SIST EN 60534-2-1:2001
(Main)Industrial-process control valves -- Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions
Industrial-process control valves -- Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions
Includes equations for predicting the flow of compressible and incompressible fluids through control valves. They are not intended for use when non-Newtonian fluids, fluid mixtures, slurries or liquid-solid conveyance systems are encountered. The equations for compressible fluids are for use with gas or vapour and are not intended for use with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures.
Stellventile für die Prozeßregelung -- Teil 2-1: Durchflußleistung - Bemessungsgleichungen für Fluide unter Einbaubedingungen
Vannes de régulation des processus industriels -- Partie 2-1: Capacité d'écoulement - Equations de dimensionnement pour l'écoulement des fluides dans les conditions d'installation
Comprend des équations permettant de prédire le débit de fluides compressibles et incompressibles dans les vannes de régulation. N0e sont pas destinées à être utilisées pour des fluides on newtoniens, des mélanges de fluides, des boues ou des systèmes de transport de particules solides en suspension dans un liquide. Les équations présentées d'appliquent aux gaz ou aux vapeurs, mais ne conviennent pas pour les fluides multiphasiques tels que les mélanges gaz-liquide, vapeur-liquide ou gaz-solide.
Industrial-process control valves - Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 60534-2-1:2001
01-april-2001
1DGRPHãþD
SIST EN 60534-2-1:1998
SIST EN 60534-2-2:1998
Industrial-process control valves - Part 2-1: Flow capacity - Sizing equations for
fluid flow under installed conditions
Industrial-process control valves -- Part 2-1: Flow capacity - Sizing equations for fluid
flow under installed conditions
Stellventile für die Prozeßregelung -- Teil 2-1: Durchflußleistung -
Bemessungsgleichungen für Fluide unter Einbaubedingungen
Vannes de régulation des processus industriels -- Partie 2-1: Capacité d'écoulement -
Equations de dimensionnement pour l'écoulement des fluides dans les conditions
d'installation
Ta slovenski standard je istoveten z: EN 60534-2-1:1998
ICS:
23.060.40 7ODþQLUHJXODWRUML Pressure regulators
25.040.40 Merjenje in krmiljenje Industrial process
industrijskih postopkov measurement and control
SIST EN 60534-2-1:2001 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN 60534-2-1:2001
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SIST EN 60534-2-1:2001
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SIST EN 60534-2-1:2001
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SIST EN 60534-2-1:2001
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SIST EN 60534-2-1:2001
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SIST EN 60534-2-1:2001
IEC 60534-2-1
Edition 1.0 1998-09
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Industrial-process control valves –
Part 2-1: Flow-capacity – Sizing equations for fluid flow under installed
conditions
Vannes de régulation des processus industriels –
Partie 2-1: Capacité d’écoulement – Equations de dimensionnement pour
l’écoulement des fluides dans les conditions d’installation
IEC 60534-2-1:1998
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SIST EN 60534-2-1:2001
IEC 60534-2-1
Edition 1.0 1998-09
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Industrial-process control valves –
Part 2-1: Flow-capacity – Sizing equations for fluid flow under installed
conditions
Vannes de régulation des processus industriels –
Partie 2-1: Capacité d’écoulement – Equations de dimensionnement pour
l’écoulement des fluides dans les conditions d’installation
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
X
CODE PRIX
ICS 23.060.40; 25.040.40 ISBN 2-8318-4751-6
® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 3 –
CONTENTS
Page
FOREWORD . 5
Clause
1 Scope . 7
2 Normative references . 7
3 Definitions. 9
4 Installation . 9
5 Symbols . 11
6 Sizing equations for incompressible fluids. 13
7 Sizing equations for compressible fluids . 17
8 Determination of correction factors . 21
Annex A (informative) Derivation of valve style modifier F . 49
d
Annex B (informative) Control valve sizing flow charts. 59
Annex C (informative) Physical constants . 67
Annex D (informative) Examples of sizing calculations . 69
Annex E (informative) Bibliography . 91
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
––––––––––––
INDUSTRIAL-PROCESS CONTROL VALVES –
Part 2-1: Flow capacity – Sizing equations for fluid flow
under installed conditions
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60534-2-1 has been prepared by subcommittee 65B: Devices, of
IEC technical committee 65: Industrial-process measurement and control.
