ISO/TR 16494-2:2019

TECHNICAL ISO/TR
REPORT 16494-2
First edition
2019-03
Heat recovery ventilators and energy
recovery ventilators — Method of test
for performance —
Part 2:
Assessment of measurement
uncertainty of performance
parameters
Reference number
©
ISO 2019
© ISO 2019
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
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Explanatory notes useful in laboratory application . 3
5.1 Uncertainty . 3
5.2 Confidence level . 4
5.3 Evaluation of uncertainties . 4
5.4 Steps in evaluation of uncertainty in measurements . 4
5.5 Uncertainty of measurements . 4
5.5.1 Uncertainty of individual measurements . 4
5.5.2 Uncertainty of a mean value from several measurements . 6
5.5.3 Uncertainty of a value obtained by using a smoothing curve . 7
6 Evaluation of uncertainty . 7
6.1 Airflow performance . 7
6.1.1 Air volume flow rate . 7
6.1.2 Air mass flow rate . 8
6.1.3 Static pressure differential . 8
6.2 Unit exhaust air transfer ratio . 9
6.2.1 Measured parameters affecting test results . 9
6.2.2 UEATR measurement . 9
6.2.3 Uncertainty calculation — General case . 9
6.3 Net supply airflow . 9
6.3.1 Net supply airflow ducted units. 9
6.3.2 Net supply airflow unducted ventilators .10
6.4 Gross effectiveness .11
6.4.1 Measured parameters affecting the measurement .11
6.4.2 Gross effectiveness measurement .11
6.4.3 Uncertainty calculation — General case .12
6.5 Coefficient of energy .12
6.5.1 Coefficient of energy: Ducted ventilators .12
6.5.2 Coefficient of energy — Unducted ventilators .14
6.6 Effective work (EW) .16
6.6.1 Measured parameters affecting the measurement .16
6.6.2 Effective work: Ducted or unducted ventilators .16
6.6.3 Uncertainty calculation — General case .16
6.6.4 Uncertainty calculation — Specific case.16
Annex A (informative) Uncertainty budget sheets .17
Annex B (informative) Determination of indirect contribution to uncertainty, U(C ) .42
I
Bibliography .43
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 86, Refrigeration and air-conditioning,
Subcommittee SC 6, Testing and rating of air-conditioners and heat pumps.
A list of all parts in the ISO 16494 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/members .html.
iv © ISO 2019 – All rights reserved

Introduction
This document is intended to be a practical guide to assist laboratory personnel in evaluating the
uncertainties in the measurement of the performance of ventilators falling under the scope of
ISO 16494:2014. It contains a brief introduction to the theoretical basis for the calculations, and
contains examples of uncertainty budget sheets that can be used as a basis for the determination of the
uncertainty of measurement.
TECHNICAL REPORT ISO/TR 16494-2:2019(E)
Heat recovery ventilators and energy recovery
ventilators — Method of test for performance —
Part 2:
Assessment of measurement uncertainty of performance
parameters
1 Scope
This document provides guidance for practical applications of those principles in the measurement
of the performance of ventilators falling under the scope of ISO 16494:2014. The references listed in
the Bibliography give detailed information on the principles and theory of uncertainty as applied to
measurements.
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 16494, Heat recovery ventilators and energy recovery ventilators — Method of test for performance
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16494 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http: //www .electropedia .org/
— ISO Online browsing platform: available at https: //www .iso .org/obp
3.1
calibration
operation that, under specified conditions, in a first step establishes a relation between the quantity
values with measurement uncertainties provided by measurement standards and corresponding
indications with associated measurement uncertainties and, in a second step, uses this information to
establish a relation for obtaining a measurement result from an indication
3.2
correction
modification applied to a measured quantity value to compensate for a known systematic effect
3.3
instrumental drift
continuous change in an indication, related neither to a change in the quantity being measured nor to a
change of any recognized influence quantity
3.4
resolution
smallest change in a quantity being measured that causes a perceptible change in the corresponding
indication
Note 1 to entry: In the case of a digital instrument, this value corresponds to the number of digits of the reading
of the instrument. This value might be different on the overall range of the instrument.
3.5
stability
ability of a measuring instrument or measuring system to maintain its metrological properties constant
with time
3.6 Type of evaluation of uncertainty
3.6.1
type A evaluation of standard uncertainty
evaluation of standard uncertainty based on any valid statistical method for treating data
Note 1 to entry: Examples are calculating the standard deviation of the mean of a series of independent
observations, using the method of least squares to fit a curve to data in order to evaluate the parameters of the
curve and their standard deviations, and carrying out an analysis of variance in order to identify and quantify
random effects in certain kinds of measurements. If the measurement situation is especially complicated, one
should consider obtaining the guidance of a statistician.
3.6.2
type B evaluation of standard uncertainty
evaluation of standard uncertainty that is usually based on scientific judgment using all the relevant
information available
Note 1 to entry: Relevant information can include previous measurement data, experience with, or general
knowledge of, the behaviour and property of relevant materials and instruments, manufacturer’s specifications,
data provided in calibration and other reports, and uncertainties assigned to reference data taken from
handbooks.
3.7
uncertainty due to the lack of homogeneity
component specific to air temperature measurements where several probes are used simultaneously
Note 1 to entry: In this case the air temperature value used is the mean of the measurements of the different probes.
4 Symbols
For the purposes of this document, the symbols defined in ISO 16494:2014 and the following apply.
Symbol Description Unit
A Nozzle throat area m
C Tracer gas concentrations at stations 1,2,3,4 10
1,2,3,4
NOTE
C Nozzle discharge coefficient 1
D
C Specific heat of dry air kJ/(kg K)
p
h Enthalpy kJ/kg
NSAR Net supply airflow ratio %
P Input power to any other electrical components in the ventilator W
aux
P Input power to all electric motors in the ventilator W
em
P Input power to ventilator W
in
NOTE Some quantities of dimension 1 are defined as ratios of two quantities of the same kind. The coherent derived unit
is the number 1. (ISO 80000-1:2009, 3.8).
2 © ISO 2019 – All rights reserved

