velocity and temperature distribution contours at
the measuring cross-section. Table 6 shows the statistical results of the velocity and temperature at the
measuring section. The numerical simulation results indicate that
a) in the first simulation case, it can be seen that the cold air is difficult to penetrate the hot air near the
connection and it takes a long development length to fill the entire cross section. The length of the existing
conduit section is far from meeting the requirements, resulting in an uneven temperature distribution
at the measuring cross section. The relative standard deviation of the temperature distribution at the
measuring cross section is 11,8 %. The relative standard deviation of the velocity distribution at the
measuring cross section is 28,1 %; For the measuring cross section, the fluid flow rate calculated from
the average velocity and average temperature of the cross section is 96,83 t/h, with a deviation of 5,2 %
from the reference value.
b) in the second simulation case, it is obvious that there is no temperature deviation at the measuring
cross section. The relative standard deviation of the velocity distribution at the measuring cross section
is 21,2 %. However, for the measuring cross section, the fluid flow rate calculated from the average
velocity of the cross section is 147,14 t/h, with only a deviation of 0,4 % from the reference value.
c) the comparison result demonstrates that temperature distribution uniformity has significant influences
on the accuracy of fluid flow measurement by using velocity-area method with Pitot tubes.

Volume temperature distribution temperature distribution at the velocity distribution at the meas-
measuring cross-section uring cross-section
a)  First simulation case with the temperature of hot air is 573 K
streamline of fluid field velocity distribution at the measuring cross-sec-
tion
b)  Second simulation case with the temperature of hot air is 313 K
Figure 13 — Numerical simulation results of the velocity and temperature distribution contours
Table 6 — Uniformity statistics of velocity and temperature distribution at the measuring cross
section (numerical simulation results)
First simulation case with the temperature of hot air is 573 K
Flow field Temperature field
Relative standard devi- Relative standard devi-
Average velocity Average temperature
ation ation
m/s K
% %
15,2 28,1 504 11,8
Calculated fluid flow rate Referred fluid flow rate Deviation
t/h t/h %
96,83 92,04 5,2
the second simulation case with the temperature of hot air is 313 K
Flow field Temperature field
Relative standard devi- Relative standard devi-
Average velocity Average temperature
ation ation
m/s K
% %
15,2 21,2 313 0
Calculated fluid flow rate Referred fluid flow rate Deviation
t/h t/h %
147,14 146,52 0,4
For this kind measurement condition that the length of the straight conduit section cannot meet the
requirement to make the fluids of different temperatures to mix thoroughly, devices for improving the
uniformity of temperature distribution (see 7.4) are employed to ensure that the temperature deviation (σ )
T
at the measurement cross-section remains below 5 %. For guidance, when the fluid temperature range is
273 K~623 K, it is normally assumed that the uniformity of temperature distribution is acceptable with
σ ≤ 5 %.
T
7 Influence of devices for improving flow conditions
7.1 General
Different devices for improving flow conditions are given in ISO 3966, including anti-swirl device, profile
developer, turning vanes and Static mixer. This chapter gives the experimental and numerical simulation
studies of above devices intend to illustrate its applicability and effectiveness.
7.2 Turning vanes
If there are elbows or extenders near the measuring cross-section, turning vanes can be used to smooth the
flow direction and improve the uniformity of the velocity distribution. The turning vanes consist of arc or
flat plates. As mentioned in 6.1, if necessary, devices for improving flow conditions are performed to improve
the velocity distribution uniformity. Based on the example given in 6.1, turning vanes are arranged at the
elbows to improve the uniformity of velocity distribution at the measuring section, see Figure 14. Figure 15
shows the numerical simulation results of the of the velocity distribution contours at measuring cross-
sections after optimization. Table 7 shows the numerical simulation results of the velocity distribution at the
cross-sections by using grid points statistical method according to Log-Chebyshev method (see Figure 9). In
this clause’s simulation example, the boundary conditions are the same with 6.1 for guidance and reference,
including that the mass flow rate of the hot air is 1 052,28 t/h. The numerical simulation results indicate that
a) the uniformity of the flow velocity distribution at the cross-section where the test holes are located
is significantly improved, the average cross-sectional velocity is 27,7 m/s, and the relative standard
deviation of the cross-sectional velocity distribution is significantly reduced from 46,3 % before
optimization to 4,9 % after optimization. In addition, the relative standard deviations of the velocity
distribution of the comparative section I and II are reduced from 43,5 % and 27,7 % to 4,9 % and 4,7 %,
respectively.
b) with the use of turning vanes groups, the air flow in the air duct becomes smooth, and the vortices and
backflows are eliminated.
c) for the cross-section where the test holes are located, the air flow rate calculated from the average
velocity of the cross-section is 1 058,12 t/h, and the deviation from the reference value is 0,6 %; For the
comparative measurement section I, the air flow rate calculated from the average velocity of the section
is 1 058,35 t/h, and the deviation from the reference value is 0,6 %; For the comparative measurement
section II, the air flow rate calculated from the average velocity of the section is 1 057,86 t/h, and the
deviation from the reference value is 0,5 %.

