24
AGA Flow Orifice Calculation Routines Set initial values. C=0.6:Y=1 1. Calculate the Normal Differential Range H =H . W W N M N M 2 2. Calculate the Orifice Sizing Factor S W 358.9628.D . .H M N 2 n N = γ 3. Calculate Reynolds Number R 6.31533.W D. D N = μ CP 4. Calculate the beta ratio β O M 2 .25 1 Y. C S = + -0 5. Calculate the discharge coefficient at infinite Reynolds Number (Typical) ( 29 C 0.5961 0.0291 0.229 0.003 1 M TapTerm INF O 2 O 8 O 1 = + - + - + β β β 6. Calculate the true discharge coefficient C=C 0.000511 10 . R 0.021 0.0049 19000 R 10 R INF 6 o D 0.7 o D 0.8 O 4 6 D 0.35 + + + β β β 7. If the fluid is gas then calculate the expansion factor ( 29 Y = 1- 0.41+ 0.35 H 27.73KP O 4 N f β 8. Repeat from step 4 until the beta ratio value changes less than 0.000001 9. Calculate orifice bore d .D O Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. For complete details of all formula and techniques refer to the AGA Report #3 and The Flow Measurement Engineering Handbook By R.W.Miller. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information. Nomenclature W M Flowrate upper range variable lb/h W N Flowrate normal flow lb/h H M Differential upper range variable inches of water H N Differential normal inches of water S M Orifice sizing factor dimensionless

Instrucalc Calculations

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Calculation by instrucalc software. Help instrument and chemical engineer to solve CV in control valve and other valve sizing

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Page 1: Instrucalc Calculations

AGA Flow Orifice Calculation RoutinesSet initial values. C=0.6:Y=11. Calculate the Normal Differential Range

H = H .WWN M

N

M

2

2. Calculate the Orifice Sizing Factor

SW

358.9628.D . .HM

N

2n N

3. Calculate Reynolds Number

R6.31533.W

D.DN=

µCP

4. Calculate the beta ratio

βOM

2 .25

1 Y.C

S= +

−0

5. Calculate the discharge coefficient at infinite Reynolds Number (Typical)

( )C 0.5961 0.0291 0.229 0.003 1 M TapTermINF O2

O8

O 1= + − + − +β β β6. Calculate the true discharge coefficient

C = C 0.000511 10 .R

0.021 0.004919000

R10RINF

6 o

D

0.7

o

D

0.8

O4

6

D

0.35

+

+ +

β ββ

7. If the fluid is gas then calculate the expansion factor

( )Y = 1- 0.41+ 0.35H

27.73KPO4 N

f

β

8. Repeat from step 4 until the beta ratio value changes less than 0.000001

9. Calculate orifice bored .DO= β

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

For complete details of all formula and techniques refer to the AGA Report #3 and The Flow Measurement Engineering Handbook By R.W.Miller. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information.

NomenclatureWM Flowrate upper range variable lb/hWN Flowrate normal flow lb/hHM Differential upper range variable inches of waterHN Differential normal inches of waterSM Orifice sizing factor dimensionless

Page 2: Instrucalc Calculations

M1 Correction for pipe sizes less than 1.8 inches see AGA Report #3D Pipe inside diameter at flowing temperature inchesd Orifice inside diameter inchesγ n Density at flow conditions lb/ft3µCP Absolute Viscosity centipoiseRD Reynolds Number dimensionlessβO Beta Ratio dimensionlessC Orifice discharge coefficient dimensionlessCINF Orifice discharge coefficient for infinite Reynolds Number dimensionlessY Gas expansion factor dimensionlessPf Upstream pressure psiak Ratio of specific heats dimensionlessTapTerm Correction for tap location see AGA Report #3

Page 3: Instrucalc Calculations

Fixed Geometry1 Calculation RoutinesAnnubar Liquid Flow1 Calculate the differential range

HW

KD F Gm

m

A f

=

2834 717 2

2

.Inches of water

2 Calculate velocity

VW

F Dn

n A

=19 65 2. γ feet per second

3 Calculate Rod Velocity. There is a minimum rod Reynolds Number below which the flowing fluid will not separate properly from the edges of the Annubar.

RP v

DW n

CP

= 1487γ

µAnnubar Gas Flow1. Calculate the differential range -

HW

KD Fm

m

A n

=

358 94 2

2

. γInches of water

2. Calculate the expansion factor -

Yd

DHP k

m

f

= − −

1 0 011332 1

12730 00342

2

..

