Viscosity: terminal velocity of a ball

A/L Physics · G.C.E. Advanced Level · Grades 12–13

Aim

To find the viscosity of glycerine from the terminal velocity of falling balls.

Apparatus

• A tall cylinder of glycerine
• Steel balls (r = 1–3 mm)
• Stopwatch and metre rule

Method

1. Mark two points 0.30 m apart on the cylinder.
2. Drop a ball and time it between the marks.
3. Work out v = 0.30 ÷ t; repeat with different radii.
4. Plot v against r²: gradient = 2(ρ − σ)g ÷ 9η.

Conclusion

Stokes’ law: v = 2r²(ρ − σ)g ÷ 9η, so v ∝ r². The gradient gives η ≈ 0.95 Pa s for glycerine.