fluid - lecture 4

8/6/2019 Fluid - Lecture 4

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THERMO-FLUID

MECHANICS 1MIET 2095

Fluid Lecture 4 Flow Measurement


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Reminder

Lab Reports due date in Week 10 (10% of totalmark)

Test and Assignment Results are now on-line


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This Lecture

Examples of application ofBernoullis Equation

And, where appropriate, in conjunction withthe Mass Conservation Equation


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Your Learning Objectives

To be able to use Bernoullis Equation and

the Mass Conservation Equation to deriveequations for some common flow and velocitymeasuring devices

To be familiar with some of the issues

relating to correct or appropriate use of someflow and velocity measuring devices


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Note that :-

Most of the relationships of interest arederived in class

Where appropriate, reference is made tocorresponding sections of Cengel and Turner(3rd Edition)

The Flow Measurement Lab Sheet is a good

source of reference


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Bernoulli Equation

p/ + v2/2 + g*z = constant

p/(*g) + v2

/(2*g) + z = constant

p + * v2/2 + *g*z = constant

Refer to Ch. 12 starting from Section 12-2


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Conditions for Bernoullis

Equation

The equation applies to

Incompressible Inviscid

steady flow along a streamline


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Viscous Effect (Flow Separation)

http://www.youtube.com/watch?v=pHCTM2QOqT4


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When the flow is irrotational, the Bernoulli equation becomes applicablebetween any two points along the flow (not just on the same streamline).

Frictional effects and components that disturb thestreamlined structure of flow in a flow sectionmake the Bernoulli equation invalid. It should notbe used in any of the flows shown here.


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Air flowing horizontally from alarge reservoir into a pipe

through a bell mouth entry

What is the relationship between flow rateand pressure difference across the entry ?


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Use Bernoulli Equation

p1/ + v12/2 + g*z1 = p2/ + v2

2/2 + g*z2 Now z1 = z2 and v1=0 (in big tank), so

p1/ = p2/ + v22

/2 Therefore v2 = [2*(p1 - p2)/]

1/2

And Q =Q2= v2*A2 = A2*[2*(p1 - p2)/]1/2


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Liquid flowing out of a large tankthrough an orifice

What is the relationship between flow rateand head drop, assuming no friction losses ?

Refer to Example 12-3


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Example: Spraying

Water into the Air


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Applications Airfoil (Wing)


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Applications - Sailing


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Applications - Spray


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Industrial Problem CavitationsCavitations can cause serious damage

http://www.youtube.com/watch?v=GpklBS3s7iU


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Applications Velocity probe

(pitot-static probe in air)

How does the air velocity relate to thepressure drop ?

Refer to Figure 12-13 and example 12-4


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Close-up of a Pitot-static probe, showing

the stagnation pressure hole and two of

the five static circumferential pressure

holes.

Static Pitot-static Probe

Streaklines produced by colored fluid introduced

upstream of an airfoil; since the flow is steady, the

streaklines are the same as streamlines and

pathlines.


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The sum of the static and dynamic pressures is called the stagnation

pressure. It represents the pressure at a point where the fluid is broughtto a complete stop isentropically.

Stagnation Pressure

The static, dynamic,

and stagnation

pressures.


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Accuracy of Pitot-Static Probe

The shape of the probe is very precise anddesigned to avoid losses. Consequently aproperly made and calibrated pitot static

probe is regarded as providing accuratevelocity information.

(Hence it was used as a reference in your

experiment)


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Velocity probe in air withvertical water manometer

Relationship between velocity andmanometer reading ?

DP = airv2/2 = waterghvert

Therefore v = {2ghvert water/air}1/2


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Velocity probe in air withsloping water manometer

Relationship between velocity and slopingmanometer reading ?

hvert

= L*sinq

q

hvert

P2P1


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Venturi meter

Relationship between inlet area, throat area,pressure drop and flow rate ?


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Venturi meter

From Bernoulli p1-p2 = 1/2(v22 - v12) = 1/2v22 (1 - v12/ v22) But v2A2 = v1A1, So v1/v2 = A2/A1 Therefore p1-p2= 1/2v2

2 (1 - A22/ A1

2)= 1/2v22 (1 - b4), where b=

d/D

So v2= {2*(p1-p2) //(1 - b4

)}1/2

, and since Q= v2 A2 Qideal= A2{2*(p1-p2) //(1 - b

4)}1/2

Qactual= CdA2{2*(p1-p2) //(1 - b4)}1/2. Cd, the discharge

coefficient, accounts for pressure losses due to friction and othernon-ideal flow effects. Cd, varies between 0.95 and 0.99 for

venturi meters.

p1 p2


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Coefficient of Discharge

Correction to ideal flow rate, to allow forpressure losses arising from viscous effects

(Used in your laboratory experiment both forthe orifice plate and the venturi meter)


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Orifice meter

Similar treatment to Venturi meter, however, Cd is smaller (mayvary between 0.5 to 0.7) with orifice meter because of biggerpressure losses.

The orifice and venturi meters are examples of obstruction flow

meters.

p1 p2


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Orifice meter losses


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Other Flow measurementtechniques

Positive Displacement Flowmeters

Turbine Flowmeters

Variable-Area Flowmeters (Rotameters)

Ultrasonic (transit time and Doppler-effect)flowmeters

Electromagnetic Flowmeters (measuresion accumulation in magnetic field)

Vortex Flowmeters.


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Other Flow measurementtechniques

Thermal (Hot-Wire and Hot-Film)Anemometers

Laser Doppler Velocimetry

Particle Image Velocimetry (See nextslides for authors research)

PIV SETUP


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PIV SETUP

UBCRICM


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t1


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t2


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Doppler Effect

When the source of the waves is moving toward the observer,each successive wave crest is emitted from a position closer tothe observer than the previous wave; causing an increase in thefrequency

While they are travelling, the distance between successive

wavefronts is reduced; so the waves "bunch together" ; reducingthe frequency.


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Other Flow Field PropertyMeasurements

There exists a plethora of sophisticatedoptical techniques that can be used to

measure other flow field properties suchas temperature and density.

E.g., PLIF-Planar laser InducedFluorescence

Laser absorption spectroscopy


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Read and Study

Chapter 12

Problems 12.12C, 12.23C, 12.24, 12.26,

12.30 Examples 12.3, 12.4

It would then be a good learning exerciseto close the books and derive the answersto the worked examples for yourself


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Next Week

Fluid momentum and forces

Steady flow Momentum Equation

Steady Flow Angular Momentum Equation

fluid - lecture 4

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