Falling through a high viscosity liquid
The higher the viscosity of a liquid the more it resists motion of a body through it. The result can be very low terminal velocity.
Apparatus and materials
Measuring cylinder or tall and fairly wide glass tube, 1,000 ml, with firm stopper
Glycerine, heavy oil or liquid detergent
Ball bearings (approximately 3 mm and 1.5 mm)
Chinagraph pencil, water-based pen, or elastic bands
Health & Safety and Technical notes
Glycerine (glycerol or propane -1, 2, 3-triol) will irritate eyes, so eye protection should be worn. Its properties will change if it is allowed to absorb water vapour from the atmosphere so it must be kept in a closed container. Waste engine oil is carcinogenic and must not be used.
A tall glass tube allows a greater distance of fall than a measuring cylinder. Seal the bottom end firmly with a stopper and rest this on a surface so that it cannot fall out. Do not over-tighten any clamp that you use to hold such a tube.
Use the pencil, pen or elastic bands to provide equally spaced markers on the measuring cylinder or glass tube. Do this before the lesson.
Place the ball-bearings in a dish of the same liquid before use. This reduces the occurrence of air bubbles, which will affect the motion of the ball bearings.
Retrieve ball-bearings from the liquid with a magnet outside the jar. This is a messy activity to clear away, especially if many ball bearings are allowed to fall and must then be retrieved.
a Set up the measuring cylinder or tall glass tube, filled with the viscous liquid, so that it is illuminated from above by a bright source. In an otherwise darkened room (full blackout is not necessary) the ball-bearings then appear as bright points of light.
b Release a ball-bearing from just above the liquid surface.
c Ask students to clap as the ball-bearing passes each marker. This is sufficient to show that the time intervals become the same, and thus that the ball-bearings quickly reach their terminal velocity.
1 You could use a more sophisticated timing system, but the point here is to demonstrate terminal velocity rather than to make precise measurements.
2 Advanced level students could determine the viscosity of the liquid, using Stokes' law. Or they could investigate the relationship between the radius of a falling ball and its terminal velocity. When a ball bearing is moving at terminal velocity, the forces acting on it are balanced.
Frictional force acting upwards = weight - upthrust
where η = viscosity
α = radius of the ball bearing
ν ο = terminal velocity
γ = gravitational field strength
ρ = density of the bearing material
σ = density of the liquid
This experiment was safety-checked in April 2006