Hand Calculation Method for Orifice Design

Chevron Corporation B-1 July 1999
Appendix B. Hand Calculation Method for Orifice Design
Abstract
This appendix explains how to perform the calculations for orifice plate design by
hand. For manual look-up of the orifice coefficient, S (given beta) or the diameter
ratio, beta (given S), the following eight figures are provided:
Orifice calculation sheets have been prepared for guidance through the orifice calcu-
lation steps. Calculation sheets filled in with appropriate examples are attached.
The four orifice calculation sheets are as follows:
• LIQUID, square-edge orifice, Form ICM-EF-59B (Figure B-9)
• LIQUID, quadrant-edge orifice, Form ICM-EF-59C (Figure B-10)
• GAS, square-edge orifice, Form ICM-EF-59D (Figure B-11)
• VAPOR/STEAM, square-edge orifice, Form ICM-EF-59E (Figure B-12)
Note that in these calculation sheets, the term "sharp edge" is used instead of
"square-edge."
Results of the hand calculations agree closely with the computer program ORIFICE.
The two types of calculations that can be performed are orifice sizing and orifice re-
ranging, except for quadrant-edge.
Figure B-1 Flange Taps - 6 Inch Pipe Size (6.056 in.); S vs. Beta for
Different R
D
Values (Based on Data from ISO 5167)
Figure B-2 Flange Taps; Pipe Size Corrections for S Values (Based on
Data from ISO 5167)
Figure B-3 Radius Taps; S vs. Beta for Different R
D
Values (Based on
Data from ISO 5167)
Figure B-4 Corner Taps; S vs. Beta for Different R
D
Values (Based on

Data from ISO 5167)
Figure B-5 Pipe Taps; S vs. Beta for Different R
D
Values (Based on
Data from ISO 5167)
Figure B-6 ASME Small Bore with Flange Taps; S vs. Beta for
Different R
D
Values—1 in. to 1-1/2 in. Pipe Size (Based
on Data from "Fluid Meters: Their Theory and Applica-
tion", 6th ed., 1971. Courtesy of ASME)
Figure B-7 ASME Small Bore with Corner Taps (.546 in.); S vs. Beta
for Different R
D
Values—1/2 in. Schedule 80 Pipe Size
(Based on Data from "Fluid Meters: Their Theory and
Application", 6th ed., 1971. Courtesy of ASME)
Figure B-8 Quadrant — Edge Data; S and Thickness Ratio vs. Beta
Appendix B Instrumentation and Control Manual
July 1999 B-2 Chevron Corporation
B1.0 Calculation Procedure
1. Fill in the STREAM PROPERTY input blocks.
2. Fill in the FLOW RATE input blocks.
3. Fill in the ORIFICE DATA input blocks.
TEMPERAURE degrees Fahrenheit for liquid and vapor/steam
degrees Rankine = °F + 460 for gas
PRESSURE PSIA for gas and vapor
LIQUID SPECIFIC GRAVITY Gb at 60 F (Gb for water =
1.00)
VAPOR/STEAM SPECIFIC GRAVITY cu.ft./lb.

for steam, use steam tables
GAS SPECIFIC GRAVITY Ideal sp. gr. is used
= M.W. gas/M.W. dry air
= Z
b
× Real sp. gr.
LIQUID KINEMATIC VISCOSITY use centistokes
GAS AND VAPOR ABSOLUTE
VISCOSITY
use centipoise
UNITS: For liquid use BPD, BPH, GPM, or GPH. For vapor use
lbs/hour; for gas use SCFH.
FULL SCALE: Flow that creates a dp across the orifice taps equal to the
maximum value of the dp transmitter range.
NORMAL: For square-edge and ASME small-bore this should be
the mid-range dp value, which equals .707 × (full-scale
flow rate)
1/3 FS: For quadrant-edge, equal to .333 × (full-scale flow rate)
TYPE OF ORIFICE PLATE Square-edge
ASME small-bore
Quadrant-edge
TYPE OF TAPS Flange, radius, corner or pipe for
square-edge
Flange or corner only for ASME
small-bore
Flange for quadrant-edge
PIPE INSIDE DIAMETER Use 3 decimal places
ORIFICE DIAMETER Entered for orifice re-ranging
calculation
Instrumentation and Control Manual Appendix B

