1 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.
2 Motion of solid particles in a fluid For a sphereStoke’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 layerseparation.Table 2.1 (Schiller and Naumann (1933) : Accuracy around 7%.
6 Special CasesNewton’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 UTIndependent 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 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 terminalVelocity 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)
25 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 thesame conditions, the same CD vesus Rep relationshipapplies, only the standard drag curve is that for a cube(y = 0.806)