IEC 60534-2-1 cancels and replaces the first edition of both IEC 60534-2, published in 1978,
and IEC 60534-2-2, published in 1980, which covered incompressible and compressible fluid
flow, respectively.
IEC 60534-2-1 covers sizing equations for both incompressible and compressible fluid flow.
This bilingual version, published in 1999-03, corresponds to the English version.
The text of this standard is based on the following documents:
FDIS Report on voting
65B/347/FDIS 65B/357/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
Annexes A, B, C, D and E are for information only.
The contents of the corrigendum of February 2000 have been included in this copy.
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 7 –
INDUSTRIAL-PROCESS CONTROL VALVES –
Part 2-1: Flow capacity – Sizing equations for fluid flow
under installed conditions
1 Scope
This part of IEC 60534 includes equations for predicting the flow of compressible and
incompressible fluids through control valves.
The equations for incompressible flow are based on standard hydrodynamic equations for
Newtonian incompressible fluids. They are not intended for use when non-Newtonian fluids,
fluid mixtures, slurries or liquid-solid conveyance systems are encountered.
At very low ratios of pressure differential to absolute inlet pressure (Δp/p ), compressible fluids
1
behave similarly to incompressible fluids. Under such conditions, the sizing equations for
compressible flow can be traced to the standard hydrodynamic equations for Newtonian
incompressible fluids. However, increasing values of Δp/p result in compressibility effects
1
which require that the basic equations be modified by appropriate correction factors. The
equations for compressible fluids are for use with gas or vapour and are not intended for use
with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures.
For compressible fluid applications, this part of IEC 60534 is valid for valves with x ≤ 0,84
T
(see table 2). For valves with x > 0,84 (e.g. some multistage valves), greater inaccuracy of
T
flow prediction can be expected.
2 2
Reasonable accuracy can only be maintained for control valves if K /d < 0,04 (C /d < 0,047).
v v
2 Normative references
The following normative documents contain provisions which, through reference in this text,
constitute provisions of this part of IEC 60534. For dated references, subsequent amendments
to, or revisions of, any of these publications do not apply. However, parties to agreements
based on this part of IEC 60534 are encouraged to investigate the possibility of applying the
most recent editions of the normative documents indicated below. For undated references, the
latest edition of the normative document referred to applies. Members of IEC and ISO maintain
registers of currently valid International Standards.
IEC 60534-1:1987, Industrial-process control valves – Part 1: Control valve terminology and
general considerations
IEC 60534-2-3:1997, Industrial-process control valves – Part 2: Flow capacity – Section 3: Test
procedures
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 9 –
3 Definitions
For the purpose of this part of IEC 60534, definitions given in IEC 60534-1 apply with the
addition of the following:
3.1
valve style modifier F
d
the ratio of the hydraulic diameter of a single flow passage to the diameter of a circular orifice,
the area of which is equivalent to the sum of areas of all identical flow passages at a given
travel. It should be stated by the manufacturer as a function of travel. See annex A
4 Installation
In many industrial applications, reducers or other fittings are attached to the control valves. The
effect of these types of fittings on the nominal flow coefficient of the control valve can be
significant. A correction factor is introduced to account for this effect. Additional factors are
introduced to take account of the fluid property characteristics that influence the flow capacity
of a control valve.
In sizing control valves, using the relationships presented herein, the flow coefficients calculated
are assumed to include all head losses between points A and B, as shown in figure 1.
