Flow Measurement
Dec 21, 2015
Flow Measurement
Flow Measurement
• Positive Displacement• Flow Obstruction• Drag Effects• Hot Wire Anemometers• Magnetic Effects• Doppler Effects• Interference Effects• Pressure Probes
Positive Displacement
Bucket & Stopwatch Methods
•Buckets for low flows•Tanks of known dimensions•Can measure either volume or weight
Accuracy limited by time and volume or weight measurements
Positive Displacement
• Fluid is captured in fixed “pockets”• Fluid flow moves pockets from inlet to outlet• Count pocket movements per unit time• Compute flow from known pocket volume
Best for incompressible fluids (i.e. liquids)
Can be used for gases if know pressure and composition
Positive Displacement
Obstruction Methods
1 2
Based on Bernoulli’s equation:
c
22
2
2
c
21
1
1
g2uP
g2uP
ρρEnergy Considerations:
Mass Flow Considerations: 222111 uAuA
Obstruction Methods
If the flow is incompressible and very little temperature change, then:
212
1
2
2 (2
)(1
1PP
g
AA
u c
22 uAQ
Obstruction Methods
Unfortunately, can’t meet the rigorous conditions for the theory to be absolutely true, so modify with an empirical coefficient:
Pg
CQ cm
2
Note: if always running same fluid at about the same conditions, then write as
PCQ m '
Obstruction Methods
Drag Effects
Fluid flowing past a body exerts a drag on the object. The body resists this force through gravitational, friction, and other forces.
• Rotameter: Discussed in experiment 2
• Turbine Flow Meter
• Vortex Shedding Flow Meter
Drag Effects
• Like a fan running in reverse
• Flow turns blades
• Count revolutions
• Calibrate flow vs rotational speed
Accurate, with modest pressure drop
Turbine Flow Meter
Drag Effects
Vortex Shedding Meter
•Turbulent flow conditions
•Vortices (circular flow patterns) are shed from downstream edge of body in the flow stream.
•Pressure sensor in body can sense departure of vortex.
•Frequency of vortex departure related to flow velocity
•Require special installation and care
Hot Wire Anemometers
As fluid flows past a hot object, extracts heat according to:
)()( 5.0bw TTubaq
velocityflowu
etemperaturwireTw
etemperaturfluidbulkTb
Hot Wire Anemometers
But the amount of heat delivered to the wire is related to the resistance of the wire, and the applied current:
)(1 0022 TTRiRiq ww
00 TetemperaturatresistancewireR
resistanceoftcoefficienetemperaturα
resistancewireR w
Hot Wire Anemometers
• Accurately measure i and Rw
• Compute q and Tw
• Compute u
Can be used in liquids and gases
Very fast response times, so can measure fluctuating flows
Magnetic Flow Meters
When a conductor moves through a magnetic field, an electric potential is induced in the conductor:
Use magnet to supply field
Measure induced potential
Calibrate to flow
Magnetic Flow Meters
Non-intrusive, so don’t disrupt flow
Minimal pressure drop
Fluid must be conductive
Relatively expensive
Doppler Effects
Wave reflected off moving particle undergoes a frequency shift (Doppler effect)
Ultrasonic probes use ultrasound
Laser Doppler Anemometer uses light
(Same principle as police radar)
Doppler Effects
• Meters fairly simple
• Need good contact with pipe
• Need fluid with particles (Actually measure particle velocity)
• Can be made in “clamp on” form, so portable
Ultrasonic meters
Doppler Effects
Laser Doppler Anemometers
Requires particles in fluid
Velocity determination requires sophisticated signal processing
Can detect velocity in very small volume, so good for turbulent flow measures
Interference Effects
Changing flow fields result in pressure changes which give rise to density changes.
The index of refraction is a function of density.
Can use this change in index of refraction to build a picture of the density, and, hence, an estimate of the velocity.
Interference Effects
The Shadowgraph
Light shining through the flow field will be bent in regions of differing density.
On leaving the flow field, some areas will have more light than others and get light and dark areas.
This is the phenomenon that is observed when you see the wavy patterns rising from a hot surface such as a road. You are seeing the density differences.
Interference Effects
Schlieren effect & Interferometers
Use lenses to send a beam through the sample.
Use sharp edge (shlieren) or split beam (interferometer) to generate interference pattern.
Produces a visual representation of the flow, but no numbers.
Interference Effects
Pressure Probes
Measure static pressure
Measure Stagnation Pressure
Compute flow from Bernoulli’s equation
2
2
0
upps
pressurestagnationps
pressurestaticp 0
Pressure Probes