A vibrating cleaner screen is fed with grain feed containing $40\%$ desired oversized fractions ($x_F = 0.40$). The overflow stream $D$ contains $90\%$ oversized fraction ($x_D = 0.90$) with an overflow recovery ratio $\frac{D}{F} = 0.38$. The underflow contains $x_B = 0.0935$ oversized fraction with $\frac{B}{F} = 0.62$. The overall effectiveness of the screen is ________ $\%$ (round off to one decimal place).
Answer Key:
80.1
Step-by-Step Solution & Explanation
Screen effectiveness is the product of recovery of desired oversize material in overflow and recovery of undersize material in underflow:
$E = E_D \times E_B = \left[ \frac{x_D D}{x_F F} \right] \times \left[ \frac{(1 - x_B) B}{(1 - x_F) F} \right]$
$E_D = \frac{0.9 \times 38}{0.4 \times 100} = \frac{34.20}{40.00} = 0.855$
$E_B = \frac{(1 - 0.0935) \times 62}{(1 - 0.4) \times 100} = \frac{0.9065 \times 62}{0.60 \times 100} = 0.937$
$E = 0.855 \times 0.937 = 0.801 = 80.1\%$