kent introl multi phase sizing

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MULTI-PHASE SIZING 0705

TS40 Control Valve Selection for

Multi-Phase Flows

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Contents

Contents _______________________________________________________________2

TS40 Control Valve Selection for Multi-Phase Fluid Flows _______________________3 TS40.1 Nomenclature __________________________________________________________________ 4 TS40.2 Multi-phase Flow Valve Sizing Procedure ____________________________________________ 5 TS40.3 Process/Application Data Requirements______________________________________________ 6

TS41 Multi-phase Sizing ___________________________________________________7 TS41.1.1 Introduction ______________________________________________________________ 7 TS41.1.2Definition of Multi-phase Parameters___________________________________________ 8 TS41.2.1Multi-phase Sizing Equations_________________________________________________ 9

TS42 Multi-phase Velocity_________________________________________________15 TS42.1 Introduction ______________________________________________________________ 15 TS42.1 Factors Influencing Velocity Limitations ________________________________________ 15 TS42.2 Basis of Velocity Calculations ________________________________________________ 16 TS42.3 Procedure ________________________________________________________________ 17

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TS40 Control Valve Selection for Multi-Phase Fluid Flows

Selection of a control valve for a multi-phase flow application involves a number of factors, which should be considered in a logical sequence. This section of the Technical Manual provides the information necessary to consider these factors, which include CV calculation, fluid velocity and noise level prediction. It is important to note that omission of these aspects could lead to incorrect selection of a control valve for a particular application.

It should be noted that the process of sizing multi-phase fluids is extremely complicated involving phase transfer of energy.

The process and application information necessary to fully specify the size and type of valve required is detailed, together with a flow chart indicating the sequence of steps involved.

The CV calculation includes consideration of the various flow regimes.

To ensure correct selection of valve size and to maximise operational life, fluid velocity calculations and limitations are detailed for the various flow regimes.

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Nomenclature

Unit Description Imp SI

CV Valve Flow Coefficient U.S. units U.S. units KV Valve Flow Coefficient S.I. units S.I. units Cf Valve Pressure Recovery Factor - - d Valve Bore Size inches mm D Pipe Bore Size inches mm P1 Upstream Pressure p.s.i.a. BarA P2 Downstream Pressure p.s.i.a. BarA ∆P Pressure Drop across Valve p.s.i. BarA ∆Psl Sizing Pressure Drop for Liquid Phase p.s.i. Bar ∆Pl(limit) Limiting Pressure Drop for Critical Flow p.s.i. Bar of liquid phase ∆Psg Sizing Pressure Drop for Gas Phase p.s.i. Bar ∆Pg(limit) Limiting Pressure Drop for Critical Flow p.s.i. Bar of gas phase ∆Psg(dissolved) Sizing Pressure Drop for dissolved vapour p.s.i. Bar T1 Inlet Temperature °F °C QL Volume Flow Rate of liquid phase U.S.gall./min m3/hr WL Mass Flow Rate of liquid phase lb/hr kg/hr Qg(ref) Volume Flow Rate of gas phase S ft3/hr Nm3/hr Wg Mass Flow Rate of gas phase lb/hr kg/hr X Gas/vapour fraction (Wg/Wtot) - - XV Gas/vapour fraction (Qg/Qtot) - - K Expansion correction factor gas phase - - G Specific Gravity - - MW Molecular Weight of gas/vapour phase - - FK γ/1.4 (γ=ratio of specific heats) - - Z Compressibility factor for gas/vapour - - Vg Gas/vapour phase Fluid Velocity ft/sec m/sec VL Liquid phase Fluid Velocity ft/sec m/sec SPL Sound Pressure Level dBA dBA B Liquid noise efficiency term - - H1 Liquid noise trim style correction dB dB Z1 Liquid noise bulk flow factor - - X Pressure Coefficient gas noise - - Y Pressure Ratio Coefficient gas noise - - Zg Gas flow bulk noise factor - - Hg Trim style attenuation factor dB dB T Valve opening reduction dB dB Subscripts 1 Upstream 2 Downstream g refers to gas/vapour phase l refers to liquid stage Tot or TOT Total Dissolved refers to dissolved gas s sizing a void fraction A flow area

TS40.1

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TS40.2

Multi-phase Flow Valve Sizing Procedure

The following flowchart details the overall sequence of steps used during the sizing and selection of a control valve for a multi phase flow application. For individual consideration of multi-phase sizing, multi-phase velocity and multi phase noise prediction, reference should be made to Sections TS41, TS42 and TS43 respectively.

