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Example 5 (12.10) Does a Ball Have a Turbulent Wake?

Calculate the Reynolds number N′R for a ball with a 7.40-cm diameter thrown at 40.0 m/s.

Strategy

We can use the Reynolds number equation calculate N’R , since all values in it are either given or can be found in tables of density and viscosity.

Reynolds number calculation

Solution

We first find the kinematic viscosity values:

2. Kinematic Viscosity
vKinematic Viscosity (m2/s)
μDynamic Viscosity (N*s/m2)
ρDensity (kg/m3)
Variables...
  valueunitslink
v
μ
ρ

Substituting values into the equation for N’R yields:

1. Reynolds number
ReReynolds number (dimensionless)
umean velocity of the object relative to the fluid (m/s)
Lcharacteristic linear dimension (m)
νkinematic viscosity (m2/s)
Variables...
  valueunitslink
ReN'R
u
L
ν

Discussion

This value is sufficiently high to imply a turbulent wake. Most large objects, such as airplanes and sailboats, create significant turbulence as they move. As noted before, the Bernoulli principle gives only qualitatively-correct results in such situations.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

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