# SIST EN 60534-2-5:2004

(Main)## Industrial-process control valves -- Part 2-5: Flow capacity - Sizing equations for fluid flow through multistage control valves with interstage recovery

## Industrial-process control valves -- Part 2-5: Flow capacity - Sizing equations for fluid flow through multistage control valves with interstage recovery

Gives equations for predicting the flow of compressible and incompressible fluids through multistage control valves. Is based on standard hydrodynamic equations for Newtonian incompressible fluids. Is applicable only to those designs of multistage multipath control valves and multistage single path control valves.

## Stellventile für die Prozessregelung -- Teil 2-5: Durchflusskapazität - Bemessungsgleichungen für Fluide durch Mehrstufenregelventile mit Druckrückgewinn zwischen den Stufen

## Vannes de régulation des processus industriels -- Partie 2-5: Capacité d'écoulement - Equations de dimensionnement pour l'écoulement des fluides dans les vannes de régulation multi-étagées avec récupération entre étages

Fournit les équations permettant de prédire le débit de fluides compressibles et incompressibles dans les vannes de régulation multi-étagées. Est fondée sur les équations de base pour les fluides newtoniens incompressibles. S'applique uniquement aux conceptions de vannes de régulation multi-étagées à chemins multiples et multi-étagées à chemin unique.

## Industrial-process control valves - Part 2-5: Flow capacity - Sizing equations for fluid flow through multistage control valves with interstage recovery

### General Information

### Standards Content (Sample)

SLOVENSKI SIST EN 60534-2-5:2004

STANDARD

marec 2004

Industrial-process control valves - Part 2-5: Flow capacity - Sizing equations for fluid

flow through multistage control valves with interstage recoveryICS 23.060.40; 25.040.40 Referenčna številka

SIST EN 60534-2-5:2004(en)

© Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

---------------------- Page: 1 ----------------------EUROPEAN STANDARD EN 60534-2-5

NORME EUROPÉENNE

EUROPÄISCHE NORM October 2003

ICS 23.060.40 ; 25.040.40

English version

Industrial-process control valves

Part 2-5: Flow capacity –

Sizing equations for fluid flow

through multistage control valves

with interstage recovery

(IEC 60534-2-5:2003)

Vannes de régulation des processus Stellventile für die Prozessregelung

industriels Teil 2-5: Durchflusskapazität –

Partie 2-5: Capacité d'écoulement – Bemessungsgleichungen für Fluide

Equations de dimensionnement durch Mehrstufenregelventile

pour l'écoulement des fluides mit Druckrückgewinn

dans les vannes de régulation zwischen den Stufen

multi-étagées avec récupération (IEC 60534-2-5:2003)

entre étages

(CEI 60534-2-5:2003)

This European Standard was approved by CENELEC on 2003-10-01. CENELEC members are bound to

comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European

Standard the status of a national standard without any alteration.Up-to-date lists and bibliographical references concerning such national standards may be obtained on

application to the Central Secretariat or to any CENELEC member.This European Standard exists in three official versions (English, French, German). A version in any other

language made by translation under the responsibility of a CENELEC member into its own language and

notified to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Czech Republic,

Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Lithuania, Luxembourg, Malta,

Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and United Kingdom.

CENELECEuropean Committee for Electrotechnical Standardization

Comité Européen de Normalisation Electrotechnique

Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1050 Brussels

© 2003 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.

Ref. No. EN 60534-2-5:2003 E---------------------- Page: 2 ----------------------

EN 60534-2-5:2003 - 2 -

Foreword

The text of document 65B/488/FDIS, future edition 1 of IEC 60534-2-5, prepared by SC 65B, Devices,

of IEC TC 65, Industrial-process measurement and control, was submitted to the IEC-CENELEC

parallel vote and was approved by CENELEC as EN 60534-2-5 on 2003-10-01.The following dates were fixed:

– latest date by which the EN has to be implemented

at national level by publication of an identical

national standard or by endorsement (dop) 2004-07-01

– latest date by which the national standards conflicting

with the EN have to be withdrawn (dow) 2006-10-01

Annexes designated "normative" are part of the body of the standard.

Annexes designated "informative" are given for information only.

In this standard, annex ZA is normative and annexes A and B are informative.

