Given equivalent diameter dp, volume Vp, and surface area sp for a non-spherical particle, its sphericity φs is expressed by________________?
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Answer: A. φs = 6 Vp/dpsp
Explanation
The equation for sphericity relates particle volume and surface area through the equivalent diameter. Multiplying volume by six and dividing by diameter and surface area yields the dimensionless ratio. This mathematical definition accurately compares any non-spherical particle shape directly against a perfect sphere. Sphericity is a crucial dimensionless parameter used in fluid mechanics and particle technology applications. Equivalent diameter represents the diameter of a sphere having the same volume as the particle. A perfect sphere has a sphericity value of exactly one by this standard geometric formulation.
Engineers use particle sphericity to calculate drag coefficients in fluid flow through packed beds. Knowing particle shape helps predict pressure drops and terminal settling velocities in processing operations. It matters significantly in fluidized bed design, pneumatic conveying, and heterogeneous chemical reactor modeling. Option B lacks the essential numerical factor of six required to normalize against spherical geometry. Option C incorrectly places the equivalent diameter and surface area terms in the numerator position. Option D inverts the required relationship entirely, resulting in an incorrect dimensional formula arrangement.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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