Subtopic: Particle size analysis for comminuted solids
Question Statement:
In a screen separator, the mass flow rates of feed, overflow and underflow are 150, 140 and 10 kg h⁻¹, respectively. Mass fraction of material in the feed and overflow are 0.9 and 0.96, respectively. The effectiveness of separation in percentage is
Options:
(A) 32
(B) 42
(C) 52
(D) 62
Official Answer Key:
D
Step-by-Step Solution & Explanation
Mass balance for the fraction of interest: F·x_F = O·x_O + U·x_U ⇒ 150×0.9 = 140×0.96 + 10×x_U ⇒ 135 = 134.4+10x_U ⇒ x_U = 0.06.
Recovery of the oversize fraction to overflow, E_A = O·x_O/(F·x_F) = 134.4/135 = 0.9956.
Recovery of the undersize fraction to underflow, E_B = U(1−x_U)/[F(1−x_F)] = 10×0.94/(150×0.1) = 9.4/15 = 0.6267.
Overall screen effectiveness, E = E_A×E_B = 0.9956×0.6267 = 0.6239 = ≈62%. Answer: (D).
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