Subtopic: Centrifugal separation of solids, liquids and gases
Question Statement:
A centrifuge with rotational speed of 1440 rpm is used for separating oil from a dispersion in which oil is present in the form of spherical globules of 47 µm diameter. The density of oil is 886 kg m⁻³. Separation occurs at an effective radius of 4 cm. Viscosity and density of water are 0.705 cP and 1000 kg m⁻³, respectively. The velocity of oil through water, in mm s⁻¹, is ___________.
Official Answer Key:
17.5 to 18.5
Step-by-Step Solution & Explanation
Stokes' law in a centrifugal field: v = d²(ρ_water − ρ_oil)·ω²·r / (18µ)
d = 47×10⁻⁶ m → d² = 2.209×10⁻⁹ m²; Δρ = 1000−886 = 114 kg/m³.
ω = 2πN/60 = 2π(1440)/60 = 150.80 rad/s → ω² = 22,739.5.
r = 0.04 m; µ = 0.705×10⁻³ Pa·s.
v = (2.209×10⁻⁹ × 114 × 22,739.5 × 0.04) / (18 × 0.705×10⁻³)
= 2.2906×10⁻⁴ / 0.01269 = 0.01805 m/s = 18.05 mm/s, within the accepted range.
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