Week # 2 MR Chapter 2
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Transcript of Week # 2 MR Chapter 2
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Week # 2MR Chapter 2
• Tutorial #2• MR # 2.1, 2.4, 2.8.
• To be discussed on Jan. 25, 2017.
• By either volunteer or class list.
MARTIN RHODES (2008) Introduction to Particle Technology , 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.
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Motion of solid particles in a fluid
For a sphere
Stoke’s law
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Standard drag curve for motion of a sphere in a fluid
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Reynolds number ranges for single particle drag coefficient correlations
At higher relative velocity, the inertia of fluid begins to dominate.
Four regions are identified: Stoke’s law, intermediate, newton’s law, boundary layer separation.
Table 2.1 (Schiller and Naumann (1933) : Accuracy around 7%.
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Single Particle Terminal Velocity
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Special Cases
• Newton’s law region:12( )
1.74 p fT
f
x gU
Intermediate region:
0.71.1 0.29 0.43, , ,T p f fU x
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To calculate UT and x
• (a) To calculate UT, for a given size x,
• (b) To calculate size x, for a given UT,
32
2
( )4Re3
f p fD
x gC
Independent of UT
3 2
( )4Re 3
P fD
P T f
gCU
Independent of size x
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Particles falling under gravity through a fluid
Method for estimating terminal velocity for a given size of particle and vice versa
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Non-spherical particles
Drag coefficient CD versus Reynolds number ReP for particles of sphericity ranging from 0.125 to 1.0
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Effect of boundaries on terminal velocity
Sand particles falling from rest in air (particle density, 2600 kg/m3)
When a particle is falling through a fluid in the presence of a solid boundary the terminalVelocity reached by the particle is less than that for an infinite fluid.
Following Francis (1933), wall factor ( )/w Df U U
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Limiting particle size for Stoke’s law in water
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Limiting particle size for Stoke’s law in air
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850
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• Where the plotted line intersects the standard drag curve for a sphere ( = 1), Rep = 130.
• The diameter can be calculated from:
Re 130 f v TP
x U
Hence sphere diameter, xv = 619 m.
• For a cube having the same terminal velocity under the same conditions, the same CD vesus Rep relationship applies, only the standard drag curve is that for a cube( = 0.806)
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