START

Select Different Trim Style

NoDetermine the CV (use 2 term equation)

Yes

Select Trim Style* (single stage)

Convert flowrates to flow by weight

Select Design CV and Valve Size

Determine gas/vapour fraction

Is Design CV OK?

Calculate Flow Velocities

Yes

Is Velocity OK?

Calculate Sound Pressure Level

Yes

Is SPL OK

Select Design CV & Valve Size

YesIs dissolved gas content known

Determine the CV (use 3 term equation)

Determine Cf value at valve opening

Re-calculate CV using appropriate equations

* Usually preferred due to interstage erosion problems on multiphase liquids

N

N

N

END

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Process/Application Data Requirements

The information required to fully specify the size and type of valve for multi-phase service applications can be broken down into different categories. For valve sizing and selection, this information can be classified as essential, preferred or additional. The following chart categorises the information required into these three areas. The information presented here relates to valve selection only, for actuator selection refer to TS8O.

Process Units Flow Units - Temp Units - Flow Condition Max Normal Minimum

1 Quantity 2 Line Fluid 3 Liquid Phase Flow Rate Gas/vapour Phase Flow Rate 4 Inlet 5 Outlet 6

Pressures P

7 Temp. at Inlet 8 SpecificGravity/Molecular Weight MW 9 Compressibility Factor, Z 10 Vapour Pressure/Ratio of Specific Heats, γ 11 Critical Pressure 12 DP Actuator Sizing 13 Design Press./Temp. 14 Line Size In/Out/Sch. 15 16 Predicted SPL (dBA) 17 Calculated Cv 18 19 Valve Size C.M. Trim 20 Body Form Design CV 21 Catalogue No. 22 End Conns. Style Rating23 Rated Press. Temp.24 Body Material 25 No of Seats Design26 Type Rings27 Char’s Flow Dir28

Trim

Material 29 Type of Bonnet 30 Packing Lub. /Lub No 31 Max. Leakage 32 Stem Dia Valve Duty

Absolute minimum flow information (essential)

Information required for full analysis (preferred)

Additional design information

Full valve specification

TS40.3

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TS41 Multi-phase Sizing

Introduction

When two phases, one incompressible and the other compressible flow together ma pipe, a number of different flow patterns may exist, such as bubble, mist, annular and slug flow. Therefore the prediction of the behaviour of the two-phase flow is very complicated. In contrast to single component flows, for which relatively simple flow equations can be derived, the flow equations for two component flows are very complicated and cannot be applied directly to the valve sizing problem. The complexity of the equations is attributable to the fact that the flow cannot be assumed to be homogeneous or in a state of thermodynamic equilibrium.

Valve manufacturers have relied heavily on the limited data available for two-phase flows through valves or flow restrictions such as orifice plates. This information is limited to certain flow conditions and even then has a high level of uncertainty.

Experimental data for such flows is in general for low pressures. In applying this to a valve sizing technique the data has to be scaled to high pressure applications. In a single-phase flow this is a relatively simple task, however, in a multi-component flow this is extremely difficult and leads to greater inaccuracies.

Introl in conjunction with a major oil company, have developed the multi-phase sizing procedure presented here. The procedure has been proven by numerous flow tests and field data, and has shown to be a reliable engineering tool for selecting control valves operating on multi-phase flow applications.

TS41.1.1

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Definition of Multi-phase Parameters

Gas Fraction

This is the ratio of the gas/vapour phase mass flow rate to the total two-phase mass flow rate.

TOTWWX =

Slip Ratio

When a two-phase fluid flows along a pipe the velocity of each phase will be different. The slip ratio is the ratio of the gas/vapour phase velocity to the liquid phase velocity.

t

g

uu

S =

Void Fraction

This is the ratio of the cross-sectional area of the gas phase to the cross-sectional area of the pipe.

AA

a g=

Gas Oil Ratio (GOR)

Used to quantify the amount of gas in relation to the amount of oil. GOR is the number of Sft3 of gas per barrel of oil.

Gas Solution Ratio, Rs

Quantifies the amount of gas dissolved in a liquid, i.e. the number of Nm3/hr of gas per m3/hr of liquid.

TS41.1.2

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Multi-phase Sizing Equations

a) Gas/Vapour Fraction

The valve sizing equations for multi-phase flows are presented for simplicity, in terms of a total mass flow rate and a gas/vapour fraction. In the event of flow rates being presented in volumetric units then the first stage in the multi-phase calculation procedure is to convert volume flows into mass flow rates.

Convert to flow by weight

IMPERIAL

USGPM to lb/hr ll QGW ××= 501

ft3/hr to lb/hr ll QGW ××= 43.62

ft3/hr to lb/hr

gW

g QTZ

MPW ×+××

=)460(72.10 1

1

S. ft3/hr to lb/hr

glWg QMW ××= 0028.0

METRIC

m3 to kg/hr ll QGW ××= 1000

m3 to kg/hr

gW

g QTZ

MPW ×+××

××=

)273(831410

1

51

Nm3/hr to kg/hr

glWg QMW ××= 0044.0

Calculate the mass flow rate

glTOT WWW +=

Calculate gas/vapour pressure

TOT

g

WW

X =

b) Sizing Pressure Drop for Liquid Phase

Calculate supercooled vapour pressure

−=

C

VVVC P

PPP 02896.0

Determine the limiting liquid phase pressure drop corresponding to the occurrence of critical flow. Refer to Table 41.1 for values of Cr

)( 12

lim Vfit PPCp −=∆

Set the liquid phase sizing pressure drop, ∆psl. If the pressure drop across the valve is less than the limiting pressure drop then the liquid phase is normal and

ppSl ∆=∆

If the pressure drop across the valve is greater than the limiting pressure drop, then the liquid phase is critical and

itlSl pp lim∆=∆

TS41.2.1

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c) Sizing Pressure Drop for Gas/Vapour Phase

Calculate limiting pressure drop for gas vapour phase

12

lim RPFCp Kfitg =∆

where ff CC ×= 33.1

and 47.0=R

Refer to Table 41.1 for values of Cf or the valve opening is known Figure 41.2.

Set the sizing pressure drop for gas/vapour phase.

If the pressure drop across the valve is less than or equal to the limiting pressure drop the gas/vapour phase is normal and

ppSg ∆=∆

If the pressure drop is greater than the limiting pressure drop then the gas/vapour phase is critical and

itgSg pp lim∆=∆

d) Calculate Phase Specific Volumes

Liquid Phase

IMPERIAL

Gl016.0

=ν

METRIC

Gl001.0

=ν

Gas/vapour Phase

IMPERIAL

( )1

46072.10PM

TZ

Wg ×

+××=ν

METRIC

( )1

2738314PM

TZ

Wg ×

+××=ν

e) Calculate the Expansion Correction Factor

γ

∆−=

121PC

pKf

where

−= 92.0

65.0

KFγ

or refer to Figure 41.1

f) Calculate Valve Flow Coefficient – Two Phase

IMPERIAL

( )sl

l

sg

gTOT p

Xp

XKWCv

∆−

+∆

×=νν 10159.0

2

METRIC

( )sl

l

sg

gTOT p

Xp

XKWCv

∆−

+∆

×=νν 10368.0

2

TS41.2.2

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TS41.2.4

g) Calculate Valve Flow Coefficient - Three Phase

On many choke applications there is a combination of oil, vapour and water in the flowing media. In such a case, the differences in the liquids specific gravity and the limiting pressure drops must be accounted for in the sizing procedure. The previous two-term equation has been modified so that the sizing pressure drop can be calculated for each liquid phase.

Water phase

The water phase sizing pressure drop is ∆pslw and ∆pslo should be calculated using the equations presented in (b) of this procedure using the water fluid properties.

