Required Practicals/Edexcel/Practical 4
4ASCP4

Investigating viscosity using Stokes' Law (CP4)

Determine the viscosity of a viscous liquid by measuring the terminal velocity of falling spheres of different radii.

Apparatus

  • Tall measuring cylinder filled with glycerol (or golden syrup)
  • Steel ball bearings of at least three different radii
  • Micrometer screw gauge
  • Ruler with two reference marks on the cylinder
  • Stopwatch and thermometer

Safety

  • Glycerol is slippery; wipe up spills immediately to prevent slipping.
  • Ball bearings dropped from height can shatter glass; lower them carefully with a thin wire hook.

Method

  1. Measure the diameter of each ball bearing at least three times using the micrometer; calculate mean radius r.
  2. Mark two horizontal lines on the cylinder at a known separation s, well below the liquid surface (to ensure terminal velocity is reached before the upper mark).
  3. Drop a ball gently into the centre of the liquid. Measure the time t to travel between the two marks; terminal velocity $v = s/t$.
  4. Repeat for each ball bearing size, three times each, and take mean velocities.
  5. Plot v against $r^2$: straight line through origin. Determine viscosity from the gradient.

Key Variables

Independent
Ball radius r
Dependent
Terminal velocity v
Controlled
Liquid temperature (viscosity is temperature-dependent); Same liquid and cylinder; Same distance s between markers

Analysis and Results

  • At terminal velocity, weight $=$ upthrust $+$ drag: $(\rho_s - \rho_l)g\frac{4}{3}\pi r^3 = 6\pi\eta r v$.
  • Rearranging: $v = \frac{2(\rho_s - \rho_l)g}{9\eta}r^2$.
  • Plot v vs $r^2$: gradient $= \frac{2(\rho_s - \rho_l)g}{9\eta}$, so $\eta = \frac{2(\rho_s - \rho_l)g}{9 \times \text{gradient}}$.
  • Record the liquid temperature; viscosity decreases significantly as temperature rises.

Common Errors

  • Not allowing the ball to reach terminal velocity before the upper timing mark (start timing marks well below the surface).
  • Dropping the ball near the cylinder wall (wall effects increase drag; always drop near the centre).
  • Not measuring liquid temperature; a change of a few degrees can significantly alter viscosity.
  • Forgetting to subtract upthrust from the weight when deriving the formula.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q14 marks
A steel ball of radius $1.5 \times 10^{-3}$ m falls at terminal velocity through glycerol. Given $\rho_{\text{steel}} = 7800$ kg m$^{-3}$, $\rho_{\text{glycerol}} = 1260$ kg m$^{-3}$, and $\eta = 1.5$ Pa s, calculate the terminal velocity.
Q23 marks
Explain why the timing marks should be positioned well below the liquid surface.
Q32 marks
A student repeats the experiment at a higher room temperature. Explain how this would affect the measured terminal velocity.