fluid - lecture 4
TRANSCRIPT
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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