Falling through a high viscosity liquid
Practical Activity for 14-16
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
- Eye protection
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.
- 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.
- Release a ball-bearing from just above the liquid surface.
- 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.
- You could use a more sophisticated timing system, but the point here is to demonstrate terminal velocity rather than to make precise measurements.
- 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
- νο = terminal velocity
- γ = gravitational field strength
- ρ = density of the bearing material
- σ = density of the liquid
This experiment was safety-tested in April 2006