SPI Sizing Equations

SmartPlant Instrumentation Sizing Equations

Version 2013

March 2013

DSPI2-PE-200008B

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Sizing Equations 1

Contents Preface .................................................................................................................................3

1 Nomenclature .....................................................................................................4 2 Control Valve Sizing..........................................................................................7

2.1 Liquid, Water ............................................................................................................ 7 2.2 Gas, Steam ................................................................................................................ 9

3 Noise Calculation ....................................................................................................11 3.1 Hydrodynamic Noise: Masoneilan Standard .......................................................... 11 3.2 Hydrodynamic Noise: IEC Standard ...................................................................... 11 3.3 Aerodynamic Noise: ISA Standard ........................................................................ 14 3.4 Aerodynamic Noise: IEC Standard ........................................................................ 17

4 Flow Meter Sizing ..................................................................................................20 4.1 Calculation of Beta Ratio ....................................................................................... 20 4.2 Calculation of Flow rate ......................................................................................... 22 4.3 Calculation of Differential range ............................................................................ 23

5 Restriction Device Sizing .......................................................................................26 5.1 Calculation of Beta Ratio ....................................................................................... 26 5.2 Calculation of Flow Rate ........................................................................................ 30 5.3 Calculation of Pressure Loss .................................................................................. 33

6 Relief Valve Sizing .................................................................................................35 6.1 Blocked Flow: Liquid Relief .................................................................................. 35 6.2 Blocked Flow: Gas Relief ...................................................................................... 36 6.3 Blocked Flow: Steam Relief ................................................................................... 38 6.4 Fire Case: Gas Expansion ....................................................................................... 39 6.5 Fire Case: Liquid Filled Vessel .............................................................................. 40

7 Thermowell Calculation .........................................................................................42

7.1.1 Define Initial Value of K f Constant: ................................................................... 42

7.1.2 Calculate Ratio of Frequency at Fluid Temperature to Frequency at 70 °F: ....... 42 7.1.3 Calculate Maximum Thermowell Length Based on Vibration Limitation: ......... 42

7.1.4 Define K f Constant: ............................................................................................ 42

7.1.5 Paragraphs 7.1.3 - 7.1.4 are repeated until current K f value equals previous K f

value

43 7.1.6 Calculate Natural Frequency for L=L1 ................................................................ 43 7.1.7 Calculate Wake Frequency .................................................................................. 43

7.1.8 Calculate Magnification Factor for L1(R 0.8) ................................................... 44

7.1.9 Define 1K, 2K

, 3Kconstants .............................................................................. 44

7.1.10 Calculate Maximum Allowable Static Gage Pressure....................................... 44 7.1.11 Calculate Maximum thermowell length based on Steady State Stress Consideration

44 7.2.1 Calculate Mounting factor ................................................................................... 45 7.2.2 Calculate Reynolds number ................................................................................. 45 7.2.3 Calculate Strouhal number ................................................................................... 45 7.2.4 Calculate Natural frequency ................................................................................ 45 7.2.5 Calculate Vortex shedding frequency .................................................................. 46

Contents

2 Sizing Equations

7.2.6 Calculate Scruton number .................................................................................... 47 7.2.7. Calculate miscellaneous parameters .................................................................... 47 7.2.8 Calculate Frequency Limit ................................................................................... 48 7.2.9 Compliance with the Frequency Limit requirement ............................................ 48 7.2.10 Compliance with the Static Stress Limit requirement ....................................... 50 7.2.11 Compliance with the Dynamic Stress Limit requirement ................................. 52 7.2.12 Compliance with the Hydrostatic Pressure Limit requirement ......................... 53

8 Standards .................................................................................................................54 8.1 Control Valve Sizing .............................................................................................. 54 8.2 Noise Calculation ................................................................................................... 54 8.3 Flow Meter Sizing .................................................................................................. 54 8.4 Relief Valve Sizing................................................................................................. 55 8.5 Thermowell Calculation ......................................................................................... 55

9 Appendix .................................................................................................................56 9.1 Square Edge Orifice ............................................................................................... 56 9.2 Quarter of Circle (Quadrant Edge) Orifice ............................................................. 57 9.3 Conical Entrance Orifice ........................................................................................ 57 9.4 Lo-Loss Tube ......................................................................................................... 57 9.5 Venturi Tube ........................................................................................................... 57 9.6 Nozzle ..................................................................................................................... 58 9.7 Eccentric Orifice ..................................................................................................... 58 9.8 Segmental Orifice ................................................................................................... 58 9.9 Restriction Device .................................................................................................. 58

Sizing Equations 3

Preface This document is a reference for sizing equations used by the SmartPlant

Instrumentation Calculation module.

Send documentation comments or suggestions to [email protected].

mailto:[email protected].?subject=Documentation%20Comments

1 Nomenclature

4 Sizing Equations

1 Nomenclature A Required effective discharge area, inch

2

A1 Exposed surface area, inch2

Ad Root diameter of thermowell, m

B Diameter at tip, in

b Fillet radius at root, m

bs Fillet radius at base for stepped thermowell, m

C Discharge coefficient

CV Valve flow coefficient, US gallon per minute of water (60 ºF) at 1 psi pressure drop

Cr Coefficient for critical flow equation, dimensionless

Cs Speed of sound, m/s

Cp Speed of sound in pipe wall, m/s

D Internal pipe diameter (upstream) at flow temperature, mm

D0 Internal pipe diameter (upstream) at ambient temperature, mm

Dt Nominal size of sensing element, in

D1 Inlet internal diameter of the pipe, mm

D2 Outlet internal diameter of the pipe, mm

Dd2 Outlet outside diameter of the pipe, m

DP Pressure differential, P1-P2 , or differential pressure transmitter range, bar

DPA Maximum allowable pressure drop, bar

DPloss Pressure loss, bar

DPn Differential pressure at normal flow rate, bar

Dbh Bleed/Vent hole diameter, mm

Dj Diameter of the jet, m

d Valve inlet diameter or orifice (throat) diameter at flow temperature, mm

db Bore diameter of thermowell, m

d0 Orifice (throat) diameter at ambient temperature, mm

E Module of Elasticity at 70 °F, psi-g

Ef Acoustical efficiency factor, dimensionless

Eref Reference value for module of elasticity, Pa-g

Eps Gas expansion factor, ratio of flow coefficient for a gas to that for a liquid at the same Reynolds

number, dimensionless

F Environment Factor, dimensionless

F1 Heat Absorption Factor, dimensionless

F2 Coefficient for subcritical flow equation, dimensionless

Fd Valve style modifier, dimensionless

Fe Environmental factor for thermowell calculation, dimensionless

FF Liquid critical pressure ratio factor, dimensionless

Fk Ratio of specific heats factor, 1/K, dimensionless

FL Liquid pressure recovery factor, dimensionless

FLP Product of the liquid pressure recovery factor of a valve with attached fittings and the piping

geometry factor, dimensionless

Fp Piping geometry factor, dimensionless

FR Reynolds number factor, dimensionless

Fs Correction factor for steam quality, dimensionless

fp Peak frequency, Hz

fo Coincidence or Natural frequency, Hz

fr Ring frequency, Hz

fw Wake frequency, Hz

Gf Liquid specific gravity (ratio of density of liquid at flowing temperature to density of water at 15.6

C), dimensionless

Preface1 Nomenclature

Sizing Equations 5

Gg Gas specific gravity (ratio of density of flowing gas to density of air with both at standard

conditions, which is equal to the ratio of molecular weight of gas to the molecular weight of air),

dimensionless

Hc Mounting factor, dimensionless

HS Segmental height at flow temperature, mm

HS0 Segmental height at ambient temperature, mm

HV Heat of vaporization, J/kg

K Specific Heat Ratio, Cp/Cv dimensionless

K1,K2,Kb1,Kb2 Effective velocity head coefficients, dimensionless

KC Cavitation index, dimensionless

KCD Relative capacity, CV/d2

KCV Valve cavitation index, dimensionless

Kb Capacity correction factor due to back pressure, dimensionless

Kcc Combination capacity factor for rupture disk at the relief valve inlet, dimensionless

Kd Effective coefficient of discharge, dimensionless

Kf Constant for thermowell calculation, dimensionless

Kn Correction factor for Napier equation, dimensionless

Kp Correction factor for overpressure, dimensionless

Ksh Superheat steam correction factor, dimensionless

Kv Correction factor for viscosity, dimensionless

Kw Correction factor for back pressure, dimensionless

L Maximum thermowell length or unsupported length of thermowell, in

La “A”-weighted sound level, dB(A)

Lg Correction for pipe Mach number, dB

Lpi Internal sound pressure level, dB

Ls Length of reduced-diameter shank for stepped thermowell, m

M Molecular weight, atomic mass units

MN Mach number in pipe, dimensionless

MN0 Mach number in valve outlet, dimensionless

Mj Mach number in the jet, dimensionless

No Number of flow passages , dimensionless

Ns Strouhal number

Nsc Scruton number

P Absolute static pressure, bar

PC Absolute thermodynamic critical pressure, bar

PV Absolute vapor pressure of liquid at inlet temperature, bar

PVC, PVCC Absolute pressure in vena contracts at subsonic and critical flow conditions, Pa

P2c, P2b, P2ce Border pressures for different noise regimes, Pa

Pa Absolute outside pipe pressure, Pa

Pb Total back pressure, psi-g

Pb1 Constant back pressure, psi-g

Pb2 Variable back pressure, psi-g

Pb3 Built-up back pressure, psi-g

Pcf Critical flow throat pressure, psi-a

Pover Overpressure, %

Ps Set pressure, psi-g

Pup Upstream relieving pressure, psi-a

R Limitation on Wake to Natural frequency ratio, dimensionless

RO Density at flow conditions (upstream), kg/m3

ROm Density of well material at ambient temperature, kg/m3

ROp Density of pipe material, kg/m3

ROs Density of the thermowell sensor at ambient temperature, kg/m3

Rf Ratio of frequency at fluid temperature to frequency at 70 °F, dimensionless

RS0 Segmental radius at ambient temperature, mm

Re Valve (pipe) Reynolds number, dimensionless

Remax, Ren Pipe Reynolds number at maximum and normal flow rate, dimensionless

1 Nomenclature

6 Sizing Equations

Rq Radius of upstream profile of Quarter of Circle (Quadrant Edge) orifice, mm

S Maximum allowable working stress, Pa-g

Sf Fatigue endurance limit, Pa-g

SRF Scale reading factor, 10Wn/Wmax

St Water in steam, %wt

T Flow temperature, K

T1 Gas temperature at relieving conditions, °R

T0 Ambient temperature, K

Tc Thermodynamic critical temperature,

TL Transmission loss, dB

TLfo Transmission loss at coincidence frequency, dB

TLfr Transmission loss across the pipe wall at the ring frequency, dB

Tw Vessel Wall Temperature, °R

t Minimum tip thickness of thermowell, m

U Velocity, m/s

V Velocity, ft/s

W Flow rate, kg/h

Wmax, Wn Maximum and normal flow rate, kg/s

Wa Sound power, W

Wm, Wms Stream powers, W

wall Pipe wall thickness, m

X Ratio of pressure drop to absolute inlet pressure (DP/P1), dimensionless

XT Pressure drop ratio factor, dimensionless

XTP Value of XT for valve-fitting assembly, dimensionless

Z Compressibility at operating conditions, dimensionless

Zb Compressibility at base conditions, dimensionless

p, pe Linear expansion coefficient of pipe and primary element material, 1/ºC

Diameter ratio of orifice or throat and inside diameter of line

Lf Correction value for cavitating flow, dB

TLfp Correction for ratio of peak frequency and coincidence frequency, dB

Acoustic efficiency factor, dimensionless

Absolute (dynamic) viscosity, Pa×s

Kinematic viscosity, centistokes

ξ Damping factor, dimensionless

Subscripts 0 First estimate

1 Upstream conditions

2 Downstream conditions

VC Vena Contracta

Preface2 Control Valve Sizing

Sizing Equations 7

2 Control Valve Sizing

2.1 Liquid, Water 2.1.1 Calculate FF :

FP

PF

V

C

0 96 0 28. .