Chevron Corporation B-3 July 1999
4. Fill in the CORRECTIONS FACTORS.
5. Calculate Pipe Reynold’s Number.
Space is provided for values in equations.
See examples on sheets provided.
6. Calculate orifice size or dp range for square-edge or ASME small-bore orifice.
Given h, Find d
Fill in equations and solve for S.
Look up beta ratio in table.
Interpolation is necessary.
Use Table in Figure B-2 to correct for pipe size other than 6-inches (2-12
inches).
Use Reynold’s number column that is closest to value calculated in step 5.
Given d, Find h
Calculate beta ratio.
Look up S in table.
Interpolation is necessary.
Use Reynold’s number that is closest to value calculated in Step 5.
See examples on sheets provided.
7. Calculation for quadrant-edge orifice size.
Use 3 decimal places
FULL SCALE DP Entered for orifice sizing calcula-
tion
Standard value = 100 inches of
water
Fa Correction for thermal expansion of orifice meter at
flowing temperature found in ASME MFC-3M Tables or
API MPMS. Chapter 14.3/AGA-3.
Y Gas expansion factor for mid-scale flow
Y

1
= correction based on upstream pressure
Y
2
= correction based on downstream pressure
Look up in table or chart - use mid-range differential
pressure (dp)
Fpv Supercompressibility correction factor
Rarely used in refinery calculations (usually set = 1.0)
Look up in table or chart when used.
Zb Compressibility factor at 60°F, 1 Atm
Rarely used in refinery calculations (usually set = 1.0)
Look up in table or chart when used.
Appendix B Instrumentation and Control Manual
July 1999 B-4 Chevron Corporation
Select a plate thickness, look up values from Figure B-8, and calculate the
differential pressure h.
If h is too large, make plate thicker; if too small, make plate thinner, and repeat
calculation. h should equal about 100 inches of water.
The permissible range of Reynold’s numbers (at 1/3 full-scale flow) for a quad-
rant-edge orifice is a function of the beta ratio:
See example on calculation sheet provided.

beta ratio 0.2 0.3 0.4 0.5 0.6
min. R
D
670.0 770.0 630.0 450.0 320.0
max. R
D
17500.0 28000.0 45000.0 70000.0 85000.0

Instrumentation and Control Manual Appendix B
Chevron Corporation B-5 July 1999
Fig. B-1 Flange Taps - 6 Inch Pipe Size (6.056 in.); S vs. Beta for Different R
D
Values (
Based on Data from ISO 5167
)
Appendix B Instrumentation and Control Manual
July 1999 B-6 Chevron Corporation
Fig. B-2 Flange Taps; Pipe Size Corrections for S Values (
Based on Data from ISO 5167
)
Instrumentation and Control Manual Appendix B
Chevron Corporation B-7 July 1999
Fig. B-3 Radius Taps; S vs. Beta for Different R
D
Values (
Based on Data from ISO 5167
)
Appendix B Instrumentation and Control Manual
July 1999 B-8 Chevron Corporation
Fig. B-4 Corner Taps; S vs. Beta for Different R
D
Values (
Based on Data from ISO 5167
)
Instrumentation and Control Manual Appendix B
Chevron Corporation B-9 July 1999
Fig. B-5 Pipe Taps; S vs. Beta for Different R
D

Values (
Based on Data from ISO 5167
)
Appendix B Instrumentation and Control Manual
July 1999 B-10 Chevron Corporation
Fig. B-6 ASME Small Bore with Flange Taps; S vs. Beta for Different R
D
Values—1 in. to 1-1/2 in. Pipe Size (
Based
on Data from "Fluid Meters: Their Theory and Application", 6th ed., 1971. Courtesy of ASME
)
Instrumentation and Control Manual Appendix B
Chevron Corporation B-11 July 1999
Fig. B-7 ASME Small Bore with Corner Taps (.546 in.); S vs. Beta for Different R
D
Values—1/2 in. Schedule 80 Pipe
Size (
Based on Data from "Fluid Meters: Their Theory and Application", 6th ed., 1971. Courtesy of ASME
)
Appendix B Instrumentation and Control Manual
July 1999 B-12 Chevron Corporation
Fig. B-8 Quadrant — Edge Data; S and Thickness Ratio vs. Beta
Instrumentation and Control Manual Appendix B
Chevron Corporation B-13 July 1999
Fig. B-9 Orifice Calculation Sheet—Liquid, Square-edge Orifice
Appendix B Instrumentation and Control Manual
July 1999 B-14 Chevron Corporation
Fig. B-10 Orifice Calculation Sheet—Liquid, Quadrant-edge Orifice
Instrumentation and Control Manual Appendix B
Chevron Corporation B-15 July 1999

Fig. B-11 Orifice Calculation Sheet—Gas, Square-Edge Orifice
Appendix B Instrumentation and Control Manual
July 1999 B-16 Chevron Corporation
Fig. B-12 Orifice Calculation Sheet—Vapor/Steam, Square-Edge Orifice