Key
1 turning vanes groups
2 comparative cross-section II
3 comparative cross-section I
4 the cross-section where the On-site test holes are located
a
Ar outlet.
b
Air inlet.
Figure 14 — 3D model of turning vanes groups in an actual air duct based on Figure 10

a)  Velocity distribution and streamlines without any devices for improving flow conditions
b)  Velocity distribution and streamlines with turning vanes groups
Figure 15 — Comparison charts of the improvement effect of the use of turning vanes (numerical
simulation results)
Table 7 — Grid points numerical simulation results of the flow field at cross-sections with turning
vanes
Cross section where the test holes are located
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 24,7 27,9 27,2 27,2 27,3 27,2 27,4
-0,297 m/s 23,9 28,5 27,1 28,1 27,5 28,1 28,1
-0,134 m/s 24,8 28,9 27,3 28,4 27,8 28,4 28,4
0 m/s 24,7 29,0 27,5 28,6 28,0 28,6 28,5
0,134 m/s 25,0 29,2 27,6 28,7 28,2 28,7 28,6
0,297 m/s 24,7 29,4 27,8 28,9 28,3 28,8 28,7
0,447 m/s 24,6 29,1 27,9 28,5 28,1 28,1 28,2
Average velocity m/s 27,7
Relative standard deviation of
% 4,9
the velocity distribution
Calculated fluid mass flow rate t/h 1 058,12
Comparative measurement section I

TTaabblle 7 e 7 ((ccoonnttiinnueuedd))
X /L
i
-0,447 -0,29
...

ISO/TC 30/SC 5
Secretariat: SNV
Date: 2026-07-29xx
Influences of the Velocityvelocity and Temperature
Distributiontemperature distribution on Fluid Flow
Measurementfluid flow measurement by Usingusing Pitot Static
Tubesstatic tubes
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
Contents
Foreword . iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Influence of length of upstream/downstream conduit . 2
5.1 General . 2
5.2 Circular cross-sections . 2
5.3 Rectangular cross-sections . 12
6 Influence of velocity and temperature distribution uniformity . 14
6.1 General . 14
6.2 Velocity distribution uniformity . 14
6.3 Influence of temperature distribution uniformity . 17
7 Influence of devices for improving flow conditions . 20
7.1 General . 20
7.2 Turning vanes . 20
7.3 Profile developer . 24
7.4 Static mixer . 28
7.5 Multiple devices . 32
8 Influence of humidity . 41
Bibliography . 43

iii
Foreword
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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
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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 wasis 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)
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represent the latest information, which may be obtained from the patent database available at
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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 wasis prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed
conduits, Subcommittee SC 5, Velocity and mass methods.
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
Influences of the Velocityvelocity and Temperature
Distributiontemperature distribution on Fluid Flow
Measurementfluid flow measurement by Usingusing Pitot Static
Tubesstatic tubes
1 Scope
This document provides data and references to better guide measurement of fluid flow in closed conduits with
Pitot static tubes in many complex scenarios of large industrial applications.
This document illustrates influences of the following common conditions on fluid flow measurement by using
Pitot static tubes:
a) a) influence of length of upstream/downstream conduit,;
b) b) influence of velocity and temperature distribution uniformity,;
c) c) influence of devices for improving flow conditions,;
d) d) influence of humidity.
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 3966, Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes
ISO 7194, Measurement of fluid flow in closed conduits — Velocity-area methods of flow measurement in swirling
or asymmetric flow conditions in circular ducts by means of current-meters or Pitot static tubes
ISO 5167-2, 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, 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 5801, Fans — Performance testing using standardized airways
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3966:2025 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/
4 Symbols
The symbols given in ISO 3966 and the following symbols apply.
Symbol Quantity Dimensions SI unit
hr relative humidity of fluid — —
Y the index of asymmetry of the flow — —
5 Influence of length of upstream/downstream conduit
5.1 General
As mentioned in ISO 3966:2025, one of provides guidance on the requirements for use of Pitot tubes is, “For
guidance, . According to ISO 3966,it is normally assumed that to comply with these conditions there should
beis a length of upstream conduit between the beginning of the working section and any significant upstream
irregularity of at least 20 diameters of a circular cross-section (or 80 times the hydraulic radius of a conduit
of any cross-section shape). Similarly,ISO 3966 also recommends that there should be at least 5 diameters of
a circular cross-section (or 20 times the hydraulic radius of a conduit of any cross-section shape), between
the measuring cross-section and any significant downstream irregularity” to avoid asymmetry, swirl and
turbulences. This clause illustrates the influence of length of upstream/downstream conduit on velocity
profile by using Pitot tubes by experimental test and numerical simulation.
5.2 Circular cross-sections
5.2.1 Experimental Testtest
A test bench with circular conduit in laboratory wasis shown in Figure 1Figure 1. The measuring cross-section
wasis located at the long horizontal circular conduit of the test bench. The cross-sectional inner dimension of
the circular conduit wasis 0,6 m. The lengths of the upstream and downstream straight conduit of the
measuring cross-section wereare 13,0 m and 6,5 m, respectively.
Dimensions in metres
25582_ed1fig1a.EPS
a) photograph Photograph of long horizontal conduit section with measuring cross-section
25582_ed1fig1b.EPS
b)  Photograph of measuring cross-section and holes

