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MAIN EQUATIONS & HISTORICAL Background Measurement of Fluid Flow in Pipes Using Orifice , Nozzle , and Venturi From Standards : ISO 5167-1 :1991 Orifice plate Corner,Flange,Radius taps - STOLZ equation Nozzle ISA1932 , Long radius with high and low beta ratio Venturi Rough cast ,Machined , fabricated Convergent and Venturi- Nozzle ISO 5167-1 /A1 :1998 Orifice plate Corner,Flange,Radius taps - Reader-Harris /Gallagher equation ASME MFC-3M-1989 Orifice plate Corner,Flange,Radius taps -STOLZ equation (from ISO 5167 :1980) Nozzle ASME Long radius with high and low beta ratio, Low beta with throat taps Venturi Rough cast , Machined , and Fabricated Convergent, Venturi-Nozzle BS 1042 - section 1.2 : 1989 Orifice plate Corner taps for pipe 25 < =D <50 mm BS 1042 - section 1.2 : 1989 Orifice plate Eccentric , Quarter circle , Conical API 2530-1985 (AGA3) 1 rev3 23/08/2022 Compilation document.doc BY JC THÉODART

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MAIN EQUATIONS & HISTORICAL Background

“ Measurement of Fluid Flow in Pipes Using Orifice , Nozzle , and Venturi ”

From Standards   :

ISO 5167-1   :1991 Orifice plate Corner,Flange,Radius taps - STOLZ equationNozzle ISA1932 , Long radius with high and low beta ratioVenturi Rough cast ,Machined , fabricated Convergent and

Venturi- Nozzle

ISO 5167-1   /A1   :1998 Orifice plate Corner,Flange,Radius taps -Reader-Harris

/Gallagher equation

ASME MFC-3M-1989

Orifice plate Corner,Flange,Radius taps -STOLZ equation

(from ISO 5167 :1980)Nozzle ASME Long radius with high and low beta ratio,

Low beta with throat tapsVenturi Rough cast , Machined , and Fabricated

Convergent, Venturi-Nozzle BS 1042 - section 1.2   : 1989

Orifice plate Corner taps for pipe 25 < =D <50 mm

BS 1042 - section 1.2   : 1989

Orifice plate Eccentric , Quarter circle , Conical

API 2530-1985 (AGA3)

Orifice plate Flange and Pipe taps -Buckingham equation

FLOW METER SHELL HANDBOOK

Restriction Equation (extrapolation from curve)Orifice Plate

1 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

Page 2: Merenje protoka - jednacine

SUMMARY

1. SYMBOLS................................................................................................................................................................... 3

2. DISCHARGE COEFFICIENT :............................................................................................................................... 4

2.1 SQUARE-EDGED ORIFICE PLATES.........................................................................................................................................................................................42.1.1 Flange Taps ............................................................................................................................................................................42.1.2 Corner taps .............................................................................................................................................................................52.1.3 Radius taps. ...........................................................................................................................................................................52.1.4 Pipe taps. ...........................................................................................................................................................................6

2.2 ORIFICE EXCEPT SQUARE EDGED ORIFICE PLATES.......................................................................................................................................................6 2.2.1 Conical..................................................................................................................................................................................................................................... 6 2.2.2 Quarter..................................................................................................................................................................................................................................... 6 2.2.3 Eccentric.................................................................................................................................................................................................................................. 6

2.3 NOZZLES........................................................................................................................................................................................................................................ 6 2.3.1 ISA 1932............................................................................................................................................................................................................................................ 6

2.3.2 Long radius with high beta ratio...........................................................................................................................................................................................6 2.3.3 Long radius with low beta ratio.............................................................................................................................................................................................7

2.3.4 Low beta with throat taps..............................................................................................................................................................................................72.4 CLASSICAL VENTURI.................................................................................................................................................................................................................. 7

2.4.1 Rough cast convergent :..........................................................................................................................................................................................................7 2.4.2 Machined convergent :...........................................................................................................................................................................................................7 2.4.3 Fabricated convergent :..........................................................................................................................................................................................................7 2.4.4 Venturi-Nozzle.................................................................................................................................................................................................................8

