Trommel critical speed N relates to drum diameter D according to_____________________?
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Answer: A. N ∝ 1/√D
Explanation
The critical speed of a trommel or tumbling mill is inversely proportional to the square root of its diameter. Centrifugal forces acting on grinding media balance gravitational forces at this calculated critical rotation speed. Mathematical derivation shows that increasing drum diameter reduces the required rotational speed for centrifuging. Critical speed defines the rotational rate at which media particles cling to the inside shell of a mill. Trommels and ball mills operate at a fraction of their critical speed to ensure proper cascading action. Dimensional analysis confirms that gravitational acceleration and drum radius govern this dynamic threshold.
Mining engineers calculate critical mill speed to optimize grinding efficiency and prevent media wear. Trommel screen sizing and rotational speed selection depend directly on drum diameter calculations. Exceeding critical speed causes grinding media to centrifuge, eliminating productive impact and attrition. Option N is proportional to square root of D incorrectly suggests larger mills require higher speeds. Option N is proportional to D violates basic dimensional homogeneity in gravitational centrifugal equations. Option N is inversely proportional to D represents an incorrect scaling relationship derived without physics.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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