Hydrodynamic entrance length: independent of Re?

[MichielM]

Hi all,
I have learned that the hydrodynamic entrance length of a channel (to form fully developed laminar flow) is correlated to the Reynolds number, because the shear effects have to propagate inwards from the walls of the channel. However recently I found out that there is a 'minimum' to the dependence on the reynolds number, for example in Deen (Analysis of transport phenomena) I find for a cylindrical tube:
$$\frac{L_v}{R}=1.18+0.112 Re$$ with $$Re=\frac{2 U R}{\nu}$$
With R the radius and $$L_v$$ the entrance length.

The Reynolds dependent term in this equation I can understand (and derive), but I do not know what effect is responsible for the 'offset'. Can anyone explain to me why this occurs?

Thanks in advance!

 

[Chestermiller]

Even for creeping flow, there has got to be some sort of entrance length. The equation is just a rough approximation.