The sphericity expression for a non-spherical particle is given by (where V and S denote particle volume and surface area, and D is the equivalent diameter)?
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Answer: A. 6.V/D.S
Explanation
Sphericity is defined mathematically as the ratio 6V/(D*S) where V is volume, S is surface area, and D is equivalent diameter. This dimensionless formula compares the surface-to-volume ratio of a sphere to that of an irregular particle. Using the equivalent diameter ensures dimensional consistency across various particle shape calculations. Particle characterization requires standardized metrics to quantify irregular shapes encountered in industry. Equivalent diameter is typically defined as the diameter of a sphere having the same volume. Sphericity always yields a value between zero and one for any non-spherical particle geometry.
Designers use sphericity values in Ergun equations to calculate pressure drop in packed beds. Fluidization velocity correlations rely heavily on accurate particle shape and sphericity inputs. Powder metallurgy and pharmaceutical manufacturing require precise particle shape descriptions for flowability. Option V/6D.S incorrectly inverts the numerator and denominator constants of the sphericity ratio. Option D.S/V represents an inverted and unscaled dimension ratio lacking proper physical meaning. Option V/D.S omits the necessary geometric constant factor derived from spherical surface formulas.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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