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 Based on Bernoulli’s equation: 1 2 Energy Considerations: Mass Flow Considerations:

Obstruction Methods If the flow is incompressible and very little temperature change, then:

Obstruction Methods Unfortunately, can’t meet the rigorous conditions for the theory to be absolutely true, so modify with an empirical coefficient: Note: if always running same fluid at about the same conditions, then write as

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 Turbine Flow Meter Like a fan running in reverse Flow turns blades Count revolutions Calibrate flow vs rotational speed Accurate, with modest pressure drop

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:

Hot Wire Anemometers But the amount of heat delivered to the wire is related to the resistance of the wire, and the applied current:

Accurately measure i and Rw Compute q and Tw Compute u 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 Ultrasonic meters 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

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

Pressure Probes