Hydrodynamic entrance length: independent of Re?

AI Thread Summary
The hydrodynamic entrance length in a channel is influenced by the Reynolds number, with a minimum dependence noted in certain equations, such as the one from Deen's "Analysis of Transport Phenomena." The equation indicates that the entrance length can be expressed as a function of Reynolds number, with an additional constant offset. This offset represents effects that are not solely dependent on the flow's inertia, suggesting that even at low Reynolds numbers, there is a necessary entrance length for flow development. The discussion seeks clarification on the nature of this offset and its implications for flow behavior, especially in scenarios like creeping flow. Understanding these dynamics is crucial for accurately predicting flow characteristics in various applications.
MichielM
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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!
 
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Even for creeping flow, there has got to be some sort of entrance length. The equation is just a rough approximation.
 

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