Annex ZA has been added by CENELEC.

__________

Endorsement notice

The text of the International Standard IEC 60534-2-5:2003 was approved by CENELEC as a

European Standard without any modification.__________

---------------------- Page: 3 ----------------------

- 3 - EN 60534-2-5:2003

Annex ZA

(normative)

Normative references to international publications

with their corresponding European publications

This European Standard incorporates by dated or undated reference, provisions from other

publications. These normative references are cited at the appropriate places in the text and the

publications are listed hereafter. For dated references, subsequent amendments to or revisions of any

of these publications apply to this European Standard only when incorporated in it by amendment or

revision. For undated references the latest edition of the publication referred to applies (including

amendments).NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant

EN/HD applies.Publication Year Title EN/HD Year

IEC 60534-1 1987 Industrial-process control valves EN 60534-1 1993

Part 1: Control valve terminology and

general considerations

IEC 60534-2-1 1998 Part 2-1: Flow capacity - Sizing EN 60534-2-1 1998

equations for fluid flow under installed

conditions

IEC 60534-2-3 1997 Part 2-3: Flow capacity - Test EN 60534-2-3 1998

procedures

---------------------- Page: 4 ----------------------

NORME

CEI

INTERNATIONALE IEC

60534-2-5

INTERNATIONAL

Première édition

STANDARD

First edition

2003-09

Vannes de régulation des processus industriels –

Partie 2-5:

Capacité d'écoulement –

Equations de dimensionnement pour l'écoulement

des fluides dans les vannes de régulation multi-

étagées avec récupération entre étages

Industrial process control valves –

Part 2-5:

Flow capacity –

Sizing equations for fluid flow through multistage

control valves with interstage recovery

© IEC 2003 Droits de reproduction réservés ⎯ Copyright - all rights reserved

Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or utilized in any

utilisée sous quelque forme que ce soit et par aucun procédé, form or by any means, electronic or mechanical, including

électronique ou mécanique, y compris la photocopie et les photocopying and microfilm, without permission in writing from

microfilms, sans l'accord écrit de l'éditeur. the publisher.International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland

Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch

CODE PRIXCommission Electrotechnique Internationale PRICE CODE

International Electrotechnical Commission

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Pour prix, voir catalogue en vigueur

For price, see current catalogue

---------------------- Page: 5 ----------------------

60534-2-5 © IEC:2003 – 3 –

CONTENTS

FOREWORD .......................................................................................................................... 5

INTRODUCTION ....................................................................................................................9

1 Scope .............................................................................................................................11

2 Normative references......................................................................................................11

3 Terms and definitions .....................................................................................................11

4 Installation ......................................................................................................................15

5 Symbols..........................................................................................................................17

6 Sizing equations for incompressible fluids.......................................................................19

6.1 Turbulent flow........................................................................................................19

7 Sizing equations for compressible fluids .........................................................................21

7.1 Turbulent flow........................................................................................................23

8 Determination of correction factors .................................................................................25

8.1 Piping geometry factor, F .....................................................................................25

8.2 Liquid pressure recovery factors F or F .............................................................25

L LP8.3 Liquid critical pressure ratio factor F ....................................................................27

8.4 Expansion factor Y ................................................................................................27

8.5 Pressure differential ratio factor x or x ..............................................................29

T TP8.6 Specific heat ratio factor F ....................................................................................29

8.7 Compressibility factor Z .........................................................................................29

8.8 Stage interaction factor k.......................................................................................31

8.9 Reheat factor r.......................................................................................................31

Annex A (informative) Physical constants ..........................................................................35

Annex B (informative) Examples of sizing calculations .........................................................37

Bibliography..........................................................................................................................55

Figure 1 – Multistage multipath trim ......................................................................................13

Figure 2 – Multistage single path trim....................................................................................15

Figure 3 – Reference pipe section for sizing..........................................................................17

Figure 4 – Liquid critical pressure ratio factor F ...................................................................33

Table 1 – Numerical constants N...........................................................................................31

Table 2 – Typical values of liquid pressure recovery factor F , and pressure differential

ratio factor x at full rated travel............................................................................................33

Table 3 – Values of the stage interaction factors k and the reheat factors r ...........................33

---------------------- Page: 6 ----------------------60534-2-5 © IEC:2003 – 5 –

INTERNATIONAL ELECTROTECHNICAL COMMISSION

––––––––––––

INDUSTRIAL-PROCESS CONTROL VALVES –

Part 2-5: Flow capacity – Sizing equations for fluid flow

through multistage control valves with interstage recovery

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, 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 60534-2-5 has been prepared by subcommittee 65B: Devices, of

IEC technical committee 65: Industrial-process measurement and control.The text of this standard is based on the following documents:

FDIS Report on voting

65B/488/FDIS 65B/502/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.This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.