2.1.2 Calculate :

106 / RO

2.1.3 Calculate KC :

KP P

P PC

V

1 2

1

2.1.4 Calculate effective velocity head coefficients:

K d D

K d D

K K K K K

b

b b

1

2

1

22

1 1

4

1 2 1 2

05 1

1

. /

/

K d D

K d D

K K K

b

i b

2

2

2

22

2 2

4

1 1

1

1

/

/

2.1.5 Calculate first value of CV:

CV

W

P P RO0

1 227 3

.

2.1.6 Calculate FP :

FK CV

dP

0

2

4

1 2

0 002141

.

/

2.1.7 Calculate KCV :

K F F FCV L L L 166667 2 428571 1869048 0 3077143. . . .

2.1.8 Calculate FLP :

F FK F CV

dLP L

i L

2

0

2

4

1 2

0 002141

.

/

2.1.9 Calculate Re :

Re

..

.

76000

0 002141

0

0 5

0

2

4

0 25

F W

RO F CV

F CV

d

D

L

L

2.1.10 Calculate DPA :

DPF

FP F PA

LP

P

F V

2

1


8 Sizing Equations

2.1.11 Calculate FR .

At this stage, the following cases for different Re are possible

2.1.11.1 Case Re 56 - Laminar flow

FR 0 019 0 67. Re .

2.1.11.2 Case 56 40000 Re - Transitional flow

2.1.11.2.1 56 620 Re Az Re/ 56 1

F Az Az Az

Az

R

6 082774 10 2 212891 10 2 844539 10

01708764 0 2925969

5 4 3 3 2 2. . .

. .

2.1.11.2.2 620 2470 Re Az Re/ 620 1

F Az AzR 9121 10 6 684 10 076143 2 2. . .

2.1.11.2.3 2470 10200 Re Az Re/ 2470 1

F Az AzR 9184 10 543 10 0883 2 2. . .

2.1.11.2.4 10200 20000 Re FR 0 97.

2.1.11.2.5 20000 30000 Re FR 0 98.

2.1.11.2.6 30000 40000 Re FR 0 99.

2.1.11.3 Case Re 40000 - Turbulent flow

FR 1

2.1.12 The condition P P DPA1 2 determines:

Case A - Cavitation and Flashing

A1 Cavitation case takes place if P PV2 , otherwise

flashing case takes place.

A2 Calculate new CV .

A2.1 ISA standard:

CVW

F P F P ROLP F V

27 3 1. ( )

A2.2 IEC standard:

CVW

F F P F P ROR LP F V

27 3 1. ( )

Case B ( P P DPA1 2 ) - Usual

B1 ISA standard:

B1.1 FR 1

CV

W

F P P ROR

27 3 1 2.

B1.2 FR 1

CV

W

F P P ROP

27 3 1 2.

B2 IEC standard:

CV

W

F F P P ROR P

27 3 1 2.

Preface2 Control Valve Sizing

Sizing Equations 9

2.1.13 Calculate the relative change in the CV:

CVCV CV

CVCV CV

0

0

0;

2.1.14 Paragraphs 2.1.6 - 2.1.13 are repeated until the relative change in the CV is less than 0.001.

2.1.15 Define “Incipient” case. The “Incipient” case takes place if

P P DPA1 2 and K KC CV

2.1.16 Calculate outlet pipe velocity:

*W [kg/s], D2 [m]

UW

D RO2

2

231416 2

. ( / )

2.2 Gas, Steam 2.2.1 Calculate XT :

X FT L 084 2.

2.2.2 Calculate effective velocity head coefficients:

K d D

K d D

K K K K K

b

b b

1

2

1

22

1 1

4

1 2 1 2

05 1

1

. /

/

K d D

K d D

K K K

b

i b

2

2

2

22

2 2

4

1 1

1

1

/

/

2.2.3 Calculate FK :

F KK / .14

2.2.4 Calculate X :

X P P P 1 2 1/

2.2.5 Calculate first value of CV:

*d [in]

CV K dCD0

2

2.2.6 Calculate FP:

FK CV

dP

0

2

4

1 2

0 002141

.

/

2.2.7 Calculate XTP:

XX

F

X K CV

dTP

T

P

T i

2

0

2

4

1

0 002411

.

2.2.8 The condition X F XK TP determines:

Case A - Critical flow

A1 Eps 0 667. .

A2 Calculate new CV :

CVW

F Eps F X P ROP k TP

27 3 1.


10 Sizing Equations

Case B ( X F XK TP ) - Usual

B1 EpsX

F XK TP

13

.

B2 Calculate new CV :

CVW

F Eps X P ROP

27 3 1.

2.2.9 Calculate the relative change in CV:

CVCV CV

CVCV CV

0

0

0;

2.2.10 Paragraphs 2.2.6 - 2.2.9 are repeated until the relative change in CV

is less than 0.001.

2.2.11 Calculate outlet pipe velocity:

*W [kg/s], D2 [m]

RO ROP

P2

2

1

UW

D RO2

2

2

231416 2

. ( / )

2.2.12 Calculate outlet Max number:

C K T Ms2 8314 /

MN U Cs 2 2/

Preface3 Noise Calculation

Sizing Equations 11

3 Noise Calculation

3.1 Hydrodynamic Noise: Masoneilan Standard 3.1.1 Calculate dP dPi C, :

dP K P Pi CV V ( )1

dP F P PC L V 2

1( )

3.1.2 Calculate hydrodynamic noise.

3.1.2.1 Case DP dPi - Flow Noise:

L CV DP walla 10 20 30 705log log log( ) .

3.1.2.2 Case dP DP dPi C - Incipient Cavitation Noise:

L CV DP wall

DP

P PK

F KP P

a

V

CV

L CV

V

10 20 30

5 14 5 0 07 70 51

2 2

log log log( )

log . . .

3.1.2.3 Case DP dPC and P PV2 - Cavitation Noise:

L CV DP wall

DP

P PK

F KP P

a

V

CV

L CV

V

10 20 30

5 14 5 0 071

2 2

log log log( )

log . . +

70.7 - [5 log(DP + 0.07 - dP ) + 6]

C

3.1.2.4 Case P PV2 - Flashing Noise:

There is no method to predict Noise for flashing case.

3.2 Hydrodynamic Noise: IEC Standard *D2 [m], P1 [Pa-a], P2 [Pa-a], Pv [Pa-a], Pc [Pa-a], W[kg/s]

3.2.1 Calculate the downstream speed of sound:

C

K T

Ms2

18314

3.2.2 Calculate Characteristic pressure ratio

X Ffz L 0842

.

3.2.3 Calculate Differential pressure ratio

XP P

P Pf

v

1 2

1

3 Noise Calculation

12 Sizing Equations

3.2.4 Calculate Ring frequency

FC

Dfz

p

d

31416 2.

3.2.5 Calculate Internal sound power level

3.2.5.1 Case Xf < Xfz - Non-cavitating flow

L E W P P ROwi f 120 10 10 10 1 2 10log( ) log( ) log( ) log( )

3.2.5.2 Case Xf => Xfz - Cavitating flow

3.2.5.2.1 Calculate Liquid critical pressure ratio factor

F P Pf v c 096 028. . ( / )

3.2.5.2.2 Calculate Differential pressure

3.2.5.2.2.1 Case P P F P F PL F v1 2

2

1

DP P P 1 2

3.2.5.2.2.2 Case P P F P F PL F v1 2

2

1

DP F P F PL F v 2

1

3.2.5.2.3 Calculate Lwi.

L E W P P RO

X

XX

X

X

wi f

fz

f

X f

fz

ffz

120 10 10 10 10

180 11

1

1 2

0 06250 8

log( ) log( ) log( ) log( )

log

..

L f


Sizing Equations 13

3.2.6 Calculate Un-weighted external sound power levels

TC RO wall

C RO D

F

FL

p p

s d

fr

fr

1

2 2

1 5

10 10 20500

500

log log

.

L Lwi wi1 2 9 .

L LD

TD

we wi

d

T

L

d

L

1 1

2

0 1

1

2

17 3715

10 1012

1 ..

log.

TC RO wall

C RO D

F

FL

p p

s d

fr

fr

2

2 2

1 5

10 10 201000

1000

log log

.

L Lwi wi2 10 2 2 9 log .

L LD

TD

we wi

d

T

L

d

L

2 2

2

0 1

2

2

17 3715

10 1012

2 ..

log.

TC RO wall

C RO D

F

FL

p p

s d

fr

fr

3

2 2

1 5

10 10 202000

2000

log log

.

L Lwi wi3 10 4 2 9 log .

L LD

TD

we wi

d

T

L

d

L

3 3

2

0 1

3

2

17 3715

10 1012

3 ..

log.

TC RO wall

C RO D

F

FL

p p

s d

fr

fr

4

2 2

1 5

10 10 204000

4000

log log

.

L Lwi wi4 10 8 2 9 log .

L LD

TD

we wi

d

T

L

d

L

4 4

2

0 1

4

2

17 3715

10 1012

4 ..

log.

TC RO wall

C RO D

F

FL

p p

s d

fr

fr

5

2 2

1 5

10 10 208000

8000

log log

.

L Lwi wi5 10 16 2 9 log .

L LD

TD

we wi

d

T

L

d

L

5 5

2

0 1

5

2

17 3715

10 1012

5 ..

log.

