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Fluid Mechanics

Chapter 8

Internal Incompressible

Viscous Flow

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Main Topics

Flow Measurement

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Flow Measurement

Now we know what Q or V is

But how do we measure them?

Flow meters

Choice of a flow meter? Accuracy

Range

Cost

Ease of reading

Service life

The simplest and cheapest that give the desired

accuracy and range

-

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Direct Methods (amount, not rate)• Collect an amount of fluid in a container over a fixed time

period

• It volume of fluid and time interval are known, Q, V can be calculated

• Compressible flows (or gas flows) are more difficult

• Advantage? No calibration required

• E.g.

Munson et al.

Flow Measurement

Water meter; or nutating disk flowmeter

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Flow Measurement

Direct Methodso Bellow type flow meter or gas meter

Contain bellows that fill and empty alternatively due to pressure of gas and motion of valves

E.g., household gas meters

Munson et al.

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Restriction Flow Meters for Internal Flows• Examples: Orifice Plate; Flow Nozzle; Venturi; Laminar Flow

Element

Flow Measurement

Venturi

Orifice Plate

Flow Nozzle

o Based on acceleration of fluid through an opening.

o Change in velocity results in change in pressure

o ΔP is measured and flowrate inferred theoretically

or empirically

From Bernoulli and continuity

Theoretical and actual flowrates can be obtained

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Flow Measurement

Traversing Methods• Examples: Pitot (or Pitot Static) Tube

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Static

(thermodynamic)

pressure

Stagnation

(total)

pressure

Pitot (total head)

tube

Flow Measurement

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Flow Measurement

Linear Flow Meters• Examples: Float Meter (Rotameter)

Munson et al.

o A float in a tapered tube

o It rises to an equilibrium height

which is a function of flowrate

o At that height, the net force on

float is zero, i.e., buoyancy, float

weight, fluid drag

o Calibration scale on tube gives

flowrate

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Flow Measurement

Linear Flow Meters• Examples: Turbine-type

Munson et al.

o The turbine rotates with an

angular velocity

o This is a function of the average

fluid velocity in the pipe.

o Magnetic sensor picks up the

velocity

o It’s calibrated for flow rate.

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Other Linear Flow Meters• Vortex; Electromagnetic; Magnetic; Ultrasonic

Flow Measurement

Others• Particle image velocimeters, hot-wire and Laser Doppler

Anemometer

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HWA or HFA Constant temperature (preferred)

Constant current

Velocity Measurements

http://www.dantecdynamics.com/Default.aspx?ID=1057

A & B = constants

King’s relation

Calibration required

o The working principle is based on the cooling effect of a flow on a heated body.

Convective heat transfer Q from a wire

placed normal to the flow is a function of

the velocity U.

Directional ambiguity

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LDA – uses Doppler effect Moving particle scatters light at different freq. origin

Velocity Measurements

http://www.dantecdynamics.com/Default.aspx?ID=1046

fD = n/λU(l1-l2)U = particle velocityλ = wavelength of light

sourcen = refractive index of

medium

No calibration required

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Target area is subdivided into smaller areas –interrogation areas

Correlation is applied to obtain particle displacement

A velocity vector is determined for each interrogation area

PIV Principles

http://www.dantecdynamics.com/Default.aspx?ID=820

Velocity Measurements

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http://media.gm.com/content/media/us/en/news/

news_detail.brand_gm.html/content/Pages/news/us/

en/2010/Aug/0804_windtunnel

http://www.seriouswheels.com/2005/2005-Pagani-Zonda-F-

Wind-Tunnel-1600x1200.htm

Flow visualization

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References

Fundamentals of Fluid Mechanics, B.R. Munson, T.H.

Okiishi, W.W. Huebsch, A.P. Rothmayer, 7th ed., Wiley, New

York (2013).

news_detail.brand_gm.html/content/Pages/news/us/en/2010

/Aug/0804_windtunnel

http://www.seriouswheels.com/2005/2005-Pagani-Zonda-F-

http://www.dantecdynamics.com/Default.aspx?ID=820

http://www.dantecdynamics.com/Default.aspx?ID=1046

http://www.dantecdynamics.com/Default.aspx?ID=1057