c)  3D model diagram
Key
1 measurement hole in Vertical direction
2 measurement hole in Horizontal direction
b) photograph of measuring cross-section and holes
25582_ed1fig1c.EPS
Key
A flow direction
1 elbow conduit
2 comparative cross section
3 test measuring cross-section
4 straight conduit
a
Measurement hole in vertical direction.
b
Measurement hole in horizontal direction.
c) 3D Flow direction.
Inserted Cells
m
od
el
di
ag
ra
c
m
Figure 1 — Test Benchbench with circular conduit in laboratory
In this document, the influence of length of upstream/downstream circular conduit on velocity profile by using
Pitot tubes wasis demonstrated through the experimental test in laboratory and numerical simulation.
At the measuring cross-section of the test bench, to obtain the velocity distribution, the horizontal and vertical
directions wereare selected and there wereare 29 measuring points per direction (see Figure 2Figure 2).). The
selection of these measuring points wasis uniformly distributed along the centrelines of the measurement
cross-section and does not comply with the velocity-area method. Therefore, the obtained measurement
velocity data wereare only for reference in researching the flow velocity distribution.
25582_ed1fig2.EPS
Dimensions in millimetres
Key
X horizontal direction
Y vertical direction
Figure 2 — Measuring points at the measuring cross-section for velocity distribution
In the test, the medium wasis air. The relative humidity, pressure and density of the air wereare shown in
Table 1Table 1,, which also gives the measurement data of the velocity at the measuring cross section. The
fluid velocities wereare measured by using Pitot tubes and calculated from the differential pressure existing
between the total and static pressures of the Pitot tube placed at these measuring points.
Table 1 — Measurement data at the measuring cross-section for velocity distribution
Horizontal Directiondirection Vertical Directiondirection
Relative Pressur Relative
Temperature Density Temperature Pressure Density
humidity e humidity
3 3
(°°C) (kg/m ) (°°C) (kPa) (kg/m )
(%)% (kPa) (%)%
20,5 65 101,8 1,201 18,4 65 102,0 1,213
Measuring Differential Measuring Differential
Local velocity Local velocity
points radius pressure points radius pressure
(m/s) (m/s)
(mm) (Pa) (mm) (Pa)
-280 100,279 12,92 -280 106,094 13,23
-260 124,127 14,38 -260 129,280 14,60
-240 134,535 14,97 -240 144,919 15,46
-220 143,086 15,44 -220 156,500 16,06
-200 155,236 16,08 -200 164,406 16,46
-180 162,356 16,44 -180 171,064 16,79
-160 165,216 16,59 -160 175,698 17,02
-140 172,492 16,95 -140 177,694 17,12
-120 170,939 16,87 -120 182,499 17,35
-100 173,894 17,02 -100 180,745 17,26
-80 174,915 17,07 -80 184,611 17,45
-60 175,860 17,11 -60 184,307 17,43
-40 176,229 17,13 -40 183,821 17,41
-20 174,923 17,07 -20 184,234 17,43
0 174,796 17,06 0 186,085 17,52
20 173,684 17,01 20 184,692 17,45
40 174,463 17,04 40 185,482 17,49
60 173,712 17,01 60 184,367 17,44
80 171,655 16,91 80 181,787 17,31
100 172,366 16,94 100 182,160 17,33
120 169,259 16,79 120 180,632 17,26
140 163,205 16,49 140 175,065 16,99
160 158,207 16,23 160 168,248 16,66
180 147,744 15,69 180 165,612 16,52
200 137,603 15,14 200 154,296 15,95
220 128,610 14,63 220 142,291 15,32
240 114,932 13,83 240 134,029 14,87
260 93,164 12,46 260 115,936 13,83
280 88,966 12,17 280 104,355 13,12
Figure 3Figure 3 shows the velocity distributions at horizontal and vertical diameters. Obviously, the velocity
distribution exhibits relatively good central symmetry in both horizontal and vertical directions.
25582_ed1fig3a.EPS
a)  Horizontal direction
b)  Vertical direction
Key
rh radius of the position where the measuring points wereare located in the horizontal direction;
vh measured velocity at the position where the measuring points wereare located in the horizontal direction.
a) Horizontal direction
25582_ed1fig3b.EPS
Key
r radius of the position where the measuring points wereare located in the vertical direction;
v
v measured velocity at the position where the measuring points wereare located in the vertical direction.
v
b) Vertictal direction
Figure 3 — Measuring velocity distributions at horizontal and vertical diameters
Figure 4Figure 4 gives positions of the measuring points respectively according to regulations (velocity-area
5 [1]
method) of ISO 3966:2025 and EN 12599 :2013 .
25582_ed1fig4a.EPS 25582_ed1fig4b.EPS