3.2.7 Calculate External A-weighted sound power level

Lwae

L L L L Lwe we we we we 10 10 10 10 10 100 1 3 2 0 1 0 0 0 1 1 2 0 1 1 0 0 1 111 2 3 4 5log . ( . ) . ( . ) . ( . ) . ( . ) . ( . )

3.2.8 Calculate External A-weighted sound pressure level

L LD

Da wae

d

10 31416 3 12

2

log .

3 Noise Calculation

14 Sizing Equations

3.3 Aerodynamic Noise: ISA Standard *D2 [m], P1 [Pa-a], P2 [Pa-a], W[kg/s]

*FL=FLP/Fp

3.3.1 Calculate the downstream parameters:

222

2

22

2

12

122

/

2/1416.3

8314

/

s

s

CUMN

DRO

WU

M

TKC

PPRORO

3.3.2 Calculate the following pressures:

Pvc = P1 - (P1-P2)/FL2

P PKVCC

K

K

1

12

1

P2c = P1 - FL2(P1-Pvcc)

= Pvcc/P2c

PP

Kb

K

K

2

111

P2ce = P1/(22)

3.3.3 Calculate Fd, Dj, Mj:

F N

D F CV F

MK

P

P

d o

j d L

j

K

K

1/2

1

2

11/2

0 0046

2

11

.


Sizing Equations 15

3.3.4 Now 5 regimes are possible:

3.3.4.1 Regime I - P P P c1 2 2

T TP

P

CK T

M

UK

K

P

P

P

RO

WW U

MNU

C

MN

W W F

f U D

VC

VC

K

K

sVC

VC

VC

VC

K

K

m

VC

VC

sVC

a m L

P VC j

1

1

1

0 5

1

1

1

1 2

2

3 6

2

8314

2

11

2

0 0001

0 2

.

/

..

. /

3.3.4.2 Common calculations for II-V Regimes:

TT

K

CKT

M

UK

K

P

P

P

RO

WW U

VCC

sVCC

VCC

VCC

VCC

K

K

ms

VCC

2

1

8314

2

11

2

1

0 5

1

1

1

1 2

2

.

/

3.3.4.3 Regime II - P P Pc vcc2 2 :

0 0001

0 2

6 6

1 2

1

2

.

.

.

.M

W WP P

P P

fM C

D

j

F

a ms

VCC

P

j sVCC

j

L

3 Noise Calculation

16 Sizing Equations

3.3.4.4 Regime III - P P Pvcc b 2 2 :

0 0001 6 62

. .M j

FL

W W

fM C

D

a ms

P

j sVCC

j

0 2.

3.3.4.5 Regime IV - P P Pb ce2 2 2 :

0 00012

2

0 35

125 1

26 6

21 2

2

.

.

.

.

/

M

W W

fC

D M

j F

a ms

P

sVCC

j j

L

3.3.4.6 Regime V - P Pce2 2 0 :

MK

M

W W

fC

D M

j

K

K

j F

a ms

P

sVCC

j j

L

2

122 1

0 00012

2

0 35

125 1

11 2

26 6

21 2

2

/

.

/

.

.

.

3.3.5 Calculate Lpi: :

L W RO C Dpi a s 10 8 108

2 2 2

2log /

3.3.6 Calculate TLfo :

T

D

D wall

P

PLfo

a

1011 10

1 2 101325

7

2

3

2

2

2

log.

/ ( )

3.3.7 Calculate fo :

fo = 5000/(12.5664D2)

3.3.8 Three cases are possible when calculating TLfp:

3.3.8.1 fpfo

TLfp = 20log(fo/fp)

3.3.8.2 fo<fp4fo

TLfp = 13log(fp/fo)

3.3.8.3 fp>4fo

TLfp = 20log(fp/4fo) + 7.8

3.3.9 Calculate transmission loss:

TL = TLfo - TLfp


Sizing Equations 17

3.3.10 Calculate Lg :

LP CV F

D P

g

L

16

1

113 10 5

1

2

2

2

log.

3.3.11 Calculate sound level

La = 5 + Lpi +TL +Lg

3.4 Aerodynamic Noise: IEC Standard *D2 [m], d [m], P1 [Pa-a], P2 [Pa-a], W[kg/s]

*FL=FLP/Fp

3.4.1 Calculate the downstream parameters:

2

22

0

2

222

2

12

122

1416.3

4

1416.3

4

8314

/

dROC

WMN

DROC

WMN

M

TKC

PPRORO

s

s

s

3.4.2 Calculate the following pressures:

Pvc = P1 - (P1-P2)/FL2

P PKVCC

K

K

1

12

1

P2c = P1 - FL2(P1-Pvcc)

= Pvcc/P2c

PP

Kb

K

K

2

111

P2ce = P1/(22)

3.4.3 Calculate Fd, Dj, Mj:

F N

D F CV F

MK

P

P

d o

j d L

j

K

K

1/2

1

2

11/2

0 0046

2

11

.

3 Noise Calculation

18 Sizing Equations

3.4.4 Now 5 regimes are possible:

3.4.4.1 Regime I - P P P c1 2 2

T TP

P

CK T

M

UK

K

P

P

P

RO

WW U

MNU

C

MN

W W F

f U D

VC

VC

K

K

sVC

VC

VC

VC

K

K

m

VC

VC

sVC

a m L

P VC j

1

1

1

0 5

1

1

1

1 2

2

3 6

2

8314

2

11

2

0 0001

0 2

.

/

..

. /

3.4.4.2 Common calculations for II-V Regimes:

TT

K

CK T

M

WW C

VCC

sVCC

VCC

ms

sVCC

2

1

8314

2

1

0 5

2

.

3.4.4.3 Regime II - P P Pc vcc2 2 :

0 0001

0 2

6 6

1 2

1

2

.

.

.

.M

W WP P

P P

fM C

D

j

F

a ms

VCC

P

j sVCC

j

L

3.4.4.4 Regime III - P P Pvcc b 2 2 :

0 0001 6 62

. .M j

FL

W W

fM C

D

a ms

P

j sVCC

j

0 2.


Sizing Equations 19

3.4.4.5 Regime IV - P P Pb ce2 2 2 :

0 00012

2

0 35

125 1

26 6

21 2

2

.

.

.

.

/

M

W W

fC

D M

j F

a ms

P

sVCC

j j

L

3.4.4.6 Regime V - P Pce2 2 0 :

MK

M

W W

fC

D M

j

K

K

j F

a ms

P

sVCC

j j

L

2

122 1

0 00012

2

0 35

125 1

11 2

26 6

21 2

2

/

.

/

.

.

.

3.4.5 Calculate Lpi: :

L W RO C Dpi a s 10 8 108

2 2 2

2log /

3.4.6 Calculate TLfr:

T

C D

C RO wall

PLfr

s

s

a

103 10

1 415 101325

13

2

2

2

2

2 2

2log

/

3.4.7 Calculate fr and fo :

fr = 5000/(3.1416D2)

fo = fr Cs2/1372

3.4.8 Three cases are possible when calculating TLfp:

3.4.8.1 fp<fo

TLfp = 20log(fo/fp) + 13log(fo/fr)

3.4.8.2 fofpfr

TLfp = 13log(fp/fr)

3.4.8.3 fp>fr

TLfp = 20log(fp/fr)

3.4.9 Calculate transmission loss:

TL = TLfr - TLfp

3.4.10 Calculate Lg :

LM

g

16

1

1 2

log

3.4.11 Calculate sound level at the outside diameter of the pipe

La0 = 5 + Lpi +TL +Lg

3.4.12 Calculate sound level at a distance of 1 m from the pipe wall

L LD

Da a

0

2

2

102

log

4 Flow Meter Sizing

20 Sizing Equations

4 Flow Meter Sizing

4.1 Calculation of Beta Ratio 4.1.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01

4.1.2 Calculate Correction factor for Steam quality (For Liquid, Water,

and Gas, Fs=1):

F Ss t 1 0 0074.

4.1.3 Calculate Scale reading factor:

SRF W Wn 10 / max

4.1.4 Calculate Differential pressure at normal flow rate:

DP DP SRFn /102

4.1.5 Calculate Pipe Reynolds number at normal flow rate:

Re.

n

nW

D

12732 103

4.1.6 Calculate first estimate for - ratio.

4.1.6.1 For Venturi tubes:

0

2

7 4 2

0 25

123 10

W

D DP RO W

n

n n.

.

4.1.6.2 For other Flow meters:

0

2

8 4 2

0 25

4 6 10

W

D DP RO W

n

n n.

.

4.1.7 Calculate Gas expansion factor (for Liquid and Water, Eps 1).

4.1.7.1 For square edge orifice with 2½D & 8D pipe taps:

Eps DP P Kn 1 0333 1145 0 7 120

2

0

5

0

13

1

1. . .

4.1.7.2 For Lo-Loss tube, Venturi tubes and Nozzles:

Eps

Q

Q

Q

Q

K K

KK

K

K

2

0

4

0

42

10 5

1

1

1

1

1

.

where QP DP

P

n1

1

4.1.7.3 For Eccentric orifices:

Eps DP P Kn 1 01926 0574 09675 4 24 3620 0

2

0

3

0

4

1

1. . . . . ( / )

4.1.7.4 For square-edge orifices specified in ISO 5167 – 2003 (flange tappings, corner tappings, and

radius tappings):

))/(1(93.0256.0351.01 /1

12

8

0

4

0

KPPEps


Eps DP P Kn 1 041 035 0

4

1

1. . ( / )

Preface4 Flow Meter Sizing

Sizing Equations 21

4.1.8 Calculate Discharge coefficient. See 9 Appendix.

4.1.9 Calculate new - ratio:

2847 05 1 0

4

2

0 5

..

W

D Eps F C DP RO

n

s n

4.1.10 Calculate the relative change in - ratio:

0

0

0;

4.1.11 Paragraphs 4.1.7 - 4.1.10 are repeated until the relative change in

the - ratio is less than 0.0001.

4.1.12 Calculate Orifice diameter at flow temperature.

4.1.12.1 For all Flow Meters except Segmental orifices:

d D

4.1.12.2 Segmental orifices.

4.1.12.2.1 Calculate Segmental radius:

RS D0 0049 .

4.1.12.2.2 Calculate Segmental height at flow temperature

using the equation:

1 12

2 12

20 5

arccos

.

HS

D

HS

D

HS

D

HS

D

For further calculation of Segmental orifices, HS and HS0 are analogous to d and d0 respectively.

4.1.13 Calculate Orifice diameter at ambient temperature.

4.1.13.1 For Lo-Loss tube, Nozzles, and Venturi tubes:

dd

T Tpe

0

01

4.1.13.2 For other orifices:

d dDbh d

T Tpe

0

2

0

1 0 55

1

.

4.1.14 For Quarter of Circle (Quadrant Edge) orifice, calculate Radius of upstream profile:

R dq

0 07571 0 06253

0 68286

. .

.

