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