Flow Measurement

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Flow Measurement
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Venturi Meter
In the venturi meter velocity is increased and
the pressure decreased in the upstream cone. The
pressure drop from points F to I can be used to
measure the rate of flow through the meter.
Venturi meters are most commonly used for
liquids, especially water.
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Ventrui meter
Mass Balance
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Venturi Meter
Mechanical Energy Balance
0
0
0
So with Mass Balance Result
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Venturi Meter
Solving for the neck velocity Vb
To account for small differences in aa and ab
introduce a correction factor Cv 0.98 0.99.
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Venturi Meter
Since friction cannot be eliminated in the
venturi meter a permanent loss in pressure
occurs. Because of the small angle of divergence
in the recovery cone, the permanent pressure loss
is relatively small (about 10 of the venturi
differential papb).
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Orifice Meter
The orifice meter consists of an accurately
machined and drilled plate concentrically mounted
between two flanges. The position of the
pressure taps is somewhat arbitrary.
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Orifice Meter
The orifice meter has several practical
advantages when compared to venturi meters.

• Lower cost
• Smaller physical size
• Flexibility to change throat to pipe diameter
  ratio to measure a larger range of flow rates

• Disadvantage
• Large power consumption in the form of
  irrecoverable pressure loss

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Orifice Meter
The development of the orifice meter equation is
similar to that of the venturi meter and gives

• where
• ratio of orifice diameter to pipe diameter
  0.5 usually
• S0 cross sectional area of orifice
• V bulk velocity through the orifice
• C0 orifice coefficient 0.61 for Re gt 30,000

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There is a large pressure drop much of which is
not recoverable. This can be a severe limitation
when considering use of an orifice meter.
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Pressure Loss inOrifice Meters
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Comparison
Venturi Orifice
High Capital Cost Low Capital Cost
Low Operating Cost(good ?p recovery) High Operating Cost (poor ?p recovery)
Not Flexible (ß fixed) More Flexibility (interchangeable)
Large Physical Size Compact
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Rotameters
Rotameters fall into the category of flow
measurement devices called variable area meters.
These devices have nearly constant pressure and
depend on changing cross sectional area to
indicate flow rate. Rotameters are extremely
simple, robust devices that can measure flow
rates of both liquids and gasses.
Fluid flows up through the tapered tube and
suspends a float in the column of fluid. The
position of the float indicates the flow rate on
a marked scale.
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Rotameters
Three types of forces must be accounted for when
analyzing rotameter performance
Buoyancy

• Flow
• Gravity
• Buoyancy

Gravity
For our analysis neglect drag effect
Flow
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Rotameter
Mass Balance Assume Gradual Taper
Flow Between Float and Tube
S3 is annular flow area at plane 3
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Rotameter

• Momentum Balance
• Note
• p3 p2
• Must account for force due to float

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Rotameter
Mechanical Energy Balance
0
(Base velocity head on smallest flow area)
Assume
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Rotameter
Combining Momentum and Mechanical Energy Balance
After Some Manipulation
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Rotameter
Assuming Sf S a discharge coefficient can be
defined
CR must be determined experimentally. As Q
increases the float rides higher, the assumption
that Sf S is poorer, and the previous
expression is more nearly correct.
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Other Flow Meters
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Turbine Meter
Measure by determining RPM of turbine (3) via
sensor (6). Turbine meters accurate but fragile.
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Coriolis Meters
When fluid is passed through a U-bend, it imposes
a force on the tube wall perpendicular to the
flow direction (Coriolis force). The deformation
of the U-tube is proportional to the flow rate.
Coriolis meters are expensive but highly accurate.