4 Flow Meter Sizing

22 Sizing Equations

4.2 Calculation of Flow rate 4.2.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01

4.2.2 Calculate Correction factor for Steam quality (For Liquid, Water,

and Gas, Fs=1):

F Ss t 1 0 0074.



d d T Tpe 0 01


d d Dbh d T Tpe 0 0

2

01 055 1.

4.2.4 Calculate - ratio.


d

D



RS D0 0049 .

4.2.4.2.2 Calculate - ratio:

1 12

2 12

20 5

arccos

.

HS

D

HS

D

HS

D

HS

D

Note: HS is calculated with the help of HS0 in accordance with paragraph 4.2.3.2.



Eps DP P K 1 0333 1145 0 7 122 5 13

1

1. . .


Eps

Q

Q

Q

Q

K K

KK

K

K

24

42

10 5

1

1

1

1

1

.

where QP DP

P

1

1


Eps DP P K 1 01926 0574 09675 4.24 3622 3 4

1

1. . . . ( / )


radius tappings):

))/(1(93.0256.0351.01 /1

12

84 KPPEps


Sizing Equations 23


Eps DP P K 1 0 41 035 4

1

1. . ( / )

4.2.6 Calculate first estimate for Flow rate:

*W0 [kg/s]

W Eps dDP RO

0

4 2

42107 10

1

.

4.2.7 Calculate Pipe Reynolds number:

*W0 [kg/s]

Re.

12732 103

0W

D


4.2.9 Calculate new Flow rate:

*W [kg/s]

W C F Eps dDP RO

s

35124 101

4 2

4.

4.2.10 For Quarter of Circle (Quadrant Edge) orifices, Lo-loss tube, Venturi tubes, and Segmental orifices, go to

the paragraph 4.2.13.

4.2.11 Calculate the relative change in Flow rate:

WW W

WW W

0

0

0;

4.2.12 Paragraphs 4.2.7 - 4.2.11 are repeated until the relative change in

the flow rate is less than 0.0001.


R dq

0 07571 0 06253

0 68286

. .

.

4.3 Calculation of Differential range 4.3.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01

4.3.2 Calculate Correction factor for Steam quality (For Liquid, Water, and

Gas, Fs=1):

F Ss t 1 0 0074.



d d T Tpe 0 01


d d Dbh d T Tpe 0 0

2

01 055 1.

4 Flow Meter Sizing

24 Sizing Equations

4.3.4 Calculate Pipe Reynolds number:

*W [kg/s]

Re.

12732 103 W

D



d

D



RS D0 0049 .

4.3.5.2.2 Calculate - ratio:

1 12

2 12

20 5

arccos

.

HS

D

HS

D

HS

D

HS

D

Note: HS is calculated with the help of HS0 in accordance with paragraph 4.3.3.2.


4.3.7 First estimate for Differential range:

DP P0 1



Eps DP P K 1 0333 1145 0 7 122 5 13

1

1. . .


Eps

Q

Q

Q

Q

K K

KK

K

K

24

42

10 5

1

1

1

1

1

.

where QP DP

P

1

1


Eps DP P K 1 01926 0574 09675 4.24 3622 3 4

1

1. . . . ( / )


radius tappings):

))/(1(93.0256.0351.01 /1

12

84 KPPEps


Eps DP P K 1 0 41 035 4

1

1. . ( / )

4.3.9 Calculate new Differential range:

*W [kg/s]

DP

W

C Eps D FRO

s

1

35124 10

4

4 2

2

1

.


Sizing Equations 25

4.3.10 For Liquid and Water, go to paragraph 4.3.13.

4.3.11 Calculate the relative change in Differential range:

DPDP DP

DPDP DP

0

0

0;

4.3.12 Paragraphs 4.3.8 - 4.3.11 are repeated until the relative change in the differential range is less

than 0.0001.


R dq

0 07571 0 06253

0 68286

. .

.

5 Restriction Device Sizing

26 Sizing Equations


5.1 Calculation of Beta Ratio 5.1.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01

5.1.2 Calculate Correction factor for Steam quality (For Liquid, Water, and Steam, Fs=1):

F Ss t 1 0 0074.

5.1.3 Calculate Scale reading factor:

SRF W Wn 10 / max

5.1.4 Calculate Differential pressure at normal flow rate:

210/SRFDPDP lossn

5.1.5 Calculate Pipe Reynolds number at normal flow rate:

D

Wnn

3102732.1Re

5.1.6 Checking for Critical flow.

5.1.6.1 Liquid / Water case

If vloss PDPP 1

then the flow is critical.

5.1.6.2 Gas/Steam case

5.1.6.2.1 Calculate first estimate for - ratio.

For Venturi tubes:

0

2

7 4 2

0 25

123 10

W

D DP RO W

n

n n.

.

For other Restriction Devices:

0

2

8 4 2

0 25

4 6 10

W

D DP RO W

n

n n.

.

Preface5 Restriction Device Sizing

Sizing Equations 27

5.1.6.2.2 Calculate Critical Pressure Ratio and define whether the flow is critical.

1

4

0

1/1

1

2

21

kk

ttpk

kF

If ratDPA

then the flow is critical. If not, the flow is Sub-Critical.


Case A. Liquid / Water – Critical flow

A1 Calculate DP.

vPPDP 1

A2 Calculate first estimate for - ratio

For Venturi tubes:

0

2

7 4 2

0 25

123 10

W

D DP RO W

n

n n.

.

For other Restriction Devices: 25.0

248

2

0106.4

nn

n

WRODPD

W

A3 Eps = 1.

A4 Calculate Discharge coefficient. See 9 Appendix.

A5 Calculate new - ratio:

2847 05 1 0

4

2

0 5

..

W

D Eps F C DP RO

n

s n

A6 Calculate the relative change in - ratio:

0

0

0;

A7 Paragraphs A4 – A6 are repeated until the relative change in the - ratio is less than 0.0001.

Case B. Gas / Steam – Critical flow

B1 Calculate Gas expansion factor

2/11/1

1

2

kk

kZ

kEps

B2 Calculate Discharge coefficient. See 9 Appendix.

1

1

PF

DPPDP

ttp

lossrat

1/

1

2

kk

kA


28 Sizing Equations

B3 Calculate first estimate for - ratio (Wn[lb/h], T[R], P1[psi-a], D[in]):

EpsDPMC

TWaa n

4

1)9625.28/(591.2195

1/1

1

2

2

kk

k

kaaam

4Daacm

am

cmamd

2

4112

D

d2

B4 Calculate Orifice diameter at flow temperature:

d D

B5 Calculate Bore Reynolds number at normal flow rate:

d

Wnn

3102732.1Re

B6 Calculate Discharge coefficient. See 9 Appendix.

B7 Calculate new - ratio in accordance with equations in paragraph B3.

Case C. Sub-Critical flow

C1 First estimate for DPn:

lossDPDPn 0

C2 Calculate first estimate for - ratio

For Venturi tubes:

25.0

2

0

47

2

01023.1

n

n

WRODPnD

W

For other Restriction Devices: 25.0

2

0

48

2

0106.4

n

n

WRODPnD

W

C3 Calculate Gas expansion factor (for Liquids/Water, Eps = 1)

For Venturi tubes and Nozzles:

Eps

Q

Q

Q

Q

K K

KK

K

K

2

0

4

0

42

10 5

1

1

1

1

1

.

where QP DP

P

n1

1

For Orifice Plates:

Eps DP P Kn 1 041 035 0

4

1

1. . ( / )

C4 Calculate Discharge coefficient. See 9 Appendix.


Sizing Equations 29

C5 Calculate new - ratio:

2847 05 1 0

4

2

0 5

..

W

D Eps F C DP RO

n

s n

C6 Calculate new DP

For Classical Venturi Tube:

For Nozzles:

For Orifice Plates:

C7 Calculate new DPn:

C8 Calculate the relative change in DPn:

00

0

0 ;; nn

n DPDPnDPn

DPDPnDP

C9 Paragraphs C3 – C8 are repeated until the relative change in the DPn is less

than 0.0001

5.1.8 Calculate Orifice diameter at flow temperature:

d D

5.1.9 Calculate Orifice diameter at ambient temperature.


dd

T Tpe

0

01

For Orifice Plates:

d dDbh d

T Tpe

0

2

0

1 0 55

1

.

238.042.0218.0 lossDP

DP

32 18.106.2014.01 lossDP

DP

25.04

25.04

1

1

C

CDPDP loss

2

max

W

WDPDP n

n


30 Sizing Equations

5.2 Calculation of Flow Rate 5.2.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01


F Ss t 1 0 0074.



d d T Tpe 0 01

For Orifice Plates:

d d Dbh d T Tpe 0 0

2

01 055 1.

5.2.4 Calculate - ratio:

d

D

5.2.5 Checking for Critical flow and some initial calculations.

5.2.5.1 Liquid / Water case

5.2.5.1.1 Calculate downstream pressure:

lossDPPP 12

5.2.5.1.2 Identify Critical flow:

If vPP 2

then the flow is critical. If not, the flow is Sub-Critical

5.2.5.1.3 Calculate Differential Pressure to be used in Flow Rate calculation.

For Critical flow:

vPPDP 1

For Sub-Critical flow:

Classical Venturi Tube:

Nozzles:

Orifice Plates:

5.2.5.1.4 Calculate first estimate for Flow Rate (W0 [kg/s]):

4

24

01

10107.2

RODP

dW

238.042.0218.0 lossDP

DP

32 18.106.2014.01 lossDP

DP

25.04

25.04

1

1

C

CDPDP loss


Sizing Equations 31

5.2.5.2 Gas/Steam case

5.2.5.2.1 Calculate Critical Pressure Ratio and define whether the flow is critical.

1

4

1/1

1

2

21

kk

ttpk

kF

If ratDPA

then the flow is critical. If not, the flow is Sub-Critical

5.2.5.2.2 Initial calculations for Critical flow.

Gas expansion factor:

2/11/1

1

2

kk

kZ

kEps

First estimate for Flow Rate (W0 [lb/h], T[R], D[in], P1[psi-a]):

ttpFEpsPT

MdW

1

5.0

2

09625.28

591.2195

5.2.5.2.3 Initial calculations for Sub-Critical flow.

Differential Pressure to be used in Flow Rate calculation:

For Classical Venturi Tube:

For Nozzles:

For Orifice Plates:

Gas expansion factor:


5.0

1

24

42

1

1

1

1

1

Q

Q

Q

QEps

K

K

KK

KK

where

1

1

P

DPPQ

1

1

PF

DPPDP

ttp

lossrat

1/

1

2

kk

kA

238.042.0218.0 lossDP

DP

32 18.106.2014.01 lossDP

DP

25.04

25.04

1

1

C

CDPDP loss


32 Sizing Equations

For Orifice Plates:

1

1

4 )/(35.041.01 KPDPEps

First estimate for Flow Rate (W0 [kg/s]):

4

24

01

10107.2

RODP

dW

5.2.6 Calculate Reynolds number.

For Gas / Steam Critical flow (Bore Reynolds number):

d

W

0

3102732.1Re

For Liquid / Water and Gas / Steam Sub-Critical flow (Pipe Reynolds number):

D

W

0

3102732.1Re


5.2.8 For Orifices in the case of Gas / Steam Sub-Critical flow, calculate DP and Gas Expansion factor:

1

1

4 )/(35.041.01 KPDPEps

5.2.9 Calculate new Flow rate:

For Gas / Steam at Critical flow:

ttpFEpsPT

MdCW

1

5.0

2

9625.28591.2195

For other cases (W [kg/s]):

W C F Eps dDP RO

s

35124 101

4 2

4.

