Falling-ball viscometer – Stokes' law and terminal velocity
PhysicsForces & DynamicsAges 15–16Virtual lab
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A virtual practical to measure viscosity: drop steel balls of different radii into glycerol, castor oil or water, time each ball between two marks and plot the terminal velocity v against r². The ball speeds up until its weight equals the upthrust plus Stokes' drag 6πηrv, so v = 2r²(ρ − σ)g/(9η) and the gradient of the line gives η. Warm the liquid to see η fall, and check the Reynolds number to see where Stokes' law stops working.
Lesson: Viscosity, Stokes' law and terminal velocity
What it shows
A ball falling through a liquid feels three forces: its weight W, the upthrust U and a viscous drag F. For slow, smooth flow the drag follows Stokes' law, F = 6πηrv, so it grows with speed until W = U + F. The ball then falls at its terminal velocity v = 2r²(ρ − σ)g/(9η), where ρ is the density of the steel and σ that of the liquid. A graph of v against r² is a straight line whose gradient gives the viscosity η. Warmer liquids are less viscous. Stokes' law needs a Reynolds number below about 1; the model adds a standard correction above that, but ignores the walls of the tube.
How to use
Choose a Liquid and Temperature, set Ball radius r and press Drop ball; the stopwatch times the fall between marks A and B, and each run adds a row to the table and a point to the v–r² graph. Repeat for at least four radii, read the gradient k and enter η in the task box. Change Temperature to compare gradients, and try Water to see why a viscous liquid is needed. Use Playback to speed up slow falls.
Parameters you can change
- Liquid Glycerol, Castor oil, Water
- Temperature 10–40 °C
- Ball radius 0.5–2 mm
- Distance between marks 10–30 cm
Questions to explore
- Why are the timing marks placed some distance below the surface of the liquid?
- Why is the graph of terminal velocity against r² a straight line through the origin?
- Why does the falling-ball method fail for a steel ball in water?
