The shape factor for a cylinder whose length equals its diameter evaluates to_________________?
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Answer: A. 1.5
Explanation
The sphericity of a cylinder whose length equals its diameter can be calculated from its surface-to-volume ratio, yielding 1.5. Substituting cylinder dimensions into the general sphericity formula produces a specific numerical ratio. A cylinder with equal length and diameter has an optimized geometry resulting in this exact value. Sphericity measures how closely a particle resembles a true sphere of identical volume. Mathematical derivation involves comparing the surface area of a sphere to the actual particle surface area. Standard geometric formulas for cylinders link volume and surface area directly to characteristic length.
Particle sphericity influences fluid flow resistance and terminal settling velocity in packed beds. Designers use sphericity values to model pressure drop across catalytic fixed-bed reactors. Granular material handling equipment design incorporates particle shape factors for accurate throughput estimation. Option 0.5 represents an incorrect calculation resulting from inverted surface and volume parameters. Option 1.0 describes the sphericity of a perfect sphere rather than an equivalent cylinder. Option 2.0 overestimates the shape factor due to incorrect dimensional scaling assumptions.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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