5.2.10 Calculate the relative change in Flow rate:

WW W

WW W

0

0

0;

5.2.11 Paragraphs 5.2.6 – 5.2.10 are repeated until the relative change in the Flow rate is less

than 0.0001.

25.04

25.04

1

1

C

CDPDP loss


Sizing Equations 33

5.3 Calculation of Pressure Loss 5.3.1 Calculate Internal pipe diameter at flow temperature:

D D T Tp 0 01


F Ss t 1 0 0074.



d d T Tpe 0 01

For Orifice plates:

d d Dbh d T Tpe 0 0

2

01 055 1.

5.3.4 Calculate Pipe Reynolds number (W [kg/s]):

Re.

12732 103 W

D


d

D


5.3.7 Calculate Critical flow rate.

For Liquid / Water:

vPPDP 1

4

24

1105124.3

RODP

dEpsFCW scr

For Gas / Steam

2/11/1

1

2

kk

kZ

kEps

ttpcr FEpsPT

MdCW

1

5.0

2

9625.28591.2195

5.3.8 Checking for Critical flow and Pressure Loss calculation.

Case A. Critical flow: W>0.999*Wcr and W<1.001*Wcr.

For this case, Pressure Loss:

vloss PPDP 1

Case B. Wrong data: W=>1.001*Wcr.

Flow rate cannot be achieved. User has to check his data.

Case C. Sub-Critical flow: W<=0.999*Wcr

C1 First estimate for Differential range:

vPPDP 10

C2 Calculate Discharge coefficient. See 9 Appendix.

C3 Calculate Gas expansion factor (for Liquid and Water, Eps 1).



34 Sizing Equations

Eps

Q

Q

Q

Q

K K

KK

K

K

24

42

10 5

1

1

1

1

1

.

where

1

01

P

DPPQ

For Orifice Plates:

1

10

4 )/(35.041.01 KPDPEps

C4 Calculate new Differential range (W [kg/s]):

DP

W

C Eps D FRO

s

1

35124 10

4

4 2

2

1

.

C5 Calculate the relative change in Differential range:

DPDP DP

DPDP DP

0

0

0;

C6 Paragraphs C3 – C5 are repeated until the relative change in the DP is less

than 0.0001.

C7 Calculate Pressure Loss

25.04

25.04

1

1

C

CDPDPloss

Preface6 Relief Valve Sizing

Sizing Equations 35

6 Relief Valve Sizing

6.1 Blocked Flow: Liquid Relief 6.1.1 Requiring ASME capacity certification

6.1.1.1 Calculate Total back pressure:

321 bbbb PPPP

6.1.1.2 Effective coefficient of discharge: Kd 0 65. (if Kd is not entered by user).

6.1.1.3 Determine Correction factor for back pressure.

6.1.1.3.1 For Conventional and Pilot operated valves,

Kw 1 .

6.1.1.3.2 For Bellows valve:

Case P Pb s/ . 016: Kw 1

Case 016 05. / . P Pb s : K P Pw b s 1152 0 95. . /

Case P Pb s/ . 0 5 : Kw 0 677.

6.1.1.4 Calculate Upstream relieving pressure:

*Pup [psi-g]

P P Pup over s 1 0 01.

6.1.1.5 Estimate Required effective discharge area:

*W [US gal/min], Pup [psi-g]

AW

K K

G

p pd W

f

up b

038

6.1.1.6 Calculate Reynolds number:

*W [US gal/min], [cP]

Re

2800

0

W G

A

f

6.1.1.7 Calculate Correction factor for viscosity:

Y ln Re / ln 10

Case Re 35: Kv 0 3.

Case 35 100 Re : 6611.062838.0 YKv

Case:

Case Re 50000 : 6.1.1.8 Calculate Required effective discharge area.

6.1.1.8.1 With Rupture disk:

A A K Kv cc 0 /

6.1.1.8.2 Without Rupture disk:

vKAA /0

6.1.2 Not requiring ASME capacity certification

6.1.2.1 Calculate Total back pressure:

321 bbbb PPPP


36 Sizing Equations

6.1.2.2 Effective coefficient of discharge: Kd 0 62. (if Kd is not

entered by user).

6.1.2.3 Determine Correction factor for back pressure.

6.1.2.3.1 For Conventional and Pilot operated valves,

Kw 1 .

6.1.2.3.2 For Bellows valve:

Case P Pb s/ . 016: Kw 1

Case 016 05. / . P Pb s : K P Pw b s 1152 0 95. . /

Case P Pb s/ . 0 5 : Kw 0 677.

6.1.2.4 Calculate correction factor for overpressure:

Y Pover / 10

Case Y 1: K Y Yp 0 2 082. .

Case 1 25 Y . : K Y Y Yp 0 037641 0 30196 0 95464 0 085443 2. . . .

Case 25 5. Y : K Yp 0 034664 0 91334. .

Case Y 5 : Kp 1086.

6.1.2.5 Estimate Required effective discharge area:

*W [US gal/min]

AW

K K K

G

p pd W p

f

s b

038 125

.

6.1.2.6 Calculate Reynolds number:

*W [US gal/min], [cP]

Re

2800

0

W G

A

f

6.1.2.7 Calculate Correction factor for viscosity:

Y ln Re / ln 10

Case Re 35: Kv 0 3.

Case 35 100 Re : K Yv 062838 06611. .

Case100 50000 Re :

K Y Y Y Yv 0 023362 035578 2 037 52507 4 22284 3 2. . . . .

Case Re 50000 : Kv 1.

6.1.2.8 Calculate Required effective discharge area.

6.1.2.8.1 With Rupture disk:

A A K Kv cc 0 /

6.1.2.8.2 Without Rupture disk:

vKAA /0

6.2 Blocked Flow: Gas Relief 6.2.1 Calculate Upstream relieving pressure:

*Pa [psi-a]

P P P Pup over s a 1 0 01.


Sizing Equations 37

6.2.2 Calculate Total back pressure:

321 bbbb PPPP

6.2.3 Calculate Critical flow throat pressure:

P PK

cf up

K K

2

1

1/

6.2.4 Effective coefficient of discharge: Kd 0 975. .

6.2.5 The condition P Pb cf (Pb [psi-a] ) determines:

Case A - Critical flow. A1 Calculate Coefficient for critical flow equation:

Case K 101. : Cr 317

Case101 2. K : C KK

r

K

K

5202

1

1

1

Case K 2 : Cr 400

A2 Calculate Capacity correction factor due to back

pressure (if Kb is not entered by user).

A2.1 For Conventional and Pilot operated valves, Kb 1 .

A2.2 For Bellows valve:

A2.2.1 Y P Pb s /

A2.2.2 Case Y 0315. : K Yb10 153 168 . .

Case Y 0315. : Kb10 1 .

A2.2.3 Case Y 0325. : K Yb20 114 043 . .

Case Y 0325. : Kb20 1 .

A2.2.4 Case Pover 20 : K Kb b 20

Case 10 20 Pover : K K P K Kb b over b b 10 20 1001 10.

Case Pover 10 : K Kb b 10

A3 Estimate Required effective discharge area:

*W [lb/h], T [°R]

AW

C K P K

T Z

Mr d up b

0

Case B ( P Pb cf ) - Subcritical flow: Bellows valve.

B1 Calculate Cr:

Case K 101. : Cr 317

Case101 2. K : C KK

r

K

K

5202

1

1

1

Case K 2 : Cr 400

B2 If Capacity correction factor due to back pressure is

not entered by user, Kb 1 .


38 Sizing Equations

B3 Estimate Required effective discharge area:

*W [lb/h], T [°R]

AW

C K P K

T Z

Mr d up b

0

Case C ( P Pb cf ) - Subcritical flow: Conventional and Pilot operated valves.

C1 Calculate Coefficient for subcritical flow equation:

*Pb [psi-a]

C1.1 R P Pb up /

C1.2

FK

KR

R

R

K

K K

2

2

1

1

1

1

/

/

C2 Estimate Required effective discharge area:

*W [lb/h], Pb [psi-a], T [°R]

A

W

F K

T Z

M P P Pd up up b

0

2735

6.2.6 For Rupture disk application, calculate Required effective discharge area:

A A Kcc 0 /

6.3 Blocked Flow: Steam Relief 6.3.1 Calculate Upstream relieving pressure:

*Pa [psi-a]


6.3.2 Calculate Correction factor for Napier equation:

Case Pup 1515: Kn 1

Case 1515 3215 Pup : K P Pn up up 01916 1000 0 2292 1061. / .

Case Pup 3215 : Kn 1

6.3.3 Calculate Superheat steam correction factor:

6.3.3.1 Y T1 27316 18 32 1000 . . /

6.3.3.2 Y Pup2 1000 /

6.3.3.3

K Y Y Y Y Y Y Y Y Y

Y Y Y

sh

0 201 1 2 0168 1 2 0 291 1 0 389 1 2 0 256 1 2

0838 1 0164 2 0 025 2 1276

2 2 2 2 2

2

. . . . .

. . . .


6.3.5 Estimate Required effective discharge area:

*W [lb/h]

AW

P K K Kup d n sh

0515

.

6.3.6 For Rupture disk application, calculate Required effective discharge area:

A A Kcc 0 /


Sizing Equations 39

6.4 Fire Case: Gas Expansion 6.4.1 Calculate Upstream relieving pressure:

*Pa [psi-a]


6.4.2 Calculate Coefficient for critical flow equation:

Case K 101. : Cr 317

Case101 2. K : C KK

r

K

K

5202

1

1

1

Case K 2 : Cr 400

6.4.3 If Heat absorption factor is entered, go to paragraph 6.4.8.

6.4.4 If Normal pressure is not entered or Normal temperature is not entered, a message appears: “Please enter

Heat absorption factor or Normal pressure and Normal temperature”.

6.4.5 Calculate Gas temperature at relieving conditions:

*Pa [psi-a], T [°R]

T TP

P

up1

6.4.6 If Vessel Wall temperature is not entered, the following message appears:

“Please enter Heat absorption factor or Vessel wall temperature”.