3. EXPANSION FACTOR FOR COMPRESSIBLE FLUIDS :....................................................................................8

3.1 SQUARE-EDGED ORIFICE PLATES.........................................................................................................................................................................................83.2 ORIFICE EXCEPT SQUARE EDGED ORIFICE PLATES...........................................................................................................................83.3 NOZZLES & VENTURI :..............................................................................................................................................................................................................8

4. PRESSURE LOSS :..................................................................................................................................................... 9

4.1 ORIFICE PLATES ( FLANGE TAPS, CORNER TAPS , RADIUS TAPS )..........................................................................................................................94.2 NOZZLES :...................................................................................................................................................................................................................................... 94.3 VENTURI :..................................................................................................................................................................... 9

5. UNCERTAINTY :...................................................................................................................................................... 10

5.1 ORIFICE PLATES (FLANGE TAPS, CORNER TAPS , RADIUS TAPS )...........................................................................................................................105.2 NOZZLES................................................................................................................................................................................................115.3 VENTURI ...............................................................................................................................................................................................11

6. LIMITS...................................................................................................................................................................... 12

6.1 SQUARE-EDGED ORIFICE PLATES.......................................................................................................................................................................................126.2 ORIFICE EXCEPT SQUARE EDGED ORIFICE PLATES.....................................................................................................................................................126.3 NOZZLES ...............................................................................................................................................................................................136.4 VENTURI . ..................................................................... ...........................................................................................................................................................14

7. MAIN EQUATION.................................................................................................................................................... 14

7.1 UNIVERSAL EQUATION..........................................................................................................................................................................................................147.2 REYNOLDS NUMBER...............................................................................................................................................................................................................147.3 THERMAL CORRECTION FACTOR......................................................................................................................................................14

8. PRACTICAL COMPUTATION OF THE UNCERTAINTY...........................................................................................................14

9. HISTORICAL BACKGROUND.........................................................................................................................................................15

10. EXEMPLES & COMPARISON FOR FLANGE TAPS ORIFICE.................................................................................................16

11. RESTRICTION ORIFICE (from SHELL HANDBOOK METER )........ .......................................................................................17

2 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

Page 3: Merenje protoka - jednacine

3 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

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1. SYMBOLS

Symbols Represented quantity Dimensions SI UNITMLT

: Mass: Length: temperature: Time

C

d

D

e

k

l

L

p1

qm

qv

RD

l

t

U

b

g

dP

Dv

e or U

k

m

n

r

t

K

Ke

K0

Coefficient of discharge

Diameter of orifice or throat of primary device at flowing conditions

Upstream international pipe diameter ( or upstream diameter of a classical Venturi ) at flowing conditions

Relative uncertainty

Uniform equivalent roughness

Pressure tap spacing from orifice plate at 20°C

Ratio of pressure tap spacing to D , L = l / D at 20°C

Static pressure of the fluid

Mass rate of flow

Volume rate of flow

Reynolds number referred to D

Thermal expansion factor

Temperature of the flowing fluid

Mean axial velocity of the fluid in the pipe

Diameter ratio b = d/D

Specific heat capacity ratio1)

Differential pressure

Pressure loss

Expansion factor

Isentropic exponent1)

Dynamic viscosity of the fluid or Absolute viscosity

Kinematic viscosity of the fluid n = m / r

Mass density of the fluid

Pressure ratio t = p2 / p1

Flow coefficient correponding to any specific set of values of D,b, and RD

Particular value of K for any specific values of D and b when RD =106db / 15

The limiting value of K for any specific values of D and b when RD becomes infintely large

dimensionless

L

L

dimensionless

L

L

dimensionless

ML-1T-2

MT-1

L3T-1

dimensionless

-1

LT-1

dimensionless

dimensionless

ML-1T-2

ML-1T-2

dimensionless

dimensionless

ML-1T-1

L2T-1

ML-3

dimensionless

dimensionless

dimensionless

dimensionless

-

m

m

-

m

m

-

Pa

kg/s

m3/s

-

°C-1

°C

m/s

-

-

Pa

Pa

-

-

Pa.s

m2/s

kg/m3

-

-

-

-

1 ) Ratio of heat capacity at constant pressure to the specific heat capacity at constant volume.For ideal gases,the ratio of the specific heatcapacities and the isentropic exponent have the same values.These values depend on the nature of the gas.