.

3. Apply the expansion factor -

HH

Ymm=2

.Repeat steps 2 and 3 again -

NomenclatureD Pipe inside diameter inchesγ N Density at flow conditions lb/cubic footFA Thermal expansion factor dimensionlessG f Specific gravity at flow temperature dimensionlessHm Differential range inches of waterk Ratio of specific heats dimensionlessK Flow coefficient dimensionlessPf Inlet pressure psiaPW Annubar width feetRD Rod Reynolds Number dimensionlessV Fluid velocity feet per secondWm Flow rate lb/hY Expansion factor dimensionlessµCP Viscosity centipoisesReferenceThe Annubar Flow Handbook Dover Industries IncAnnubar Is a registered trademark of Dover Industries Inc

Page 4: Instrucalc Calculations

Elbow Flowmeter1.. Calculate the Reynolds Number -

R6.31533.W

D.DM

CP

2.. Calculate the discharge coefficient -

KSM = +rD

rD

Rb

b

D2

6 52

0 5

.

.

3.. Calculate the differential range -

HW

K F DM

m

SM A n

=

358 9268 2

2

. γ inches of water

NomenclatureD Pipe inside diameter inchesγ n Density lb/cubic footFA Thermal expansion factor dimensionlessHm Differential range inches of waterK SM Discharge coefficient dimensionlessrb Elbow mean radius inchesWm Flow rate lb/hµCP Viscosity centipoises

Target Meters1. Calculate the Reynolds Number -

R6.31533.W

D.DCP

2. Calculate the flow rate -

W KFB

BD FA

T

Tn T= −

358 9268 5 941939 1

2

. . γ lb/h

3. Calculate target force -

FW

KTN=

6296 4

2

. pounds

NomenclatureBT Target ratio (Target diameter/Bore diameter) dimensionless

(Supplied by manufacturer)D Pipe inside diameter inchesγ N Density lb/cubic footFA Thermal expansion factor dimensionlessK Discharge coefficient dimensionless

(Supplied by manufacturer)W Flow rate lb/hµCP Viscosity centipoises

Page 5: Instrucalc Calculations

Integral Flow Orifice Assemblies1. Calculate the Reynolds Number -

R6.31533.W

d.dCP

2. Calculate the discharge coefficient -

C A D E F∞ = + + +β β β2 4 8

B G H J= + +β β2 4

C C BRd= ∞ + −0 5.

(Values of A,D,E,F,G,H and J vary with design and size. See manufacturers data)(C for Jewel insert is 0.995)

3. Calculate the expansion factor -

( )YH

P kf1

41 0 41 0 3527 73

= − +. ..

β

4. Calculate flow rate -

WCF Y d HA n=

358 9268

1

12

4

. γ

β lb/h

Nomenclatured Orifice bore diameter inchesD Pipe inside diameter inchesγ n Density lb/cubic footFA Thermal expansion factor dimensionlessC Discharge coefficient dimensionlessH Differential range inches waterk Ratio of specific heats (Gas only) dimensionlessPf Inlet pressure psiaRd Orifice Reynolds Number dimensionlessW Flow rate lb/hβ Beta ratio (d/D) dimensionlessµCP Viscosity centipoises

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

For complete details of all formula and techniques refer to The Flow Measurement Engineering Handbook By R.W.Miller and Foxboro Technical Information T! 037 087. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information.

Page 6: Instrucalc Calculations

Control Valve Calculation RoutinesLiquid1 Calculate the vena-contracta pressure drop -

P P 0.96 0.28P

PPVC 1

VAP

CVAP= − −

2 Calculate the critical drop -

P F PCRIT L VC= 2

3 Calculate preliminary valve sizing coefficient -

CW

PGV

f

=500 ∆

4. Calculate Reynolds Number -

RF W

F C

F C

dEVd

CP L V

L V= +

34 6

8901

2 2

2

1

4.

µ5. Calculate Reynolds Number Factor -

FCCR

VS

VT

= −

1044 0 358

0 655

. ..

Where -

CF

W

G PVSS

CP

f

=

123500

0 6667µ

.

and -

FF

F

F C

dSd

L

L V= +

0 6667

333

2 2

2

0 1667

8901

.

.

.

