Stokes’ Law

For a body falling in a fluid, the resistive force creating a viscous drag between the fluid and the body is given by:

From purely dimensional considerations (Stokes did the hard part of proving the constant) for two small steel balls, one having a radius exactly twice the other, the bigger one would fall through a fluid four times faster (it had eight times the weight, and twice the drag force for the same velocity, and the drag force is proportional to the velocity). If this sounds a bit muddled, don’t worry because for quite small terminal velocities we can draw a free body diagram like this. Weight acts down and upthrust +viscous drag acts upwards.

Given that U = weight of displaced fluid = density of fluid x volume x g and weight W is density of ball material x volume x g

We can write:

so we can use this equation to measure viscosity using Stokes’ Law. All we have to do is make viscosity the subject. Everything else (two densities, radius and terminal velocity) is easy enough to measure. You might like to compare this with an earlier post with experimental detail. For IB students, this is a useful extension