NOTE : Subscript 1 refers to the upstream conditions.Subscript 2 refers to the downstream conditions.Standard acceleration due to gravity , 9.806650 m/s2

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2. DISCHARGE COEFFICIENT :

2.1 SQUARE EDGED ORIFICE PLATES :

2.1.1 Flange taps :

ISO5167-1

50 < D £ 58.62

L1 = 0.433

L’2 = 25.4/DC

RDL

05959 0 0312 21 0184 8 0 0029 2 5 106 0 75

0 039 4 1 4 10 0337 2

3. . . . . ..

. . 'b b b b b b

D > 58.62 L1 = L’2 = 25.4/D CRD

L L

05959 0 0312 21 0184 8 0 0029 2 5 106 0 75

0 09 14 1 4 1

0 0337 23. . . . . .

.

. . 'b b b b b b

ASME

50.8 £ D £ 58.62

L1 = 0.433

L’2 = 25.4/D

C RD D

05959 0 0312 21 0184 8 9171 2 5 0 75 0 039 4 1 4 1

08560 1 3. . . . . . . . .b b b b b b

D > 58.62 L1 = L’2 = 25.4/DC RD D D

05959 0 0312 21 0184 8 9171 2 5 0 75 2 2860 1 4 1 4 1

08560 1 3. . . . . . . . .b b b b b b

where 91.706 = 0.0029 * (106)0.75

0.8560 = 0.0337 * 25.4 2.286 = 0.09 * 25.4

ISO-Ad1

D < 71.12 mm L1 = L’2 = 25.4/D

M’2 = 2 L’2 / 1-b

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e--10L1 - 0.123 e -7 L

1 ) (1-0.11A) b4/1-b4

0.031(M’2 - 0.8 M’21.1)b1.3 + 0.011( 0.75-b ) (2.8 - D/25.4)

D ³ 71.12 mm

A = 19000b / RD 0.8

e = 2.718281828459

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e--10L1 - 0.123 e -7 L1 ) (1-0.11A) b4/1-b4

- 0.031(M’2 - 0.8 M’21.1)b1.3

API 2530

D (inches) at 20°C

C K 1 4b

K

KE

d

e0

61

15

10

K KE

RD

0 1

b

KD D D D D

D

e

0 59930 007

0 3640 076

0 4 161

0 0705

0 0090 034

05

653 0 7

45

5

2 3

2

2

5

2

..

..

. . ..

..

.

.

b b b

b

E dD

830 5000 9000 42005302 3

0 5b b b

.

Note : Any negative factor , such as b - 0.7 )5/2 when b is less than 0.7 , should be taken as equal to zero so that the whole term [(65/D2 ) + 3](b-0.7)5/2 drops out of the equation.

5 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

theodart, 01/03/-1,
Page 6: Merenje protoka - jednacine

2.1.2 Corner taps :

ISO5167-1

L1 = L’2 = 0 CD

0 5959 0 0312 0184 0 0029102 1 8 2 5

6 0 75

. . . .Re

. .

.

b b b

ASME

L1 = L’2 = 0 C RD 05959 0 0312 0184 91712 1 8 2 5 0 75. . . .. . .b b b where :

91.706 = 0.0029 * (106)0.75

ISO-Ad1

D < 71.12 mm

L1 = L’2 = 0

M’2 = 2 L’2 / 1 - b

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e-10L1 - 0.123 e --10L1) (1-0.11A) b4/1-b4

0.031(M’2 - 0.8 M’21.1)b1.3 + 0.011( 0.75-b ) (2.8 - D/25.4)

D ³71.12 mm

A = 19000b / RD 0.8

e = 2.718281828459

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e-10L1 - 0.123 e -10L1) (1-0.11A) b4/1-b4

- 0.031(M’2 - 0.8 M’21.1)b1.3

BS1042

25£ D <50 L1 = L’2 = 0 CRD

05959 0 0312 0184 0 0029102 1 8 2 5

6 0 75

. . . .. .

