Stoke's law:

At low velocities, the frictional force on a spherical body moving through a fluid at constant velocity is equal to 6p times the product of the velocity, the fluid viscosity, and the radius of the sphere. An equation relating the terminal settling velocity of a smooth, rigid sphere in a viscous fluid of known density and viscosity to the diameter of the sphere when subjected to a known force field. When small spherical bodies move through a viscous medium, the bodies drag the layers of the medium that are in contact with them. This dragging results in relative motion between different layers, which are away from the body. The Stoke's law expression is given as:

F_d = 6πμRV

Where F_d is the frictional force acting on the interface between the fluid and the particle, μ is the fluid's viscosity, R is the radius of the spherical object, and V is the particle's velocity. Stokes's law can also be used to find the viscosity of the same liquid at different temperatures. Objects move much more slowly through very cold liquids than through warm liquids. If the density of the material of the sphere is r and that of the liquid s, then

effective gravitational force = weight - upthrust

= 4/3[pr³ (r - s)]

Therefore we have for the viscosity (h) is calculated as,

Viscosity (h) = 2gr²(r -s)/9v where v is the terminal velocity of the sphere.

From the formula it can be seen that the frictional drag is smaller for large spheres than for small ones, and therefore the terminal velocity of a large sphere is greater than that for a small sphere of the same material. Stokes's law is the basis of the falling sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid.