ISO 6358-2:2013

INTERNATIONAL ISO
STANDARD 6358-2
First edition
2013-05-01
Pneumatic fluid power —
Determination of flow-rate
characteristics of components using
compressible fluids —
Part 2:
Alternative test methods
Transmissions pneumatiques — Détermination des caractéristiques
de débit des composants traversés par un fluide compressible —
Partie 2: Méthodes d’essai alternatives
Reference number
©
ISO 2013
© ISO 2013
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ii © ISO 2013 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and units . 2
5 Test installation . 2
5.1 Test circuit for discharge test . 3
5.2 Test circuit for charge test . 3
5.3 General requirements . 4
5.4 Requirements for the tank (item 4) . 5
5.5 Special requirements . 7
6 Test procedures . 8
6.1 Test conditions . 8
6.2 Measuring procedures . 9
6.3 Calculation of characteristics .12
7 Presentation of test results .16
8 Identification statement (reference to this part of ISO 6358) .17
Annex A (informative) Evaluation of measurement uncertainty .18
Annex B (normative) Test method to determine and calibrate the volume of an isothermal tank .24
Annex C (informative) Isothermal tank stuffing .30
Annex D (informative) Test method to determine isothermal performance .33
Annex E (informative) Equations for calculation of flow-rate characteristics .36
Annex F (informative) Procedures for calculating critical back-pressure ratio, b, and subsonic
index, m, by the least-square method using the Solver function in Microsoft Excel .39
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International
Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 6358-2 was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee SC 5,
Control products and components.
This first edition of ISO 6358-2, together with ISO 6358-1 and ISO 6358-3, cancels and replaces
ISO 6358:1989, which has been technically revised. However, ISO 6358-2 and ISO 6358-3 are new
standards whose scopes were not included in ISO 6358:1989.
ISO 6358 consists of the following parts, under the general title Pneumatic fluid power — Determination
of flow-rate characteristics of components using compressible fluids:
— Part 1: General rules and test methods for steady-state flow
— Part 2: Alternative test methods
— Part 3: Method for calculating steady-state flow-rate characteristics of assemblies
iv © ISO 2013 – All rights reserved

