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Figure 6-9. Total drag coefficient for a smooth sphere versus Reynolds number 2
The Reynolds number (commonly denoted N r or R n ) is a dimensionless number that
represents the speed of fluid flow around an object. It's a little more than just a speed
measure, since it includes a characteristic length for the object and the viscosity and
density of the fluid. The formula for the Reynolds number is:
R n = (v L)/υ
R n = (v L ρ)/µ
where v is speed, L is a characteristic length of the object (diameter for a sphere), υ is
the kinematic viscosity of the fluid, ρ is the fluid mass density, and µ is the absolute
viscosity of the fluid. For the Reynolds number to work out as a dimensionless number
velocity, length and kinematic viscosity must have units of m/s, m, and m 2 /s, respectively,
within the SI system.
This number is useful for non-dimensionalizing data measured from tests on an object
of given size (like a model) such that you can scale the data to estimate the data for
similar objects of different size. Here “similar” means that the objects are geometrically
similar, just different scales, and that the flow pattern around the objects is similar. For
a sphere the characteristic length is diameter, so you can use drag data obtained from a
small model sphere of given diameter to estimate the drag for a larger sphere of different
2. The curve shown here is intended to demonstrate the trend of C d versus R n for a smooth sphere. For more
accurate drag coefficient data for spheres and other shapes, refer to any college-level fluid mechanics text, such
as Robert L. Daugherty, Joseph B. Franzini, and E. John Finnemore's Fluid Mechanics with Engineering Ap‐
plications (McGraw-Hill).
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