Xlw is the fraction of water present by weight, i.e.

TOT

lw

WWX =

Oil phase

The oil phase sizing pressure drop is ∆pslo and should be calculated using the procedure presented in (b) using the liquid hydrocarbon (oil) fluid properties.

Xlo is the fraction of oil present by weight, i.e.

TOT

lwlw W

WX =

The sizing equations are:-

IMPERIAL

slw

lwlw

slo

lolo

sg

gTOT p

XpX

pXK

WCv∆

+∆

+∆

×=ννν2

0159.0

METRIC

slw

lwlw

slo

lolo

sg

gTOT p

XpX

pXK

WCv∆

+∆

+∆

×=ννν2

0368.0

h) Calculate Valve Flow Coefficient - Gas Solution Ratio Known (Dissolved Gas Content)

If the gas solution ratio is known this means that the amount of dissolved gas within the liquid phase can be calculated. This dissolved gas will come out of solution as the fluid flows through the valve. The effect of this on the sizing can be taken into account by utilizing the procedure detailed below. This will lead to more a accurate calculation of the flow coefficient.

Xfree is the free gas content by weight

Xdissolved is the dissolved gas content by weight

The sizing pressure drop for the dissolved gas can be determined from the equation below.

−=∆

Cfsg P

PPCdissolvedp 11

2 02896.0)(

The sizing equation becomes:

IMPERIAL

)(

2

0159.0dissolvedsg

lodissolved

slw

lwlw

slo

lolo

sg

gfreeTOT p

Xp

Xp

XpKX

WCv∆

+∆

+∆

+∆

×=νννν

METRIC

)(

2

0368.0dissolvedsg

lodissolved

slw

lwlw

slo

lolo

sg

gfreeTOT p

Xp

Xp

XpKX

WCv∆

+∆

+∆

+∆

×=νννν

Note: The sizing pressure drops ∆ and lop slwp∆

should be calculated using the procedure shown on TS41.2.1 and using the respective fluid properties.

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TS41.2.4

Table 41.1 Valve Pressure Recovery and Incipient Cavitation Coefficients

Valve Type Trim Style Trim Size Flow Direction Cf K1

Microspline All sizes Over 0.95 0.95

Full Under Over

0.9 0.85

0.8 0.81

Contoured Reduced Under

Over 0.9 0.8

0.8 0.82

Ported All sizes Over or under 0.93 0.9

Series 10

HF, HFD, HFT All sizes Over or under 1 0.95

Full Under Over

0.9 0.85

0.8 0.81 Contoured

Reduced Under Over

0.9 0.8

0.8 0.82

Ported All sizes Over or under 0.93 0.9 Series 14

HF All sizes Over or under 1 0.95

Ported Full Over or under 0.92 0.9

HF All sizes Over or under 0.97 0.95

XHF All sizes Over or under 0.98 0.95

HFD All sizes Over or under 0.99 0.95

Series 12

XHFD,HFT,XHFT All sizes Over or under 0.97 0.95

Contoured Full Reduced Over and under 0.9

0.8 0.87 0.84 Series 20

HF, HFD, HFT All sizes Over and under 1 0.95

Series 30/31 ‘V’ Port All sizes Mixing and diverting 0.91 0.9

4 Stage All sizes Over 1* 0.95* Series 51/57

7 Stage All sizes Over 1* 0.95*

Vane <30% Open Through 0.98

0.9 0.9 0.75 Series 61/62

Vane and baffle <30% Open Through 1**

0.98** 0.9 0.9

Contoured Full Under Over

0.9 0.45

0.8 0.84

Reduced Under Over

0.95 0.5

0.8 0.82




Series 70/71

HFT All sizes Over or under 0.99 0.95



XHF All sizes Over or under 0.97 0.92


Series 72/73/74

XHFD ,HFT, XHFT All sizes Over or under 0.99 0.95

Cylindrical All sizes Through 0.95 0.90 Fixed area

Flat All sizes Through 0.92 0.90

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TS41.2.5

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Figure 41.2 Valve Pressure Recovery Values for Different Valve Series as a function of Valve Openings

TS41.2.6

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TS42.1

TS42 Multi Phase Velocity

Introduction

In selecting a valve for a multi-phase flow application one of the major considerations is the effect of fluid velocity. High fluid velocities can lead to erosion and vibration problems. The higher velocity of the gas/vapour phase will tend to lead to an increase in the mean flow velocity of the liquid phase leading to the possibility of an erosion problem. This section covers the limitations imposed because of the possible effects of high flow velocities and includes the velocity calculation procedures for multi-phase fluids along with the recommended velocity limits.

