GATE AG 2022 • Q62 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Mechanics and energy requirement in size reduction of agriculture produce

Question Statement:

Sweet sorghum with an initial average particle size of 4.0 mm was pulverized using a burr mill at two different gap settings between stones. The average feed rate of the material is 200 kg h⁻¹. The resultant flour was analyzed by IS sieves for particle size determination and was found to be 0.336 mm and 0.306 mm for the first and second gap settings, respectively. Using Kick's law, if the power required to grind the sorghum at first setting is 7.2 kW, the power requirement in kW with the second setting is ___________. [round off to two decimal places]

Official Answer Key:

7.40 to 7.55

Step-by-Step Solution & Explanation

• Kick's law: Power ∝ ln(D1/D2), where D1=initial size, D2=final (product) size. • P1/P2 = ln(D1/Dp1)/ln(D1/Dp2): ln(4.0/0.336)=2.4769; ln(4.0/0.306)=2.5701 • P2 = P1 × [ln(4.0/0.306)/ln(4.0/0.336)] = 7.2 × (2.5701/2.4769) = 7.2×1.03763 = 7.47 kW Computed value: 7.47 kW (within official range 7.40–7.55)

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