A second important flow at small Reynolds numbers is Stokes' flow--the flow
of a viscous fluid around a sphere of radius a, which is moving with a
speed U.
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The derivation of the actual velocity field and the resulting drag force D
are too complicated to derive here, so I'll just quote the result:
This is usually referred to as Stokes' law . Note that the result is independent of the fluid density, in accordance with our earlier observation that the fluid density shouldn't influence the drag at low Reynolds numbers. From this expression we can derive the terminal velocity of a small sphere in air, by equating the drag force with the weight, with the result that . Note that this result requires that the Reynolds number be small, so we would need to verify that was indeed small at the end of a calculation. Stokes' law is important in determining things such as the settling of dust (from a volcanic explosion, say), or the sedimentation of small particles (pollutants) in a river.
At this point it is useful to introduce yet another dimensionless number,
the coefficient of drag 
, which provides a measure of the drag on a
solid body. The coefficient of drag is defined as
where A is the projected area of the object in the plane perpendicular to
the flow. For the Stokes' flow, 
, and the coefficient of drag is
with 
. In fact, dimensional analysis tells us that
for the flow of any incompressible fluid about a sphere,
where 
is some undetermined, dimensionless function of the
Reynolds number; however, we know that when 
, 
. Some important dimensionless numbers commonly encountered
in fluid mechanics are listed in Table 3.2.
| Number | Symbol | Definition | Importance |
| Mach | Ma | U/c | If  for incompressible flow. |
| Reynolds | Re |  | Measures the relative importance of viscosity. |
| Drag coefficient | |  | Dimensionless measure of the drag. |
| Lift coefficient |  |  | Dimensionless measure of the lift. |
Footnotes:
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Alternatively, the fluid velocity at infinity could be U, in which
case D would be the force required to hold the sphere stationary in
the stream.
