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**Week # 2 MR Chapter 2 Tutorial #2**

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.

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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: Intermediate region:

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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, Independent of UT 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 to 1.0

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**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)

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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: 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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1 Lecture #5 of 25 Moment of inertia Retarding forces Stokes Law (viscous drag) Newton’s Law (inertial drag) Reynolds number Plausibility of Stokes law.

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