Symbol Description Unit
ps Static pressure Pa
pv Velocity pressure Pa
P Nozzle Pressure Pa
v
P Power value of moving air W
vma
Q Gross airflow volume m /s
Airflow rate calculated using the data from test “I” as described in ISO 16494:2014
Q m /s
i
B.2.1.1 through B.2.2.2.
qm Air mass flow rate kg/s
i
Q Supply airflow m /s
SA
Q Net supply airflow m /s
SANet
qm Net supply mass flow rate kg/s
2,net
t Time s
T Temperature K
V Air volume in test chamber m
v’ Specific Volume m /kg
n
Same as
U Expanded uncertainty of a measurement
measurand
Same as
u Standard uncertainty of a measurement
measurand
UEATR Unit exhaust air transfer ratio %
NOTE
COE Coefficient of Energy 1
EW Effective Work W
e Effectiveness Ratio
ρ Density kg/m
NOTE Some quantities of dimension 1 are defined as ratios of two quantities of the same kind. The coherent derived unit
is the number 1. (ISO 80000-1:2009, 3.8).

Subscript Description
sensible Indicates parameter refers to sensible energy
latent Indicates parameter refers to latent energy
total Indicates parameter refers to total (enthalpic) energy
ducted Indicates parameter refers to a ducted ventilator
unducted Indicates parameter refers to an unducted ventilator
1,2,3,4 Refers to station 1, 2, 3 or 4
SA Supply air
SANet Net supply air
5 Explanatory notes useful in laboratory application
5.1 Uncertainty
No measurement of a real quantity can be exact; there is always some uncertainty involved in the
measurement. Uncertainty may arise because of measuring instruments not being exact, because the
conditions of the test are not precise, or for many other reasons, including human error. Uncertainty
may be expressed as a range of test results (e.g. 10 kW ± 0,1 kW), or as a fraction or percentage of the
test result (e.g. 10 kW ± 1 %).
5.2 Confidence level
Confidence level refers to the probability that the true result of a measurement lies within the range
stated by the uncertainty. For example, if the measurement of a power is given as 10,0 kW ± 1 % at a
confidence level of 95 %, this means that there is not more than 5 % probability that the true value
of the power is outside the range 9,90 kW to 10,10 kW. A confidence level of 95 % is usually used for
engineering measurements; this provides a good compromise between reliability of measurements and
the cost of making those measurements.
5.3 Evaluation of uncertainties
Two types of uncertainty evaluation are recognized by ISO/IEC Guide 98-3. A type A evaluation involves
statistical methods of evaluation of the uncertainties, and may only be used where there are repeated
measurements of the same quantity. A type B evaluation is one using any other means, and may require
the use of knowledge of the measurement system, such as calibration certificates for instruments and
experience in determining what factors may produce uncertainties in the measurement.
5.4 Steps in evaluation of uncertainty in measurements
To evaluate the uncertainty in a measurement, it is necessary to follow a series of steps.
a) A mathematical model of the measurement system is developed, that lists all the factors that
contribute to the measurement.
b) Examination of this model will determine the magnitude of the contribution of each source of
uncertainty to the final measurement uncertainty.
c) In many cases the units of the final measurement will differ from the units of the various
measurements involved. For example, the measurement of the effective work of an energy-recovery
ventilator will involve measurements such as temperatures, pressures, and electrical power. In
these cases, it is necessary to determine weighting factors to describe the effect that uncertainties
in these measurements will have on the final measurement of capacity. These weighting factors are
known as sensitivity coefficients.
d) Once all the factors contributing to the final measurement are evaluated, together with their
sensitivity coefficients, they are combined to give the overall uncertainty in the final measurement.
5.5 Uncertainty of measurements
5.5.1 Uncertainty of individual measurements
The uncertainty of measurement of each individual measurement should take into account the different
components of uncertainties as described below, where appropriate.
4 © ISO 2019 – All rights reserved

