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
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
3 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
4 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
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
6 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
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
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
.
9 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
10 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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%
11 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
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
13 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
14 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
.
15 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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.
16 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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 :
17 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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
18 rev3 09/04/2023 Compilation document.doc BY JC THÉODART
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