Fluid Mechanics: Terminal Velocity MCQ

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Terminal VelocityHardQuestion 30958

Question

In oil of viscosity 5 Pa·s, a 1 mm radius steel sphere (ρ = 8000 kg/m³) falls. Terminal velocity is (ρ_oil = 800 kg/m³, g = 10 m/s²):

A
1.56 m/s
B
0.156 m/s
C
3.1×10⁻³ m/s
D
0.0156 m/s
Correct

Correct answer

0.0156 m/s

Explanation

v_t = 2r²(ρ_s−ρ_f)g/(9η) = 2×(10⁻³)²×(8000−800)×10/(9×5) = 2×10⁻⁶×72000/45 = 144000×10⁻⁶/45 = 3.2×10⁻³/0.2... recalculating: 2×10⁻⁶×7200×10/45 = 2×10⁻⁶×1600 = 3.2×10⁻³/45... v_t = 2×(10⁻³)²×7200×10/(9×5) = 2×10⁻⁶×72000/45 = 0.00320 m/s ≈ 0.0032 m/s.

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