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where r 1 is the upstream fluid density. When Y ¼ 1, the flow is incompressible, and Equation 10.12
reduces to Equation 10.10. Equation 10.12 represents the most general form of the working
equation for volume flow rate determination when using an obstruction meter.
The expansion factor, Y, depends on several values: the b ratio, the gas specific heat ratio, k, and
the relative pressure drop across the meter, p 1 À p 2
ð
Þ p 1 , for a particular meter type, that is,
Y ¼ f b; k; p 1 À p 2
ð
Þ =p 1
½
. As a general rule, compressibility effects should be considered if
p 1 À p 2
ð
Þ =p 1 ! 0:1.
Standards
The flow behaviors of the most common obstruction meters, namely the orifice plate, venturi, and
flow nozzle, have been studied to such an extent that these meters are used extensively without
calibration. Values for the discharge coefficients, flow coefficients, and expansion factors are
tabulated and available in standard U.S. and international flow handbooks along with standardized
construction, installation, and operation techniques (1, 3, 4, 16). Equations 10.10 and 10.12 are very
sensitive to pressure tap location. For steam or gas flows, pressure taps should be oriented on the top
or side of the pipe; for liquids, pressure taps should be oriented on the side. We discuss the
recommended standard tap locations with each meter (1, 4). A nonstandard installation or design
requires an in situ calibration.
Orifice Meter
An orifice meter consists of a circular plate having a central hole (orifice). The plate is inserted into a
pipe so as to effect a flow area change. The orifice hole is smaller than the pipe diameter and
arranged to be concentric with the pipe’s i.d. The common square-edged orifice plate is shown in
Figure 10.4. Installation is simplified by housing the orifice plate between two pipe flanges. With
this installation technique any particular orifice plate is interchangeable with others of different b
value. The simplicity of the design allows for a range of b values to be maintained on hand at modest
expense.
For an orifice meter, plate dimensions and use are specified by engineering standards (1, 4).
Equation 10.12 is used with values of A 0 and b based on the orifice (hole) diameter, d 0 . The plate
thickness should be between 0.005 d 1 and 0.02 d 1 , otherwise a taper must be added to the
downstream side (1, 4). The exact placement of pressure taps is crucial to use standard coefficients.
Standard pressure tap locations include (1) flange taps where pressure tap centers are located
25.4 mm (1 in.) upstream and 25.4 mm (1 in.) downstream of the nearest orifice face, (2) d and
d/2 taps located one pipe diameter upstream and one-half diameter downstream of the upstream
orifice face, and (3) vena contracta taps. Nonstandard tap locations always require in situ meter
calibration.
Values for the flow coefficient, K 0 ¼ Re d 1 ; b
ð
Þ and for the expansion factor, Y ¼
f b; k; p 1 À p 2
ð
Þ =p 1
½
for a square-edged orifice plate are given in Figures 10.5 and 10.6 based
on the use of flange taps. The relative instrument systematic uncertainty in the discharge coefficient
(3) is $0.6% of C for 0:2 b 0:6 and b% of C for all b > 0.6. The relative instrument systematic
uncertainty for the expansion factor is about 4ðp 1 À p 2 Þ=p 1
½
% of Y. Realistic estimates of the
overall systematic uncertainty in estimating Q using an orifice meter are between 1% (high b) and
3% (low b) at high Reynolds numbers when using standard tables. Although the orifice plate
represents a relatively inexpensive flow meter solution with an easily measurable pressure drop,
430 Chapter 10 Flow Measurements
13:4:37 Page 430
where r 1 is the upstream fluid density. When Y ¼ 1, the flow is incompressible, and Equation 10.12
reduces to Equation 10.10. Equation 10.12 represents the most general form of the working
equation for volume flow rate determination when using an obstruction meter.
The expansion factor, Y, depends on several values: the b ratio, the gas specific heat ratio, k, and
the relative pressure drop across the meter, p 1 À p 2
ð
Þ p 1 , for a particular meter type, that is,
Y ¼ f b; k; p 1 À p 2
ð
Þ =p 1
½
. As a general rule, compressibility effects should be considered if
p 1 À p 2
ð
Þ =p 1 ! 0:1.
Standards
The flow behaviors of the most common obstruction meters, namely the orifice plate, venturi, and
flow nozzle, have been studied to such an extent that these meters are used extensively without
calibration. Values for the discharge coefficients, flow coefficients, and expansion factors are
tabulated and available in standard U.S. and international flow handbooks along with standardized
construction, installation, and operation techniques (1, 3, 4, 16). Equations 10.10 and 10.12 are very
sensitive to pressure tap location. For steam or gas flows, pressure taps should be oriented on the top
or side of the pipe; for liquids, pressure taps should be oriented on the side. We discuss the
recommended standard tap locations with each meter (1, 4). A nonstandard installation or design
requires an in situ calibration.
Orifice Meter
An orifice meter consists of a circular plate having a central hole (orifice). The plate is inserted into a
pipe so as to effect a flow area change. The orifice hole is smaller than the pipe diameter and
arranged to be concentric with the pipe’s i.d. The common square-edged orifice plate is shown in
Figure 10.4. Installation is simplified by housing the orifice plate between two pipe flanges. With
this installation technique any particular orifice plate is interchangeable with others of different b
value. The simplicity of the design allows for a range of b values to be maintained on hand at modest
expense.
For an orifice meter, plate dimensions and use are specified by engineering standards (1, 4).
Equation 10.12 is used with values of A 0 and b based on the orifice (hole) diameter, d 0 . The plate
thickness should be between 0.005 d 1 and 0.02 d 1 , otherwise a taper must be added to the
downstream side (1, 4). The exact placement of pressure taps is crucial to use standard coefficients.
Standard pressure tap locations include (1) flange taps where pressure tap centers are located
25.4 mm (1 in.) upstream and 25.4 mm (1 in.) downstream of the nearest orifice face, (2) d and
d/2 taps located one pipe diameter upstream and one-half diameter downstream of the upstream
orifice face, and (3) vena contracta taps. Nonstandard tap locations always require in situ meter
calibration.
Values for the flow coefficient, K 0 ¼ Re d 1 ; b
ð
Þ and for the expansion factor, Y ¼
f b; k; p 1 À p 2
ð
Þ =p 1
½
for a square-edged orifice plate are given in Figures 10.5 and 10.6 based
on the use of flange taps. The relative instrument systematic uncertainty in the discharge coefficient
(3) is $0.6% of C for 0:2 b 0:6 and b% of C for all b > 0.6. The relative instrument systematic
uncertainty for the expansion factor is about 4ðp 1 À p 2 Þ=p 1
½
% of Y. Realistic estimates of the
overall systematic uncertainty in estimating Q using an orifice meter are between 1% (high b) and
3% (low b) at high Reynolds numbers when using standard tables. Although the orifice plate
represents a relatively inexpensive flow meter solution with an easily measurable pressure drop,
430 Chapter 10 Flow Measurements