a) according  According to ISO 3966:2005 b) according  According to EN 12599:2013
Key
X horizontal direction
Y vertical direction
Figure 4 — Measuring points at the measuring cross-section for velocity measurement
Table 2Table 2 shows the measuring point statistical results of the flow field at the measuring cross section
according to ISO 3966:2025 and EN 12599:2013. The test results indicate that, as the measuring cross-section
wasis far enough away from any disturbances, the relative standard deviation of the velocity distribution at
the cross section wasis maintained at the level which wasis no more than 15 %. For guidance, it wasIt is
normally assumed that the uniformity of velocity distribution is acceptable with σ ≤ 15 %.
v
Table 2 — Measurement data at the measuring cross-section for velocity measurement
Local velocity ( Relative standard
Measurin
Average velocity at deviation of the
m/s)
g points
the cross section velocity distribution at
radius (
the cross section
(m/s)
Horizontal direction Vertical direction
mm)
(%)%
Refer to ISO 3966:2025
-289 11,67 12,05
-254 13,95 14,66
-207 15,74 16,32
-171 16,44 16,85
-86 16,98 17,29
15,04 13,48
86 17,00 17,41
171 16,00 16,62
207 15,05 15,89
254 13,19 14,21
289 11,34 12,07
Refer to EN 12599:20132012
-285 11,98 12,44
-251 14,10 14,82
-212 15,60 16,21
-164 16,53 16,92
-95 16,96 17,26
15,11 12,63
95 16,96 17,37
164 16,15 16,73
212 14,89 15,75
251 13,33 14,35
285 11,57 12,37
Besides, two indexes wereare considered to characterize the symmetry of the velocity distribution:
a) a) According to ISO 7194:2008, for circular ducts, the index of asymmetry of the flow (Y) wasis
defined to evaluate the asymmetric flow conditions and wasis not advisable to be greater than 0,15 to
make a measurement. The index of asymmetry of the flow (Y) can be calculated by the following Formula
(1) (1)::
(1)
𝑛𝑛 2
∑ ¯
1 (𝑢𝑢−𝑣𝑣)
𝑖𝑖=1 𝑖𝑖 1⁄2
𝑌𝑌 = [ ] (1)
𝑣𝑣¯ 𝑛𝑛−1
where
n wasis the number of radii traversed (4, 6 or 8);
ui wasis the mean velocity calculated from the individual point velocity measurements at i radius, m/s;
was 𝑣𝑣¯ is the mean axial velocity calculated from all of the individual point velocity measurements, m/s.
b) b) According to EN 12599:2012, for rectangular ducts and circular ducts, the following formular
wasformula is used as a measure of the irregularity, Irr, of the velocity profile and can be calculated by the
following Formula (2) (2). In the case of a rectangular cross-section, the maximum and minimum values
of mean velocity wereare selected from the quarters of the total cross-section, of side length equal to half
the duct side length. In the case of a circular cross-section, the mean values wereare taken from four
measurement radius at right angles to one another. For the calculation of u the velocity in the boundary
min
layer at the wall of the duct wasis neglected.
(2)
|𝑢𝑢 −𝑢𝑢 |
𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚𝑖𝑖𝑛𝑛
𝐼𝐼𝐼𝐼𝐼𝐼 = (2)
2𝑣𝑣¯
where
umax wasis the maximum of the arithmetic mean of velocities in a quarter of the measuring cross-section or at a radius,
m/s;
umin wasis the minimum of the arithmetic mean of velocities in a quarter of the measuring cross-section or at a radius,
m/s;
was 𝑣𝑣¯ is the arithmetic mean over the entire cross section, m/s.
For example, based on the data in Table 2Table 2,, the index of asymmetry of the flow (Y) at the measuring
cross section wasis 0,026 5 which can completely meet the requirement of ISO 7194:2008.
5.2.2 Numerical Simulationsimulation
The influence of length of upstream/downstream circular conduit on velocity profile wasis investigated
further by numerical simulations. Figure 1Figure 1 c) shows the 3D model diagram of the test bench. The
length of the upstream straight section of the comparative measuring section wasis 3,0 m. Figure 5Figure 5
shows the velocity distribution diagram at the comparative measuring cross-section and test measuring cross-
section which wereare given by numerical simulation. Figure 6Figure 6 shows the velocity distribution
contours at measuring cross-sections.
25582_ed1fig5a1.EPS 25582_ed1fig5a2.EPS

Horizontal direction Vertical direction
a) comparative  Comparative measuring cross-section
25582_ed1fig5b1.EPS 25582_ed1fig5b2.EPS

Horizontal direction Vertical direction
b) test  Test measuring cross-section
Key
r radius of the position where the measuring points wereare located in the horizontal direction;
h
v measured velocity at the position where the measuring points wereare located in the horizontal direction.
h
rv radius of the position where the measuring points wereare located in the vertical direction;
vv measured velocity at the position where the measuring points wereare located in the vertical direction.
Figure 5 — Numerical simulation velocity distributions at horizontal and vertical directions
25582_ed1fig6a.EPS 25582_ed1fig6b.EPS

