Hydrodynamic entrance length: independent of Re?

In summary, the hydrodynamic entrance length of a channel is correlated to the Reynolds number, but there is a minimum dependence on it. This was discovered in Deen's analysis of transport phenomena, where the equation for a cylindrical tube shows an offset term in addition to the Reynolds dependent term. It is not fully understood what causes this offset.
  • #1
MichielM
23
0
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:
[tex]\frac{L_v}{R}=1.18+0.112 Re[/tex] with [tex]Re=\frac{2 U R}{\nu}[/tex]
With R the radius and [tex]L_v[/tex] 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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  • #2
Even for creeping flow, there has got to be some sort of entrance length. The equation is just a rough approximation.
 

Related to Hydrodynamic entrance length: independent of Re?

1. What is the concept of hydrodynamic entrance length?

Hydrodynamic entrance length refers to the distance in a pipe or channel where the flow pattern transitions from laminar to turbulent. It is typically measured from the point where the flow enters the pipe to the point where it becomes fully developed.

2. How is the hydrodynamic entrance length related to Reynolds number?

The hydrodynamic entrance length is independent of Reynolds number, meaning it does not change with varying flow rates. This is because the transition from laminar to turbulent flow occurs due to the geometry of the pipe, and not the fluid's velocity.

3. What factors affect the hydrodynamic entrance length?

The hydrodynamic entrance length is primarily affected by the pipe's geometry, such as its diameter and roughness. Other factors that may influence it include the fluid's viscosity, density, and velocity profile at the entrance.

4. Why is it important to consider the hydrodynamic entrance length?

It is essential to determine the hydrodynamic entrance length in a pipe or channel because it affects the accuracy of flow measurements and can impact the efficiency of heat transfer processes. Understanding this length helps in designing more efficient fluid systems and predicting flow behavior.

5. Can the hydrodynamic entrance length be calculated?

Yes, the hydrodynamic entrance length can be calculated using empirical equations or by conducting experiments. However, it is important to note that these calculations may not be accurate in all cases, and experimental data is usually preferred for more precise results.

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