---------------------- Page: 7 ----------------------60534-2-5 © IEC:2003 – 7 –

The committee has decided that the contents of this publication will remain unchanged until 2007.

At this date, the publication will be• reconfirmed;

• withdrawn;

• replaced by a revised edition, or

• amended.

---------------------- Page: 8 ----------------------

60534-2-5 © IEC:2003 – 9 –

INTRODUCTION

This part of IEC 60534 includes equations for predicting flow which are the same as IEC

60534-2-1. The differences in this multistage standard are:a) the equation for the calculation of expansion factor Y (equation 18);

b) the non-inclusion of the section on sizing for laminar flow;

c) the inclusion of stage interaction factor k (8.8) and reheat factor r (8.9);

d) the addition of Tables for multistage valves for values of F and x

L T.

The test data used to validate the method for numbers of stages from one to five was

obtained from sizing tests carried out in accordance with IEC 60534-2-3 using air as the test

5 5medium at pressures varying from 5 × 10 Pa to 13,5 × 10 Pa and at temperatures of

approximately 300 K. Some data was obtained under plant conditions using steam at

5 5pressures varying from 12 × 10 Pa to 110 × 10 Pa and temperatures from 460 K to 750 K.

The method is applicable to any number of stages but has only been validated up to five

stages.If valve specific coefficients (such as K or C , F , and x ) cannot be determined by

v v L Tappropriate test procedures in IEC 60534-2-3, values supplied by the manufacturer should

then be used.---------------------- Page: 9 ----------------------

60534-2-5 © IEC:2003 – 11 –

INDUSTRIAL-PROCESS CONTROL VALVES –

Part 2-5: Flow capacity – Sizing equations for fluid flow

through multistage control valves with interstage recovery

1 Scope

This part of IEC 60534 includes equations for predicting the flow of compressible and

incompressible fluids through multistage 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 (∆p/p ), compressible

fluids 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 ∆p/p result in compressibility effects

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.This standard is applicable only to those designs of multistage multipath control valves and

multistage single path control valves.2 Normative references

The following referenced documents are indispensable for the application 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.IEC 60534-1:1987, Industrial-process control valves – Part 1: Control valve terminology and

general considerationsIEC 60534-2-1:1998, Industrial-process control valves – Part 2-1: Flow capacity – Sizing

equations for fluid flow under installed conditionsIEC 60534-2-3:1997, Industrial-process control valves – Part 2-3: Flow capacity – Test

procedures3 Terms and definitions

For the purposes of this document, the terms and definitions given in IEC 60534-1 and the

following apply.---------------------- Page: 10 ----------------------

60534-2-5 © IEC:2003 – 13 –

3.1

multistage control valves

a globe control valve where the trim has several stages which are separated by a gap (see

Figures 1 and 2). The geometrical contour of the apertures in all stages must be similar.

The ratio of the second stage flow coefficient C to the first stage flow coefficient C must not

exceed 1,80. The ratio of the flow coefficient C of the other stages to their previous stage

must not exceed 1,55 and must be uniform within a tolerance of ± 9 %. Normally for

incompressible fluids the flow coefficients of the stages are approximately equal, a slightly

smaller flow coefficient C being allocated to a particular stage only if it is required to take

a higher pressure drop.3.2

gap

the distance between adjacent stages

3.3

multistage multipath control valves

a globe control valve where the trim has multiple flow passages having several stages which

are separated by a gap (see Figure 1). The gap should conform to the values calculated from

the following equation with a tolerance of +15 % and –10 % (see Figures 1 and 2).