Flow
l l
I
I1 2 Pressure
2 Pressur
1
Pressur
Pressure
tap
tap
tap
tap
A B
Control valve with or without attached fittings
IEC 588/99
l = two nominal pipe diameters
1
l = six nominal pipe diameters
2
Figure 1 – Reference pipe section for sizing
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 11 –
5 Symbols
Symbol Description Unit
C Flow coefficient (K , C ) Various (see IEC 60534-1)
v v
(see note 4)
C Assumed flow coefficient for iterative purposes Various (see IEC 60534-1)
i
(see note 4)
d Nominal valve size mm
D Internal diameter of the piping mm
D Internal diameter of upstream piping mm
1
D Internal diameter of downstream piping mm
2
D Orifice diameter mm
o
Valve style modifier (see annex A) 1 (see note 4)
F
d
F Liquid critical pressure ratio factor 1
F
F Liquid pressure recovery factor of a control valve without attached fittings 1 (see note 4)
L
F Combined liquid pressure recovery factor and piping geometry factor of a 1 (see note 4)
LP
control valve with attached fittings
F Piping geometry factor 1
P
F Reynolds number factor 1
R
F Specific heat ratio factor 1
γ
M Molecular mass of flowing fluid kg/kmol
N Numerical constants (see table 1) Various (see note 1)
p Inlet absolute static pressure measured at point A (see figure 1) kPa or bar (see note 2)
1
p Outlet absolute static pressure measured at point B (see figure 1) kPa or bar
2
p Absolute thermodynamic critical pressure kPa or bar
c
p Reduced pressure (p /p ) 1
r 1 c
p Absolute vapour pressure of the liquid at inlet temperature kPa or bar
v
Differential pressure between upstream and downstream pressure taps kPa or bar
Δp
(p – p )
1 2
3
Q Volumetric flow rate (see note 5) m /h
Re Valve Reynolds number 1
v
T Inlet absolute temperature K
1
T Absolute thermodynamic critical temperature K
c
T Reduced temperature (T /T ) 1
r 1 c
t Absolute reference temperature for standard cubic metre K
s
W Mass flow rate kg/h
x 1
Ratio of pressure differential to inlet absolute pressure (Δp/p )
1
x Pressure differential ratio factor of a control valve without attached fittings 1 (see note 4)
T
at choked flow
x Pressure differential ratio factor of a control valve with attached fittings at 1 (see note 4)
TP
choked flow
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 13 –
Symbol Description Unit
Expansion factor 1
Y
Z Compressibility factor 1
2
Kinematic viscosity m /s (see note 3)
ν
3
ρ Density of fluid at p and T kg/m
1 1 1
ρ /ρ Relative density (ρ /ρ = 1,0 for water at 15 °C) 1
1 o 1 o
Specific heat ratio 1
γ
Velocity head loss coefficient of a reducer, expander or other fitting 1
ζ
attached to a control valve or valve trim
Upstream velocity head loss coefficient of fitting 1
ζ
1
Downstream velocity head loss coefficient of fitting 1
ζ
2
Inlet Bernoulli coefficient 1
ζ
B1
ζ Outlet Bernoulli coefficient 1
B2
NOTE 1 – To determine the units for the numerical constants, dimensional analysis may be performed on the
appropriate equations using the units given in table 1.
2 5
NOTE 2 – 1 bar = 10 kPa = 10 Pa
–6 2
NOTE 3 – 1 centistoke = 10 m /s
NOTE 4 – These values are travel-related and should be stated by the manufacturer.
NOTE 5 – Volumetric flow rates in cubic metres per hour, identified by the symbol Q, refer to standard conditions.
The standard cubic metre is taken at 1 013,25 mbar and either 273 K or 288 K (see table 1).
6 Sizing equations for incompressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors, and pertinent service conditions for control valves handling
incompressible fluids. Flow coefficients may be calculated using the appropriate equation
selected from the ones given below. A sizing flow chart for incompressible fluids is given in
annex B.
6.1 Turbulent flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-choked flow conditions are derived from the basic formula as given in IEC 60534-1.
6.1.1 Non-choked turbulent flow
6.1.1.1 Non-choked turbulent flow without attached fittings
2
Applicable ifΔ
()
[]LF1 v
The flow coefficient shall be determined by
Qρ/ρ
1o
C= (1)
NpΔ
1
NOTE 1 – The numerical constant N depends on the units used in the general sizing equation and the type of flow
1
coefficient: K or C .
v v
NOTE 2 – An example of sizing a valve with non-choked turbulent flow without attached fittings is given in annex D.