Introduction
In pneumatic fluid power systems, power is transmitted and controlled through a gas under pressure within
a circuit. Components that make up such a circuit are inherently resistive to the flow of the gas and it is
necessary, therefore, to define and determine the flow-rate characteristics that describe their performance.
ISO 6358:1989 was developed to determine the flow-rate characteristics of pneumatic valves, based upon
a model of converging nozzles. The method included two characteristic parameters: sonic conductance,
C, and critical pressure ratio, b, used in a proposed mathematical approximation of the flow behaviour.
The result described flow performance of a pneumatic valve from choked flow to subsonic flow, based
on static pressure. This new edition uses stagnation pressure instead, to take into account the influence
of flow velocity on the measurement of pressures.
Experience has demonstrated that many pneumatic valves have converging–diverging characteristics
that do not fit the ISO 6358:1989 model very well. Furthermore, new developments have allowed the
application of this method to additional components beyond pneumatic valves. However, this now
requires the use of four parameters (C, b, m, and Δp ) to define the flow performance in both the choked
c
and subsonic flow regions.
This part of ISO 6358 describes a set of three flow-rate characteristic parameters determined from test
results. These parameters are described as follows and are listed in decreasing order of priority:
— The sonic conductance, C, corresponding to the maximum flow rate (choked) is the most important
parameter. This parameter is defined by the upstream stagnation conditions.
— The critical back-pressure ratio, b, representing the boundary between choked and subsonic
flow is second in importance. Its definition differs here from the one in ISO 6358:1989 because it
corresponds to the ratio of downstream to upstream stagnation pressures.
— The subsonic index, m, is used if necessary to represent more accurately the subsonic flow behaviour.
For components with a fixed flow path, m is distributed around 0,5. In these cases, only the first two
characteristic parameters C and b are necessary. For many other components, m will vary widely. In
these cases, it is necessary to determine C, b, and m.
Several changes to the test equipment were made to overcome apparent violations of the theory
of compressible fluid flow. This included expanded inlet pressure-measuring tubes to satisfy the
assumptions of negligible inlet velocity to the item under test and to allow the inlet stagnation pressure
to be measured directly. Expanded outlet tubes allow the direct measurement of downstream stagnation
pressure to better accommodate the different component models. The difference between stagnation
pressure at upstream and downstream of component means a loss of pressure energy.
ISO 6358-3 can be used to calculate without measurements an estimate of the overall flow-rate
characteristics of an assembly of components and piping, using the characteristics of each component
and piping determined in accordance with this part of ISO 6358 or ISO 6358-1.
The discharge and charge test methods specified in this part of ISO 6358 have the following advantages
over the test method specified in ISO 6358-1:
a) an air source with a large flow-rate capacity is not required;
b) components with larger flow-rate capacity can be tested more easily;
c) energy consumption is minimised; and
d) test time is shortened in the discharge test, and noise level is decreased in the charge test.
It should be noted that performance characteristics measured in accordance with this edition of ISO 6358
will differ from those measured in accordance with ISO 6358:1989.
INTERNATIONAL STANDARD ISO 6358-2:2013(E)
Pneumatic fluid power — Determination of flow-rate
characteristics of components using compressible fluids —
Part 2:
Alternative test methods
1 Scope
This part of ISO 6358 specifies a discharge test and a charge test as alternative methods for testing
pneumatic fluid power components that use compressible fluids, i.e. gases, and that have internal
flow passages that can be either fixed or variable in size to determine their flow-rate characteristics.
However, this part of ISO 6358 does not apply to components whose flow coefficient is unstable during
use, i.e. components that exhibit remarkable hysteretic behaviour (because they can contain flexible
parts that deform under the flow) or that have an internal feedback phenomenon (such as regulators),
or components that have a cracking pressure such as non-return (check) valves and quick-exhaust
valves. In addition, it does not apply to components that exchange energy with the fluid during flow-rate
measurement, e.g. cylinders, accumulators, etc.
NOTE This part of ISO 6358 does not provide a method to determine if a component has hysteretic behaviour;
ISO 6358-1 does provide such a method.
Table 1 provides a summary of which parts of ISO 6358 can be applied to various components.
Table 1 — Application of ISO 6358 test methods to components
Constant Variable
upstream pressure test upstream pressure test
ISO 6358-1 ISO 6358-1
Components
ISO 6358-2
constant ISO 6358-2 variable
discharge
upstream charge test upstream
test
pressure test pressure test
Group 1 Directional control valves yes yes yes yes
Flow control valves yes yes yes yes
Connectors yes yes yes yes
Valve manifolds yes yes yes yes
Group of components yes yes yes yes
Group 2 Filters and lubricators yes no no no
Non-return (check) valves yes no no no
Tubes and hoses yes no no no
Group 3 Silencers and exhaust oil mist
no no yes yes
separators
Blow nozzles no no yes yes
Quick-exhaust valves no no yes yes
Cylinder end heads no no yes yes
The charge test cannot be performed on components that do not have downstream port connections.
This part of ISO 6358 specifies requirements for the test installation, the test procedure, and the
presentation of results.
Evaluation of measurement uncertainties is described in Annex A. Requirements for a method to test
the volume of an isothermal tank are given in Annex B. Guidance on the isothermal tank is given in
Annex C. Requirements for a method to test isothermal performance are given in Annex D. Guidance
on the equation for calculating characteristics is given in Annex E. Guidance on calculating flow-rate
characteristics is given in Annex F.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 1219-1, Fluid power systems and components — Graphical symbols and circuit diagrams — Part 1:
Graphical symbols for conventional use and data-processing applications
ISO 5598, Fluid power systems and components — Vocabulary
ISO 6358-1, Pneumatic fluid power — Determination of flow-rate characteristics of components using
compressible fluids — Part 1: General rules and test methods for steady-state flow
3 Terms and definitions
For the purposes of this document, the terms and definitions in ISO 5598 and ISO 6358-1 apply.
4 Symbols and units
4.1 The symbols and units shall be in accordance with ISO 6358-1 and Table 2.
Table 2 — Symbols and units
a
Reference Description Symbol Dimension SI units Practical units
5.5.2 Time t T s s
3 3 3
5.4.3 Tank volume V L m dm
a
T = time; L = length
4.2 The numerals used as subscripts to the symbols shall be in accordance with ISO 6358-1 and Table 3.
Table 3 — Subscripts
Subscript Meaning
3 Tank conditions
4.3 The graphic symbols used in Figures 1 and 2 are in accordance with ISO 1219-1.
5 Test installation
CAUTION — Figures 1 and 2 illustrate basic circuits that do not incorporate all the safety
devices necessary to protect against damage in the event of component failure. It is important
that those responsible for carrying out the test give due consideration to safeguarding both
personnel and equipment.
2 © ISO 2013 – All rights reserved