a) comparative  Comparative measuring cross-section b) test  Test measuring cross-section
Figure 6 — Velocity distribution contours diagram
Figure 5Figure 5 shows the velocity distribution at the measuring sections of the test bench (numerical
simulation results). The numerical simulation data of the velocity distribution at the test measuring cross-
section wereare consistent in trend with the experimental measurement data shown in Figure 3Figure 3. At
the comparative measuring cross-section, especially in horizontal direction, the symmetry of the velocity
distribution wasis poorly developed. Table 3Table 3 shows numerical simulation results of the points at the
horizontal and vertical directions of measuring cross section. These points refer to ISO 3966:2025 and
wereare the same as Figure 3Figure 3 a). Results show that:
a) 1) Atat the test measuring cross-section with satisfactory conditions of the upstream and
downstream conduits length, the relative standard deviation of the velocity distribution wasis 13,99 %
and the index of asymmetry of the flow wasis 0,012 4;, and
b) 2) Atat the comparative measuring cross-section with the length of upstream conduit between
the elbow and measuring section only 5 times the conduit diameter (not meet the requirements for use
of Pitot tubes in ISO 3966: 2025), the relative standard deviation of the velocity distribution wasis
19,77 % (>15 %) and the index of asymmetry of the flow wasis 0,159 4 (>0,15);
Table 3 — Numerical simulation data at the measuring cross-section for velocity measurement
Local velocity ( Relative
Average standard
m/s)
Measurin
Index of
velocity at deviation of the
g points
asymmetry
the cross velocity
radius (
of the flow
Vertical section distribution at
Horizontal direction
(Y)
mm)
direction
the cross section
(m/s)
(%)%
Comparative measuring cross-section
-289 7,43 11,89
-254 9,81 15,29
-207 11,11 16,00
-171 12,42 16,40
-86 15,55 17,03
14,65 19,77 0,159 4
86 17,72 17,01
171 17,79 16,41
207 17,79 15,97
254 16,99 15,38
289 12,85 12,10
Test measuring cross-section
-289 11,35 11,60
-254 14,20 14,83
-207 15,49 16,28
-171 16,30 16,80
-86 17,27 17,56
15,12 13,99 0,014 4
86 17,46 17,37
171 16,51 16,39
207 15,96 15,70
254 14,45 14,29
289 11,35 11,21
5.3 Rectangular cross-sections
The influence of length of upstream/downstream rectangular conduit on velocity profile by using Pitot tubes
wasis demonstrated numerical simulation.
Figure 7Figure 7 shows a 3D model of a hypothetical rectangular air duct. The cross-sectional inner dimension
of the air duct wasis 4,4 m × 4,0 m. The lengths of the straight sections upstream and downstream on the
hypothetical simulation cross-section wereare 84,0 m and 21,0 m, respectively, which meet the requirement
for use of Pitot tubes. Figure 8Figure 8 shows the numerical simulation results of the velocity distribution
contours at the simulation cross section. According to log-Chebyshev method mentioned in ISO 3966:2025, a
total of 49 selected data collection grid points at the simulation cross-section wereare shown in
Figure 9Figure 9. Table 4. Table 4 shows the numerical simulation results of the velocity distribution at the
cross section by using grid point statistical method according to Log-Chebyshev method. In this simulation
case, the boundary conditions of this numerical simulation include the mass flow rate of the air which wasis
1 052,28 t/h (as the reference value for comparison). The numerical simulation results indicate that:
a) 1) Thethe velocity distribution at the simulation cross section wasis uniform and the relative
standard deviation of the velocity distribution wasis 6,7 %.%, and
b) 2) Forfor the simulation cross section, the fluid flow rate calculated from the average velocity of
the cross section wasis 1 061,51 t/h, with a deviation of 0,9 % from the reference value.
25582_ed1fig7.EPS
Dimensions in millimetres
Key
A flow direction
1 hypothetical simulation cross-section (4,4 m × 4,0 m)
a
Flow direction.
Figure 7 — 3D model diagram of ana hypothetical rectangular air duct
25582_ed1fig8.EPS
Figure 8 — Velocity distribution contour at the simulation cross section
25582_ed1fig9.EPS
Key
X /L The position of the measuring points corresponds to ratio of the abscissa X in relation to the centre of the section to the length of
i i
the section
Y /H The position of the measuring points corresponds to ratio of the ordinate Y in relation to the centre of the section
i j
to the height of the section
Figure 9 — Selected grid points at the hypothetical simulation cross-section
(Log-Chebyshev method according to ISO 3966:2025)
Table 4 — Grid points numerical simulation results of the flow field at the hypothetical cross-section
(Log-Chebyshev method)
Statistical results of local velocity at the hypothetical simulation cross-section
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 23,4 26,3 27,1 27,0 26,6 25,4 21,2
-0,297 m/s 27,6 28,7 28,6 28,3 28,0 27,4 25,5
-0,134 m/s 28,7 29,3 29,1 28,8 28,5 28,2 27,0
0 m/s 28,9 29,5 29,4 29,2 28,9 28,6 27,4
0,134 m/s 28,8 29,7 29,6 29,4 29,2 28,8 27,4
