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Week # 2
MR Chapter 2
• Tutorial #2
• MR # 2.1, 2.4, 2.8.
• To be discussed on Jan. 27, 2021.
• 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:
1
2( )1.74
p f
T
f
x gU
Intermediate region:
0.7
1.1 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,
3
2
2
( )4Re
3
f p f
D
x gC
Independent of UT
3 2
( )4
Re 3
P fD
P T f
gC
U
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 terminal
Velocity 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 (y = 1), Rep = 130.
• The diameter can be calculated from:
Re 130f v T
P
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
(y = 0.806)