5.1 Test circuit for discharge test
A suitable test circuit as shown in Figure 1 shall be used for the discharge test. See 5.3.5.
6 7 8 9 10
11 12
p
1 p
1 2 3 13
p
NOTE See Table 4 for the key to test circuit components.
Figure 1 — Test circuit for discharge test
5.2 Test circuit for charge test
A suitable test circuit as shown in Figure 2 shall be used for the charge test.
6 7 8 9 10
p
p
1 2
11 12
17 13 3 18
p
14 15
NOTE See Table 4 for the key to test circuit components.
Figure 2 — Test circuit for charge test
Table 4 — Key to test circuit components shown in Figures 1 and 2
Relevant
Key item
subclause or Description Additional requirements
number
paragraph
Compressed gas source and filter for discharge
1 5.3.2
test
Adjustable pressure regulator for discharge
2 -
test
3 - Shut-off valve
4 5.4 Tank
5 - Temperature-measuring instrument
6 5.3.7 Upstream pressure-measuring tube
7 5.3.7 Upstream transition connector
8 - Component under test
9 5.3.7 Downstream transition connector
10 5.3.7 Downstream pressure-measuring tube
11 5.3.10 Pressure transducer
12 5.3.10 Pressure transducer
13 5.3.4 and 5.3.9 Flow control solenoid valve (optional) The sonic conductance of this
flow control valve shall be about
four times larger than that of the
component under test.
14 - Barometer
15 - Digital recorder
16 5.3.10 Pressure transducer
17 - Suction port for charge test
18 - Vacuum pump for charge test
5.3 General requirements
5.3.1 The component under test shall be installed and operated in the test circuit in accordance with
the manufacturer’s operating instructions.
5.3.2 For the discharge test, a filter shall be installed which provides a standard of filtration specified
by the manufacturer of the component under test.
5.3.3 A test set-up shall be constructed from the items listed in Table 4. Items 1 through 8, 11, and 14 through
16 are required for the discharge test. Items 3 through 12 and 14 through 18 are required for the charge test.
5.3.4 If the component under test has no control mechanism for shifting its position, install a flow
control solenoid valve (item 13) upstream of pressure-measuring tube (item 6) in order to start the test.
5.3.5 Items 9, 10, and 12 are not required for the discharge test when the component under test does
not have a downstream port. See the special instructions in 6.2.3.3.
5.3.6 The distance between the tank (item 4) and the upstream pressure-measuring tube (item 6) for
the discharge test, or between the tank (item 4) and downstream pressure-measuring tube (item 10) for
charge test, shall be as short as possible. The volumes of all components and conductors in Figures 1 and
4 © ISO 2013 – All rights reserved

2 between items 3 and 13 (if item 13 is used) or between items 3 and 8 (if item 13 is not used) shall be
added to the volume of the tank.
5.3.7 The pressure-measuring tubes (items 6 and 10) and the transition connectors (items 7 and 9)
shall be in accordance with ISO 6358-1. It is not necessary to have a temperature-measuring connection
in the pressure-measuring tubes because the temperature is measured in the tank.
5.3.8 For any locations where liquid can collect, installation of a drain separator is recommended.
5.3.9 The shifting time of the flow control solenoid valve (item 13) shall be sufficiently short to limit the
transient time at the beginning of test data collection.
5.3.10 When connecting pressure measuring instruments, the dead volume shall be limited as much as
possible to avoid long response time, delays, and phase lag for measurements.
5.4 Requirements for the tank (item 4)
5.4.1 Structure
The tank shall be suitably structured as shown in Figure 3 and consist of the components listed in
Table 5. Dimensions of the flow port shall conform to the dimensions given in Table 6.
The tank shall conform to any local, national, and/or regional regulations and standards related to
pneumatic containers.
The ratio of the height of the tank to its diameter should not exceed 2:1.
The junction of the flow port with the internal surface of the tank shall be convergent shaped so as to
avoid pressure loss. The dimensions and arrangement of connection ports other than the flow port are
determined by the test operator.
Key
a
Measuring ports (temperature and pressure)
b
Source port
c
Flow port
Figure 3 — Structure of the tank
Table 5 — Key to tank components
Key item number Description Comments
1 Lid
2 Tank body
3 Gasket
4 Flange fastener (nut and bolt) Six or more pieces, equally arranged
5 Metal net See 5.4.2.
6 Stuffed material See 5.4.2.
7 Drain valve
6 © ISO 2013 – All rights reserved

