ME411 Engineering Measurement & Instrumentation•McLeod gauge •Trapped gas in capillary (isothermal compression) •Capillary force, Boyle’s law and gh of Hg •Barometer •Inverted

ME411Engineering Measurement

& Instrumentation

Winter 2017 – Lecture 10

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Basic concepts

• By definition, P = F/A and is isotropic

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Hydrostatic pressure

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Pressure reference instruments

• McLeod gauge• Trapped gas in capillary (isothermal

compression)• Capillary force, Boyle’s law and gh of

Hg

• Barometer• Inverted tube in a bath of fluid used to

measure atmosphere• Rise of fluid (usually Hg low vapor

pressure) gives the pressure• Needs to be corrected for temperature

effects

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Pressure reference instruments

• Manometer• Height difference gh gives difference in pressure, P

• Inclined manometer• Low pressure application

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Known!

Less relative error

These techniques suited to static (or slowly varying) measurements and not necessarily easily integrated into a system

Pressure transducers

• Actually a sensor & transducer

• Elastic element deforms or deflects under pressure (sensor)

• Secondary element converts elastic deflection to an observable signal (transducer) voltage, mechanical rotation of a pointer etc

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Bourdon Tube

• Mechanical dial gauge

• Deflection of tube due to different internal and external pressures

• Measurements from 104 to 109 Pa with error generally 0.5 – 2%

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Diaphragm

• Sensing element: Thin, elastic, circular plate supported along its circumference pressure difference across membrane causes a deflection

• Membranes can be metal, non-metal, plastic, neoprene etcmaterial selection determined by pressure range and fluid it is contact with

• Have good linearity and resolution• Can be designed to have low mass & stiffness gives a

wide frequency response, high natural frequency, small damping ratio and short rise/settling times

• Well suited for both static and transient measurements!

• Need to add a 2nd element to translate the deflection into a usable signal (transducer)

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Diaphragm

• Transducer options:• Strain gauge resistance

depends on applied strain

• Capacitance fixed metal plate forms a capacitor. Capacitance varies with deflection and can be measured through a change in voltage

• Piezoelectric deformation of a piezoelectric crystal induces a surface charge which can be measured

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Pressure calibration

• Static calibration comparison with reference pressure measurement techniques (gh, dead weight tester etc)

• Dynamic calibration rise time determined from step change in P (shock tube)

• Frequency response found from period pressure input (eg. reciprocating piston cylinder)

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Pressure measurement in moving Fluids

• 2 contributions static pressure and dynamic pressure (ie. additional pressure due to fluid flow)

• We can measure the static pressure with pressure taps to flow

• We can measure total pressure by inserting a tube and stopping the flow (Pitot tube)

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Pitot tube

• If we connect the static pressure and total pressure tubes together, we form the basis of a Pitot static tube (Prandtl tube) way to measure velocity!

• From Bernoulli, we know that dynamic pressure is:

12

2

1

2

1

1

2

and 2

2

D

T D S S

T S

UP

UP P P P

P PU

So a Pitot-static tube provides a pointwise means to measure velocity

Velocity Measurement Techniques

• Two broad types:• Local (pointwise) velocity profiles

• Global flow rate vs P physics can be inferred

• Pointwise velocity measurements:• Pitot-static tube

• Thermal anemometry

• Doppler anemometry

• Global velocity measurements• PIV

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Pointwise measurements can be determined at multiple locations to create a velocity field but this is rather tedious particularly if you want well a well resolved velocity field

Velocity Measurement Techniques

Thermal anemometry

• Basic principle measure heat transfer out of a fin

• Two types hot wire and hot film

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Velocity Measurement Techniques

Doppler anemometry

• Basic principle Doppler effect think radar gun for speed checking

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Velocity Measurement Techniques

Particle image velocimetry

• Expensive, technically advanced

• But full-field, essentially instantaneous

• Only suitable for systems that have “optical access” and particles to scatter the light!

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Things to consider

• Spatial resolution

• Velocity range

• Sensitivity (K)

• Dynamic velocity or static?

• Probe access (blockage, optical access etc)

• Operating environment (hostile, flammable?)

• Calibration

• Cost

• Ease of use

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Image credits

• All images from Figliola and Beasley, Mechanical Measurements 5th edition unless otherwise stated

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