6. Calculate the pressure recovery and piping geometry factors

Kd

DB11

4

1= −

K

dDB2

2

4

1= −

K

dD1

2

12

2

0 5 1= −

. K

dD2

2

22

2

1= −

( )F F

K K F C

dLP LB L v=

++

1 12 2

4

0 5

8901

.

( )F

K K K K C

dpB B v=

+ + −+

1 2 1 22

4

0 5

8901

.

7 Calculate the final valve size -Turbulent flow -

Ce inaryC

FVV

P

=Pr lim

or Transitional flow -

Ce inaryC

FVV

R

=Pr lim

or Laminar flow -C CV VS=

or Choked or flashing flow -

CW

F P GV

LP CRIT f

=500 ∆

Page 7: Instrucalc Calculations

8 Calculate the noise levelSL LogC Log P Log tV= + − +10 20 30 5∆ ( )

For incipient cavitation add --

( )5 112 2

∆PP P

K

F KLog P PVAP

c

L cVAP

−−

+ −

For full cavitation subtract from incipient cavitation --

( )5 1Log P PCrit∆ ∆+ −Gas1 Calculate the pressure drop ratio factors

XP

P11

= ∆F

Kk =

14.2 Calculate the minimum size for sonic velocity

dWP

TMmin .= 0 0454

2

1

inches3 Calculate the preliminary valve size

CW

X PV

N

=63 3 1 1. γ

4 Calculate the piping geometry factor

Kd

DB11

4

1= −

K

dDB2

2

4

1= −

K

dD1

2

12

2

0 5 1= −

. K

dD2

2

22

2

1= −

( )F

K K K K C

dpB B v=

+ + −+

1 2 1 22

4

0 5

8901

.

5 Calculate the pressure drop ratio factor

( )X

X

F

X K K C

dTPT

P

T B v=+

+

2

1 12

4

1

10001

6 Calculate the expansion factor

YX

F Xk T

= −13

1

7 Calculate the final size

FinalCe inaryC

F YVV

P

=Pr lim

8 Calculate the valve sound pressure levelGas

SL Log C F P P DT

tSLv L G1 1 2

2 13

10 28=

Steam

( )( )SL Log C F PP D T tv L SH1 1 22 6 310 11000 1 0 0007= +η . /

9 Calculate the outlet noise

( )SL Log P d D M T SLs G2 22 2

22

110 018= +.

Page 8: Instrucalc Calculations

10. If SL SL1 2 7− ≥

then

SL SL= 1

ElseSL SL SL= +1 2

Two Phase Flow1 Calculate the vena-contracta pressure drop

P P 0.96 0.28PP

PVC 1VAP

CVAP= − −

2 Calculate the critical drop

P F PCRIT L VC= 2

3 Calculate the specific volumes of the gas and liquid

vgN

= 1γ

vGl

f

= 0 016033.

4 Calculate the volume fraction and the weight fraction of the gas

Vw v

w v w vgg g

g g f f

=+

fw

w wgg

g f

=+

5 Calculate the pressure drop ratio factors

XP

P11

= ∆F

Kk =

14.6 Calculate the expansion factor

YX

F Xk T

= −13

1

7 Calculate the effective specific volume for the mixture

( )v

f v

Y Y

f

Geg g g

f

= +−

2

1

63 3.8 Calculate the preliminary valve size

( )C

w w vX Pv

f g e=+

63 3 1 1.9 Calculate the piping geometry factor

Kd

DB11

4

1= −

K

dDB2

2

4

1= −

K

dD1

2

12

2

0 5 1= −

. K

dD2

2

22

2

1= −

( )F

K K K K C

dpB B v=

+ + −+

1 2 1 22

4

0 5

8901

.

