Reduction ratio in fine crushing: assuming a typical fine-crushing duty where average feed size Df = 50 mm and average product size Dp = 5 mm, what is the reduction ratio (Df/Dp)?

Introduction / Context:
Reduction ratio is a fundamental sizing parameter in comminution, defined as the ratio of characteristic feed size to characteristic product size. For crushing equipment selection and stage design, engineers often estimate reduction ratios to meet target top sizes economically.

Given Data / Assumptions:

• The original database prompt omitted specific sizes; applying the Recovery-First Policy, we use a standard fine-crushing example.
• Average feed size, Df = 50 mm.
• Average product size, Dp = 5 mm.
• Definition: reduction ratio R = Df / Dp.

Concept / Approach:
For crushers, a common working definition is R = Df/Dp (using characteristic sizes like F80/P80 or averages). Fine crushing stages typically deliver reduction ratios from about 5 to 10 per stage depending on machine and material. The assumed values reflect a realistic fine-crushing step.

Step-by-Step Solution:
Write formula: R = Df / Dp.Substitute values: Df = 50 mm, Dp = 5 mm.Compute: R = 50 / 5 = 10.

Verification / Alternative check:
Comparing with vendor literature, a single fine-crushing stage (e.g., impact or cone) commonly achieves R in the 6–10 range, so 10 is plausible for selected duty and settings.

Why Other Options Are Wrong:
0.5 and 2: far below typical fine-crushing ratios for the given sizes.5: would correspond to Df/Dp = 25/5 or 50/10, not our stated 50/5 example.

Common Pitfalls:
Mixing up definitions (using Dp/Df) or confusing top size with average or P80; always check the definition used in your calculation.

Final Answer:
10