6.4.7 Calculate Heat absorption factor:

T [°R]

FT T

C K T

w

r d

1 014061

1

1 25

0 6506

.

.

.

6.4.8 Estimate Required effective discharge area:

*W [lb/h], T [°R]

AF A

Pup

0

1 1

6.4.9 If Normal pressure is not entered or Normal temperature is not entered

or Molecular Mass is not entered or Vessel wall temperature is not

entered, a message appears: “Maximum discharge cannot be calculated

because Normal pressure or Normal temperature or Molecular Mass or

Vessel wall temperature is not entered”. Then go to paragraph 6.4.11.

6.4.10 Calculate Maximum discharge:

*Pa [psi-a], W[lb/h]

W A M PT T

Tup

w

01406 1

1

1

1 25

1 1506.

.

.

6.4.11 For Rupture disk application, calculate Required effective discharge

area:

A A Kcc 0 /


40 Sizing Equations

6.5 Fire Case: Liquid Filled Vessel 6.5.1 Calculate Maximum discharge:

*HV [Btu/lb], W[lb/h]

WF A

HV

21000

10 82.

6.5.2 Calculate Upstream relieving pressure:

*Pa [psi-a]


6.5.3 Calculate Total back pressure:

321 bbbb PPPP

6.5.4 Calculate Critical flow throat pressure:

P PK

cf up

K K

2

1

1/


6.5.6 The condition P Pb cf (Pb [psi-a] ) determines:

Case A - Critical flow. A1 Calculate Coefficient for critical flow equation:

Case K 101. : Cr 317

Case101 2. K : C KK

r

K

K

5202

1

1

1

Case K 2 : Cr 400

A2 Calculate Capacity correction factor due to back

pressure (if Kb is not entered by user).

A2.1 For Conventional and Pilot operated valves, Kb 1 .

A2.2 For Bellows valve:

A2.2.1 Y P Pb s /

A2.2.2 Case Y 0315. : K Yb10 153 168 . .

Case Y 0315. : Kb10 1 .

A2.2.3 Case Y 0325. : K Yb20 114 043 . .

Case Y 0325. : Kb20 1 .

A2.2.4 Case Pover 20 : K Kb b 20

Case 10 20 Pover : K K P K Kb b over b b 10 20 1001 10.

Case Pover 10 : K Kb b 10

A3 Estimate Required effective discharge area:

*W [lb/h], T [°R]

AW

C K P K

T Z

Mr d up b

0

Case B ( P Pb cf ) - Subcritical flow: Bellows valve.

B1 Calculate Cr:

Case K 101. : Cr 317


Sizing Equations 41

Case101 2. K : C KK

r

K

K

5202

1

1

1

Case K 2 : Cr 400

B2 If Capacity correction factor due to back pressure is

not entered by user, Kb 1 .

B3 Estimate Required effective discharge area:

*W [lb/h], T [°R]

AW

C K P K

T Z

Mr d up b

0

Case C ( P Pb cf ) - Subcritical flow: Conventional and Pilot operated valves.

C1 Calculate Coefficient for subcritical flow equation:

*Pb [psi-a]

C1.1 R P Pb up /

C1.2

FK

KR

R

R

K

K K

2

2

1

1

1

1

/

/

C2 Estimate Required effective discharge area:

*W [lb/h], Pb [psi-a], T [°R]

A

W

F K

T Z

M P P Pd up up b

0

2735

6.5.7 For Rupture disk application, calculate Required effective discharge

area:

A A Kcc 0 /

7 Thermowell Calculation

42 Sizing Equations


7.1 ASME PTC 1974

7.1.1 Define Initial Value of K f Constant:

If Dt=1/4 then K f

=2.075

If Dt=3/8 then K f

=2.445

If Dt=9/16 then K f

=3.02

If Dt=11/16 then K f

=3.40

If Dt=7/8 then K f

=3.965

7.1.2 Calculate Ratio of Frequency at Fluid Temperature to Frequency at 70 °F:

* T[°F]

For Austenitic steel,

R f 0.99996 - 0.0000036111 T - 0.0000000742 T2

For Ferrite steel, R f 1.0101- 0.000138 T + 0.000000267 T - 0.000000000336 T2 3

7.1.3 Calculate Maximum Thermowell Length Based on Vibration Limitation:

* ROmaterial[lb/in3]

)64.2/()(1 VROmaterialRBEKRL ff

7.1.4 Define K f Constant:

Case L 3.5

If Dt=1/4 then K f

=2.06

If Dt=3/8 then K f

=2.42

If Dt=9/16 then K f

=2.97


=3.32

If Dt=7/8 then K f

=3.84

Case 3.5<L 6

If Dt=1/4 then K f

=2.07

If Dt=3/8 then K f

=2.45

If Dt=9/16 then K f

=3.01


=3.39

If Dt=7/8 then K f

=3.96

Case 6<L 9

If Dt=1/4 then K f

=2.08

If Dt=3/8 then K f

=2.46

Preface7 Thermowell Calculation

Sizing Equations 43

If Dt=9/16 then K f

=3.05


=3.44

If Dt=7/8 then K f

=4.03

Case 9<L 13.25

If Dt=1/4 then K f

=2.09

If Dt=3/8 then K f

=2.47

If Dt=9/16 then K f

=3.06


=3.46

If Dt=7/8 then K f

=4.06

Case 13.25<L 20

If Dt=1/4 then K f

=2.09

If Dt=3/8 then K f

=2.47

If Dt=9/16 then K f

=3.07


=3.47

If Dt=7/8 then K f

=4.08

Case 20<L

If Dt=1/4 then K f

=2.09

If Dt=3/8 then K f

=2.47

If Dt=9/16 then K f

=3.07


=3.48

If Dt=7/8 then K f

=4.09

7.1.5 Paragraphs 7.1.3 - 7.1.4 are repeated until current K f value equals previous K f

value

7.1.6 Calculate Natural Frequency for L=L1

* ROmaterial[lb/in3]

ROmaterialL

REKfn

ff

2

1

7.1.7 Calculate Wake Frequency

B

VfW 64.2


44 Sizing Equations

7.1.8 Calculate Magnification Factor for L1(R 0.8)

2

2

2

2

11

R

R

f

f

f

f

F

n

w

n

w

M

7.1.9 Define 1K, 2K

, 3Kconstants

If Dt=1/4 then {

1K =0.412; 2K =37.5;

3K =0.116}

If Dt=3/8 then {

1K =0.334; 2K =42.3;

3K =0.205}

If Dt=9/16 then {

1K =0.223; 2K =46.8;

3K =0.389}

If Dt=11/16 then {

1K =0.202; 2K =48.7;

3K =0.548}

If Dt=7/8 then {

1K =0.155; 2K =50.1;

3K =0.864}

7.1.10 Calculate Maximum Allowable Static Gage Pressure

*Pmax [psi-g]. Convert from UOM used for pressure.

*S [psi-g]

SKP 1max

7.1.11 Calculate Maximum thermowell length based on Steady State Stress Consideration

*L2 [inch]

*ROfluid [lb/ft3]

*P [psi-g] – operating pressure

MFROfluid

PKS

V

KL

1

322


Sizing Equations 45

7.2 ASME PTC 2010

7.2.1 Calculate Mounting factor

*L [m]

7.2.1.1 Threaded connection:L

AH d

c 9.01

7.2.1.2 Other connection types:

2)]/(5.11[

/61.01

d

dc

Ab

LAH

7.2.2 Calculate Reynolds number

*B [m]

/Re ROBU

7.2.3 Calculate Strouhal number

7.2.3.1 Re < 1,300 Re)/221(22.0 sN

7.2.3.2 Re > 500,000 22.0sN

7.2.3.3 1,300 ≤ Re ≤ 500,000

3

10

2

10 ]1300(Re/[0095.0]1300(Re/[0248.0213.0 LogLogNs

7.2.4 Calculate Natural frequency

*L [m], B[m], E[Pag]

7.2.4.1 Calculate average outside diameter

7.2.4.1.1 Tapered thermowell: 2/)( BAD da

7.2.4.1.2 Other thermowells: da AD

7.2.4.2 Calculate approximate natural frequency

64/)(1416.344

ba dDI

4/)(1416.3

22

bam dDROm

2

5.02 1

)(1416.32

867.1

Lm

IEfa

7.2.4.3 Calculate correction factor Hf

7.2.4.3.1 Tapered and straight thermowell:


46 Sizing Equations

)]/(8.01[3

2

)/(1.11

])/1()/1(1[99.0ab Dd

a

ddf

LD

ABABH

7.2.4.3.2 Stepped thermowell:

Case A: db = 0.66 cm

Case A1: B = 2.22cm: c1=1.41, c2=-0.949, c3=-0.091, c4=1.132, c5=-1.714, c6=0.865, c7=0.861,

c8=1.00, c9=9.275, c10=-7.466

Case A2: B = 1.27cm:

c1=1.407, c2=-0.839, c3=-0.022, c4=1.022, c5=-2.228, c6=1.594, c7=1.313,

c8=0.362, c9=8.299, c10=-5.376

For both A1 and A2:

])/([)/(])/([ 43211 cBAcLLcBAcy dsd

])/([)/(])/([ 87652 cBAcLLcBAcy dsd

])/([ 109 cBAcBet d

BetBetBet

f yyH /1

21 )(

Case A3: Other values of db:

1fH

Case B: Other values of B: 1fH

7.2.4.4 Calculate correction factor Haf

m

afRO

ROH

21

7.2.4.5 Calculate correction factor Has

]1)/(

1[

21

2

bam

sas

dDRO

ROH

7.2.4.6 Calculate natural frequency with ideal support

asaffan HHHff 0

7.2.4.7 Calculate natural frequency of the mounted thermowell

cnn Hff 0

7.2.5 Calculate Vortex shedding frequency

*B[m]

BUNf ss /


Sizing Equations 47

7.2.6 Calculate Scruton number

*B [m]

])/(1[)/(1416.3 22 BdRORON bmsc

7.2.7. Calculate miscellaneous parameters

*B [m], L[m], E[Pag]

7.2.7.1 Parameter Gsp

7.2.7.1.1 Tapered and straight thermowell:

])/(1[1416.33

)/21(1642

2

dbd

dsp

AdA

ABLG

7.2.7.1.2 Stepped thermowell:

])/(1[1416.3

])/1()/1(/[1642

22

dbd

sddsp

AdA

LLABABLG

7.2.7.2 Parameter Grd (for stepped thermowell only):

])/(1[1416.3

1642

2

BdB

LG

b

srd

7.2.7.3 Stress concentration factor

7.2.7.3.1 Threaded connections:

3.2tK

7.2.7.3.2 Other connections

Case A: b is unknown or Ad/b > 33:

2.2tK

Case B: b is known and Ad/b ≤ 33:

bAK dt /033.01.1

7.2.7.4 Stress concentration factor at support plane (for stepped thermowell only)

Case A: bs is unknown or B/bs > 33:

2.21 tK


48 Sizing Equations

Case B: bs is known and B/bs ≤ 33:

st bBK /033.01.11

7.2.7.5 Temperature de-rating factor:

reft EEF /

7.2.8 Calculate Frequency Limit

7.2.8.1 Low density gases: Nsc > 2.5 and Re < 100000

nfFrL 8.0

7.2.8.2 General case: other values of Nsc and Re

nfFrL 4.0

7.2.9 Compliance with the Frequency Limit requirement

7.2.9.1 Initial evaluation of compliance

7.2.9.1.1 The thermowell is in compliance with the Frequency Limit requirement, if

FrLf s

Go to 7.2.10

7.2.9.1.2 The thermowell is in non-compliance with the Frequency Limit requirement if

FrLf s and )100000(Re)5.2( andNsc

Go to 7.2.10

7.2.9.2 Evaluate compliance with Cyclic Stress Limit for General case

7.2.9.2.1 Calculate velocity for in-line resonance

7.2.9.2.1.1 Re < 1,300

ROBUROBN

fBVR

s

n

22)

221(

2

7.2.9.2.1.2 1,300 ≤ Re < 500,000

)1300(Re/10LogR

RRaR 0496.00285.0 2

)]2

(1[2

10UN

fBLog

N

aR

N

fBVR

s

n

ss

n


Sizing Equations 49

7.2.9.2.1.3 Re ≥ 500,000

s

n

N

fBVR

2

7.2.9.2.2 Calculate cyclic drag stress at the root

)2/(1 Fm

205.0 VRROPd

PdFmGSd sp

7.2.9.2.3 Calculate combined drag and lift stresses

SdKS t max

7.2.9.2.4 Calculate fatigue stress limit

fet SFFLimit

7.2.9.2.5 Compliance with cyclic stress limit

7.2.9.2.5.1 Tapered and straight thermowell

7.2.9.2.5.1.1 Not complied with the cyclic stress limit and frequency limit if

LimitS max

Go to 7.2.10

7.2.9.2.5.1.2 Complied with the cyclic stress limit if LimitS max

Set new frequency limit: nfFrL 8.01

Go to 7.2.9.3

7.2.9.2.5.2 Stepped thermowell

7.2.9.2.5.2.1 Not complied with the cyclic stress limit and frequency limit if

LimitS max

Go to 7.2.10

7.2.9.2.5.2.2 Case LimitS max

7.2.9.2.5.2.2.1 Calculate:

PdFmGSd rd 1

111max SdKS t


50 Sizing Equations

7.2.9.2.5.2.2.2 Not complied with the cyclic stress limit and frequency limit if

LimitS 1max

Go to 7.2.10

7.2.9.2.5.2.2.3 Complied with the cyclic stress limit if LimitS 1max

Set new frequency limit: nfFrL 8.01

Go to 7.2.9.3

7.2.9.3 Re-evaluate compliance with the frequency limit requirement if cyclic stress is acceptable

7.2.9.3.1 The thermowell is in compliance with the Frequency Limit requirement, if

1FrLf s

7.2.9.3.2 The thermowell is in non-compliance with the Frequency Limit requirement if

1FrLf s

7.2.10 Compliance with the Static Stress Limit requirement

*B [m], P[Pag], S[Pag]

7.2.10.1 Calculate radial, tangential, and axial stresses due to the external pressure:

PSr

2

2

)/(1

)/(1

db

db

Ad

AdPSt

2)/(1 db Ad

PSa

7.2.10.2 Calculate steady-state drag stress at the root:

27.0 UROPD

7.2.10.3 Calculate steady-state stress due to the drag force:

PDGSd sp

7.2.10.4 Calculate maximum stress

SaSdS max

7.2.10.5 Calculate left-hand side of the Von Mises criteria:

22

max

2

max )()()[(5.0 SrStStSSrSLHS

7.2.10.6 Calculate right-hand side of the Von Mises criteria:

SRHS 5.1


Sizing Equations 51

7.2.10.7 Compliance

7.2.10.7.1 Tapered and straight thermowell

7.2.10.7.1.1 Not complied with the static stress limit if

RHSLHS

7.2.10.7.1.2 Complied with the static stress limit if

RHSLHS

7.2.10.7.2 Stepped thermowell

7.2.10.7.2.1 Not complied with the static stress limit if

RHSLHS

Go to 7.2.11

7.2.10.7.2.2 Case RHSLHS

7.2.10.7.2.2.1 Calculate:

2

2

)/(1

)/(11

Bd

BdPSt

b

b

2)/(11

Bd

PSa

b

PDGSd rd 1

111max SaSdS

22

1max

2

1max )1()1()[(5.01 SrStStSSrSLHS

7.2.10.7.2.2.2 Not complied with the static stress limit if

RHSLHS 1

7.2.10.7.2.2.3 Complied with the static stress limit if

RHSLHS 1


52 Sizing Equations

7.2.11 Compliance with the Dynamic Stress Limit requirement

7.2.11.1 Calculate parameters:

ns ffr /

21

11

rFm

ns ffr /21

211

12

rFm

7.2.11.2 Calculate drag and lift stresses at the root:

205.01 UROPD

25.01 UROP

12 PDFmGSd sp

111 PFmGS sp

7.2.11.3 Calculate combined drag and lift stresses:

22

max 1SSdKS t

7.2.11.4 Calculate fatigue stress limit:

fet SFFLimit

7.2.11.5 Compliance

7.2.11.5.1 Tapered and straight thermowell

7.2.11.5.1 Not complied with the dynamic stress limit if

LimitS max

7.2.11.5.2 Complied with the dynamic stress limit if

LimitS max

7.2.11.5.2 Stepped thermowell

7.2.11.5.1 Not complied with the dynamic stress limit if

LimitS max

Go to 7.2.12


Sizing Equations 53

7.2.11.5.2 Case LimitS max

7.2.11.5.2.1 Calculate:

121 PDFmGSd rd

1111 PFmGS rd

22

11max 111 SSdKS t

7.2.11.5.2.2 Not complied with the dynamic stress limit if

LimitS 1max

7.2.11.5.2.3 Complied with the dynamic stress limit if

LimitS 1max

7.2.12 Compliance with the Hydrostatic Pressure Limit requirement

*B [m], P[Pag], S[Pag]

7.2.12.1 Calculate pressure rating for the shank:

]0833.0)/(2

167.2[66.0

bdBBSPc

7.2.12.2 Calculate external pressure rating for the tip:

2)(13.0 bd

tSPt

7.2.12.3 Calculate pressure rating of the thermowell:

),(Pr PtPcMINating

7.2.12.4 Compliance

7.2.12.4.1 Not complied with the hydrostatic pressure limit if

Pating Pr

7.2.12.4.2 Complied with the hydrostatic pressure limit if

Pating Pr

8 Standards

54 Sizing Equations

8 Standards

8.1 Control Valve Sizing ISA S75.01 (1995)

IEC 60534-2-1 (1998)

8.2 Noise Calculation Masoneilan OZ 3000E (1984) - Hydrodynamic Noise

ISA S75.17 (1991) - Aerodynamic Noise

IEC 534-8-3 (1995)

IEC 534-8-4 (1994)

8.3 Flow Meter Sizing 8.3.1 Square Edge Orifice Standard Flange Tappings ISO*/ Miller**

Corner Tappings ISO / Miller

Radius Tappings ISO / Miller

Small-Bore Honed-Orifice Meter Run with Corner Tappings Miller

Small-Bore Honed-Orifice Meter Run with Flange Tappings Miller

Pipe Tappings (2.5D & 8D) Miller

AGA Report 3 (Flange Tappings) AGA Rep.3***

AGA Report 3 (Pipe Tappings) AGA Rep.3

8.3.2 Quarter of Circle (Quadrant Edge) Orifice

Flange Tappings BS 1042****

Corner Tappings BS 1042

Radius Tappings BS 1042

8.3.3 Conical Entrance Orifice Miller

8.3.4 Lo-Loss Tube Miller

8.3.5 Venturi Tube

Classical venturi tube with an “as cast” convergent section ISO / Miller

Classical venturi tube with a machined convergent section ISO / Miller

Classical venturi tube with a rough-welded sheet-iron convergent section ISO / Miller

Universal Venturi Tube Miller

8.3.6 Nozzle

ISO Long Radius Nozzle ISO

ASME Long Radius Nozzle Miller

ISA 1932 Nozzle ISO / Miller

Venturi Nozzle ISO / Miller

8.3.7 Eccentric Orifice

Diametrically Opposite Flange Tappings Miller

Side (90) Flange Tappings Miller

Diametrically Opposite Vena Contracta Tappings Miller

Side (90) Vena Contracta Tappings Miller

Preface8 Standards

Sizing Equations 55

8.3.8 Segmental Orifice

Flange Tappings Miller

Vena Contracta Tappings Miller

Note: * ISO 5167-1 (1991), ISO 5167-1 (1998), or ISO 5167 (2003)

** Flow Measurement Engineering Handbook by R.W. Miller, 3rd edition

(1996)

*** ANSI/API 2530 (1991) [AGA Report 3]

**** British standard 1042. Section 1.2 (1989)

8.4 Relief Valve Sizing API RP 520, seventh edition (January 2000)

8.5 Thermowell Calculation ASME PTC 19.3 (1974)

ASME PTC 19.3 TW (2010)

9 Appendix

56 Sizing Equations

9 Appendix

Formulae for Discharge Coefficient Notation

B - ratio

C Discharge Coefficient

D Internal Pipe Diameter, mm

Di Internal Pipe Diameter, inch

Re Pipe Reynolds Number at Normal Flow Rate

Rd Bore Reynolds Number at Normal Flow Rate

9.1 Square Edge Orifice 9.1.1 Flange Tappings

9.1.1.1 ISO 5167-1 (1991) and Miller If D<58.62

C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75-0.85598*B^3/D+

0.039*B^4/(1-B^4)

Else C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75-0.85598*B^3/D+

2.286*B^4/(D*(1-B^4))

9.1.1.2 ISO 5167-1 (1998) and ISO 5167 (2003)

If D<71.12

C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*25.4/D)-0.123*exp(-7*25.4/D))*(1-

0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*25.4/D/(1-B)-0.8*(2*25.4/D/(1-

B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

Else C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*25.4/D)-0.123*exp(-7*25.4/D))*(1-

0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*25.4/D/(1-B)-0.8*(2*25.4/D/(1-

B))^1.1)*B^1.3

9.1.2 Corner Tappings

9.1.2.1 ISO 5167-1 (1991) and Miller C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75

9.1.2.2ISO 5167-1 (1998) and ISO 5167 (2003)