Table 1 — Components of uncertainties for individual measurements
Value from
Coverage factor,
Source of un- Evaluation calibration Probability Standard
k (ISO/IEC Guide
certainty basis certificate or distribution uncertainty
a
99:2007, 2.38)
actual value
U
Calibration
Calibration U Normal 2
u =
certificate
U
Resolution Specifications U Rectangular u =
2 23× 2
23×
— —
u
Calibration (see 5.5.1 (see 5.5.1
Correction U (see 5.5.1
certificate NOTE 1 and NOTE 1 and
NOTE 1 and NOTE 2)
NOTE 2) NOTE 2)
U
Calibration
Drift U Rectangular u =
4 3 4
certificate
Standard devi-
S
Stability (in 5
s =
Mean S ation on a mean N
T
time)
N
value
T
a
Number larger than one by which a combined standard measurement uncertainty is multiplied to obtain an expanded
measurement uncertainty.
The expanded uncertainty, U, is thus calculated as follows.
a) If the calibration correction is applied:
 
S
2 2 2 22 5
 
Uu=×2 ++uu ++uu + (1)
1 2 3 4 i
 
N
T
 
NOTE 1 If the calibration correction value U is applied directly, then the evaluated value of u = 0. In case
3 3
that the averaged value of deviations at several calibration points is applied as correction factor, the value
of u arising from incomplete correction is evaluated from the variance of deviations remaining after the
correction value has been applied to each calibration data.
b) If the calibration correction is not applied:
 
S
2 2 22 5
 
Uu=×2 ++uu+ u + +U (2)
1 2 4 i 3
 
N
T
 
NOTE 2 Avoid calculating the expanded uncertainty without applying the correction. However, if the
correction value is small compared to the uncertainty, it could be decided that correction is not needed. If
the value of the calibration correction U is entered in Formula (2), then u = 0.
3 3
5.5.2 Uncertainty of a mean value from several measurements
If several sensors are used for determining a mean value, this mean value is calculated with the
following formula:
N
T
∑ i
i=1
T = (3)
m
N
where
T is the mean value;
m
T is the value measured by the sensor i;
i
N is the number of sensors.
The uncertainty of this mean value should be calculated from the uncertainty of each individual
measurement to which an additional component for homogeneity is added as follows, assuming the
individual measurements to be correlated:
N
 
uT
()
i
∑  s 
 
i=1
uT = +
()
m  
 
N
N
 
 
 
leading to:
2 2
N N
   
2 2
uT UT
() ()
∑∑i   ii  
  s   s
i==1 i 1
UT =×22uT =× + =×2 + (4)
() ()
   
mm
   
N 2×N
N N
   
   
   
where
u(T ) is the combined standard uncertainty on the mean value;
m
U(T ) is the expanded uncertainty on the mean value (k = 2, confidence level approximately 95 %);
m
u(T) is the standard measurement uncertainty of the sensor i, determined according to Table 1;
i
U(T) is the expanded measurement uncertainty of the sensor i, determined according to Table 1;
i
s is the standard deviation on the mean value (calculating from the N individual measurements, T).
i
NOTE 1 According to ISO/IEC Guide 98-3:2008, 5.2.2 NOTE 1, for the very special case where all of the input
estimates are correlated with correlation coefficients equal to +1, the uncertainty of measurements with the
following formula:
N
 
 
uy = cu x
() ()
ci i
∑
 
i=1
 
N 2
 
N
 
uT
()
 
i
∑
uT
()
i−1
∑ i
   
i−1
Leads to, for the mean value, T = =� (5)
()
m
 
N N
 
 
NOTE 2 See ISO 3534-1 for guidance in evaluating the uncertainty of the mean value obtained from repeated
measurements of the same parameter.
6 © ISO 2019 – All rights reserved