.

b b b

2.1.3 Radius Taps

ISO5167-1 L1 = 1 L’2 = 0.47

CRD

L L

05959 0 0312 21 0184 8 0 0029 2 5 106 0 75

0 09 14 1 4 1

0 0337 23. . . . . .

.

. . 'b b b b b b

ASME

L1 = 0.433 L’2 = 0.47 C RD

05959 0 0312 21 0184 8 9171 2 5 0 75 0 039 4 1 4 1

0 01584 3. . . . . . . . .b b b b b b

where : 91.706 = 0.0029 * (106)0.75

0.01584 = 0.0337 * 0.47 0.03897 = 0.09 * 0.433

ISO-Ad1

D < 71.12 mm

L1 = 1

L’2 = 0.47

M’2 = 2 L’2 / 1 - b

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e-10L1 - 0.123 e -7 L1 ) (1-0.11A) b4/1-b4

0.031(M’2 - 0.8 M’21.1)b1.3

+ 0.011( 0.75-b ) (2.8 - D/25.4)

D ³71.12 mm

A = 19000b / RD 0.8

e = 2.718281828459

C = 0.5961 + 0.0261b 2 - 0.216b 8+ 0.000521 106 b /RD 0.7

+ (0.0188 + (0.0063 A)b3.5 (106/ RD)0.3 + ( 0.043 + 0.080e-10L1 - 0.123 e -7 L1 ) (1-0.11A) b4/1-b4

- 0.031(M’2 - 0.8 M’21.1)b1.3

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Page 7: Merenje protoka - jednacine

2.1.4 Pipe taps

API 2530

D (inches) at Tf

C K 1 4b

K

KE

d

e0

61

15

10

K KE

RD

0 1

b

KD D D De

059250 0182

0 4400 06

0 9350 225

135143

0 252 5 145

2..

..

..

..

.b b b b E dD

830 5000 9000 4200875

752 3b b b

E dD

905 5000 9000 42008752 3b b b

where 905 = 830 + 75

2.2 ORIFICE EXCEPT SQUARE-EDGED

2.2.1 Conical with Corner taps

BS1042conical R≤ 5000 * β C = 0.734 rev2conical R≥ 5000 * β C = 0.730 rev2

2.2.2 Quarter with Corner taps

BS1042

quarter

C 0 73823 0 3309 11615 2 15084 3. . . .b b b

2.2.3 Eccentric with Corner taps and Flange taps

BS1042

eccentric

C 0 9355 16889 30248 2 17989 3. . . .b b b

2.3 NOZZLES

2.3.1 ISA 1932

ISO-5167-1

ISA 1932

15.161015.40033.0200175.01.42262.0990.0

DRC bbb

2.3.2 Long radius with high beta ratio

ISO5167-1

0.25 £ b £ 0.8056105.000653.09965.0

DRC b

ASME

Long Radius with high beta

ratio

0.5 £ b £ 0.8056105.000653.09975.0

DRC b

7 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

Page 8: Merenje protoka - jednacine

2.3.3 Long radius with low beta ratio

ISO5167-1 0.2 £ b £ 0.5 C

RD

0 9965 0 00653

05 10605

. ..

.

b

ASME

Long radius with low beta ratio

0.2 £ b £ 0.5 C RD

0 9975 0 00653

05 10605

. ..

.

b

2.3.4 Low beta with throat taps

ASME

low beta with throat taps

0.2 5 £ b £ 0.5 C RD

0 9975 0 00653

05 10605

. ..

.

