# Definition of the Reynolds number

The Reynolds number is defined as $Re = \frac{\rho u L}{\mu}$, with the fluid's density $\rho$ and its viscosity $\mu$. The constants $u$ and $L$ are according to wikipedia the "velocity of the fluid with respect to the object" and a "characteristic linear dimension". Now I am a little bit confused by this terms: when one observes a flowing fluid with no obstacle/object, how can one define these properties?

If you look at a flow of a fluid through a channel in which an obstacle is placed, these constants can be set without any problem. But what happens, if we remove the obstacle? What is now a characteristic length scale?