10 Calculate the final size

Ce inaryC

FvV

P

=Pr lim

11 Sound level calculated using the liquid calculations above.

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical

Page 9: Instrucalc Calculations

calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

NomenclatureCV Valve sizing coefficient dimensionlessd Nominal valve size inchesD1 Inside diameter of inlet piping inchesD2 Inside diameter of outlet piping inchesγ n Fluid density at operating temp and pressure pounds per cubic footFd Valve style modifier dimensionlessk Ratio of specific heats dimensionlessFK Ratio of specific heats factor dimensionlessFL Rated pressure recovery factor dimensionlessFLP Combined liquid pressure recovery factor dimensionlessFP Piping geometry factor dimensionlessFR Reynolds number factor dimensionlessGf Specific gravity at flow temperature dimensionlessM Molecular weight dimensionlessMS Mach number at flow conditions dimensionlessP1 Upstream absolute pressure psiaP2 Downstream absolute pressure psiaPc Critical pressure psiaPVAP Vapor pressure psia∆P Valve pressure drop psiSL Sound pressure level dBASLG Gas property factor dBAt Pipe wall thickness inchesT1 Absolute upstream temperature degRTSH Steam superheat temperature degFREV Reynolds number dimensionlessve Effective two phase specific volume ft3/lbv f Specific volume of liquid ft3/lbvg Specific volume of gas ft3/lbVg Volume fraction of gas dimensionlessW Total rate of flow lb/hw f Rate of liquid flow lb/hw g Rate of gas flow lb/h

Page 10: Instrucalc Calculations

X1 Pressure drop ratio dimensionlessX T Rated pressure drop ratio factor dimensionlessX TP Value of XT for valve/reducer assembly dimensionlessY Expansion factor dimensionlessη Acoustic efficiency dimensionless

ReferencesControl Valve Sizing Equations ANSI/ISA S75.01Masoneilan Noise Control Manual Masoneilan - DresserISA Handbook of Control Valves. J. W. Hutchison

Page 11: Instrucalc Calculations

ISO Flow Element Calculation RoutinesRoutines are similar all devices except that the discharge coefficient formulas vary.The gas restriction orifice is checked for critical flow, see RO Sonic Gas Routine.Set initial values. C=0.6:Y=1

1. Calculate the Normal Differential Range

H = H .WWN M

N

M

2

2. Calculate the SM Factor

SW

358.9628.D .F . .HM

N

2A n N

3. Calculate Reynolds Number

R6.31533.W

D.DN

p

4. Calculate the beta ratio

βOM

2 .25

1 Y.C

S= +

−0

5. Calculate the discharge coefficient at infinite Reynolds NumberTypical for corner taps

C 0.5959 0.3121 0.184INF O2.1

O8= + −β β

6. Calculate the true discharge coefficient

C = Cb

RINFDn +

Where typically

b 91.71 O2.5= β

and n = 0.75 for corner taps7. If the fluid is gas then calculate the expansion factor

( )Y = 1- 0.41+ 0.35H

27.73KPO4 N

f

β

8. Repeat from step 4 until the value of the beta ratio changes less than 0.000001

9. Calculate orifice bored .DO= β

R. O. Sonic Gas Routine1. Check for sonic velocity

P P2

k 1SONIC f

kk

k 1=

+

2. If the discharge pressure is more than -

PSONIC then use pipe tap calculationElse

Y SW

359D .F .PT P

M

2A N f

3. Calculate Beta Ratio

βO = 0.6991Y ST P0.4919

Page 12: Instrucalc Calculations

4. Calculate orifice bored .DO= β

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

For complete details of all formula and techniques refer to the ISO 5167 and The Flow Measurement Engineering Handbook By R.W.Miller. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information.

NomenclatureWM Flowrate upper range variable lb/hWN Flowrate normal flow lb/hHM Differential upper range variable inches of waterHN Differential normal inches of waterSM Orifice sizing factor dimensionlessD Pipe inside diameter at flowing temperature inchesd Orifice inside diameter inchesγ n Density at flow conditions lb/ft3µCP Absolute Viscosity centipoiseRD Reynolds Number dimensionlessβO Beta Ratio dimensionlessC Orifice discharge coefficient dimensionlessCINF Orifice discharge coefficient for infinite Reynolds Number dimensionlessY Gas expansion factor dimensionlessPf Upstream pressure psiak Ratio of specific heats dimensionlessFA Thermal expansion factor dimensionlessPSONIC Downstream pressure for sonic velocity psia

Page 13: Instrucalc Calculations

Fixed Geometry2 Calculation RoutinesRotametersLiquid Calculation1. Calculate the equivalent flow in US gallons per minute of water -

( )Q

W

G G Gm

m

f F f

=−188 814.

US gallons per minute -2. Calculate the sizing viscosity -

( )µ

µCS

CP

f F fG G G=

2 6496.

centistokes3. Calculate the Maximum allowable viscosity -.

