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The
drag coefficient, CD, associated with a sphere is shown plotted
against of Reynolds number, Re =rVD/m.
Both axes of the plot are logarithmic. For a given body size, D, fluid
density, r,
and dynamic viscosity, m,
the Reynolds number scales as the velocity, V, of the fluid with respect
to the sphere.
In
the Reynolds number range below about 5, the drag coefficient is large
and increases with decreasing Re. This region is known as "Stokes flow"
and FD = 3pmDV,
where D is the diameter of the sphere and V the velocity. The drag increases
linearly with the velocity.
Between
103 < Re < 105 the drag coefficient is about
0.5 and approximately constant. In this range the viscous forces are less
important than the pressure forces acting on the sphere. It is in this
range that the drag increases as the square of the speed. |
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