When a body moves through a fluid it experiences a resistive force because the the presence of the fluid. Every fluid has a property called viscosity – the resistance of a fluid to any body moving through it. Thicker, more viscous materials resist more the movement of bodies through them than thinner, less viscous materials.
The viscosity of a material is described by it's coefficient of viscosity,
Under conditions of low velocity and non turbulent motion, the force experience by a sphere moving through a fluid is described by Stoke's Law:
For this case, of a sphere moving through a fluid, a free body diagram is shown below.
On the diagram above, the upthrust U is equal to the weight of fluid displaced. If the density of the fluid is
and the density of the body is
the mass of fluid displaced is
and the weight of fluid displaced is
and we can write the weight of the body similarly as
If the body is travelling at it's terminal velocity all the forces balance and
If we know the viscosity, the terminal velocity
is given by
If we measure the terminal velocity, the viscosity
is given by