If D<71.12

C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080-0.123)*(1- 0.11*(19000*B/Re)^0.8))*(B^4/(1-

B^4))-0.031*(2*0/(1-B)-0.8*(2*0/(1-B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

Else C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080-0.123)*(1- 0.11*(19000*B/Re)^0.8))*(B^4/(1-

B^4))-0.031*(2*0/(1-B)-0.8*(2*0/(1-B))^1.1)*B^1.3

9.1.3 Radius Tappings

9.1.3.1 ISO 5167-1 (1991) and Miller C = 0.5959+0.0312*B^2.1-0.184^B^8+0.0029*B^2.5*(10^6/Re)^0.75+0.039*B^4/(1-B^4)-

0.015839*B^3

9.1.3.2 ISO 5167-1 (1998) and ISO 5167 (2003)

If D<71.12

C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*1)-0.123*exp(-7*1))*(1-

0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0.47/(1-B)-0.8*(2*0.47/(1-

B))^1.1)*B^1.3+0.011*(0.75-B)*(2.8-D/25.4)

Preface9 Appendix

Sizing Equations 57

Else C = 0.5961+0.0261*B^2-0.216B^8+0.000521*(10^6*B/Re)^0.7+(0.0188+0.0063*(19000*B/

Re)^0.8)*B^3.5*(10^6/Re)^0.3+(0.043+0.080*exp(-10*1)-0.123*exp(-7*1))*(1-

0.11*(19000*B/Re)^0.8))*(B^4/(1-B^4))-0.031*(2*0.47/(1-B)-0.8*(2*0.47/(1-B))^1.1)*B^1.3

9.1.4 Small-Bore Honed-Orifice Meter Run with Corner Tappings C = (0.5991+0.0044/Di+(0.3155+0.0175/Di)*(B^4+2^B^16)+(0.52/Di-0.192+

(16.48-1.16/Di)*(B^4+4*B^16))*(Re^(-0.5)))*((1-B^4)^0.5)

9.1.5 Small-Bore Honed-Orifice Meter Run with Flange Tappings

C = (0.5980+0.468*(B^4+10^B^12)+(0.87+8.1*B^4)*(Re^(-0.5)))*((1-B^4)^0.5)

9.1.6 Pipe Tappings (2.5D & 8D) C = 0.5959+0.461*B^2.1+0.48^B^8+0.039*B^4/(1-B^4)+0.0029*B^2.5*(10^6/Re)^0.75

9.1.7 AGA Report 3 (Flange Tappings) A0 = 830-5000*B+9000*B^2-4200*B^3+530/Di^0.5

A1 = 0.5993+0.007/Di+(0.364+0.076/Di^0.5)*B^4

A2 = 0

If B<(0.07+0.5/Di) A2 = 0.4*(1.6-1/Di)^5*(0.07+0.5/Di-B)^(5/2)

A3 = 0

If B<0.5 A3 = (0.5-B)^(3/2)*(0.009+0.034/Di)

A4 = 0

If B>0.7 A4 = (B-0.7)^(5/2)*(65/Di^2+3)

K0 = (A1+A2-A3+A4)/(1+0.000015*A0)

EF = A0*Di*B

C = (1-B^4)^0.5*K0*(1+EF*B/Re)

9.1.8 AGA Report 3 (Pipe Tappings) A0 = 905-5000*B+9000*B^2-4200*B^3+875/Di

A1 = 0

If B<0.25 A1 = (0.25-B)^(5/2)*(1.43/Di^0.5)

K0 = 0.5925+0.0182/Di+(0.440-0.06/Di)*B^2+(0.935+0.225/Di)*B^5+1.35*B^14+A1

EP = A0*Di*B

C = (1-B^4)^0.5*K0*(1+EP*B/Re)

9.2 Quarter of Circle (Quadrant Edge) Orifice C = 0.73823+0.3309*B-1.1615^B^2+1.5084*B^3

9.3 Conical Entrance Orifice If Re5000*B C = 0.734

Else C = 0.730

9.4 Lo-Loss Tube C = 1.005-0.471*B+0.564^B^2-0.514*B^3

9.5 Venturi Tube 9.5.1 Classical venturi tube with an “as cast” convergent section

C = 0.984

9.5.2 Classical venturi tube with a machined convergent section

C = 0.995

9.5.3 Classical venturi tube with a rough-welded sheet-iron convergent section

C = 0.985

9.5.4 Universal Venturi Tube

C = 0.9797

9 Appendix

58 Sizing Equations

9.6 Nozzle 9.6.1 ISO Long Radius Nozzle

C = 0.9965-0.00653*(B^0.5)*(10^6/Re)^0.5

9.6.2 ASME Long Radius Nozzle

C = 0.9975-6.53*B^0.5*Re^-0.5

9.6.3 ISA 1932 Nozzle

C = 0.99-0.2262*B^4.1-( 0.00175*B^2-0.0033*B^4.15)*(10^6/Re)^1.15

9.6.4 Venturi Nozzle

C = 0.9558-0.196*B^4.5

9.7 Eccentric Orifice 9.7.1 Diametrically Opposite Flange Tappings

If D 100 C = 0.5875+0.3813*B^2.1+0.6898^B^8-0.1963*B^4/(1-B^4)-0.3366*B^3+

(7.3-15.7*B+170.8^B^2-399.7*B^3+332.2*B^4)/(Re)^0.75

Else C = 0.5949+0.4078*B^2.1+0.0547^B^8+0.0955*B^4/(1-B^4)-0.5608*B^3+

(-139.7+1328.8*B-4228.2^B^2+5691.9*B^3-2710.4*B^4)/(Re)^0.75

9.7.2 Side (90) Flange Tappings

If D 100 C = 0.6284+0.1462*B^2.1-0.8464^B^8+0.2603*B^4/(1-B^4)-0.2886*B^3+

(69.1-469.4*B+1245.6^B^2-1287.5*B^3+486.2*B^4)/(Re)^0.75

Else C = 0.6276+0.0828*B^2.1+0.2739^B^8-0.0934*B^4/(1-B^4)-0.1132*B^3+

(-103.2+898.3*B-2557.3^B^2+2977*B^3-1131.3*B^4)/(Re)^0.75

9.7.3 Diametrically Opposite Vena Contracta Tappings

If D 100 Dp1 100

DC = 0.6261+0.1851*Bet0^2.1-0.2879*Bet0^8+0.1170*Bet0^4/(1-

Bet0^4)- 0.2845*Bet0^3+(23.3 - 207*Bet0+821.5*Bet0^2-

1388.6*Bet0^3+900.3*Bet0^4)/(Re1)^0.75

Else DC = 0.6276+0.0828*Bet0^2.1+0.2739*Bet0^8-0.0934*Bet0^4/(1-Bet0^4)-

0.1132*Bet0^3+( 55.7-471.4*Bet0+1721.8*Bet0^2-2722.6*Bet0^3+

1569.4*Bet0^4)/(Re1)^0.75

9.7.4 Side (90) Vena Contracta Tappings

If D 100 DC = 0.5917+0.3061*Bet0^2.1+0.3406*Bet0^8-0.1019*Bet0^4/(1-Bet0^4)-

0.2715*Bet0^3+(-69.3+556.9*Bet0-1332.2*Bet0^2+1303.7*Bet0^3-

394.8*Bet0^4)/(Re1)^0.75

Else DC = 0.6016+0.3312*Bet0^2.1-1.5581*Bet0^8+0.6510*Bet0^4/(1-Bet0^4)-

0.7308*Bet0^3+( 52.8-434.2*Bet0+1571.2*Bet0^2-2460.9*Bet0^3+

1420.2*Bet0^4)/(Re1)^0.75

9.8 Segmental Orifice 9.8.1 Flange Tappings

If D 100 C = 0.5866+0.3917*B^2.1+0.7586^B^8-0.2273*B^4/(1-B^4)-0.3343*B^3

Else C = 0.6037+0.1598*B^2.1-0.2918^B^8+0.0244*B^4/(1-B^4)-0.0790*B^3

9.8.2 Vena Contracta Tappings

If D 100 C = 0.5925+0.3380*B^2.1+0.4016^B^8-0.1046*B^4/(1-B^4)-0.3212*B^3

Else C = 0.5922+0.3932*B^2.1+0.3412^B^8-0.0569*B^4/(1-B^4)-0.4628*B^3

9.9 Restriction Device 9.9.1 Critical Flow

Preface9 Appendix

Sizing Equations 59

9.9.1.1 Square Edge Orifice (Liquid/Water) C = 0.6

9.9.1.2 Thick Plate Square Edge Orifice (Liquid/Water) C = 0.899

9.9.1.3 Classical Venturi Tube C = 0.985

9.9.1.4 Square Edge Orifice (Gas/Steam) C = 0.83932

9.9.1.5 Toroidal Throat Venturi Nozzle C = 0.99354 - 1.525/Rd^0.5

9.9.1.6 Cylindrical Throat Venturi Nozzle If Rd<3.5*10^5 C = 1 - 7.21/Rd^0.5

If 3.5*10^5<=Rd<2.5*10^6 C = 0.9887

If 2.5*10^6<Rd C = 1 - 0.222/Rd^0.2

9.9.1.7 ASME Long Radius Nozzle If Rd<3.5*10^5 C = 1 - 7.21/Rd^0.5

If 3.5*10^5<=Rd<2.5*10^6 C = 0.9887

If 2.5*10^6<Rd C = 1 - 0.222/Rd^0.2

9.9.2 Sub-Critical Flow

9.9.2.1 Square Edge Orifice (Liquid/Water), Thick Plate Square Edge Orifice (Liquid/Water) , and Square

Edge Orifice (Gas/Steam)

L1 = 25.4/D

L2 = 25.4/D

A = (19000 * B/Re)^0.8

M = 2 * L2 / (1 - B)

C = 0.5961 + 0.0261*B^2 - 0.216 *B^8 + 0.000521*(1000000*B/Re)^0.7 +

(0.0188+0.0063*A) * B^3.5 * (1000000/Re)^0.3 + (0.043+0.080*exp(-10*L1) -

0.123*exp(-7*L1)) * (1 - 0.11*A)*(B^4/(1 - B^4)) - 0.031*(M - 0.8*M^1.1)*B^1.3.

IF D < 71.12 THEN C = C +0.011*(0.75 - B) * (2.8 - Di)

9.9.2.2 Classical Venturi Tube C = 0.984

9.9.2.3 Toroidal Throat Venturi Nozzle C = 0.9558-0.196*B^4.5

9.9.2.4 Cylindrical Throat Venturi Nozzle C = 0.9558-0.196*B^4.5

9.9.2.5 ASME Long Radius Nozzle C = 0.9975-6.53*(B^0.5)*(1/Re)^0.5

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