### Sphericity of Cylinder

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

Calculations:

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

Volume of particle = π rc2 h = π x 0.52 x 3 = 2.356 cm3

Radius of sphere of volume 2.356 cm3:

4πrs3 / 3 = 2.356

rs = 0.8255 cm

Surface area of sphere of same volume as the particle = 4 π rs2 = 4 x πx 0.82552 = 8.563 cm2

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

Sphericity (φ s) = 8.563/10.996 = 0.779

Sphericity could also be found from the formula,

Sphericity (φ s) = 6 Vp / (DpSp)

Where Vp = volume of particle

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

Sp = surface area of particle

Vp = π rc2 h = 2.356 cm3

Dp = 2 rs = 2 x 0.8255 = 1.651 cm

Sp = 2 π rc (h + rc) = 10.996 cm2

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