Size Reduction and Material Handling: Mechanics and energy requirement in size reduction of agriculture produce; particle size analysis for comminuted solids; size separation by screening; fluidization of granular solids-pneumatic, bucket, screw and belt conveying; cleaning and grading; effectiveness of separation; centrifugal separation of solids, liquids and gases; homogenization; filtration and membrane separation.
A cream separator has discharge radii of 6 cm and 9 cm and the density of cream and skim milk are 860 and 1035 kg/m³ respectively. The ideal radius (m) for placing the feed inlet is
Options:
(A) 0.085
(B) 0.098
(C) 0.113
(D) 0.174
Official Answer Key:
D
Step-by-Step Solution & Explanation
In a disc-bowl centrifugal separator, cream (lighter phase) migrates toward the axis and discharges at the smaller radius (r_cream = 0.06 m), while skim milk (heavier) is thrown outward and discharges at the larger radius (r_skim = 0.09 m). The 'neutral zone' (ideal feed radius, rn) is where the centrifugal pressures built up on both sides — from rn to r_cream by the cream, and from rn to r_skim by the skim milk — are equal (analogous to a hydrostatic balance under centrifugal 'gravity'):
ρ_cream(rn² − r_cream²) = ρ_skim(rn² − r_skim²)
rn² = (ρ_cream·r_cream² − ρ_skim·r_skim²)/(ρ_cream − ρ_skim)
rn² = (860×0.06² − 1035×0.09²)/(860−1035) = (860×0.0036 − 1035×0.0081)/(−175) = (3.096 − 8.3835)/(−175) = (−5.2875)/(−175) = 0.030214
rn = √0.030214 = 0.1738 ≈ 0.174 m. Answer: (D) 0.174.
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