As the sphere falls so its velocity increases until it reaches a velocity known as the terminal velocity. At this velocity the frictional drag due to viscous forces is just balanced by the gravitational force and the velocity is constant. At this speed:

Viscous drag = 6phrv = Weight = mg

If the density of the material of the sphere is r and that of the liquid s, then effective gravitational force = weight – upthrust = 4/3pr

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