µ µCP CS fG= centipoises

Gas calculation1. Calculate the equivalent flow -

QW

Gm

m

F n

=5 862. γ

Standard cubic feet of air equivalent.NomenclatureQm Calculated equivalent water flow US gallons per minuteWm Desired quantity of flowing fluid lb/hγ n Gas density lb per cubic footG f Specific gravity of flowing fluid dimensionlessGF Specific gravity of float dimensionlessµCS Rotameter viscosity immunity ceiling centistokesµCP Viscosity of flowing fluid centipoises

Vortex meters1. Calculate the flow area -

AW

Vm

n

=3600 γ square feet

2. Calculate the maximum and minimum flowrate -W A VMAX SEL MAX n= 3600 γ lb/h W A VMIN SEL Min n= 3600 γ lb/h

3. For liquids callculate the Reynolds Number -

RW

DDm

CP

=6 31533.

µNomenclatureA Flow area for required flow square feetASEL Cross section area of selected meter square feet

Supplied by manufacturer (Bore area - Element area)D Pipe inside diameter at flowing temperature Inchesγ n Density at flow conditions lb/ft3RD Reynolds Number dimensionlessWm Required flowrate lb/hWMAX Flowrate upper range variable lb/h

Page 14: Instrucalc Calculations

WMIN Flowrate lower range variable lb/h

V Velocity at Wm feet per secondVMAX Velocity at WMAX feet per second

(Supplied by the manufacturer)VMIN Velocity at WMIN feet per second

(Supplied by the manufacturer)µCP Absolute Viscosity centipoise

Wedge Flowmeter1. Set Y = 12. Calculate the differential range -

hW

F YKm

m

a d n

=

358 9626 2

2

. γ inches of water

3. If fluid is gas then calculate the expansion factor -

YhP

n= −

1 0 012

0 541

0 3

..

4. Repeat from 2 until error is less than 0.00001NomenclatureWm Desired quantity of flowing fluid lb/hγ n Fluid density lb per cubic footHm Differential range inches of waterK

d2 Wedge coefficient dimensionlessP1 Inlet pressure psiaY Gas expansion factor dimensionlessβ Wedge ratio ( Supplied by the manufacturer ) dimensionlessFluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

Page 15: Instrucalc Calculations

Relief Valve Calculation RoutinesFire size Liquid Vaporization1. Calculate the wetted area -

( )A X D D LW V V V= +Σ πsquare feet

2. Calculate vaporized liquid -

WFA

LmW

HV

=21000 0 82.

lb/h3. Calculate the pressure ratio -

rP

P= 2

1

Limited to a minimum of -

21

1

k

k

k

+

4. Calculate the specific heat ratio coefficient -

C kk

k

k=

+

+−

5202

1

1

1

5. Calculate the back pressure correction factor -Standard valves

KF

Crb = −

73512

Where -

Fk

kr

rr

k

k

k

2

21

11

1=

−−

Bellows valves

( )K rOV

PbP

ININ= − − +

−16 0 3 11860

700 04

2

. . ..ε (Typical)

6. Calculate the required area

AW

K CP KT ZM

m

d b

f=1 square inches

7. Calculate maximum allowable back pressure -

KAA

KbCALC

VALVEbMAX

=

Standard valvesIterate to find r

Maximum back pressure -= −rP1 14 7. psig

Bellows valvesMaximum back pressure -

( )P

P K

OVIN

INP

bIN

MAX16 0 3

11860

70

0 04

2

. .

.

.− −

+

−ε

psig (Typical)

Page 16: Instrucalc Calculations

Fire size Gas Expansion1. Calculate the wetted area -

( )A X D D LW V V V= +Σ πsquare feet

2. Calculate pressure ratio -

rPP

= 2

1

Limited to a minimum of -

21

1

k

k

k

+

3. Calculate the specific heat ratio coefficient -

C kk

kk

=+

+−

5202

1

11

4. Calculate the back pressure correction factor -Standard valves

KF

Crb = −

73512

Where -

Fk

kr

rr

k

k

k

2

21

11

1=

−−

Bellows valves

( )K rOV

PbP

ININ= − − +

−16 0 3 11860

700 04

2

. . ..ε (Typical)

5. Calculate the relief temperature -

( )TP

PTf

nn=

++1

14 7460

. degR6. Calculate the relief valve factor -

( )F

K C

T T

Td

W f

f

/

.

.