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 15 –
6.1.1.2 Non-choked turbulent flow with attached fittings
2
Applicable ifΔ
LP P 1 F v
The flow coefficient shall be determined as follows:
ρ /ρ
Q
1 o
C= (2)
NF Δp
1 P
NOTE – Refer to 8.1 for the piping geometry factor F .
P
6.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated from the following equations.
6.1.2.1 Choked turbulent flow without attached fittings
2
Applicable ifΔ≥p F p −F × p
()
LF1 v
[]
The flow coefficient shall be determined as follows:
Q ρ/ρ
1 o
C= (3)
NF p−×F p
1L 1 Fv
NOTE – An example of sizing a valve with choked flow without attached fittings is given in annex D.
6.1.2.2 Choked turbulent flow with attached fittings
2
Applicable ifΔ≥p F / F p −F × p
()( )
LP P 1 F v
The following equation shall be used to calculate the flow coefficient:
Q ρ/ρ
1 o
C= (4)
Np F −×Fp
1 LP 1 Fv
6.2 Non-turbulent (laminar and transitional) flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-turbulent flow conditions are derived from the basic formula as given in IEC 60534-1.
This equation is applicable if Re < 10 000 (see equation (28)).
v
6.2.1 Non-turbulent flow without attached fittings
The flow coefficient shall be calculated as follows:
Q ρ /ρ
1 o
C= (5)
NF Δp
1 R
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 17 –
6.2.2 Non-turbulent flow with attached fittings
For non-turbulent flow, the effect of close-coupled reducers or other flow-disturbing fittings is
unknown. While there is no information on the laminar or transitional flow behaviour of control
valves installed between pipe reducers, the user of such valves is advised to utilize the
appropriate equations for line-sized valves in the calculation of the F factor. This should result
R
in conservative flow coefficients, since additional turbulence created by reducers and
expanders will further delay the onset of laminar flow. Therefore, it will tend to increase the
respective F factor for a given valve Reynolds number.
R
7 Sizing equations for compressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors and pertinent service conditions for control valves handling
compressible fluids. Flow rates for compressible fluids may be encountered in either mass or
volume units and thus equations are necessary to handle both situations. Flow coefficients may
be calculated using the appropriate equations selected from the following. A sizing flow chart
for compressible fluids is given in annex B.
7.1 Turbulent flow
7.1.1 Non-choked turbulent flow
7.1.1.1 Non-choked turbulent flow without attached fittings
Applicable if x < F x
[]
γ T
The flow coefficient shall be calculated using one of the following equations:
W
C= (6)
NY xpρ
611
W TZ
1
C = (7)
NpY xM
81
Q MT Z
1
C = (8)
NpY x
91
NOTE 1 – Refer to 8.5 for details of the expansion factor Y.
NOTE 2 – See annex C for values of M.
7.1.1.2 Non-choked turbulent flow with attached fittings
Applicable if x < F x
[]
γ TP
The flow coefficient shall be determined from one of the following equations:
W
C= (9)
NF Y xpρ
61P 1
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 19 –
W TZ
1
C = (10)
NFpY xM
81P
Q MT Z
1
C = (11)
NFpY x
91P
NOTE 1 – Refer to 8.1 for the piping geometry factor F .
P
NOTE 2 – An example of sizing a valve with non-choked turbulent flow with attached fittings is given in annex D.
7.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated as follows.
7.1.2.1 Choked turbulent flow without attached fittings
Applicable if x ≥ F x
[]γ T
The flow coefficient shall be calculated from one of the following equations:
W
C= (12)
0,667NFx pρ
61γT1
W TZ
1
C= (13)
0,667Np Fx M
81 γ T
Q MT Z
1
C=
(14)
0,667Np Fx
91 γ T
7.1.2.2 Choked turbulent flow with attached fittings
Applicable if x ≥ F x
[]γ TP
The flow coefficient shall be determined using one of the following equations:
W
C= (15)
0,667NF F x pρ
61PTγ P1
TZ
W
1
C= (16)
0,667NF p Fx M
81PTγP
MT Z
Q
1
C= (17)
0,667NF p Fx
91PTγP
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 21 –
7.2 Non-turbulent (laminar and transitional) flow
The equations for the flow rate of a Newtonian fluid through a control valve when operating
under non-turbulent flow conditions are derived from the basic formula as given in IEC 60534-1.