b

2.4 CLASSICAL VENTURI

2.4.1 Rough cast convergent :

ISO5167-1

-

RD ³ 2 * 105 C = 0.984

ASME

- RD ³ 2 * 105 C = 0.984

2.4.2 Machined convergent :

ISO5167-1

-

RD ³ 2 * 105 C = 0.995

ASME

- RD ³ 2 * 105 C = 0.995

2.4.3 Fabricated convergent :

ISO5167-1

-

RD ³ 2 * 105 C = 0.985

ASME

- RD ³ 2 * 105 C = 0.984

8 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

Page 9: Merenje protoka - jednacine

2.4.4 Venturi-Nozzle

ISO5167-1

- - C = 0.9858 - 0.196 b4.5

3. EXPANSION FACTOR FOR COMPRESSIBLE FLUIDS :

3.1 SQUARE-EDGED ORIFICE : (FLANGE , CORNER ,RADIUS TAPS )

ISO5167-1

all taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

ISO-Ad1

all taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

ASME

all taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

BS1042

25 £ D < 50

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

API2530

Flange taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

Pipe taps

ifp2 / p1 ³ 075 Y

p

kp12 5 13

1

1 0 333 1145 0 7 12

. . .b b b D

3.2 ORIFICE EXCEPT SQUARE-EDGED :ECCENTRIC

BS1042

Corner taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

3.3 NOZZLES & VENTURI :

ISO5167-1

ifp2 / p1 ³ 075

e t

b

b t

tt1

2

11 4

1 42

11

1

12

.

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Page 10: Merenje protoka - jednacine

ASME

ifp2 / p1 ³ 075 e t

b

b t

tt1

2

11 4

1 42

11

1

12

.

4. PRESSURE LOSS :

4.1 ORIFICE PLATES ( FLANGE TAPS, CORNER TAPS , RADIUS TAPS )

ISO5167-1

- - D Dvb b

b b

1

1

4 2

4 2

C

Cp

or approximately

DDv bp 1 1 9.

ISO-Ad1

- - D Dvb b

b b

1

1

4 2

4 2

C

Cp

ASME

- - D Dvb b

b b

1

1

4 2

4 2

C

Cp

BS1042

for 25 £ D < 50 - D Dvb b

b b

1

1

4 2

4 2

C

Cp

API2530Pipe and

Flange taps D Dv b b b ( . . )1 0 24 052 0162 3 p Miller source

4.2 NOZZLES :

ISO5167-1

- - D Dvb b

b b

1

1

4 2

4 2

C

Cp

ASME

- -D Dv b b b ( . . . )1 0 014 2 06 1182 3 p

4.3 VENTURI :

ISO5167-1Generally within 5% to 20%

ASMEDv b b 0 436 086 059 2. . . for 15° divergent

Generally within 5% to 20%D 0 218 0 42 0 38 2. . .b b for 7° divergent

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Page 11: Merenje protoka - jednacine

5. UNCERTAINTY :

5.1 ORIFICE PLATES (FLANGE TAPS, CORNER TAPS , RADIUS TAPS )

Standard

C (Discharge coefficient) e 1 (Expansibility factor)

ISO5167-1Flange tapsCorner tapsRadius taps 0.6% for b £ 0.6 4

1

Dp

p%

b% for 0.6 < b £ 0.75 41

Dp

p%

ISO-Ad1Flange tapsCorner tapsRadius taps

0.5% for b £ 0.6 41

Dp

p%

(1.667b - 0.5 )% for 0.6 < b £ 0.754

1

Dp

p%

ASMEFlange tapsCorner tapsRadius taps

0.6% for b £ 0.6 41

Dp

p%

b% for 0.6 < b £ 0.754

1

Dp

p%

BS1042

Conical b% for 0.6 < b £ 0.754

1

Dp

p%

Quarter 2 % for b > 0.316 and 2.5% when b £ 0.316 33 (1 - e1) %

Eccentric 1 % for b £ 0.75 and 2.5% when b > 0.75 33 (1 - e1) %

BS1042

for 25 £ D < 50 0.6% for b£ 0.64

1

Dp

p%

API2530

Flange taps 0.5% for 0.15 £ b £ 0.7 if Dp/p1 < 55 then 0.5% else 0.7%

1 % for b ³ 0.7 or b £ 0.15 if Dp/p1 < 55 then 0.5% else 0.7%

Pipe taps 0.75 % for 0.2 £ b £ 0.67 if Dp/p1 < 55 then 0.5% else 0.7%

1.5 % for b ³ 0.67 or b £ 0.2if Dp/p1 < 55 then 0.5% else 0.7%

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Page 12: Merenje protoka - jednacine

5.2 NOZZLES :

Standard C (Discharge coefficient) e 1 (Expansibility factor)