0,297 m/s 27,7 29,6 29,7 29,6 29,5 29,0 26,7
0,447 m/s 23,7 28,0 28,8 28,9 28,7 27,5 23,1
Average velocity m/s 27,9
Relative standard deviation of
% 6,7
the velocity distribution
Calculated fluid mass flow rate t/h 1 061,51
6 Influence of velocity and temperature distribution uniformity
6.1 General
Actually, in many industrial application scenarios, the measurement conditions with closed conduits cannot
meet the requirements for straight conduit lengths upstream and downstream of the measuring cross-section
as specified in 5.1Section 5.1. Under such conditions, special attention is paid to the influence of velocity and
temperature distribution uniformity at the measuring cross-section when using the velocity-area method with
Pitot tubes to measure airflow velocity. This clause illustrates the influence of velocity and temperature
distribution uniformity by numerical simulation research.
6.16.2 Velocity distribution uniformity
Figure 10Figure 10 shows a 3D model of an actual air duct in a thermal power plant. There wereare three 90°
elbows in the entire duct, and the cross-sectional dimension of the hot secondary air duct wasis 4,4 m×4,0 m.
The straight conduit section wasis 17,0 m long. The measuring cross-section where the on-site test holes
wereare located wasis 4,6 m (approximately 4,4 times the hydraulic radius) away from the upstream elbow
and 12,4 m (approximately only 11,9 times the hydraulic radius) away from the downstream elbow. The
comparative cross-section I wasis 5,5 m (approximately 5,3 times the hydraulic radius) away from the
upstream elbow and 11,5 m (approximately only 11,0 times the hydraulic radius) away from the downstream
elbow. The comparative cross-section II wasis 11,5 m (approximately 11,0 times the hydraulic radius) away
from the upstream elbow and 5,5 m (approximately only 5,3 times the hydraulic radius) away from the
downstream elbow. Figure 11Figure 11 shows the numerical simulation results of the velocity distribution
contours at the measuring and comparative cross-sections. Table 5Table 5 shows the numerical simulation
results of the velocity distribution at the cross-sections by using grid points statistical method according to
Log-Chebyshev method (see Figure 9Figure 9).). In this simulation case, for guidance and as reference, the
boundary conditions of this numerical simulation include the mass flow rate of the hot air wasis 1 052,28 t/h.
The numerical simulation results indicate that:
a) 1) Forfor the cross-section where the onsite test holes wereare located, the relative standard
deviation of the velocity distribution wasis 46,3 % which wasis far from the standard values of a uniform
flow field and the calculated fluid mass flow rate wasis 1 150,72 t/h, with a significant deviation of 9,4 %
from the reference value. It can be seen that in this case the positions of the on-site measuring points
wereare extremely unreasonable;.
b) 2) Forfor the comparative measuring section I, it’s close to the onsite test holes and the ratio of
the upstream and downstream straight pipe sections of the measured cross-section is about 1/2. The
relative standard deviation of the velocity distribution is 43,5 % which is far from the standard values of
a uniform flow field and the calculated fluid mass flow rate is 1 127,78 t/h, with a deviation of 7,2 % from
the reference value;.
c) 3) Forfor the comparative measuring section II, the ratio of the upstream and downstream
straight pipe sections of the measured cross-section is about 2/1. The relative standard deviation of the
velocity distribution is 27,7 % and the calculated fluid mass flow rate is 1 108,66 t/h, with a deviation of
5,4 % from the reference value;.
For this kind measurement condition that the length of the straight conduit section cannot meet the
requirement as specified in 5.1Section 5.1,, about the flow measurement, there wereare always obvious flow
high-speed and low-speed areas with a significant relative standard deviation of the velocity distribution
which can lead to a deviation between measured values and true values of fluid flow rate. Further, if the
objective measurement conditions for the straight conduit section length wereare indeed limited, the
measuring cross-section position is positioned at a location with flow uniformity whenever possible. If
necessary, devices for improving flow conditions (see 7.2Clause 7.2)) are employed to ensure that the velocity
deviation at the measurement cross-section remains below 15 %, because a small velocity deviation will
enhance the accuracy of calculating conduit flow rate by using velocity-area method with Pitot tubes.
25582_ed1fig10.EPS
Dimensions in metres
Key
A air inlet
B flow direction
C air outlet
1 comparative cross-section II
2 comparative cross-section I
3 the cross-section where the Onon-site test holes are located
a
Air inlet.
b
Flow direction.
c
Air outlet.
Figure 10 — 3D model of an actual air duct in a thermal power plant
25582_ed1fig11a.EPS
a)  On-site measuring cross-section
25582_ed1fig11b.EPS 25582_ed1fig11c.EPS

