Stokes Flow Around a Sphere

This design shows how a liquid will flow around a stationary sphere under certain conditions.  The curved streamlines indicate the path of a particle dropped into the fluid. Regions where the streamlines are closer together correspond to the fluid moving faster. If we kept looking further and further away from the sphere, the impact of the sphere on the streamlines would decrease until they were all uniformly spaced. 

Mathematicians find these streamlines by solving the Stokes equations, so this kind of flow is called Stokes flow. It corresponds to flows that happen very slowly, on very small scales, and/or in very thick liquids. For example, these are the streamlines that would represent the flow if you dropped a billiard ball in a vat of honey. When the necessary conditions for Stokes flow aren't satisfied (for example, if the ball was dropped into water), the flow has turbulence! This makes the flows much more difficult to model mathematically. The field of maths that investigates these kinds of problems is called fluid mechanics.