Rosin–Rammler Equation Example 2

 

 Numerical Example 2

Scenario:
A crusher product is analyzed and found to have the following Rosin–Rammler parameters:

  • D63.2 = 40 mm
  • λ = 2.0

Question:
What percentage of the material is smaller than 20 mm?

Step-by-Step Calculation

1. Insert values into the Rosin–Rammler equation:
   P(20) = 1 – exp[ – ( 20 / 40 )^2.0 ]

2. Simplify the fraction:
   20 / 40 = 0.5

3. Apply exponent 2.0:
   0.5^2.0 = 0.25

4. Compute exponential term:
   exp(–0.25) ≈ 0.7788

5. Final step:
   1 – 0.7788 = 0.2212

Final Answer:
Approximately 22.1% of the material is smaller than 20 mm.




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