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Week # 2 MR Chapter 2

This tutorial discusses Stoke's law and the motion of solid particles in a fluid. It covers the standard drag curve for a sphere, Reynolds number ranges, and correlations for drag coefficients. The effects of boundaries, non-spherical particles, and terminal velocity estimation are also explored.

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Week # 2 MR Chapter 2

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  1. Tutorial #2 MR # 2.1, 2.4, 2.8. To be discussed on Jan. 29, 2020. By either volunteer or class list. Week # 2MR Chapter 2 MARTIN RHODES (2008) Introduction to Particle Technology , 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.

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

  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 UT and x • (a) To calculate UT, for a given size x, • (b) To calculate size x, for a given UT, Independent of UT 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 CD versus Reynolds number ReP for particles of sphericity ranging from 0.125 to 1.0

  10. Effect of boundaries on terminal velocity 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 ( ) Sand particles falling from rest in air (particle density, 2600 kg/m3)

  11. Limiting particle size for Stoke’s law in water

  12. Limiting particle size for Stoke’s law in air

  13. 850

  14. Where the plotted line intersects the standard drag curve for a sphere (y = 1), Rep = 130. • The diameter can be calculated from: Hence sphere diameter, xv = 619 mm. • 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)

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