A tray type paddy separator is used to separate paddy from a binary mixture of paddy and brown rice fed at the rate of 1600 kg h⁻¹. Mass fractions of paddy in feed, separated paddy and separated rice are 0.2, 0.7 and 0.02, respectively. The mass of 1000 paddy grains is 24.5 g. Separation effectiveness and number of paddy grains recycled per second, respectively are
Options:
(A) 0.35 and 7373
(B) 0.93 and 3733
(C) 0.76 and 3773
(D) 0.83 and 3361
Official Answer Key:
D
Step-by-Step Solution & Explanation
Mass balance (F=1600 kg/h at x_F=0.2 paddy; paddy-rich stream P at x_P=0.7; rice-rich stream R at x_R=0.02):
F = P + R = 1600; paddy balance: 0.2(1600) = 0.7P + 0.02R = 0.7P + 0.02(1600−P)
320 = 0.68P + 32 → P = 423.5 kg/h; R = 1176.5 kg/h.
Separation effectiveness (product of the two component-recovery efficiencies):
Paddy-recovery efficiency, E_p = (P·x_P)/(F·x_F) = (423.5×0.7)/(1600×0.2) = 296.5/320 = 0.9264
Rice-recovery efficiency, E_r = [R·(1−x_R)]/[F·(1−x_F)] = (1176.5×0.98)/(1600×0.8) = 1152.9/1280 = 0.9007
Overall effectiveness, E = E_p × E_r = 0.9264 × 0.9007 = 0.834 ≈ 0.83, matching option (D)'s first value.
Grains recycled per second: the paddy impurity remaining in the rice-rich (reject) stream R is the material that must be recycled: paddy mass in R = 0.02 × 1176.5 = 23.53 kg/h.
Mass of one paddy grain = 24.5 g / 1000 = 0.0245 g.
Grains/h = 23,530 g / 0.0245 g ≈ 960,000 grains/h ≈ 267 grains/s by this direct impurity-mass route — this does not reproduce the keyed 3361 grains/s, and the exact circulating-load convention used in the official solution (which typically multiplies the reject-stream mass, not only its paddy fraction, by a recycle ratio tied to the separator's internal recirculation loop) could not be reconstructed to full confidence from the given data alone. The effectiveness value (0.83) is independently verified; the grains/s figure (3361) is reported per the official key, and option (D) is adopted overall, but the second sub-value is flagged as unresolved in this independent re-derivation.
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