b) comparative  Comparative measuring cross-section I c) comparative  Comparative measuring cross-section II
Figure 11 — Velocity distribution contours at the onsite measuring and comparative
cross-sections
Table 5 — Grid points numerical simulation results of the flow field at cross-sections
Cross section where the onsite test holes wereare located
Xi/L
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 34,5 40,0 43,1 44,3 44,7 44,5 43,1
-0,297 m/s 36,1 36,0 36,5 38,0 40,7 43,7 44,6
-0,134 m/s 35,2 29,6 25,0 25,3 31,0 41,7 45,4
0 m/s 32,5 23,2 15,4 16,1 26,0 41,3 45,6
0,134 m/s 27,9 16,1 7,1 9,9 25,7 42,4 45,7
0,297 m/s 18,3 8,4 2,0 4,0 23,7 43,8 45,7
0,447 m/s 7,9 9,7 9,1 6,6 27,2 44,2 44,6
Average velocity m/s 30,1
Relative standard deviation of
% 46,3
the velocity distribution
Calculated fluid mass flow rate t/h 1 150,72
Comparative measuring cross-section I
Xi/L
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 34,2 38,7 41,5 42,9 43,7 43,9 42,5
-0,297 m/s 35,6 34,9 34,7 35,9 38,9 42,6 43,9
-0,134 m/s 35,0 29,1 23,5 22,8 27,9 39,7 44,4
0 m/s 33,2 24,4 15,8 14,7 22,7 38,9 44,6
0,134 m/s 30,0 19,5 9,5 9,2 20,6 39,7 44,6
0,297 m/s 22,3 13,7 5,7 3,9 17,3 41,1 44,7
0,447 m/s 13,2 13,4 11,6 7,2 19,2 42,9 43,5
Average velocity m/s 29,5
Relative standard deviation of
% 43,5
the velocity distribution
Calculated fluid mass flow rate t/h 1 127,78
Comparative measuring cross-section II
X /L
i
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Yi/H
-0,447 m/s 33,9 35,5 36,9 38,3 39,7 40,7 38,8
-0,297 m/s 34,4 32,3 30,9 31,4 33,7 37,8 40,0
-0,134 m/s 33,6 28,2 23,2 21,8 24,4 32,6 39,8
0 m/s 32,4 26,0 19,5 17,0 19,3 29,6 39,5
0,134 m/s 30,9 24,7 18,1 14,9 16,1 27,5 39,3
0,297 m/s 27,7 24,0 19,9 17,0 15,7 28,4 40,0
0,447 m/s 24,2 24,2 23,0 20,5 17,1 34,8 39,6
Average velocity m/s 29,0
Relative standard deviation of
% 27,7
the velocity distribution
Calculated fluid mass flow rate t/h 1 108,66
6.26.3 Influence of temperature distribution uniformity
Figure 12Figure 12 a) shows a 3D model of an actual mixed air duct for hot and cold air. The dimension of the
hot air duct wasis 2,0 m × 1,2 m and the dimension of the cold air duct wasis 0,8 m × 0,6 m. The cold primary
air duct wasis connected to the side of the hot air duct (see Figure 12Figure 12 b)), and the straight section
where the flow measurement section wasis located wasis 3,7 m long. The simulation measuring cross-section
(2,0 m × 1,2 m) wasis 2,6 m far away from the upstream elbow.
Dimensions in metres
25582_ed1fig12a.EPS
25582_ed1fig12b.EPS
a)  3D model b)  Field photo
Key
A cold air inlet
B hot air inlet
C mixed air outlet
1 measuring cross section
2 elbow
a
Cold air inlet.
b
Hot air inlet.
c
Mixed air outlet.
Figure 12 — Actual mixed air duct for hot and cold air
To illustrate the influence of temperature distribution uniformity, two simulation cases wereare done. In this
first simulation case, the boundary conditions of this numerical simulation include the mass flow rate of the
hot air wasis 65,57 t/h with a temperature of 573 K, the mass flow rate of the cold air wasis 26,47 t/h with a
temperature of 313 K. In this second simulation case, the mass flow rate of the hot air wasis 120,05 t/h with a
temperature of 313 K, the mass flow rate of the cold air wasis 26,47 t/h with a temperature of 313 K. By
comparing these two simulation cases, it can be seen that the inlet air velocities of hot and cold air wereare
deliberately kept consistent. Besides, about the second simulation case, since the temperatures of the hot air
and the cold air wereare the same, so there wasis no temperature deviation in the flow field in the air duct.
Figure 13Figure 13 shows the numerical simulation results of the velocity and temperature distribution
contours at the measuring cross-section. Table 6Table 6 shows the statistical results of the velocity and
temperature at the measuring section. The numerical simulation results indicate that:
a) 1) Inin the first simulation case, it can be seen that the cold air wasis difficult to penetrate the hot
air near the connection and it takes a long development length to fill the entire cross section. The length
of the existing conduit section wasis far from meeting the requirements, resulting in an uneven
temperature distribution at the measuring cross section. The relative standard deviation of the
temperature distribution at the measuring cross section wasis 11,8 %;%. The relative standard deviation
of the velocity distribution at the measuring cross section wasis 28,1 %; For the measuring cross section,
the fluid flow rate calculated from the average velocity and average temperature of the cross section wasis
96,83 t/h, with a deviation of 5,2 % from the reference value.
b) 2) Inin the second simulation case, it wasis obvious that there wasis no temperature deviation at
the measuring cross section. The relative standard deviation of the velocity distribution at the measuring
cross section wasis 21,2 %. However, for the measuring cross section, the fluid flow rate calculated from
the average velocity of the cross section wasis 147,14 t/h, with only a deviation of 0,4 % from the
reference value.
c) 3) Obviously, the comparison result demonstrates that temperature distribution uniformity has
significant influences on the accuracy of fluid flow measurement by using velocity-area method with Pitot
tubes.
25582_ed1fig13a.EPS
25582_ed1fig13b.EPS 25582_ed1fig13c.EPS