Factors Influencing Velocity Limitations

Selection of pipework systems includes the consideration of fluid velocity which is limited for the following reasons

1) reduction in pressure loss,

2) to reduce/eliminate vibration potential,

3) to minimise erosion damage.

A control valve is considered as a major part of the pipework system and the flow velocity is limited for similar reasons.

Although valve and piping velocity limits apply to mean inlet/outlet flow velocities, it should be noted that the flow through a control valve being highly turbulent would exhibit areas of flow velocity much higher than the mean flow velocity. Additionally, dependant on the trim configuration the flow may impinge directly onto the valve body wall. These factors, together with levels of energy dissipation, mechanical vibration response, and the material of construction influence the recommended maximum levels presented in Table 42.1. and 42.2.

Effect of Valve/Trim Style

Reference to Table 42.1 and 42.2 will reveal varying velocity limits for different valve sizes, trim styles and body material. The reasons for these changes are related to the varying flow paths through the different configurations. For example the recommended velocity levels are higher for cage guided trims because the highest flow velocities, occurring just downstream of the minimum flow area, are contained within the more erosion resistant valve trim. Additionally, in cage guided valves the high levels of energy dissipation are controlled by splitting the flow into small jets with the impingement contained within the guide.

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Basis of Velocity Calculation

If the % flash is given or can be calculated then the relative velocities of the two phases, liquid and vapour, can be approximated. A measure of the different phase velocities is given by the slip ratio, s. This is the ratio of the vapour phase to the liquid phase velocity. An expression used to determine this value is shown below.

21

1

−+= XXs

v

l

ρρ

It is evident by examining this expression that as the % flash increases so does the slip ratio, and hence the vapour flow velocity. Furthermore, when the vapour density approaches the liquid density, s tends to 1, and the vapour velocity is almost equal to the liquid velocity.

TS42.2

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TS42.4

Procedure

a) Determine the liquid density and downstream vapour density.

METRIC

1000×= Glρ 42.1

)273(831410

2

52

2 +×××

=TMP W

vρ 42.2

IMPERIAL

43.62×= Glρ 42.3

)460(72.10 2

22 +×

×=

TMP W

vρ 42.4

b) Determine the slip ratio.

21

1

−+= XXs

v

l

ρρ

42.05

c) Calculate the liquid and vapour phase mass flow rate.

TOTV WXW ×= 42.06

( ) TOTl WXW ×−= 1 42.07

d) Calculate the downstream vapour and liquid phase volume flow rates.

22

V

VV

WQρ

= l

llWQρ

= 42.08

e) Calculate the downstream vapour volume ratio where:

TOT

Vv Q

QX 2= 42.09

lVTOT QQQ += 2

f) Determine the void fraction and phase flow areas.

( )( )sXXXa

VV

V

−+=

1 42.10

Liquid phase flow area

totl AaA )1( −= 42.11

Vapour phase flow area

totV aAA = 42.12

Note: use the correct area units in the above equations i.e. m2 for METIC or ft2 for IMPERIAL

g) Determine the liquid phase flow velocity.

3600×

=l

ll A

QV 42.13

h) Determine the vapour phase flow velocity.

36002

×=

V

VV A

QV 42.14

i) Check that the phase velocities do not exceed their recommended maximum levels, see Table 42.1. The vapour phase flow velocity should not exceed 253m/s (830 ft/sec) or 0.3 Mach. For the complete set of velocity limits for gas/vapour flows refer to Table 42.2.

In the case that the % flash cannot be determined then the valve size is selected based upon the design CV and making reference to the line size.

