ITP: Entrance Length

Now that we have defined external and internal flows, we need to point out that at the beginning of an internal flow we often have a "transition period" as the flow gets "used to" the idea of being an internal flow as opposed to an external flow.


The entrance region/length in a flow is the length of conduit necessary for the flow to transition from being an external flow to an internal flow. In the entrance region, the velocity changes in the direction of flow as it adjusts from the profile externally and at the inlet to a "fully-developed" profile where the effects of the walls are felt across the entire channel.


Fully-developed flow is what we call it when the velocity profile does not change along the direction of flow (axial direction), i.e. two different axial locations in conduit have same velocity profile.

As you might imagine the distance required as an entrance region depends on the width of the channel/pipe (as we need the frictional wall effects to "diffuse" to the center). What may not be obvious (yet) is that the necessary length also depends on the character of the flow (i.e., laminar vs turbulent), so that (for laminar flows in a cylindrical pipe):

$\displaystyle{\frac{L_e}{D} \cong 0.0575 Re}$

for turbulent flows in a cylindrical pipe:

$\displaystyle{\frac{L_e}{D} \cong 4.4 Re^{1/6}}$


These expressions will change slightly for different geometries. Also, if a pipe has a bend or other obstruction in it, we need to start all over again!


Explain the meaning of fully-developed flow and calculate the entrance region length necessary for a pipe flow.