ISO/TR 20461:2023

TECHNICAL ISO/TR
REPORT 20461
Second edition
2023-02
Determination of uncertainty for
volume measurements of a piston-
operated volumetric apparatus using
a gravimetric method
Détermination de l’incertitude de mesure pour les mesurages
volumétriques des appareils volumétriques à piston au moyen de la
méthode gravimétrique
Reference number
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 S c op e . 1
2 Nor m at i ve r ef er enc e s . 1
3 Terms and definitions . 1
4 Modelling the measurement.1
5 G eneral procedure for the uncertainty calculation . 3
6 S tandard uncertainty components associated with the measuring system
(gravimetric measurement procedure) . 4
6.1 G eneral information on standard uncertainty components estimation. 4
6.2 S tandard uncertainty of weighing (balance indication) . 5
6.3 S tandard uncertainty of temperature . 5
6.4 S tandard uncertainty of water density . 6
6.5 S tandard uncertainty of air density . 6
6.6 S tandard uncertainty of weights density . 7
6.7 S tandard uncertainty related to air cushion effects . 7
7 S tandard uncertainty components associated with the POVA . 7
7.1 S tandard uncertainty of cubic expansion coefficient . 7
7.2 S tandard uncertainty of resolution . 8
7.3 S tandard uncertainty of setting . 8
8 S tandard uncertainty components associated with the liquid delivery process .8
8.1 R epeatability (experimental standard deviation) . 8
8.2 Reproducibility . 8
9 C ombined standard uncertainty of measurement associated with the volume V .9
ref
10 Sensitivity coefficients .9
11 Choice of an appropriate coverage factor (k) .10
12 Expanded uncertainty of measurement associated with the volume V .10
ref
13 E xample for determining the uncertainty of the volume measurement of POVA .10
13.1 M easurement conditions . 10
13 . 2 R e s u lt s . .13
13.2.1 C alculations . .13
13.2.2 Uncertainty in use and corrections for pressure changes .13
13.2.3 General remarks .13
13.2.4 Note on the conformity of the ISO 8655 series with ISO/IEC Guide 98-3 .13
Annex A (informative) Approaches for the estimation of uncertainty in use of a single
delivered volume .14
Annex B (informative) Volume correction due to pressure changes .17
Bibliography .18
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 48, Laboratory equipment.
This second edition cancels and replaces the first edition (ISO/TR 20461:2000), which has been
technically revised and cancels ISO/TR 20461:2000/Cor 1:2008.
The main changes are as follows:
— the term “standard deviation of the mean delivered volume” has been replaced in this document by
“repeatability” according to ISO/IEC Guide 99 ;
— a new uncertainty calculation example has been supplied;
— new uncertainty components have been added, namely, reproducibility, air cushion and resolution;
— a new Annex A concerning approaches for the estimation of uncertainty in use of a single delivered
volume has been added;
— a new Annex B concerning volume correction due to pressure changes has been added.
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
Introduction
The example given in this document is informative and supports the requirements found in
ISO 8655-6:2022, 9.6 and ISO 8655-7:2022, 4.2, to perform an estimation of measurement uncertainty
when calibrating POVA according to the measurement procedures described in these documents and
the principles of ISO/IEC Guide 98-3.
The revision of this document coincides with a major revision of the ISO 8655 series in 2022, reflecting
the state-of-the-art measurement procedures and approaches for the estimation of measurement
uncertainty.
v
TECHNICAL REPORT ISO/TR 20461:2023(E)
Determination of uncertainty for volume measurements
of a piston-operated volumetric apparatus using a
gravimetric method
1 S cope
This document gives detailed information regarding the evaluation of uncertainty for the gravimetric
[1]
reference measurement procedure specified in ISO 8655-6 and the gravimetric procedure specified
[1] [16]
in ISO 8655-7:2022 , Annex A, according to the ISO/IEC Guide 98-3 .
This document also includes the determination of other uncertainty components related to the liquid
delivery process of a piston-operated volumetric apparatus (POVA), e.g. repeatability and handling.
Furthermore, it provides examples for the calculation and application of the uncertainty of the mean
delivered volume and the uncertainty in use of a single delivered volume.
2 Normat ive 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 8655-1, Piston-operated volumetric apparatus — Part 1: Terminology, general requirements and user
recommendations
ISO/IEC Guide 2, Standardization and related activities — General vocabulary
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 8655-1, ISO/IEC Guide 2 and
ISO/IEC Guide 99 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 Modelli ng the measurement
In the gravimetric reference measurement procedure, a quantity of water is delivered by the instrument
under calibration (POVA) into a vessel that is weighed on a balance. Ambient conditions are recorded so
that the liquid density and air density can be determined and, consequently, the delivered volume can
be calculated from this data.
Furthermore, the influence of possible evaporation and possible temperature difference of the
POVA from the reference calibration temperature are taken into consideration as corrections in the
mathematical model of the calibration.
The general formula for calculation of the volume at the reference temperature of 20 °C, V (at a
reference temperature of 27 °C, V ), from the balance indication of the delivered water as described in
[2] [1]
ISO 4787 and the ISO 8655 series , is given by Formula (1). When a liquid other than water is used,
Formula (1) is modified accordingly.
ρ
1  
A
Vm=−mm+ × ×−11×−[]γ ()tt− (1)
()
refL Eevap   Wref
ρρ− ρ
 
WA B
where
V is the calculated volume at the reference temperature, in ml;
ref
m is the balance indication of the weighing vessel after water delivery, in g;
L
m is the balance indication of the weighing vessel before water delivery, in g (m = 0 in case the
E E
balance was tared with the weighing vessel);
m is the estimated evaporated mass within a test cycle, in g;
evap
ρ is the density of air, in g/ml, at the temperature, humidity and atmospheric pressure of the
A
test, see Formula (3);
ρ is the density of the reference weights (typically 8 g/ml);
B
ρ is the density of water at the test temperature (in units of °C), in g/ml, calculated with the
W
“T
...