What it shows

For a body to reach terminal velocity when falling through a fluid, the drag force (given by Stoke's Law) coupled with the buoyant force (from Archimedes' principle) need to balance the falling object's weight. Leaving derivations to other great texts you end up with

where ρ=density of fluid, ρ₀=density of object, R=object's radius and η=fluid's viscosity. This demo uses a suitably viscous silicone fluid ¹   to study the effects of object size on terminal velocity.

How it works

The objects used are steel ball bearings, dropped into a 2L measuring cylinder full of silicone fluid. The balls reach terminal velocity pretty fast (within the first centimeter) so their timed descent can be measured successive graduations as they head to the bottom. Terminal velocity goes as the square of the radius of the ball, and the value for the viscosity can be obtained from a graph of v_T vs. R². The value obtained for the Dow silicone is 1.16×10⁵ centipoise (116 pascal sec) at 20°C.

table 1. dependence of terminal velocity on ball diameter.

Setting it up

To get measurements, a video camera with can illustrate the separation between two graduations (on our cylinder, ² convenient graduations to use are the 200ml markings which are 4cm apart). Bright illumination from behind using a light box makes the balls clear.

Comments

The way to remove the ball bearings from the bottom of the cylinder is to draw them up the wall using a powerful magnet (such as a samarium cobalt). Put a lid on the cylinder and leave the magnet sitting on it so the balls drip dry. They can then be washed clean with water.

1 Dow Corning 200 Fluid. Dow Corning Corp., Midland, MI 48640
2 EXAX 20025 2L measuring cylinder