ISO5167-1

ISA-1932 0 8%. 0 6. .. ... .for b £ 21

Dp

p%

b%......for .....0.6 < b £0.752

1

Dp

p%

Long radius nozzle

0 8%. 0 6. .. ... .for b £ 21

Dp

p%

ASME

Throat taps 0.5%2

1

Dp

p%

High ratio 2%2

1

Dp

p%

Low ratio 2%2

1

Dp

p%

5.3 VENTURI :

ISO5167-1

Venturi-nozzle (1.2+1.5b4) 4 100 8

1

b Dp

p%

Rough castconvergent 0.7 % 4 100 8

1

b Dp

p%

Machinedconvergent 1 % 4 100 8

1

b Dp

p%

Fabricatedconvergent 1.5 % 4 100 8

1

b Dp

p%

ASME

Rough castconvergent

1 % 4 100 8

1

b Dp

p%

Machinedconvergent

1 %4 100 8

1

b Dp

p%

Fabricatedconvergent

1 %4 100 8

1

b Dp

p%

12 rev3 09/04/2023 Compilation document.doc BY JC THÉODART

Page 13: Merenje protoka - jednacine

6. LIMITS

6.1 SQUARE EDGED ORIFICE PLATES

Standard d D b ReD mini

ISO5167

Flange taps 12.5 £ d 50 £ D £ 1000 0.2 £ b £ 0.75 1260 *b2 * D £ RD

Corner taps 12.5 £ d 50 £ D £ 1000 0.2 £ b £ 0.75 RD ³ 5000 ....for b £ .45

RD ³ 10000 ....for b> 0.45

Radius taps 12.5 £ d 50 £ D £ 1000 0.2 £ b £ 0.75 1260 *b2 * D £ ReD

ISO-Ad1

Flange taps 12.5 £ d 50 £ D £ 1000 0.1 £ b £ 0.75 RD ³ 4000 andRD ³ 170b2D

Corner taps 12.5 £ d 50 £ D £ 1000 0.1 £ b £ 0.75 RD ³ 4000 for 0.1 £ b £ 0.5

RD ³ 16000b2 .for b> 0.5

Radius taps 12.5 £ d 50 £ D £ 1000 0.1 £ b £ 0.75RD ³ 4000 for 0.1 £ b £ 0.5

RD ³ 16000b2 .for b> 0.5

ASME

Flange taps 12.5 £ d 50 £ D £ 900 0.2 £ b £ 0.75 1260 b2 D £ RD

Corner taps 12.5 £ d 50 £ D £ 900 0.2 £ b £ 0.75 RD ³ 5000 ....for b £ 0.45

RD ³ 10000 ....for b> 0.45

Radius taps 12.5 £ d 50 £ D £ 900 0.2 £ b £ 0.75 1260 b2 D £ RD

API2530

Flange taps 12.5 £ d 50 £ D £ 750 0.1 £ b £ 0.75 RD ³ 4000

Pipe taps 12.5 £ d 50 £ D £ 750 0.1 £ b £ 0.75 RD ³ 4000

Standard d D b C b2 (1-b4)-0.5 RD

BS 1042

for 25 £ D < 50 d > 6 25 £ D £ 50 0.23 £ b < 0.7 0.032 £ C b2 (1-b4)-0.5 £ 0.35 RD ³ 40000 b2 for 0.23 £ b £ 0.5

RD ³ 10000 for 0.5 £ b £ 0.7

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Page 14: Merenje protoka - jednacine

6.2 ORIFICE PLATES (EXCEPT SQUARE EDGED)

Standard d D b C b2 (1-b4)-0.5 RD

BS 1042

Conical d > 6 25 £ D £500 0.1 £ b < 0.316 0.007 £C b2 (1-b4)-0.5 £ 0.074 80 £ RD £ 2 * 105 b

Quarter d ³ 15 25 £ D £ 500 0.245 £ b £ 0.6 0.046 £C b2 (1-b4)-0.5 £ 0.326 RD(mini)= 1000b +9.4*106(b-0.24)8

RD £ 105 b

Eccentric d ³ 50 100 £ D £ 1000 0.46 £ b £ 0.84 0.136 £C b2 (1-b4)-0.5 £ 0.423 2*105£ RD £ 106 b