These equations are applicable if Re < 10 000 (see equation (28)). In this subclause, the
v
density correction of the gas is given by (p + p )/2 due to non-isentropic expansion.
1 2
7.2.1 Non-turbulent flow without attached fittings
The flow coefficient shall be calculated from one of the following equations:
W T
1
C= (18)
NF Δp p +p M
()
27R 12
Q MT
1
C= (19)
NF Δp p()+p
22R 12
NOTE – An example of sizing a valve with small flow trim is given in annex D.
7.2.2 Non-turbulent flow with attached fittings
For non-turbulent flow, the effect of close-coupled reducers or other flow-disturbing fittings is
unknown. While there is no information on the laminar or transitional flow behaviour of control
valves installed between pipe reducers, the user of such valves is advised to utilize the
appropriate equations for line-sized valves in the calculation of the F factor. This should result
R
in conservative flow coefficients since additional turbulence created by reducers and expanders
will further delay the onset of laminar flow. Therefore, it will tend to increase the respective F
R
factor for a given valve Reynolds number.
8 Determination of correction factors
8.1 Piping geometry factor F
P
The piping geometry factor F is necessary to account for fittings attached upstream and/or
P
downstream to a control valve body. The F factor is the ratio of the flow rate through a control
P
valve installed with attached fittings to the flow rate that would result if the control valve was
installed without attached fittings and tested under identical conditions which will not produce
choked flow in either installation (see figure 1). To meet the accuracy of the F factor of ±5 %,
P
the F factor shall be determined by test in accordance with IEC 60534-2-3.
P
When estimated values are permissible, the following equation shall be used:
1
F = (20)
P
2
Σζ C
i
1+
2
N
d
2
In this equation, the factor Σζ is the algebraic sum of all of the effective velocity head loss
coefficients of all fittings attached to the control valve. The velocity head loss coefficient of the
control valve itself is not included.
Σζ=+ζ ζ +ζ −ζ (21)
12 BB1 2
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SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 23 –
In cases where the piping diameters approaching and leaving the control valve are different,
the ζ coefficients are calculated as follows:
B
4
d
ζ =−1 (22)
B
D
If the inlet and outlet fittings are short-length, commercially available, concentric reducers, the
ζ and ζ coefficients may be approximated as follows:
1 2
2
2
d
Inlet reducer: ζ=−05, 1 (23)
1
D
1
2
2
d
Outlet reducer (expander): ζ=−10, 1 (24)
2
D
2
2
2
d
Inlet and outlet reducers of equal size: ζ+=ζ 15, 1− (25)
12
D
The F values calculated with the above ζ factors generally lead to the selection of valve
P
capacities slightly larger than required. This calculation requires iteration. Proceed by
calculating the flow coefficient C for non-choked turbulent flow.
NOTE – Choked flow equations and equations involving F are not applicable.
P
Next, establish C as follows:
i
CC=13, (26)
i
Using C from equation (26), determine F from equation (20). If both ends of the valve are the
i P
same size, F may instead be determined from figure 2. Then, determine if
P
C
≤C (27)
i
F
P
If the condition of equation (27) is satisfied, then use the C established from equation (26).
i
If the condition of equation (27) is not met, then repeat the above procedure by again
increasing C by 30 %. This may require several iterations until the condition required in
i
equation (27) is met. An iteration method more suitable for computers can be found in annex B.
For graphical approximations of F , refer to figures 2a and 2b.
P
8.2 Reynolds number factor F
R
The Reynolds number factor F is required when non-turbulent flow conditions are established
R
through a control valve because of a low pressure differential, a high viscosity, a very small
flow coefficient, or a combination thereof.