5.5.3 Uncertainty of a value obtained by using a smoothing curve
If a value, V(m), is determined from a measurement m and the use of a smoothing curve, then the term:
uV m
()()
should be replaced by:
 
∂V
 
 |mu⋅ mu+ Vm  (6)
() ()
()
ii smooth
 
∂m
 
 
 
where
u(m ) is the standard uncertainty on each measurement m (determined according to
i i
Table 1);
u (V(m)) is the standard uncertainty component due to the smoothing of the law. Usually,
smooth
this term is evaluated as the maximum deviation between the smoothing curve
and the experimental measurements;
∂V
|m is the derivative of the smoothing curve with respect to measurement m .
i i
∂m
6 Evaluation of uncertainty
6.1 Airflow performance
6.1.1 Air volume flow rate
6.1.1.1 Measured parameters affecting the measurement
— Discharge coefficient;
— Nozzle throat area;
— Nozzle pressure;
— Specific volume.
6.1.1.2 Air volume flow rate measurement
Air volume flow rate is calculated as follows:
QC= AP2'v (7)
Dv n
where
C is the nozzle(s) discharge coefficient (dimensionless);
D
A is the nozzle(s) throat area (m );
P is the nozzle pressure (Pa);
v
v’ is the specific volume (m /kg).
n
6.1.1.3 Uncertainty calculation — Specific case
When the air volume flow rate is determined by using a nozzle chamber, the calculation of the relative
uncertainty of measurement is made as follows:
22 2 2
         
uQ uC uA up uv'
() () () () ()
D v n
  =  +  +  +  (8)
         
Q C A 2p 2v'
D v n
         
When the air volume flow rate is determined by using a nozzle chamber, the calculation of the absolute
uncertainty of measurement is made as follows:
uQ = uC Ap22vu''+ AC pv +
()() () ()
() ()
Dv nD vn
(9)
   
up CA 2pv' uv''CA 2pv
() ()
vD vn nD vn
  + 
   
2p 2v'
v n
   
6.1.2 Air mass flow rate
6.1.2.1 Measured parameters affecting the measurement
— Air volume flow rate;
— Air density.
6.1.2.2 Air mass flow rate
When mass flow rates are calculated, they can be determined from the relevant air volume flow rate by
the following formula:
qm =Q ρ (10)
ii i
where
qm is the relevant air volume flow rate i (m /s);
i
ρ is the density of air stream i (kg/m ).
i
6.1.2.3 Uncertainty calculation — General case
uqmu= Quρρ+ Q (11)
() ()() ()()
ii ii i
6.1.3 Static pressure differential
6.1.3.1 Measured parameters affecting the measurement
— Inlet pressure;
— Outlet pressure.
6.1.3.2 Static pressure differential
Static pressure differential is described by the following formulae:
ps =−ps ps (12)
21− 21
8 © ISO 2019 – All rights reserved

ps =−ps ps (13)
43− 43
where ps is the static pressure at station n (Pa).
n
6.1.3.3 Uncertainty calculation — General case
2 2
upsu= ps + ups (14)
() () ()
() ()
21− 2 1
2 2
upsu= ps + ups (15)
() ()() ()()
43− 4 3
6.2 Unit exhaust air transfer ratio
6.2.1 Measured parameters affecting test results
— Tracer gas concentrations.
6.2.2 UEATR measurement
The unit exhaust air transfer ratio is calculated as follows:
CC−
UEATR= ×100 (16)
CC−
where
UEATR is the unit exhaust air transfer ratio (%);
C is the tracer gas concentration at entering supply air(station 1);
C is the tracer gas concentration at leaving supply air (station 2);
C is the tracer gas concentration at entering exhaust air (station 3).
6.2.3 Uncertainty calculation — General case
The uncertainty calculation is given by the general formula:
 
 
 
  CC−+uC
uC CC− ()()
() ()
2 21 1
2 21
 
 
uUEATR = ×100 + −− ×100 +
()  
 
CC−  CC−  
() () CC−+uC
  ()
31 31 ()
31 1
 
 
 
 
(17)
 
