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Week # 2 MR Chapter 2 Tutorial #2 MR # 2.1, 2.4, 2.8. To be discussed on Jan. 28, 2015. By either volunteer or class list. MARTIN RHODES (2008) Introduction.

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Presentation on theme: "Week # 2 MR Chapter 2 Tutorial #2 MR # 2.1, 2.4, 2.8. To be discussed on Jan. 28, 2015. By either volunteer or class list. MARTIN RHODES (2008) Introduction."— Presentation transcript:

1 Week # 2 MR Chapter 2 Tutorial #2 MR # 2.1, 2.4, 2.8. To be discussed on Jan. 28, 2015. By either volunteer or class list. MARTIN RHODES (2008) Introduction to Particle Technology, 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.

2 Motion of solid particles in a fluid For a sphere Stoke’s law

3 Standard drag curve for motion of a sphere in a fluid

4 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%.

5 Single Particle Terminal Velocity

6 Special Cases Newton’s law region: Intermediate region:

7 To calculate U T and x (a) To calculate U T, for a given size x, (b) To calculate size x, for a given U T, Independent of U T Independent of size x

8 Particles falling under gravity through a fluid Method for estimating terminal velocity for a given size of particle and vice versa

9 Non-spherical particles Drag coefficient C D versus Reynolds number Re P for particles of sphericity ranging from 0.125 to 1.0

10 Effect of boundaries on terminal velocity Sand particles falling from rest in air (particle density, 2600 kg/m 3 ) 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 ( )

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12 Limiting particle size for Stoke’s law in water

13 Limiting particle size for Stoke’s law in air

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25 Where the plotted line intersects the standard drag curve for a sphere (  = 1), Re p = 130. The diameter can be calculated from: Hence sphere diameter, x v = 619  m. For a cube having the same terminal velocity under the same conditions, the same C D vesus Re p relationship applies, only the standard drag curve is that for a cube (  = 0.806)

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