Subtopic: Particle size analysis for comminuted solids
Question Statement:
Sorghum flour obtained from a grinder was analyzed by IS sieves for particle size determination. The data obtained are as follows:
The average particle size of the flour, in mm, is __________. (Rounded off to 3 decimal places)
Official Answer Key:
0.230 to 0.260
Step-by-Step Solution & Explanation
Step 1 — sieve apertures. An IS sieve number denotes the aperture in units of 0.1 mm:
IS 100 = 1.00 mm, IS 70 = 0.70 mm, IS 50 = 0.50 mm, IS 40 = 0.40 mm, IS 30 = 0.30 mm, IS 20 = 0.20 mm.
Step 2 — assign a representative size to each retained fraction, taken as the mean of the retaining sieve and the next finer sieve in the stack:
Step 3 — mass-weighted average particle size:
d̄ = Σ(Wᵢ dᵢ)/ΣWᵢ = 62.045/250.0 = 0.248 mm
Important note on convention. If instead each fraction is represented by the mean of the two sieves that bound it (the retaining sieve and the coarser sieve it passed through) — the convention used in several textbooks — the representative sizes become 0.85, 0.60, 0.45, 0.35, 0.25 and 0.10 mm, giving d̄ = 0.354 mm, which lies outside the official range. The official key of 0.230–0.260 is reproduced only by the retaining-sieve/next-finer-sieve pairing used above. This convention should be noted, since the two approaches differ by roughly 40 %.
SECTION 7: DAIRY AND FOOD ENGINEERING
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