Chemical Engineering - Mechanical Operations - Discussion

For a cylinder with L=D,,volume= π*r2*h,we get volume=2*π*r3.
The surface area of a sphere S.A.=4*π*r2.
S.A.of cylinder=2* π*r(h+r)=6*π*r2
Sphericity= S.A of the sphere of same volume as the particle/S.A. of the particle = 2/3=0.66.
Shape factor=1/0.66 = 1.51.

Surface shape factor is the reciprocal of sphericity. So, the answer is 1.15.

Spphercity for cylinder (length =diameter) = 0.785.
Shape factor = 1/Sphercity.
= 1/0.785,
= 1.27,
So, option (A) is correct Answer.

0.785 is correct.
Using formula VP = a dp^3.
VP = volumes of the particle , a shape factor, do diameter of the particle.

Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size.

Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, Shape factors are often normalized, that is, the value ranges from zero to one.

The shape factor is the reciprocal of sphericity.
Sphericity = surface area of sphere/surface area of particle.
Surface area of sphere = 4×π× r^2.

Here the particle is a cylinder
So, the surface area of the cylinder =2×π×r(r+h).
L = D
So, h = D = 2r.

On substituting we get.
Sphericity = (4×π× r^2)/(=2×π×r(r+2r).
= 4/6=2/3.
Therefore shape factor = 1/sphericity = 3/2 = 1.5.