An indented cylinder type rice grader has been fed with milled rice containing 18 % brokens. After separation, head rice stream contains 3 % brokens and the broken stream carried away 4 % head rice. The effectiveness of the given rice grader on the basis of head rice separation, in fraction, is __________. (Rounded off to 3 decimal places)
Official Answer Key:
0.840 to 0.860
Step-by-Step Solution & Explanation
Take the feed as 1 kg basis. Let H = mass of head rice stream, B = mass of broken stream.
Composition (head rice fractions):
Feed: x_F = 1 − 0.18 = 0.82
Head rice stream: x_H = 1 − 0.03 = 0.97
Broken stream: x_B = 0.04
Step 1 — material balance on head rice:
H + B = 1
0.97H + 0.04B = 0.82
0.97H + 0.04(1 − H) = 0.82
0.93H = 0.78 ⇒ H = 0.8387 kg, B = 0.1613 kg
Step 2 — effectiveness. Overall effectiveness is the product of the recovery of the desired material in its own stream and the rejection of the undesired material:
E = [H·x_H/(F·x_F)] × [B(1 − x_B)/(F(1 − x_F))]
First factor (head rice recovered in head stream):
(0.8387 × 0.97)/0.82 = 0.81355/0.82 = 0.9921
Second factor (brokens rejected into broken stream):
(0.1613 × 0.96)/0.18 = 0.15484/0.18 = 0.8602
Step 3 — effectiveness:
E = 0.9921 × 0.8602 = 0.853
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