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.

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

Standard drag curve for motion of a sphere in a fluid

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%.

Single Particle Terminal Velocity

Special Cases Newton’s law region: Intermediate region:

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

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

Non-spherical particles Drag coefficient CD versus Reynolds number ReP for particles of sphericity ranging from 0.125 to 1.0

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)

Limiting particle size for Stoke’s law in water

Limiting particle size for Stoke’s law in air

850

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)