Table 6 — Thread size of flow port
Tank volume, V,
Thread size
in m
V ≤ 0,0025 G 1/8
0,0025 < V ≤ 0,0063 G 1/4
0,0063 < V ≤ 0,014 G 3/8
0,014 < V ≤ 0,032 G 1/2
0,032 < V ≤ 0,066 G 3/4
0,066 < V ≤ 0,100 G 1
0,100 < V ≤ 0,190 G 1 1/4
0,190 < V ≤ 0,310 G 1 1/2
0,310 < V ≤ 0,510 G 2
0,510 < V ≤ 0,730 G 2 1/2
0,730 < V ≤ 1,100 G 3
5.4.2 Stuffed material
The stuffed material, which is used to reduce the change in air temperature, shall be resistant to
corrosion and pressure and shall be distributed evenly in the tank. If copper wires are used as the
−5 −5
stuffed material, wires of equivalent diameter 3 × 10 m to 5 × 10 m shall be stuffed in the tank at a
−4 3
density of 3 × 10 kg/m .
NOTE The equivalent diameter means the diameter of the cross-sectional area of a noncircular shape
assumed as equivalent to the diameter of the cross-sectional area of a circular shape.
The stuffed material shall be wrapped with a metallic net to prevent it from flowing out of the flow port.
It is desirable that a suitable frame supports the stuffed material to prevent it from leaning inside the
tank. Further information is given in Annex C.
5.4.3 Volume
The volume of the tank, V, in m should be calculated using Formula (1):
VC≥×510 (1)
where
C is the estimated sonic conductance of the component under test, in m /(s∙Pa)(ANR).
NOTE 1 The tank volume is the net value obtained by subtracting the volume of the stuffed material from the
volume of the empty air tank.
NOTE 2 The test method to determine the tank volume is given in Annex B.
5.5 Special requirements
5.5.1 The special requirements given in 5.6 of ISO 6358-1 apply for this part of ISO 6358.
5.5.2 The digital recorder shall be set to sample pressure at a time interval determined in accordance
with Formulae (2) or (3). Approximately 1000 pressure data points will be obtained during discharge or
charge tests. These criteria have an effect on the calculations performed in 6.3.
— For discharge tests:
V
−8
Δt≈×25, 10 (2)
C
— For charge tests:
V
−8
Δt≈×15, 10 (3)
C
where
Δt is the time interval for sampling pressure, in s;
C is the estimated sonic conductance of the component under test, in m /(s∙Pa)(ANR);
V is the tank volume, in m .
6 Test procedures
6.1 Test conditions
6.1.1 Test fluid
6.1.1.1 Air should be used as the test fluid. If a different fluid is used, it shall be stated in the test report.
6.1.1.2 The gas shall be filtered and conditioned to comply with the recommendations of the
manufacturer of the component under test.
6.1.2 Checks
Periodically check that the pressure-tapping holes are not blocked by liquids or solid particles.
6.1.3 Test measurements
6.1.3.1 Each set of test readings shall be recorded after steady-state conditions of temperature and
pressure in the tank have been reached. The variations of pressures and temperature indications shall not
exceed the limits given in the column “Allowed test conditions variation” of Table 7.
6.1.3.2 Pressure and temperature shall be measured within the measurement accuracy specified in Table 7.
Table 7 — Measurement accuracy and allowed test condition of parameters
Allowed test condition
Parameter Measurement accuracy
variation
Volume ±1 % -
Time ±1 % -
Upstream pressure ±0,5 % ±1 %
Downstream pressure ±0,5 % ±1 %
Tank pressure ±0,5 % ±1 %
Temperature ±1 K ±3 K
6.1.3.3 Flow-rate conditions in each flow path shall be maintained constant within the component
while taking measurements to ensure there is no inadvertent movement of component parts.
8 © ISO 2013 – All rights reserved