The F factor is determined by dividing the flow rate when non-turbulent flow conditions exist
R
by the flow rate measured in the same installation under turbulent conditions.
---------------------- Page: 19 ----------------------
SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 25 –
Tests show that F can be determined from the curves given in figure 3 using a valve Reynolds
R
number calculated from the following equation:
14/
22
NF Q FC
4 d Li
=+
Re 1 (28)
v
4
ν CF
ND
iL 2
This calculation will require iteration. Proceed by calculating the flow coefficient C for turbulent
flow. The valve style modifier F converts the geometry of the orifice(s) to an equivalent
d
circular single flow passage. See table 2 for typical values and annex A for details. To meet
a deviation of ±5 % for F , the F factor shall be determined by test in accordance with
d d
IEC 60534-2-3.
NOTE – Equations involving F are not applicable.
P
Next, establish C as per equation (26).
i
Apply C as per equation (26) and determine F from equations (30) and (31) for full size trims
i R
or equations (32) and (33) for reduced trims. In either case, using the lower of the two F
R
values, determine if
C
≤C (29)
i
F
R
If the condition of equation (29) is satisfied, then use the C established from equation (26). If
i
the condition of equation (29) is not met, then repeat the above procedure by again increasing
C by 30 %. This may require several iterations until the condition required in equation (29) is
i
met.
2
For full size trim where C/d ≥ 0,016 N and Re ≥ 10, calculate F from the following
i 18 v R
equations:
12/
03, 3F Re
Lv
F =+1 log (30)
R 10
14/
10000
n
1
for the transitional flow regime,
where
N
2
n = (30a)
1
2
C
i
2
d
or
0,026
F = n Re (not to exceed F = 1) (31)
R 1 v R
F
L
for the laminar flow regime.
1 – F Re
NOTE Use the lower value of from equations (30) and (31). If < 10, use only equation (31).
R v
NOTE 2 – Equation (31) is applicable to fully developed laminar flow (straight lines in figure 3). The relationships
expressed in equations (30) and (31) are based on test data with valves at rated travel and may not be fully
accurate at lower valve travels.
2
NOTE 3 – In equations (30a) and (31), C /d must not exceed 0,04 when K is used or 0,047 when C is used.
i v v
---------------------- Page: 20 ----------------------
SIST EN 60534-2-1:2001
60534-2-1 © IEC:1998 – 27 –
2
For reduced trim valves where C /d at rated travel is less than 0,016 N and Re ≥ 10,
i 18 v
calculate F from the following equations:
R
12/
03, 3F Re
Lv
F =+1 log (32)
R 10
14/
10 000
n
2
for the transitional flow regime,
where
2 / 3
C
i
n = 1+N (32a)
2 32
2
d
or
0,026
F = n Re (not to exceed F = 1) (33)
R 2 v R
F
L
for the laminar flow regime.
NOTE 1 – Select the lower value from equations (32) and (33). If Re < 10, use only equation (33).
v
NOTE 2 – Equation (33) is applicable to fully developed laminar flow (straight lines in figure 3).
8.3 Liquid pressure recovery factors F or F
L LP
8.3.1 Liquid pressure recovery factor without attached fittings F
L
F is the liquid pressure recovery factor of the valve without attached fittings. This factor
L
accounts for the influence of the valve internal geometry on the valve capacity at choked flow.
It is defined as the ratio of the actual maximum flow rate under choked flow conditions to a
theoretical, non-choked flow rate which would be calculated if the pressure differential
used was the difference between the valve inlet pressure and the apparent vena contracta
pressure at choked flow conditions. The factor F may be determined from tests in accordance
L
with IEC 60534-2-3. Typical values of F versus percent of rated flow coefficient are shown in
L
figure 4.
8.3.2 Combined liquid pressure recovery factor and piping geometry factor
with attached fittings F
LP
F is the combined liquid pressure recovery factor and piping geometry factor for a control
LP
valve with attached fittings. It is obtained in the s
...
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