 
CC− CC−
() ()
21 21
 
 
− ×100
 
 C −C 
() Cu− CC−
()()
33 1
 
 
6.3 Net supply airflow
6.3.1 Net supply airflow ducted units
6.3.1.1 Measured parameters affecting test results
— UEATR;
— Supply airflow.
6.3.1.2 NSAR measurement
Net supply airflow for ducted units is calculated as follows:
NSAR
Q =×Q (18)
SANetSA
where
Q is the net supply airflow (m /s);
SANet
Q is the supply airflow (m /s);
SA
NSAR is the net supply airflow ratio (%).
where
NSAR=−100 EATR (19)
and
UEATR is the unit exhaust air transfer ratio (%).
6.3.1.3 Uncertainty calculation for ducted units — General case
2 2
   
uUEATR 100−UEATR
() ()
uQ = ×Q  + ×uQ  (20)
() ()
SANetSASA
   
100 100
   
6.3.2 Net supply airflow unducted ventilators
6.3.2.1 Measured parameters affecting test results
— Chamber volume;
— Tracer gas concentration;
— Time.
6.3.2.2 NSAR measurement
Net supply airflow for unducted ventilators is calculated as follows:
QQ=−Q (21)
SANet 12
where
CC−
()
V
io
Q = ln (22)
i
t CC−
()
to
10 © ISO 2019 – All rights reserved

where, when corrected to standard temperature and density:
Q is the net supply airflow (m /s);
SANet
Q is the average of the three calculated overall airflow rates with the unit under test in oper-
ation as described in ISO 16494:2014 B.2.1.1 and B.2.1.2 (m /s);
Q is the average of the three calculated natural airflow rates of the test chamber with the ven-
tilator removed as described in ISO 16494:2014 B.2.2.1 and B.2.2.2 (m /s);
Q is the airflow rate calculated using the data from a test ‘i’ as described in ISO 16494:2014
i
B.2.1.1, B.2.1.2, B.2.2.1 and B.2.2.2 (m /s);
V is the air volume in the test chamber (m );
t is the length of time elapsed since the start of test unit operation (s);
C is the initial tracer gas concentration in the test chamber (average of all measurement points);
i
C is the tracer gas concentration in outdoor air (station 1);
o
C is the tracer gas concentration in the test chamber after t seconds (average of all measure-
t
ment points).
6.3.2.3 Uncertainty calculation for unducted units — General case
2 2
uQ =uQ +uQ (23)
() () ()
SANet 1 2
General uncertainty formula for Q :
i
 
   
 CC−  CC− CC−
uV () ut V (() ()
() () V
io io io
 
   
uQ = ln + ln + ln +
()  
i
 
 
t CC−  CC−  t  
() () Cu− CC−
tu− tt ()
to () to ()
ii o
 
   
 
(24)
 
 
 
 
Cu− CC−
CC− CC−+uC ()
() () ()()
() tt o
V io to o V
 
 
 
 
ln + ln
 
 
 
t   t CC−
CC− CC−+uC ()
() ()  
()  to 
to io o
 
 
 
 
6.4 Gross effectiveness
6.4.1 Measured parameters affecting the measurement
— Dry-bulb temperature;
— Absolute humidity;
— Enthalpy.
6.4.2 Gross effectiveness measurement
The gross sensible, latent or total effectiveness of an HRV or ERV at test conditions is calculated by the
following formula:
xx−
ε = (25)
xx−
where x equals one of the following for the test condition under consideration:
x is the dry-bulb temperature (for sensible effectiveness), °C; or
x is the absolute humidity ratio (for latent effectiveness), kg water/kg dry air; or
x is the total enthalpy (for total effectiveness), J/kg.
6.4.3 Uncertainty calculation — General case
2 2
   
     
xu− xx− ux
()() ()() xx−
xx− xx− ()
2 11 2 2
12 12
  
   
 
u ε = − + + − (26)
()
 xx−  xx−  xx− 
xu− xx− ()
() xx−−ux
13 () 13 13 ( ()))
11 3
13 3
     