6.2 Measuring procedures
6.2.1 Requirements for testing to publish catalogue ratings
If data are to be used for publishing ratings in a catalogue, a sample consisting of a minimum of five test
units selected from a random production lot shall be tested in accordance with the following procedures.
6.2.2 Selection of measuring procedure
Either the procedure described in 6.2.3 or the procedure described in 6.2.4 shall be selected in accordance
with the scope of this part of ISO 6358.
6.2.3 Measuring procedures for discharge test
6.2.3.1 Set the pressure of the pressure regulator (item 2) at 700 kPa (7 bar), and open the shut-off
valve (item 3) to charge air into the tank (item 4). Leave the tank in this state until temperature and
pressure in the tank reach steady-state conditions.
6.2.3.2 Close the shut-off valve (item 3) and measure the initial pressure, p , using pressure transducer
16, initial temperature, T , using the temperature-measuring instrument (item 5) in the tank, and
atmospheric pressure using the barometer (item 14).
6.2.3.3 Open the component under test (item 8) or the solenoid valve (item 13) to discharge air from
the tank (item 4) into the atmosphere. Measure pressure in the tank, p , upstream pressure, p , and
3 1
downstream pressure, p , during discharge using the pressure transducers (items 16, 11, and 12), and
record the values using the digital recorder (item 15) as shown in Figure 4. If the downstream transition
connector cannot connect to a component under test, measure atmospheric pressure as downstream
pressure, p .
Y
X
a b
Key
X time
Y pressure
1 upstream pressure
2 downstream pressure
3 pressure in the tank
4 atmospheric pressure
a
choked flow region
b
subsonic flow region
NOTE The broken line indicates the upstream pressure, p , when solenoid valve 13 is used to start the test.
But the upstream pressure, p , begins at the maximum value if the component under test can perform the shift to
start the test.
Figure 4 — Pressure response in the tank during discharge
6.2.4 Measuring procedures for charge test (see Figure 2)
6.2.4.1 Reduce the pressure in the tank (item 4) to approximately 2 kPa absolute (0,02 bar absolute)
using the vacuum pump (item 18). Then, close the shut-off valve (item 3) and leave the tank in this state
until the pressure in the tank reaches steady-state conditions. Measure the initial pressure, p , using the
pressure transducer (item 16), initial temperature, T , using the temperature-measuring instrument
(item 5) in the tank, and the atmospheric pressure using the barometer (item 14).
6.2.4.2 Open the component under test (item 8) or the solenoid valve (item 13) to charge the air from
the atmosphere into the tank. Measure pressure in the tank, p , upstream pressure, p , and downstream
3 1
pressure, p , during charge using the pressure transducers (items 16, 11, and 12), and record the values
using the digital recorder (item 15) as shown in Figure 5.
10 © ISO 2013 – All rights reserved

Y
a b
X
Key
X time
Y pressure
1 upstream pressure
2 downstream pressure
3 pressure in the tank
4 atmospheric pressure
a
choked flow region
b
subsonic flow region
NOTE The broken line indicates the upstream pressure, p when a solenoid valve 13 is used to start the test.
1,
But the upstream pressure, p , begins at the maximum value if the component under test can perform the shift to
start the test.
Figure 5 — Pressure response in the tank during charge
6.3 Calculation of characteristics
6.3.1 Sonic conductance, C
6.3.1.1 Smoothing of pressure in the tank, p
Perform a calculation to smooth the raw pressure data in the tank from a 21-point moving average by
using Formula (4).
ij=+10
pp' = (4)
33()ji∑ ()
ij=−10
where
p is the pressure in the tank, in Pa (i = 1, 2, ···, n);
3(i)
p’ is the pressure in the tank after moving average processing, in Pa ( j = 11, 12, ···, n-10);
3( j)
n is the number of pressure data points measured during the discharge test or the charge test.
6.3.1.2 Conductance characteristics curve
Calculate the conductance, C , for each value of j over the measured region shown in Figure 4 for the
e
discharge test, or Figure 5 for the charge test, by using Formulae (5) or (6). Describe the conductance
versus the pressure ratio on the graph as shown in Figures 7 or 8:
— for discharge test
Vp''−p
()
31()jj−+03()10
C = (5)
e()j
20pRρΔtT T
10()j 0 3
— for charge test
12 © ISO 2013 – All rights reserved

