E1C10 09/14/2010
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ultrasonic transducer is mounted to the outside of a pipe wall. A wave of frequency f on the order of
100 kHz to 1 MHz is emitted. The emitted wave is bounced back by particles suspended in the
moving fluid, and this scattered wave is detected by the transducer. The scattered waves travel at a
slightly different frequency, the difference being the Doppler frequency f D . The flow rate is
Q ¼ UA ¼
pd
2
1 af D
8f cos u
¼ K 1 f D
ð10:29Þ
These devices can measure time-dependent flow rates. Instrument systematic uncertainty is $2%
(95%) of the flow rate.
Positive Displacement Meters
Positive displacement meters contain mechanical elements that define a known volume filled with
the fluid being metered. The free-moving elements are displaced or rotated by the action of the
moving fluid. A geared counting mechanism counts the number of element displacements to provide
a direct reading of the volume of fluid passed through the meter, 8. This metering method is common
to water, gasoline, and natural gas meters.
To be used as volume flow rate meters, volume measurement can be used in conjunction with a
timer, so that
Q ¼ 8=t
ð10:30Þ
These units serve applications needing ruggedness and accuracy in steady flow metering. Common
applications are metering related to domestic water and natural gas consumption.
Diaphragm meters contain two opposing flexible bellows coupled by linkages to exhaust valves
that alternately displace a known volume of fluid through the meter. Through the coupled linkage,
the flow of fluid through one bellows drives the motion of the opposite bellows. Thus, as entering gas
causes one bellows to expand within its chamber sealed by a closed valve, the gas in the opposite
bellows exhausts through an open valve to allow its bellows to collapse; this alternating motion
cycles the gears of its counter register (output display). Such ‘‘dry gas’’ meters are common to
natural gas or propane lines for volume measurement. Thomas Glover invented the first diaphragm
meter in 1843, and modern meters retain the major elements of his design.
Wobble meters contain a disk that is seated in a chamber. The flow of liquid through the
chamber causes the disk to oscillate so that a known volume of fluid moves through the chamber
with each oscillation. The disk is connected to a counter that records each oscillation as volume is
displaced. Wobble meters are used for domestic water applications, where they must have an
uncertainty of no greater than 1% of actual delivery.
Frequently found on oil trucks and at the gasoline pump, rotating vane meters use rotating cups
or vanes that move about an annular opening, displacing a known volume with each rotation.
With any of these meters, uncertainty can be as low as 0.2% (95%) of actual delivery. Because
of the good accuracy of these meters, they are often used as local working standards to calibrate
other types of volume flow meters.
10.7 MASS FLOW METERS
There are many situations in which the mass flow rate is the quantity of interest. Mass flow rate
demands measuring the mass flux per unit volume, rU , to yield _
m ¼ rUA.
454 Chapter 10 Flow Measurements
13:4:40 Page 454
ultrasonic transducer is mounted to the outside of a pipe wall. A wave of frequency f on the order of
100 kHz to 1 MHz is emitted. The emitted wave is bounced back by particles suspended in the
moving fluid, and this scattered wave is detected by the transducer. The scattered waves travel at a
slightly different frequency, the difference being the Doppler frequency f D . The flow rate is
Q ¼ UA ¼
pd
2
1 af D
8f cos u
¼ K 1 f D
ð10:29Þ
These devices can measure time-dependent flow rates. Instrument systematic uncertainty is $2%
(95%) of the flow rate.
Positive Displacement Meters
Positive displacement meters contain mechanical elements that define a known volume filled with
the fluid being metered. The free-moving elements are displaced or rotated by the action of the
moving fluid. A geared counting mechanism counts the number of element displacements to provide
a direct reading of the volume of fluid passed through the meter, 8. This metering method is common
to water, gasoline, and natural gas meters.
To be used as volume flow rate meters, volume measurement can be used in conjunction with a
timer, so that
Q ¼ 8=t
ð10:30Þ
These units serve applications needing ruggedness and accuracy in steady flow metering. Common
applications are metering related to domestic water and natural gas consumption.
Diaphragm meters contain two opposing flexible bellows coupled by linkages to exhaust valves
that alternately displace a known volume of fluid through the meter. Through the coupled linkage,
the flow of fluid through one bellows drives the motion of the opposite bellows. Thus, as entering gas
causes one bellows to expand within its chamber sealed by a closed valve, the gas in the opposite
bellows exhausts through an open valve to allow its bellows to collapse; this alternating motion
cycles the gears of its counter register (output display). Such ‘‘dry gas’’ meters are common to
natural gas or propane lines for volume measurement. Thomas Glover invented the first diaphragm
meter in 1843, and modern meters retain the major elements of his design.
Wobble meters contain a disk that is seated in a chamber. The flow of liquid through the
chamber causes the disk to oscillate so that a known volume of fluid moves through the chamber
with each oscillation. The disk is connected to a counter that records each oscillation as volume is
displaced. Wobble meters are used for domestic water applications, where they must have an
uncertainty of no greater than 1% of actual delivery.
Frequently found on oil trucks and at the gasoline pump, rotating vane meters use rotating cups
or vanes that move about an annular opening, displacing a known volume with each rotation.
With any of these meters, uncertainty can be as low as 0.2% (95%) of actual delivery. Because
of the good accuracy of these meters, they are often used as local working standards to calibrate
other types of volume flow meters.
10.7 MASS FLOW METERS
There are many situations in which the mass flow rate is the quantity of interest. Mass flow rate
demands measuring the mass flux per unit volume, rU , to yield _
m ¼ rUA.
454 Chapter 10 Flow Measurements