   
6.5 Coefficient of energy
6.5.1 Coefficient of energy: Ducted ventilators
6.5.1.1 Measured parameters affecting the measurement
— Enthalpy;
— Net supply mass flow rate at station 2;
— Unit exhaust air transfer ratio;
— Specific volume of supply air at station 2;
— Static pressure;
— Dynamic pressure;
— Input power.
6.5.1.2 Coefficient of Energy — Measurement
The coefficient of energy (COE) of a ducted ventilator is described by the following formula:
qm hh− ×1000 +P
()
()21,netv2 ma
COE = (27)
ducted
P
in
where
h is the enthalpy of the air at station 1 (kJ/kg of dry air);
h is the enthalpy of the air at station 2 (kJ/kg of dry air);
qm is the net supply mass flow rate at station 2 (kg/s);
2,net
P is the power value of moving air (J/s);
vma
P is the input power to ventilator (W).
in
12 © ISO 2019 – All rights reserved

and
 UEATR 
qm =−qm 1 (28)
22,net  
 
and
 
 
Pp=+spvq2 mv (29)
vman nn2, et s
∑
 
n=1 
where
v is the specific volume of the supply air (m /kg);
s
ps is the external static pressures at the inlet(s) and outlet(s) (Pa);
n
pv is the dynamic pressure at the inlet(s) and outlet(s) (Pa).
n
and
PP=+P (30)
in em aux
where
P is the input power to all electric motors in the ventilator (W);
em
P is the input power to any other electrical components in the ventilator (W).
aux
6.5.1.3 Uncertainty calculation — General case
   
uqmh −h ×1000 qm uh ×1000
() ()
()() ()()
22,net 1 2,neet 2
   
uCOE = + +
()
ducted
   
P P
   
in in
   
(31)
 
 
qm uh ×1000 −uP qm hh− ×+1000 PP
() () ()
()() uP  {}
21,net () in 22,net 1 vma
vma
 
 
+ +
 
     
P P
   Pu− P P 
in in ()
  in in in
   
where
 
uUEATR 
2   ()
 UEATR 
uqmu= qm 1− +qm  (32)
() ()  
 
2,net 2   2
 
 
100 100
 
 
 
 
and
4 4
2 2 2
uP = upsq2 m v + upvq2 m v +
∑ ∑
() () ()
() () ( ))
vman 2,,Net s n 2 Net s
n=1 n=1
(33)
2 2
4 4
   
 ps +pv 2uqm v  + ps +pv 2qm uv()
∑ ∑
()
nn 2,,Net s nn 2 Nett s
   
n=1 n=1
   
and
2 22
uP =uP +uP (34)
() () ()
in em aux
6.5.1.4 Uncertainty calculation — Specific case
When moisture transfer is not of interest (sensible-only ventilators) or does not occur the substitution
described in ISO 16494:2014, 8.7.3 can be made.
   
uqmC TT− ×1000 qm Cu T ×1000
() ()
()() ()()
22,net p 1 2,,netp 2
   
uCOE = + +
()
ducted
   
P P
   
in in
   
 
qm Cu T ×1000
()()  
( )) uP
21,netp ()
vma
 
+  +
 
 
P P
 
in in
 
 
(35)
 
−uP qm CT −T ×+1000 P
() (()
in {}22,netp 1 vma
 
+
 
Pu− PP
 () 
in in in
 
 
qm ⋅−uC()(T TT )×1000
()
2,netp 2 1
 
 
P
in
 
6.5.2 Coefficient of energy — Unducted ventilators
6.5.2.1 Measured parameters affecting the measurement
— Enthalpy;
— Net supply mass flow rate at station 2;
— Unit exhaust air transfer ratio;
— Specific volume of supply air at station 2;
— Input power.
6.5.2.2 Coefficient of energy — Measurement
The coefficient of energy (COE) of an unducted ventilator is described by the following formula:
qm hh− ×1000
()
21,net 2
COE = (36)
unducted
P
in
where
h is the enthalpy of the air at station 1 (kJ/kg of dry air);
h is the enthalpy of the air at station 2 (kJ/kg of dry air);
qm is the net supply mass flow rate (kg/s);
2,net
P is the input power to ventilator (W).
in
14 © ISO 2019 – All rights reserved

and
 UEATR 
qm =−qm 1 (37)
22,net  
 
and
PP=+ P (38)
in em aux
where
P is the input power to all electric motors in the ventilator (W);
em
P is the input power to any other electrical components in the ventilator (W).
aux
6.5.2.3 Uncertainty calculation — General case
2 2
   
uqmh −h ×1000 qm uh ×1000
() ()()
()() ()
22,net 1 2,,net 2
   
uCOE = + +
()
unducted
 
 
P P
   
in in
   
(39)
 
 
qm uh ×1000
()()
() uP qm hh− ×1000
21,net () ()
in 22,net 1
 
 
+
  2
P  
 
in Pu− PP
()
in in in
 
 
where
 
 
uUEATR
2  UEATR  ()
 
uqmu= qm 1− +qm  (40)
()  
()
2,net  2  2
 
 
 