Vp''−p
()
31()jj+−03()10
C = (6)
e()j
20pRρΔtT T
10()j 0 3
where
C is the conductance of a component under test, in m /(s∙Pa)(ANR) ( j = 21, 22, …, n − 20); see
e( j)
Figure 6 for a description of how these data are organized;
p is the upstream pressure, in Pa;
1( j)
p’ is the pressure in the tank after smoothing before 10 points, in Pa;
3( j-10)
p’ is the pressure in the tank after smoothing after 10 points, in Pa;
3( j+10)
V is the volume of the tank, in m ;
R is the gas constant, in J/(kg·K); [for air, R = 287 J/(kg·K)];
ρ is the mass density of air at the standard reference atmosphere, in kg/m ;
T is the absolute temperature at standard reference atmosphere, in K;
T is the absolute temperature in the tank at start of discharge, in K;
Δt is the time interval for sampling pressure determined in 5.5.2, in s.

1 10 20 30 n
Measured pressure p
3(i)
i=1,2,…, n
n-10
1112 13
Smoothing pressure p’
3(j)
j=11,12,…, n-10
n-20
21 22 23
Conductance C
….
e(j)
j=21,22,…, n-20
Figure 6 — Value of j in C
e(i)
6.3.1.3 Calculation of sonic conductance, C
Calculate the sonic conductance, C, by averaging the saturated region of the conductance, C , as shown
e
in Figures 7 or 8. The saturated region is characterized by several values of the conductance that are at
maximum values compared to all others. However, this does not include the transient values obtained
immediately after starting a charge or discharge.
If the C coefficients vary significantly in the choked flow region, the component could be considered
e
to exhibit pressure dependence. In this case, first repeat the procedure in 6.2.3.1 through 6.2.3.3 at
the upper limit of the pressure range of the component, then determine the K and C coefficients in
p
accordance with 6.3.3.
a
Y
C
X
Key
X back-pressure ratio p /p
2 1
Y conductance C
e
a
saturated region
Figure 7 — Conductance characteristics for discharge test
a
Y
C
X
Key
X back-pressure ratio p /p
2 1
Y conductance C
e
a
saturated region
Figure 8 — Conductance characteristics for charge test
6.3.2 Critical back-pressure ratio, b, and subsonic index, m
6.3.2.1 Calculate the critical back-pressure ratio, b, and subsonic index, m, from Formula (7) by the least-
square method using all of pressure ratios, p /p , and conductance ratios, C /C, in the subsonic flow region
2 1 e
determined in 6.3.1. See Annex F for the calculation, giving attention to the second paragraph in F.2.2.1.
14 © ISO 2013 – All rights reserved

m
 
 p 
 
−b
 
C p
 
e 1
 
=−1 (7)
 
C  1−b 
 
 
 
 
 
6.3.2.2 If the value of the subsonic index, m, calculated in 6.3.2.1 is between 0,48 and 0,52, its value
may be corrected to 0,5 to reduce the number of characteristic parameters. In this case, recalculate the
corresponding critical back-pressure ratio, b, in accordance with 6.3.2.1, with m = 0,5.
6.3.3 Pressure dependence coefficient, K
p
Taking C as the value of conductance for the maximum upstream pressure, plot the pressure dependence
max
as shown in Figure 9 using the test result stated in 6.2.3, then find the correlative line in the range of the
conductance ratio close to 1. The plot on this line can be considered to define the choked flow region. The
slope of this line is the value of the pressure dependence coefficient, K . When selecting a conductance
p
ratio and upstream pressure at two positions on this line, K can be calculated by using Formula (8).
p
C
low
1−
C
max
K = (8)
p
pp−
11max low
where
p is the lower upstream pressure of the linear dependence.
1low
Y 2 1
a
b c
0 X
Key
X upstream pressure p
Y conductance ratio C /C
e max
1 first data point, taken at maximum upstream pressure
2 second point on the line
3 correlative line
4 test results
a
conductance ratio C /C
low max
b
upstream pressure p
1low
c
upstream pressure p
1max
Figure 9 — Plot of conductance ratio versus upstream pressure
7 Presentation of test results
7.1 All measurements and the results of calculations shall be tabulated by the testing laboratory.
7.2 If data are to be used for publishing ratings in a catalogue, the average of results from the test units
for each characteristic listed in 7.3 shall be reported.
7.3 The following performance characteristics related to flow-rate capacity, which are calculated in
accordance with 6.3, shall be stated:
a) sonic conductance, C, [also see item d) below],
b) critical back-pressure ratio, b,
c) subsonic index, m, and
d) if necessary, pressure dependence coefficient, K , upstream pressure, p , and sonic conductance,
p 1max
C at the upstream pressure value p .
max 1max
16 © ISO 2013 – All rights reserved

