Subtopic: Mechanics and energy requirement in size reduction of agriculture produce
Question Statement:
The lighter liquid layer and the interphase layer in a basket centrifuge, rotating at a speed of 1000 rpm, are 0.1025 m and 0.105 m away from the center, respectively. Considering the densities of lighter and heavier liquids as 920 kg m⁻³ and 1015 kg m⁻³, the differential pressure in horizontal direction required to maintain the interphase layer in kPa is ______________ (rounded off to 3 decimal places, Consider π = 3.14).
Official Answer Key:
2.610 to 2.620
Step-by-Step Solution & Explanation
Angular speed, ω = 2πN/60 = 2×3.14×1000/60 = 104.667 rad/s.
The pressure built up by the lighter-liquid layer (from its free surface at r₁=0.1025 m out to the interface at r₂=0.105 m) supplies the differential pressure that positions/maintains the liquid-liquid interface:
ΔP = ρ_light×ω²×(r₂²−r₁²)/2 = 920×(104.667)²×(0.105²−0.1025²)/2
= 920×10,955.1×(0.011025−0.01050625)/2 = 920×10955.1×0.00051875/2 = 2614.2 Pa ≈ 2.614 kPa. Within official range 2.610–2.620.
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