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.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We can use $N_{R}^{'} = \frac{ρ vL}{η}$ to calculate $N_{R}^{'}$ , since all values in it are either given or can be found in tables of density and viscosity.
Solution
Substituting values into the equation for $N_{R}^{'}$ yields
$\begin{array}{l} N_{R}^{'} & = & \frac{ρ vL}{η} = \frac{(1.29 {kg/m}^{3}) (40.0 m/s) (0.0740 m)}{1.81 \times 10^{- 5} 1.00 Pa \cdot s} \\ = & 2.11 \times 10^{5} . \end{array}$
12.56
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.

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