A falling ball viscometer is used to determine the dynamic viscosity of sunflower oil. The viscometer has a tube length of 10 cm with the ball diameter of 0.68 mm. The densities of oil and the ball are 921 kg m⁻³ and 2420 kg m⁻³, respectively. If the ball takes 44.5 s to fall from top of the tube, the viscosity of the oil in Pa s is ________. [round off to three decimal places]. (Take g = 9.81 m s⁻²)
Official Answer Key:
0.165 to 0.172
Step-by-Step Solution & Explanation
• Terminal velocity v = L/t = 0.1/44.5 = 0.0022472 m/s
• Stokes' law for a falling sphere: μ = d²(ρs−ρf)g / (18v)
• d² = (0.00068)² = 4.624×10⁻⁷ m²; (ρs−ρf) = 1499 kg/m³
• Numerator = 4.624×10⁻⁷ × 1499 × 9.81 = 6.800×10⁻³
• μ = 6.800×10⁻³ / (18×0.0022472) = 6.800×10⁻³/0.040450 = 0.168 Pa·s
Computed value: 0.168 Pa·s (within official range 0.165–0.172)
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