e) From these characteristics the performance of the component can be predicted using Formulae (E.1)
and (E.2) of Annex E of ISO 6358-1 and compared.
7.4 The record of the calibration of measuring devices shall be available.
8 Identification statement (reference to this part of ISO 6358)
Use the following statement in test reports, catalogues, and sales literature when electing to comply
with this International Standard:
“Flow-rate characteristics of pneumatic components determined in accordance with the discharge
test or charge test of ISO 6358-2, Pneumatic fluid power — Determination of flow-rate characteristics of
components — Part 2: Alternative test methods”
Annex A
(informative)
Evaluation of measurement uncertainty
A.1 General
The ISO guide of the uncertainty in measurement (GUM:2000) provides the current international
consensus method for estimating the measurement uncertainty. There are different possibilities to
estimate measurement uncertainty, the strict mathematical way is described most extensively in the GUM,
but the other pragmatic methods that are in conformity with GUM can be used. The most important rule
is: effort and expenditure for determination of uncertainties should be clearly guided by the principle ”fit
for purpose”, that is, it should be good enough to meet the requirements of the user of the measurement
data, but it should not be overdone in light of the application. This annex uses this principle.
GUM groups uncertainty components into type A and type B according to the way data were obtained.
Type A components are calculated by statistical means from repeated measurements, while type B
components are taken from other sources, e.g. reference material, calibration certificates, accepted
values of constants, resolution, instability, environmental conditions.
In practice, however, a combined approach will be the most suitable; this combined approach will
apply very often, as it is impossible to estimate each uncertainty individually. In this case, type B will
be used with reference materials and quality control materials to avoid some systematic measuring
error. The single uncertainties are combined applying the law of propagation of uncertainty. The type A
uncertainty estimate is an estimate derived from the statistical analysis of experimental data. This type
of uncertainty evaluation is preferred when the value of a measurand will be the average of several test
results or is in relation with non-independent variables.
A.2 Evaluation of measurement uncertainty of the sonic conductance, C, using type B
A.2.1 Measurand conductance, C
e
According to this part of ISO 6358, the most important flow-rate characteristic parameter of a pneumatic
component is the sonic conductance, C. The equation relating measurand conductance, C , and evolution
e
of the conductance during the charge or discharge test can be expressed using either Formulae (E.3) or
(E.8); following these equations, the quantity subject to measurement, and input quantities are:
1 T V dp dp
3 3 3
Cs==()ign fp(,TV,, ) (A.1)
e 13
ρ p T RT dt dt
01 03
A.2.2 Identification of uncertainty of input quantities
According to Formula (A.1), the input quantities subject to measurement are:
a) p – upstream stagnation pressure
Uncertainty follows the accuracy of measuring instrument: ±Δp = ±0,5 %
Method of measurement of stagnation pressure (wall taping): Δp = +0,3 %
b) T – upstream stagnation temperature
Uncertainty follows the accuracy of measuring instrument: ±ΔT = ±1 K
18 © ISO 2013 – All rights reserved

It must be noted here that all measurement instabilities are included in the previous limits of
uncertainty. If it is not, the reality in this range of instability must be added at the previous ΔT. However,
the temperature variation (decreasing in the discharge case or increasing in charge case) must be less
than 3K from the isothermal tank. That is the condition for the validity of the isothermal assumption
of air inside the tank and the flow rate can be calculated by only recording the pressure response.
c) V – volume of isothermal tank
Uncertainties will follow the evaluation of Formula (B.14)
d) dp /dt – change in pressure in the tank
Uncertainty will follow the accuracy of measuring instrument and the time base (sampling period).
A.2.3 Sensitivity coefficient
Sensitivity coefficients are obtained from partial derivatives of the model function f with respect to the
input quantities. For the evolution of conductance, C :
e
T dp
∂f 1 V
3 3
= for the input p (A.2)
∂p T RT dt
ρ p
1 03
∂f 1 V dp
= for the input T (A.3)
∂T RT T dt
T
3 30
2ρ p
T
∂f 1 T V dp
3 3
= for the input (A.4)
dp  ρ p T RT dt
3 01 03
∂
 
dt
 
A.2.4 Expression of absolute standard uncertainty
The absolute standard uncertainty for the measured conductance, C , is given by:
e
dp
∂f ∂f ∂f
ΔΔCp= + ΔΔT + (A.5)
e 1 3
∂p ∂T dt dp
 