Table 42.1 Recommended Maximum Velocities for Liquid Service

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TS42.4

Maximum Velocity Valve Size Carbon Steel Alloy Steel Bronze, Cu/Ni Alloys

Valve Type Valve Rating Trim Style

in mm ft/s m/s ft/s m/s ft/s m/s

Series 10/14/20 All Contoured

0.5-2 3-6 8-14 16-18

20 24

15-50 80-150 200-350 400-450

500 600

41 34 29 22 18 12

12.5 10.4 8.9 6.7 5.5 3.7

46 34 29 22 18 12

14 10.4 8.9 6.7 5.5 3.7

25 20 17 13 11 7

7.6 6.2 5.2 4

3.4 2.1

All Ported + HF family

1-12 14-20

24

25-300 350-500

600

43 35 25

13.1 10.7 7.6

52 43 35

15.8 13.1 10.7

26 21 15

7.9 6.4 4.6

Series 12/51 All Ported + HF family

1-12 14-20

24

25-300 350-500

600

43 (60) 35 (50)

25 (35)

13.1 (18.3)10.7 (15.2)7.6 (10.7)

52 (70) 43 (60)

35 (50)

15.8 (21.3) 13.1 (18.3)

10.7 (15.2)

26 (35) 21 (30)

15 (21)

7.9 (10.7) 6.4 (9.1)

4.6 6.4)

Series 30/31 Up to and including ANSI 600

"V" Port 1-2 3-6 8-12

25-50 80-150 200-300

31 26 19

9.5 8

5.8

35 26 19

10.7 8

5.8

19 16 11

5.8 4.9 3.4

Series 61/62 Up to and including ANSI 300

Vane 4-12 14-24 >24

100-300 350-600

>600

25 15 10

7.6 4.6 3

25 15 10

7.6 4.6 3

15 9 6

4.6 2.7 1.8

Series 70/71 All Contoured All sizes All sizes Refer to Series 10 velocity limits Series

70/71/72 73/74/57

All Ported + HF family

1-12 14-20

24

25-300 350-500

600

48 (65) 40 (55)

30 (42)

14.6 (19.8)12.2 (16.8)9.1 (12.8)

57 (75) 48 (65)

40 (55)

17.4 (22.9) 14.6 (19.8)

12.2 (16.8)

29 (39) 24 (29)

18 (25)

8.8 (11.9) 7.3 (8.8)

5.5 (7.6)

TABLE 42.2. Recommended Maximum Velocities for Gas/Vapour

Valve

Type

Valve

Rating

Trim

Style Valve Size

Maximum Inlet

Velocity

Maximum Outlet

Velocity

Max. Outlet Mach no. for

Required Noise Level

in mm ft/s rn/s ft/s rn/s >95 dBA <95 dBA <85 dBA

0.5-2 15-50 340 104

3-6 80-150 295 90

8-14 200-350 265 81

16-18 400-450 190 58

20 500 150 46

Up to and

including

ANSI 600

Contoured

24 600 115 35

1-12 25-300

14-20 350-500

Series

10//14/20

All Ported +

HF family 24 600

475 144

830 253 0.65 0.5 0.3

1-12 25-300

14-20 350-500 830 253 0.65 0.5 0.3 Series 12 All Ported +

HF family 24 600

475 144

(1150) (350) (0.9) (0.7) (0.4)

1-2 25-50 226 78

3-6 80-150 220 67 Series 30/31

Up to and

including

ANSI 600

‘V’ Port

8-12 200-300 200 61

640 195 0.65 0.5 0.3

4-12 100-300 200 61

14-24 350-600 100 30 Series 61/62

Up to and

including

ANSI 300

Vane

>24 >600 80 24

350 107 0.65 0.5 0.3

Series 70/71 All Contoured All sizes Refer to Series 10

velocity limits Sonic 0.65 0.5 0.3

1-12 25-300

14-20 350-500 0.65 0.5 0.3 Series 70/71

72/73 All

Ported +

HF family 24 600

475 144 Sonic

(0.9) (0.7) (0.4)

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Documents

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