CENTRE OF MASS
5. In the above problem, the velocity of cen-
tre of mass of the system is
a) 14.2 ms
b) 15 ms
c) 18.5 ms
d) 16.7 ms
Answers
Answer:
The separability of minerals by gravity separation relies on a particle's settling rate in a
fluid. The terminal velocity of solid spheres settling in a fluid is described by Stokes' Law for
fine particles (Eq. (15.3)) or Newton's Law for coarse particles (Eq. (15.4)). Both these
equations include particle density as well as particle size.
vT = B^-2—tiLi— for viscous resistance (Stokes'Law) (15.3)
1 oji
vT = I B'-Ps pF^ for turbulent resistance (Newton's Law) (15.4)
V
3CD PF
where d = particle diameter,
ps, PF = density of solid and fluid respectively,
CD = the drag coefficient,
|a = fluid viscosity and
g = gravitational acceleration.
Stokes' equation is said to apply to conditions where the particle Reynolds number is less
than 1 and Newton's equation applies for Reynolds numbers > 1000. For particles of quartz
in water, this represents an upper size limit of around 110 um for Stokes' Law and a lower
limit of around 3.5 mm for Newton's Law. Thus for particles of quartz between 110 microns
and 3.5 mm neither equation accurately describes the settling rate of objects and this size
range represents a major size range of interest in gravity separation. A number of researchers
have developed empirical correlations to fill this size gap. Dietrich [3] derived a correlation
from a data set of 252 values using dimensionless parameters, W and D , and incorporating
shape and angularity factors:
W* = .
V T P F (15.5)
(pp) ^
and
D* = (PSPFMNP F (156 )
H
where dN = nominal diameter of the largest projected area. An irregular particle will
settle in a stable orientation when the largest projected area is perpendicular
to the settling direction.
Dietrich's dimensionless parameters are related by the expression:
W* = R310R
'
+R2