.=−

014061 25

0 6506

7. Calculate the required area -

AF A

PW=

/

1 square inches8. Calculate the flow rate -

W K ACPMTm d

f

= 1

lb/h9. Calculate maximum allowable back pressure -

KAA

KbCALC

VALVEbMAX

=

Standard valves --Iterate to find r

Maximum back pressure -= −rP1 14 7. psig

Page 17: Instrucalc Calculations

Bellows valves -Maximum back pressure -

( )P

P K

OVIN

INP

bIN

MAX16 0 3

11860

70

0 04

2

. .

.

.− −

+

−ε

psig (Typical)10. Calculate gas valve reaction force in pounds force

( )161

46028 97

1. . . .

..

A P C

TM

VALVE

f +

11. Calculate the gas valve sound pressure level (dBA @ 3 feet)

( )85 10

460

3 4210++

LOG

W k T

MM f. .

. .

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

NomenclatureA Relief area square inchesA W Wetted area square feetC Specific heat ratio coefficient dimensionlessDV Vessel diameter feet

F /Relief valve factor dimensionless

K d Coefficient of discharge dimensionlessK b Gas back pressure correction factor dimensionlessk Ratio of specific heats dimensionlessK p Overpressure correction factor dimensionlessLHV Latent heat of vaporization at flow temp. Btu per poundLV Vessel length, tangent to tangent feetOV % overpressure dimensionlessM Molecular weight dimensionless

Pbmax Maximum back pressure factor dimensionlessPin Set pressure psigPn Operating pressure psigP1 Relieving pressure psiaP2 Back pressure psiar Pressure ratio dimensionlessTf Relief temperature degRTn Operating temperature degF

Page 18: Instrucalc Calculations

Wm Flow rate lb/hX1 Vessel wetted portion dimensionlessZ Compressibility factor dimensionless

Page 19: Instrucalc Calculations

Relief Valve Calculation RoutinesLiquid Relief Known flow1. Calculate the back pressure factor -Standard valves -

K W = 1Bellows valves.-

KP

PWIN

OUT

= −

117.

2. Calculate the relief area -

( )A

W

K K K G P Pm

d p w f OUT

=−19008 4 1.

3. Calculate viscosity correction factor

RW

AD

m

cp

=5 6.

µ

KR R

RvD D

D

=− −1892 0 6

0 047

. ln.ln.ln. .

.

If the Reynolds Number is greater than 50000 then -K v = 1

If the Reynolds Number is less than 100 then -K Ln Rv D= −0 26 0 6. . . .

If the Reynolds Number is less than 15 then -

KR

vD=

154. Calculate the viscosity corrected area -

AA

K v

=

5. Calculate the maximum allowable back pressure.-Standard valves

P P

WK K K K A

GB IN

m

d p w v

fMAX

= −

19008 4

2

.

Bellows valves Calculate

KP

PWIN

OUT

= −

117.

Calculate A in formula 2

Increment POUT until A equals the selected valve area

Gas Relief Known Flow1. Calculate the pressure ratio -

rPP

= 2

1

Limited to a minimum of -

Page 20: Instrucalc Calculations

21

1

k

k

k

+

2. Calculate the specific heat ratio coefficient

C kk

k

k=

+

+−

5202

1

1

1

3. Calculate the back pressure correction factor -Standard valves

KF

Crb = −

73512

Where -

Fk

kr

rr

k

k

k

2

21

11

1=

−−

Bellows valves (Typical) --

( )K rOV

PbP

ININ= − − +

−16 0 3 11860

700 04

2

. . ..ε

4. Calculate the required area -

AW

K CP KT ZM

m

d b

f=1 square inches

5. Calculate maximum allowable back pressure -

KAA

KbCALC

VALVEbMAX

=

Standard valves -Iterate to find r

Maximum back pressure= −rP1 14 7. psig

Bellows valvesMaximum back pressure -

( )P

P K

OVIN

INP

bIN

MAX16 0 3

11860

70

0 04

2

. .

.

.− −

+

−ε

psig (Typical)

Steam Relief Known Flow -1. Calculate the pressure ratio -

rPP

= 2

1

Limited to a minimum of -

21

1

k

k

k

+

2. Calculate the superheat correction factor -K T T LogPSH SH SH= + −1 0 00004 0 00012 1. .

3. Calculate the back pressure correction factor -

Page 21: Instrucalc Calculations

Standard valves

KF

Crb = −

73512

Where -

Fk

kr

rr

k

k

k

2

21

11

1=

−−

Bellows valves -

( )K rOV

PbP

ININ= − − +

−16 0 3 11860

700 04

2

. . ..ε (Typical)

4. Calculate the required area

AW

K P K Km

d SH b

=515 1. square inches

5. Calculate the maximum allowable back pressure factor

KAA

KbCALC

VALVEbMAX

=

Standard valvesIterate to find r

Maximum back pressure= −rP1 14 7. psig

Bellows valves -Maximum back pressure

( )P

P K

OVIN

INP

bIN

MAX16 0 3

11860

70

0 04

2

. .

