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 isand the density of the body isthe mass of fluid displaced isand the weight of fluid displaced isand we can write the weight of the body similarly asIf the body is travelling at it's terminal velocity all the forces balance and
If we know the viscosity, the terminal velocityis given by
If we measure the terminal velocity, the viscosityis given by