100 100
 
 
 
 
and
2 22
uP =uP +uP (41)
() () ()
in em aux
6.5.2.4 Uncertainty calculation — Specific case
When moisture transfer is not of interest (sensible-only ventilators) or does not occur, the substitution
described in ISO 16494:2014, 8.7.3 can be made.
 
uqmc TT− ×1000
()
()()
22,netp 1
 
uCOE = +
()
unducted,sensible
 
P
 
in
 
2 2
   
qm cu T ×1000 qm cu T ×1000
()() ()()
() ()
22,,netp 2 netp 11
   
+ + (42)
   
P P
   
in in
   
 
 
qm uC TT−×1000
−uqP mc TT− ×1000
() () ()
22,netp 1
in 22,netp 1
 
 
+
 
  P
P −uP P in
()
inninin
 
 
6.6 Effective work (EW)
6.6.1 Measured parameters affecting the measurement
— COE;
— P
in.
6.6.2 Effective work: Ducted or unducted ventilators
The effective work (EW) of a ducted or unducted ventilator is described by the following formula:
EW =×PCOE−1 (43)
()
in
6.6.3 Uncertainty calculation — General case
uEWu= PC×−OE 1 +×Pu COE (44)
() ()() () ()()
in in
6.6.4 Uncertainty calculation — Specific case
When moisture transfer is not of interest (sensible-only ventilators) or does not occur, the substitution
described in ISO 16494:2014, 8.7.3 can be made.
2 2
uEWu= PC×−OE 1 +×Pu COE (45)
() () () ( ))
() ()
sensible in sensible in sensible
16 © ISO 2019 – All rights reserved

Annex A
(informative)
Uncertainty budget sheets
The following (18) budget sheets, presented as tables, are given in this annex as an example of
uncertainty calculations using an uncertainty budget sheet approach.
— Table A.1 — Uncertainty budget sheet for air volume flow rate Q
— Table A.2 — Uncertainty budget sheet for air mass flow rate qm
i
— Table A.3 — Uncertainty budget sheet for static pressure differential(s) ps , ps
2-1 4-3
— Table A.4— Uncertainty budget sheet for unit exhaust air transfer ratio UEATR
— Table A.5 — Uncertainty budget sheet for net supply airflow Q
SANet
— Table A.6 — Uncertainty budget sheet for net supply mass airflow qm
2,net
— Table A.7 — Uncertainty budget sheet for power value of moving air P
vma
— Table A.8 — Uncertainty budget sheet for gross effectiveness, sensible ε
sensible
— Table A.9 — Uncertainty budget sheet for gross effectiveness, latent ε
latent
— Table A.10 — Uncertainty budget sheet for gross effectiveness, total ε
total
— Table A.11 — Uncertainty budget sheet for coefficient of energy, ducted ventilator, total COE
ducted
— Table A.12 — Uncertainty budget sheet for coefficient of energy, ducted ventilator, sensible
COE
ducted,sensible
— Table A.13 — Uncertainty budget sheet for coefficient of energy, unducted ventilator, total COE
unducted
— Table A.14 — Uncertainty budget sheet for coefficient of energy, unducted ventilator, sensible
COE
unducted,sensible
— Table A.15 — Uncertainty budget sheet for effective work, total EW
— Table A.16 — Uncertainty budget sheet for effective work, sensible EW
sensible
— Table A.17 — Uncertainty budget sheet for airflow rate from test i, used to determine net supply
airflow for unducted ventilators using the attenuation method Q
i
— Table A.18 — Uncertainty budget sheet for net supply airflow Q for unducted ventilators using
SANet
the attenuation method
In the normative sections of this document, most of the numbered formulae for determination of
uncertainty yield the absolute uncertainty u(Q).
The following budget sheets yield first the relative uncertainty u(Y)/Y, and the absolute uncertainty
u(Q) is calculated by multiplying the value of Q by u(Y)/Y.
Alternate forms of the formulae which yield the relative uncertainty u(Y)/Y are shown in the tables and
are labelled as “(rel)”.
These budget sheets are only an example of the budget sheet method of calculation for guidance.
Laboratories may use appropriate data depending on the test methods and instrumentation used. For
minimum uncertainty in test results it is essential that an appropriate method is adopted for each test.
If the functional relationship is a product or quotient, i.e. the output quantity is obtained from only the
multiplication or division of the input quantities, this can be transformed to a linear addition by the use
of relative values.
p1 p2 pN
In all cases of the general form Y = c X X …X in which the exponents p are known positive or
1 2 N i
negative numbers having negligible uncertainties, then the combined standard relative uncertainty
u(Y)/Y can be calculated from the relative standard uncertainty of all of the sources of uncertainty as
follows (see ISO/IEC Guide 98-3:2008, 5.1.6):
n
 
uY pu x
() ()
ii
= (A.1)
 