1 3 3
∂
 
dt
 
If the relative or percentage standard uncertainty is desired, it is given by:
ΔC
e
ΔC %=100 (A.6)
e
C
e
A.3 Evaluation of measurement uncertainty of the sonic conductance, C, using
Type A
A.3.1 Measurand sonic conductance, C
According to this part of ISO 6358, the most important flow-rate characteristic parameter of a pneumatic
component is the sonic conductance, C. The evolution of conductance, C , is defined by Formula (A.1)
e
can be plotted over the ratio of downstream pressure to upstream pressure, p /p . These curves show
2 1
correlatively the pressure variation and the conductance characteristics variation. See 6.3.1.3 of this
part of ISO 6358.
A.3.2 Expression of standard uncertainty
If the measurement points in the choked flow region are considered, an estimate of the measurand is
obtained that will be the average of several data points, as follows:
n
C= C (A.7)
i
∑
n
i=1
where
n is number of measurement points in the choked flow region (n > 1);
C is the result of data measurement at i.
i
The experimental standard deviation, s , characterizes the variability of observed values, C , in the
c i
choked flow region, as follows:
in=
CC−
()
i
∑
i=1
s = (A.8)
c
n−1
This experimental standard deviation of the sonic conductance measurement can be taken as an
estimate of uncertainty (type A).
A.4 Evaluation of measurement uncertainty of the critical back-pressure ratio, b,
and subsonic index, m, using type B
A.4.1 Measurands
According to this part of ISO 6358, the second most important flow-rate characteristic parameter of a
pneumatic component is the critical back-pressure ratio, b. The subsonic index, m, is eventually used
to represent the subsonic flow behaviour. The equation relating measurands b and m, i.e. the quantity
subject to measurement, and input quantities is:
m
 
 p 
 
−b
 
C p
 
e 1
 
=−1 (A.9)
 
C  1−b 
 
 
 
 
 
This equation is solved by the non linear least square method (NLLSQ) with the variables as follows:
C
e
y = (A.10)
i
C
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p
2,i
x = (A.11)
i
p
1,i
The difference between an observed value and the value given by the model is:
m
 
xb−
   
i
δ =−y 1− (A.12)
 
ii  
1−b
 
 
 
The sum of squared difference will be the least values (see Annex G). The NLLSQ are conceptually
inadequate to generate a statistical estimator of uncertainty. A pragmatic way to estimate the variability
of b and m can be to use the NLLSQ with the minimum and maximum values of C found in A.3.2.
A.4.2 Identification and expression of uncertainty
As mentioned in A.4.1, the functional relationship between the measurands b and m and the influence
quantities is an arduous task. In this paragraph, two calculations will focus on the upper and lower
limits of these characteristics. The uncertainty of these flow-rate characteristics will be defined here as
limits associated with the NLLSQ calculation results from maximum and minimum sonic conductance
determined in the choked flow region. In these conditions:
Cs− →→NLLSQb,m (A.13)
{} []
c
Cmin
Cs− →→NLLSQb,m (A.14)
{} []
c
Cmax
From these calculation results, the maximum absolute differences between these limits and the best
values attributable to these measurands are the two values: Δb and Δm . These values are now
max max
considered as the uncertainty of the result of a measurement, which is expressed as:
bb± Δ for the critical back-pressure ratio
max
(A.15)
mm± Δ for the subsonic index
max
(A.16)
NOTE These calculations show that:
a) concerning the choked flow region of the conductance curve, the comparison of results can be done directly
by comparing the values of sonic conductance, C; but
b) concerning the subsonic flow region of the conductance curve, the comparison of each parameter b and
m independently is not sufficient to compare the results. It is necessary to add a graphical comparison
of conductance curves, because the variations of each parameter C, b, and m can compensate to give an
equivalent subsonic flow region of the conductance curve.
A.
...