1 1,589gap = totalholearea of adjacent upstreamstageat rated travel× ×

where

the total hole area is in mm ;

l is the travel, in mm;

Ds is the outside diameter of adjacent upstream stage, in mm;

minimum gap limit = 4 mm;

maximum gap limit = 44 mm.

Gap

IEC 2141/03

NOTE This is one example of a multistage trim.

Figure 1 – Multistage multipath trim

---------------------- Page: 11 ----------------------

60534-2-5 © IEC:2003 – 15 –

3.4

multistage single path control valves

a globe control valve where the trim has one flow passage having several stages which are

separated by a gap (see Figure 2). The gap should be within the following minimum and

maximum limits:minimum gap = 0,60 times the seat diameter of the previous stage;

maximum gap = 1,10 times the seat diameter of the previous stage.

Seat diameter

IEC 2142/03

NOTE This is one example of a multistage trim.

Figure 2 – Multistage single path trim

4 Installation

In applications for single stage valves, the influence of reducers and other fittings may be

2 2significant. For multistage valves with C /d ≤ 0,01 (K /d ≤ 0,0086) they have virtually

v vno effect.

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 3.

Gap---------------------- Page: 12 ----------------------

60534-2-5 © IEC:2003 – 17 –

Flow

l l

1 2

Pressure tap Pressure tap

A B

Control valve with or without attached fittings

IEC 2143/03

Key

l = two nominal pipe diameters

l = six nominal pipe diameters

Figure 3 – Reference pipe section for sizing

5 Symbols

Symbol Description Unit

C Flow coefficient (K , C ) Various (see IEC 60534-1)

v v

(see Note 3)

C Assumed flow coefficient for iterative purposes Various (see IEC 60534-1)

(see Note 3)

d Nominal valve size mm

D Internal diameter of the piping mm

D Internal diameter of upstream piping mm

D Internal diameter of downstream piping mm

D Orifice diameter mm

F Liquid critical pressure ratio factor 1

F Liquid pressure recovery factor of a control valve without attached fittings 1 (see Note 3)

F Combined liquid pressure recovery factor and piping geometry factor of a 1 (see Note 3)

control valve with attached fittingsF Piping geometry factor 1

Specific heat ratio factor 1

k Stage interaction factor 1

M Molecular mass of flowing fluid kg/kmol

N Numerical constants (see Table 1) Various (see Note 1)

n Number of stages 1

p Inlet absolute static pressure measured at point A (see Figure 1) kPa or bar (see Note 2)

p Outlet absolute static pressure measured at point B (see Figure 1) kPa or barp Absolute thermodynamic critical pressure kPa or bar

p Reduced pressure (p /p)1

r 1 c

p Absolute vapour pressure of the liquid at inlet temperature kPa or bar

Differential pressure between upstream and downstream pressure taps kPa or bar

(p – p )

1 2

Q Volumetric flow rate (see Note 4) m /h

r Reheat factor 1

---------------------- Page: 13 ----------------------

60534-2-5 © IEC:2003 – 19 –

Symbol Description Unit

T Inlet absolute temperature K

T Absolute thermodynamic critical temperature K

T Reduced temperature (T /T)1

r 1 c

t Absolute reference temperature for standard cubic metre K

W Mass flow rate kg/h

x Ratio of pressure differential to inlet absolute pressure (∆p/p ) 1

x Pressure differential ratio factor of a control valve without attached fittings 1 (see Note 3)

at choked flowx Pressure differential ratio factor of a control valve with attached fittings at 1 (see Note 3)

choked flowY Expansion factor 1

Z Compressibility factor 1

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 o 1 o

Specific heat ratio 1

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

NOTE 3 These values are travel-related and should be stated by the manufacturer.

NOTE 4 Volumetric flow rates in m /h, identified by the symbol Q, refer to standard conditions. The standard cubic

metre is taken at 1013,25 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 those given in this Clause.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 flow6.1.1.1 Non-choked turbulent flow without attached fittings

Applicable if ∆p < F()p − F x p .

L 1 F v

The flow coefficient shall be determined by

Q ρ / ρ

1 o

C = (1)

N ∆p

NOTE 1 The numerical constant N depends on the units used in the general sizing equation and the type of flow

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 B.

