Sphericity of Cylinder

Calculate the sphericity of a cylinder of dia 1 cm and height 3 cm.

Calculations:

${\displaystyle \text{Sphericity}({�}_{�})=\frac{\text{surface area of sphere of same volume as the particle}}{\text{surface area of particle}}}$

Volume of particle = π r_c² h = π x 0.5² x 3 = 2.356 cm³

Radius of sphere of volume 2.356 cm³:

4πr_s³ / 3 = 2.356

r_s = 0.8255 cm

Surface area of sphere of same volume as the particle = 4 π r_s² = 4 x πx 0.8255² = 8.563 cm²

Surface area of particle = 2 π r_c (h + r_c) = 2 x π x 0.5 x (3 + 0.5) = 10.996 cm²

Sphericity (φ _s) = 8.563/10.996 = 0.779

Sphericity (φ _s) = 6 V_p / (D_pS_p)

Where V_p = volume of particle

D_p = Equivalent diameter of particle. (Equivalent diameter is defined as the diameter of a sphere of equal volume)

S_p = surface area of particle

V_p = π r_c² h = 2.356 cm³

D_p = 2 r_s = 2 x 0.8255 = 1.651 cm

S_p = 2 π r_c (h + r_c) = 10.996 cm²

φ _s = 6 x 2.356 / (1.651 x 10.996) = 0.779