6.3 NOZZLES :

ISO5167

ISA 1932-

50 £ D £ 500 0.3 £ b £ 0.8RD ³ 7* 104 ....for b < 0.44

RD ³ 20000 ....for b ³ 0.44

High beta ratio 50 £ D £ 630 0.2 £ b £ 0.8 104 £ RD £ 107

Low beta ratio 50 £ D £ 630 0.2 £ b £ 0.5 104 £ RD £ 107

ASME

High beta ratio 100 £ D £ 750 0.5 £ b £ 0.8 104 £ RD £ 6 * 106

Low beta ratio 100 £ D £ 750 0.2 £ b< 0.5 104 £ RD £ 6 * 106

Low beta ratio

with Throat taps 100 £ D £ 750 0.25 £ b< 0.5 104 £ RD £ 6 * 106

6.4 VENTURI

ISO5167

Rough cast convergent

100 £ D £ 800 0.3 £ b £ 0.75 2 * 105 £ RD £ 2 * 106

Machined convergent

50 £ D £ 250 0.4 £ b £ 0.75 2 * 105 £ RD £ 1 * 106

Fabricated convergent

200 £ D £ 1200 0.4 £ b £ 0.75 2 * 105 £ RD £ 2 * 106

Venturi-nozzle50£d 65 £ D £ 500 0.316 £ b £ 0.775 1 * 105 £ RD £ 2 * 106

ASME

Rough cast convergent

100 £ D £ 1200 0.3 £ b £ 0.75 2 * 105 £ RD £ 6 * 106

Machined convergent

50 £ D £ 250 0.3 £ b £ 0.75 2 * 105 £ RD £ 6 * 106

Fabricated convergent

100 £ D £ 1200 0.3 £ b £ 0.75 2 * 105 £ RD £ 6 * 106

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7. MAIN EQUATION

7.1 UNIVERSAL EQUATION

Q C d pm

e b r12 4 0 5

141 2

.*D

and

C Q

D pme b

b r1

2

4 211

4

2

D

7.2 REYNOLDS NUMBER

RQ

DDm

4

mand

RR

dD b

7.3 THERMAL CORRECTION FACTOR

ld = coefficient of thermal expansion for orifice

dd T

Td( )

( )

( )20

1 201

1

l

lD = coefficient of thermal expansion for pipe

DD T

TD

( )( )

( )20

1 201

1

l

8. PRACTICAL COMPUTATION OF THE UNCERTAINTY :

(from ISO 5167)

eq

q

C

C

D

D

d

d

p

pm

m

ee

bb

b

rr

2

1

1

2 4

4

2 2

4

2 2 2

1

1

2 0 5

2

1

2

1

1

4

1

4

DD

.

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9. HISTORICAL BACKGROUND (MILLER SOURCES)

The differential -producing flowmeters are the most widely used in industrial process-measurement and control applications.The square-edged concentric orifice is selected for 80% of all liquid , gas , and vapour (steam) applications.

The Ohio State University (1935) test report and the Buckinghan fitting equations for the various tapping arrangements have been used by ASME and AGA since 1935.The ability to predict coefficients from measured dimensions led to the full commercialization of the orifice flowmeter.

In the late 1950s , work in USA was combined with European practice and ISO Standards R541 (1967) for orifices and nozzles and R781 (1968) for venturis were issued.In 1960 ,ASME initiated a study to derive by regression analysis , a simpler and more accurate coefficient prediction equation for flange-tapped orifice. The results was not encouraging.

In 1975 , J .Stolz proposed a universal orifice equation to the ISO orifice flowmeter subcommittee. He proposed , based on logical rules to combine the Ohio State data into a single dimensionless equation suitable for flange , corner , and D-and D/2 taps.

The orifice prediction equation appears in ISO Standard 5167 (1980) , which combines Standards R541 and R781 into a single differential-produced standard.Based on the Dowdell and Chen (1970) investigation and subsequent papers by Miller , the ASME Fluid

Meters Research Committee (1981) adopted the ISO5167 (1980) equation.

For the measurement of natural gas , AGA 3 (ANSI/API 2530,1985)is usually required for contractual purposes ; in it , the Buckinghan equations for flange and pipe taps are presented.

