E1C10 09/14/2010
13:4:41 Page 459
The tangential and centripetal accelerations remain of minor consequence due to the tube
stiffness in the directions in which they act. However, at high mass flow rates they can excite modes
of vibration in addition to the driving mode, v, and response mode, v c . In doing so, they affect the
meter linearity and zero error (drift), which affects mass flow uncertainty and meter turndown.
Essentially, the magnitude of these undesirable effects is inherent to the particular meter shape and is
controlled, if necessary, through tube-stiffening members.
Another interesting problem occurs mostly in meters of small tube diameter where the tube
mass may approach the mass of the fluid in the tube. At flow rates that correspond to flow transition
from a laminar to turbulent regime, the driving frequency can excite the flow instabilities
responsible for the flow transition. The fluid and tube can go out of phase, reducing the response
amplitude and its corresponding torque. This affects the meter’s calibration linearity, but a good
design can contain this effect to within 0.5% of the meter reading.
The meter principle is unaffected by changing fluid properties, but temperature changes affect
the overall meter stiffness, an effect that can be compensated for electronically. A very desirable
feature is an apparent insensitivity to installation position. Commercially available Coriolis flow
meters can measure flow rate with an instrument systematic uncertainty to 0.25% (95%) of mass
flow rate, but 0.10% is achievable. Turndown is about 20:1. The meter is also used as an effective
densitometer.
10.8 FLOW METER CALIBRATION AND STANDARDS
While a fundamental primary standard for flow rate does not exist per se, there are a number of
calibration test code procedures in place, and government and private bureaus that perform
calibrations. The general procedure for the calibration of in-line flow meters requires establishing
a steady flow in a calibration flow loop and then determining the volume or mass of flowing fluid
passing through the flow meter in an accurately determined time interval. Such flow loop calibration
systems are known as provers. Often calibration is by comparison to a meter of proven accuracy.
Several methods to establish the flow rate are discussed.
In liquids, variations of a ‘‘catch-and-weigh’’ technique are often employed in flow provers.
One variation of the technique consists of a calibration loop with a catch tank as depicted in
Figure 10.25. Tank A is a large tank from which fluid is pumped back to a constant head reservoir,
which supplies the loop with a steady flow. Tank B is the catch-and-weigh tank into which liquid can
be diverted for an accurately determined period of time. The liquid volume is measured, either
directly using a positive displacement meter, or indirectly through its weight, and the flow rate
deduced through time. The ability to determine the volume and the uncertainty in the initial and final
time of the event are fundamental limitations to the accuracy of this technique. Neglecting
installation effects, the ultimate limits of uncertainty (at 95%) in the flow rate of liquids are on
the order of 0.03%, a number based on u meter $ 0:02%; u 8 $ 0:02%; and u t $ 0:01%.
Flow meter calibration by determining the pipe velocity profile is particularly effective for
in situ calibration in both liquids and gases, provided that the gas velocity does not exceed about
70% of the sonic velocity. Velocity traverses at any cross-sectional location some 20 to 40 pipe
diameters downstream of any pipe fitting in a long section of straight pipe are preferred.
Comparison calibration against a local standard flow meter is another common means of
establishing the flow rate through a prover. Flow meters are installed in tandem with the standard and
directly calibrated against it. Turbine and vortex meters and Coriolis mass flow meters have
consistent, highly accurate calibration curves and are often used as local standards. Other provers
10.8 Flow Meter Calibration and Standards 459
13:4:41 Page 459
The tangential and centripetal accelerations remain of minor consequence due to the tube
stiffness in the directions in which they act. However, at high mass flow rates they can excite modes
of vibration in addition to the driving mode, v, and response mode, v c . In doing so, they affect the
meter linearity and zero error (drift), which affects mass flow uncertainty and meter turndown.
Essentially, the magnitude of these undesirable effects is inherent to the particular meter shape and is
controlled, if necessary, through tube-stiffening members.
Another interesting problem occurs mostly in meters of small tube diameter where the tube
mass may approach the mass of the fluid in the tube. At flow rates that correspond to flow transition
from a laminar to turbulent regime, the driving frequency can excite the flow instabilities
responsible for the flow transition. The fluid and tube can go out of phase, reducing the response
amplitude and its corresponding torque. This affects the meter’s calibration linearity, but a good
design can contain this effect to within 0.5% of the meter reading.
The meter principle is unaffected by changing fluid properties, but temperature changes affect
the overall meter stiffness, an effect that can be compensated for electronically. A very desirable
feature is an apparent insensitivity to installation position. Commercially available Coriolis flow
meters can measure flow rate with an instrument systematic uncertainty to 0.25% (95%) of mass
flow rate, but 0.10% is achievable. Turndown is about 20:1. The meter is also used as an effective
densitometer.
10.8 FLOW METER CALIBRATION AND STANDARDS
While a fundamental primary standard for flow rate does not exist per se, there are a number of
calibration test code procedures in place, and government and private bureaus that perform
calibrations. The general procedure for the calibration of in-line flow meters requires establishing
a steady flow in a calibration flow loop and then determining the volume or mass of flowing fluid
passing through the flow meter in an accurately determined time interval. Such flow loop calibration
systems are known as provers. Often calibration is by comparison to a meter of proven accuracy.
Several methods to establish the flow rate are discussed.
In liquids, variations of a ‘‘catch-and-weigh’’ technique are often employed in flow provers.
One variation of the technique consists of a calibration loop with a catch tank as depicted in
Figure 10.25. Tank A is a large tank from which fluid is pumped back to a constant head reservoir,
which supplies the loop with a steady flow. Tank B is the catch-and-weigh tank into which liquid can
be diverted for an accurately determined period of time. The liquid volume is measured, either
directly using a positive displacement meter, or indirectly through its weight, and the flow rate
deduced through time. The ability to determine the volume and the uncertainty in the initial and final
time of the event are fundamental limitations to the accuracy of this technique. Neglecting
installation effects, the ultimate limits of uncertainty (at 95%) in the flow rate of liquids are on
the order of 0.03%, a number based on u meter $ 0:02%; u 8 $ 0:02%; and u t $ 0:01%.
Flow meter calibration by determining the pipe velocity profile is particularly effective for
in situ calibration in both liquids and gases, provided that the gas velocity does not exceed about
70% of the sonic velocity. Velocity traverses at any cross-sectional location some 20 to 40 pipe
diameters downstream of any pipe fitting in a long section of straight pipe are preferred.
Comparison calibration against a local standard flow meter is another common means of
establishing the flow rate through a prover. Flow meters are installed in tandem with the standard and
directly calibrated against it. Turbine and vortex meters and Coriolis mass flow meters have
consistent, highly accurate calibration curves and are often used as local standards. Other provers
10.8 Flow Meter Calibration and Standards 459