∑
Y x
 
i
 
i=
18 © ISO 2019 – All rights reserved

Table A.1 — Uncertainty budget sheet for air volume flow rate Q
Relative standard uncertainty of each
Uncertainty of each factor
value
Units of
Input quantity and/or Measured
Symbol measure-
Probabil- Standard
pu x
source of uncertainty value ()
Expanded ii
ment
ity distri- Divisor uncertainty
uncertainty
x
bution u(x )
i
i
uC()
D
Nozzle Coefficient C — 0,909 0,001 Normal 2 0,000 5 0,055 %
D
C
D
uA
()
Nozzle Area A m 0,005 0,000 1 Normal 2 0,000 05 1,00 %
A
uP()
v
Nozzle Pressure Pv Pa 124,6 2,5 Normal 2 1,25 0,502 %
2P
v
uV'
()
n
Specific Volume v’ m /kg 0,868 8 0,011 Normal 2 0,005 5 0,317 %
n
2V'
n
Air volume flow rate Q m3/s 0,065 0 ← calculated value per Formula (7)
Combined standard relative
1,16 %
uncertainty u(Y)/Y
Formu- By uncertain-
QC= AP2'v
Dv n
la (7) ty budget Expanded absolute uncertainty U(Q) 0,001 55
Expanded relative uncertainty U(Y)/Y 2,32 %
Combined standard relative
1,16 %
22 2 2
uncertainty u(Y)/Y
uQ  uC  uA  uP  u vv' 
() () () () () By formula at
D v n
(rel)
= ++ +
         
left Expanded relative uncertainty U(Y)/Y 2,32 %
Q C A 2P 2v'
   D     v   n 
For expanded uncertainty, coverage factor k = 2

20 © ISO 2019 – All rights reserved
Table A.2 — Uncertainty budget sheet for air mass flow rate qm
Relative standard uncertainty of each
Uncertainty of each factor
Value of
value
Units of
Input quantity and/or standard
Symbol measure-
source of uncertainty uncertainty pu x
()
Measured Expanded Probability
ii
ment
Divisor
u(x )
value uncertainty distribution
i
x
i
uQ()
i
Air volume flow rate Q m /s 0,066 9 0,001 55 Normal 2 0,000 775 1,16 %
i
Q
i
u ρ
()
i
Air density as tested ρ kg/m 1,151 ,015 Normal 2 0,007 5 0,65 %
i
ρ
i
Air mass flow rate qm kg/s 0,077 0 ← calculated value per Formula (10)
i
Combined standard relative
1,33 %
uncertainty u(Y)/Y
Formula By uncertain-
qm =Q ρ
(10) ii i ty budget Expanded absolute uncertainty U(Q) 0,002 05
Expanded relative uncertainty U(Y)/Y 2,66 %
Combined standard relative
1,33 %
22 2
uncertainty u(Y)/Y
uqm  uQ  u ρ 
() () () By formula at
i i i
(rel)
=+
     
left Expanded relative uncertainty U(Y)/Y 2,66 %
qm Q ρ
 i   i   i 
For expanded uncertainty, coverage factor k = 2

Table A.3 — Uncertainty budget sheet for static pressure differential ps
2-1
Uncertainty of each Factor Standard uncertainty of each value
Value of
Units of
Input quantity and/or standard
N
 
Symbol measure-
Measured Expanded Probability
source of uncertainty uncertainty 2
Divisor
 
uy()= cu()x
ment
value uncertainty distribution ci∑ i
u(x )
 
i
 i=1 
Inlet pressure ps Pa −20 2,5 Normal 2 1,250 1,250
ups
1 ()
Outlet pressure ps Pa 30 2,5 Normal 2 1,250 1,250
2 up()s
Static pressure
ps Pa 50 ← calculated value per Formula (12)
2-1
differential
Combined standard uncertainty u (Q) 1,768
c
Formula By uncertain-
ps =−ps ps  (see ISO/IEC Guide 98-3:2008, 5.1.5) Expanded absolute un
...