.

.− −

+

−ε

psig (Typical)6. Calculate gas valve reaction force in pounds force

( )161

46028 97

1. . . .

..

A P C

TM

VALVE

f +

7. Calculate the gas valve sound pressure level (dBA @ 3 feet)

( )85 10

460

3 4210++

LOG

W k T

MM f. .

. .

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

NomenclatureA Relief area square inchesG f Specific gravity at flowing temperature dimensionlessK d Coefficient of discharge dimensionless

Page 22: Instrucalc Calculations

K b Gas back pressure correction factor dimensionlessk Ratio of specific heats dimensionlessK p Overpressure correction factor dimensionlessK SH Superheat correction factor dimensionlessK w Liquid back pressure correction factor dimensionlessK v Viscosity correction factor dimensionlessOV % overpressure dimensionlessM Molecular weight dimensionlessPbmax Maximum back pressure factor dimensionlessPin Set pressure psigPout Back pressure psigP1 Relieving pressure psiaP2 Back pressure psiar Pressure ratio dimensionlessTf Relief temperature degRTsh Superheat degFRD Reynolds number dimensionlessWm Flow rate lb/hZ Compressibility factor dimensionlessµCP Absolute viscosity centipoises

Page 23: Instrucalc Calculations

Relief Valve Calculation RoutinesEntrapped liquid - heat exchanger -1 Calculate the flow rate -

WBHCm =

lb/hEntrapped liquid - pipeline -1. Calculate the flow rate.-

W D LBGm f= 13 62 2. lb/h(for a temperature rise of 5 degF per hour)

Both are common from here -2 Calculate the back pressure factor -Standard valves -

K W = 1Bellows valves -

KP

PWIN

OUT

= −

117.

3 Calculate the relief area -

( )A

W

K K K G P Pm

d p w f OUT

=−19008 4 1.

square inches4 Calculate viscosity correction factor -

RW

AD

m

cp

=5 6.

µ

KR R

RvD D

D

=− −1892 0 6

0 047

. ln.ln.ln. .

.

If the Reynolds Number is greater than 50000 then -K v = 1

If the Reynolds Number is less than 100 then -K Ln Rv D= −0 26 0 6. . . .

If the Reynolds Number is less than 15 then -

KR

vD=

155. Calculate the viscosity corrected area -

AA

K v

=

6 Calculate the maximum allowable back pressure -Standard valves -

P P

WK K K K A

GB IN

m

d p w v

fMAX

= −

19008 4

2

.

psigBellows valves - Calculate

KP

PWIN

OUT

= −

117.

Page 24: Instrucalc Calculations

Calculate A in formula 3

Increment POUT until A equals the selected valve area

Heat Exchanger Tube Failure -

( )A

AK

P P P

PTUBE

d

TUBE SHELL b

SHELL

MAX=− −15

185

.

.square inches

The tube pressure must be greater than 150% of the shell pressure. The ruptured tube is assumed to provide a flow area of one tube and a flow coefficient of 0.62. The is no allowance in

the formula for flashing or thermal expansion. K d is 1 for 25% overpressure, 0.82 for 16% and 0.62 for 10%.

Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.

NomenclatureA Relief area square inchesA TUBE Tube cross section area square inchesB Liquid cubical expansion at flow temp per degFC Liquid specific heat BTU/lb/degFG f Specific gravity at flowing temperature dimensionlessH Total heat transfer BTU/hourK d Coefficient of discharge dimensionlessK p Overpressure correction factor dimensionlessK w Liquid back pressure correction factor dimensionlessK v Viscosity correction factor dimensionlessOV % overpressure dimensionlessM Molecular weight dimensionlessPbmax Maximum back pressure psigPSHELL Shell maximum allowable working pressure psigPTUBE Tube maximum allowable working pressure psigPin Set pressure psigPout Back pressure psigr Pressure ratio dimensionlessTf Relief temperature degRRD Reynolds number dimensionlessWm Flow rate lb/hµCP Absolute viscosity centipoise