The first investigation of a flow nozzle dates back to the nineteen century. In 1930 Germany standardized on an ISA(1932) nozzle geometry.

The ISA was replaced by the the present International Organisation for Standardization(ISO).In the USA the long-radius flow nozzle was developed at Ohio state university primarily for the measurement of the steam flows. The need for improved accuracy when testing steam turbines led to the development of the ASME throat-tap nozzle.

The commercial success of the orifice , venturi , and nozzle led to the development of continually improved secondary measuring elements. This , coupled with test work and user familiary , led to the further development of primary element such as the segmental , eccentric , conical orifice.

In 1997 the Committee ISO/TC30 adopted equation of Reader-Harris/Gallagher for orifices. It replaced J.Stolz equation and becomes Amendment 1 to ISO5167-1 :1991/A1:1998.

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10 EXEMPLES & COMPARISON FOR FLANGE TAPS ORIFICE

COMPARISON for orifice flange tapped

ISO 5167-1 :1991 ISO 5167-1 Ad1: 1995 ASME AGA 3

J.Stolz equation Reader-Harris/Gallagher J.Stolz equation Buckingham equation

DATA   : fluid : gas

flow = 51720 kg/h

Rho(b) = 1.293 kg/m3

P(b) = 1.013 mbar

T(b)= 0°

Rho(f)= 6.671 kg :m3

P(f) = 6 bar

T(f)=40°

viscosity = 0.017 cpo

cp/cv =1.4

deltap = 500 mbar

Pipe diameter = 300 mm

DATA   : fluid : gas

flow = 51720 kg/h

Rho(b) = 1.293 kg/m3

P(b) = 1.013 mbar

T(b)= 0°

Rho(f)= 6.671 kg :m3

P(f) = 6 bar

T(f)=40°

viscosity = 0.017 cpo

cp/cv =1.4

deltap = 500 mbar

Pipe diameter = 300 mm

DATA   : fluid : gas

flow = 51720 kg/h

Rho(b) = 1.293 kg/m3

P(b) = 1.013 mbar

T(b)= 0°

Rho(f)= 6.671 kg :m3

P(f) = 6 bar

T(f)=40°

viscosity = 0.017 cpo

cp/cv =1.4

deltap = 500 mbar

Pipe diameter = 300 mm

DATA   : fluid : gas

flow = 51720 kg/h

Rho(b) = 1.293 kg/m3

P(b) = 1.013 mbar

T(b)= 0°

Rho(f)= 6.671 kg :m3

P(f) = 6 bar

T(f)=40°

viscosity = 0.017 cpo

cp/cv =1.4

deltap = 500 mbar

Pipe diameter = 300 mm

Results for d (20°) :

187.2825035 mm

Results for d (20°) :

187.37130403 mm

Results for d (20°) :

187.28235 mm

Results for d (20°) :

187.3735 mm

Deviations :%

column 2 :0.047

column 3 :0

column 4 :0.048

Deviations :%

column 1 :0.047

column 3 :0.047

column 4 :0.0011

Deviations :%

column 1 :0

column 2 :0.047

column 4 :0.048

Deviations :%

column 1 :0.048

column 2 :0.0011

column 3 :0.048

Conclusion   : Choice of Standards is contractual but to limit contests the choice should be for the latest edition of ISO.

11 RESTRICTION ORIFICE :

11.1 DISCHARGE COEFFICIENT :

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Page 18: Merenje protoka - jednacine

15 > D > 50 mm

and

0.1≥ β ≥ 0.2

C = 0.6097 for liquids

C = 0.519 for gas and steam

D ≥ 50 mm

and

β ≥ 0.2

432 5509.03199.04582.00178.05894.0 bbbb C

11.2 EXPANSION FACTOR -

Same as square edge flange taps (ISO - 5167 )

all taps

ifp2 / p1 ³ 075 e b1 1 0 41 0 35 4

1 . .

Dp

kp

11.3 LIMITATIONS

d D β

all taps Not limited 15 £ D £ not limited 0.1 £ b £ not critical

11.4 PRESSURE TAPPINGS

Pressure tappings are not essential , altough a line pressure indication upstream and downstream of the restriction orifice is recommended for checking of the behaviour of the device

END

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