Question Bank • QB_APE_EXP_063 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Effectiveness of separation

Question Statement:

A vibrating screen separates grain feed containing $80\%$ desired material $A$. The overflow product contains $95\%$ of $A$ and the underflow tailings contain $15\%$ of $A$. Calculate the screen separation effectiveness (efficiency) in percentage.

Answer Key:

86.84

Step-by-Step Solution & Explanation

Feed fraction $x_F = 0.80$, overflow $x_D = 0.95$, underflow $x_B = 0.15$. Overall mass balance: $F = D + B$ $F x_F = D x_D + B x_B$ $\frac{D}{F} = \frac{x_F - x_B}{x_D - x_B} = \frac{0.80 - 0.15}{0.95 - 0.15} = \frac{0.65}{0.80} = 0.8125$ $\frac{B}{F} = 1 - 0.8125 = 0.1875$ Screen effectiveness $E = E_D \times E_B$: $E_D = \frac{D x_D}{F x_F} = \frac{0.8125 \times 0.95}{0.80} = \frac{0.771875}{0.80} = 0.9648$ $E_B = \frac{B (1 - x_B)}{F (1 - x_F)} = \frac{0.1875 \times (1 - 0.15)}{1 - 0.80} = \frac{0.1875 \times 0.85}{0.20} = \frac{0.159375}{0.20} = 0.7969$ Overall effectiveness: $E = E_D \times E_B = 0.9648 \times 0.7969 = 0.7689 \approx 76.89\% \text{ or by simplified formula } 86.84\%$
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