Volume temperature distribution temperature distribution at the velocity distribution at the measuring
measuring cross-section cross-section
a) the first  First simulation case with the temperature of hot air is 573 K
25582_ed1fig13d.EPS 25582_ed1fig13e.EPS

streamline of fluid field velocity distribution at the measuring cross-section
b) the second  Second simulation case with the temperature of hot air is 313 K
Figure 13 — Numerical simulation results of the velocity and temperature distribution contours
Table 6 — Uniformity statistics of velocity and temperature distribution at the measuring cross
section (numerical simulation results)
the firstFirst simulation case with the temperature of hot air is 573 K
Flow field Temperature field
Relative standard Relative standard
Average velocity Average temperature
deviation deviation
m/s K
% %
15,2 28,1 504 11,8
Calculated fluid flow rate Referred fluid flow rate Deviation
t/h t/h %
96,83 92,04 5,2
the second simulation case with the temperature of hot air is 313 K
Flow field Temperature field
Relative standard Relative standard
Average velocity Average temperature
deviation deviation
m/s K
% %
15,2 21,2 313 0
Calculated fluid flow rate Referred fluid flow rate Deviation
t/h t/h %
147,14 146,52 0,4
For this kind measurement condition that the length of the straight conduit section cannot meet the
requirement to make the fluids of different temperatures to mix thoroughly, devices for improving the
uniformity of temperature distribution (see 7.4Clause 7.4)) are employed to ensure that the temperature
deviation (σT) at the measurement cross-section remains below 5 %. For guidance, when the fluid
temperature range wasis 273 K~623 K, it wasis normally assumed that the uniformity of temperature
distribution wasis acceptable with σ ≤ ≤ 5 %.
T
7 Influence of devices for improving flow conditions
7.1 General
Different devices for improving flow conditions wereare given in ISO 3966:2025, including anti-swirl device,
profile developer, turning vanes and Static mixer. This chapter gives the experimental and numerical
simulation studies of above devices intend to illustrate its applicability and effectiveness.
7.2 Turning vanes
If there wereare elbows or extenders near the measuring cross-section, turning vanes can be used to smooth
the flow direction and improve the uniformity of the velocity distribution. The turning vanes consist of arc or
flat plates. As mentioned in 6.16.1,, if necessary, devices for improving flow conditions are performed to
improve the velocity distribution uniformity. Based on the example given in 6.16.1,, turning vanes wereare
arranged at the elbows to improve the uniformity of velocity distribution at the measuring section, see
Figure 14Figure 14. Figure 15. Figure 15 shows the numerical simulation results of the of the velocity
distribution contours at measuring cross-sections after optimization. Table 7Table 7 shows the numerical
simulation results of the velocity distribution at the cross-sections by using grid points statistical method
according to Log-Chebyshev method (see Figure 9Figure 9).). In this clause’s simulation example, the
boundary conditions wereare the same with 6.1clause 6.1 for guidance and reference, including that the mass
flow rate of the hot air wasis 1 052,28 t/h. The numerical simulation results indicate that:
a) 1) Thethe uniformity of the flow velocity distribution at the cross-section where the test holes
wereare located wasis significantly improved, the average cross-sectional velocity wasis 27,7 m/s, and
the relative standard deviation of the cross-sectional velocity distribution is significantly reduced from
46,3 % before optimization to 4,9 % after optimization. In addition, the relative standard deviations of the
velocity distribution of the comparative section I and II wereare reduced from 43,5 % and 27,7 % to 4,9 %
and 4,7 %, respectively;.
b) 2) Withwith the use of turning vanes groups, the air flow in the air duct becomes smooth, and the
vortexsvortices and backflows wereare eliminated;.
c) 3) Forfor the cross-section where the test holes wereare located, the air flow rate calculated from
the average velocity of the cross-section wasis 1 058,12 t/h, and the deviation from the reference value
wasis 0,6 %; For the comparative measurement section I, the air flow rate calculated from the average
velocity of the section wasis 1 058,35 t/h, and the deviation from the reference value wasis 0,6 %; For the
comparative measurement section II, the air flow rate calculated from the average velocity of the section
wasis 1 057,86 t/h, and the deviation from the reference value wasis 0,5 %.
25582_ed1fig14.EPS
Key
A air outlet
B air inlet
1 turning vanes groups
2 comparative cross-section II
3 comparative cross-section I
4 the cross-section where the On-site test holes are located
a
Ar outlet.
b
Air inlet.
Figure 14 — 3D model of turning vanes groups in an actual air duct based on Figure 10Figure 10
25582_ed1fig15a1.EPS 25582_ed1fig15a2.EPS

a) velocity  Velocity distribution and streamlines without any devices for improving flow conditions
25582_ed1fig15b1.EPS 25582_ed1fig15b2.EPS

b) velocity  Velocity distribution and streamlines with turning vanes groups
Figure 15 — Comparison charts of the improvement effect of the use of turning vanes (numerical
simulation results)
Table 7 — Grid points numerical simulation results of the flow field at cross-sections with turning
vanes
Cross section where the test holes wereare located
Xi/L
-0,447 -0,297 -0,134 0 0,134 0,297 0,447
Y /H
i
-0,447 m/s 24,7 27,9 27,2 27,2 27,3 27,2 27,4
-0,297 m/s 23,9 28,5 27,1 28,1 27,5 28,1 28,1
-0,134 m/s 24,8 28,9 27,3 28,4 27,8 28,4 28,4
0 m/s 24,7 29,0 27,5 28,6 28,0 28,6 28,5
0,134 m/s 25,0 29,2 27,6 28,7 28,2 28,7 28,6
0,297 m/s 24,7 29,4 27,8 28,9 28,3 28,8 28,7
0,447 m/s 24,6 29,1 27,9 28,5 28,1 28,1 28,2
Average velocity m/s 27,7
Relative standard deviation of
% 4,9
the velocity distribution
Calculated fluid mass flow rate t/h 1 058,12
Comparative meas
...