---------------------- Page: 14 ----------------------60534-2-5 © IEC:2003 – 21 –

6.1.1.2 Non-choked turbulent flow with attached fittings

Applicable if ∆p < [()F / F()p − F x p ]

LP p 1 F v

The flow coefficient shall be determined as follows:

Q ρ / ρ

1 o

C = (2)

N F ∆p

1 p

NOTE Refer to 8.1 for the piping geometry factor F .

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

Applicable if ∆p ≥ F()p − F x p

L 1 F v

The flow coefficient shall be determined as follows:

Q ρ / ρ

1 o

C = (3)

N F p − F x p

1 L 1 F v

NOTE An example of sizing a valve with choked flow without attached fittings is given in Annex B.

6.1.2.2 Choked turbulent flow with attached fittingsApplicable if ∆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)

N F p − F x p

1 LP 1 F v

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 those given in this Clause.

---------------------- Page: 15 ----------------------60534-2-5 © IEC:2003 – 23 –

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:

C = (5)

N Y x p ρ

6 1 1

W T Z

C = (6)

N p Y xM

8 1

Q MT Z

(7)

C =

N p Y x

9 1

NOTE 1 Refer to 8.4 for details of the expansion factor Y.

NOTE 2 See Annex A 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:

C = (8)

N F Y xp ρ

6 p 1 1

W T Z

C = (9)

N F p Y xM

8 p 1

Q MT Z

C = (10)

N F p Y x

9 p 1

NOTE 1 Refer to 8.1 for the piping geometry factor F .

NOTE 2 An example of sizing a valve with non-choked turbulent flow with attached fittings is given in Annex B.

7.1.2 Choked turbulent flowThe 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 . The maximum value for Fγx in equations 11 to 13 shall not exceed 1.

γ T T---------------------- Page: 16 ----------------------

60534-2-5 © IEC:2003 – 25 –

The flow coefficient shall be calculated from one of the following equations:

(11)

C =

N Y F x p ρ

6 γ T 1 1

W T Z

C = (12)

N p Y F x M

8 1 γ T

Q MT Z

(13)

C =

N p Y F x

9 1 γ T

7.1.2.2 Choked turbulent flow with attached fittings

Applicable if x ≥ F x . The maximum value for Fγx in equations 14 to 16 shall not exceed 1.

γ TPThe flow coefficient shall be determined using one of the following equations:

(14)

C =

N F Y F x p ρ

6 p γ TP 1 1

W T Z

(15)

C =

N F p Y F x M

8 p 1 γ TP

Q MT Z

C = (16)

N F p Y F x

9 p 1 γ TP

8 Determination of correction factors

8.1 Piping geometry factor, F

For graphical approximations of F , refer to Figures 2a and 2b in IEC 60534-2-1.

2 2

F can be taken as one for C /d less than or equal to 0,01 (or K /d less than or equal to

p v v2 2

0,008 6). For higher ratios of C /d (or K /d ) see IEC 60534-2-1.

v v

8.2 Liquid pressure recovery factors F or F

L LP

8.2.1 Liquid pressure recovery factor without attached fittings F

F is the liquid pressure recovery factor of the valve without attached fittings. This factor

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 with

IEC 60534-2-3. Typical values of F are shown in Table 2.---------------------- Page: 17 ----------------------

60534-2-5 © IEC:2003 – 27 –

8.2.2 Combined liquid pressure recovery factor and piping geometry factor F

F is the combined liquid pressure recovery factor and piping geometry factor for a control

2 2valve with attached fittings. F equals F when C /d is less than or equal to 0,01 (or K /d

LP L v v2 2

is equal to or less than 0,008 6. For higher ratios of C /d (or K /d ), see IEC 60534-2-1.

v v8.3 Liquid critical pressure ratio factor F

F is the liquid critical pressure ratio factor. This factor is the ratio of the apparent vena

contracta pressure at choked flow conditions to the vapour pressure of the liquid at inlet

temperature. At vapour pressures near zero, this factor is 0,96.Values of F may be determined from the curve in Figure 5 or approximated from the following

equation:F = 0,96 − 0,28 (17)

8.4 Expansion factor Y

The expansion factor Y accounts for the change in density as the fluid passes from the valve

inlet to the vena contracta (the location just downstream of the orifice where the jet stream

area**...**

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