# Sphericity

## 2. Sphericity

Sphericity (f) associates different size definitions and is defined by Waddell as the volume surface area of a sphere per particle surface area. Therefore, it can be represented as follows: In addition, it is demonstrated that sphericity can be the ratio between the surface/volume (dsv) and volume (dv) diameters: The following statement is valid whether the particle is spherical or not: Two additional calculation methods can be used as well:  the ones proposed by Massarani and Peçanha (1989) and by taking the Ergun’s equation (1952) as a starting point for the total pressure fall of the bed.

The Massarani and Peçanha and method consists of determining the inscribed diameter (dCI) and circumscribed diameter (dCC) of a given particle, which are obtained through the projecting of their shadow on a still and stable surface.  Therefore, sphericity can be defined as: The Ergun (1952) method consists of applying the pressure drop equation through a fixed bed, i.e., Rep < 10: where: DP: bed pressure dropl; H0: fixed bed height; U: superficial gas velocity; mg: gas viscosity; dp:mean particle diameter; e: bed porosity, f: sphericity.

The sphericity is obtained by the straight line inclination through thegraph of pressure drop as a function of superficial gas velocity.