Calculating the hydrodynamic entry length of a cicular pipe.

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Discussion Overview

The discussion focuses on calculating the hydrodynamic entry length of laminar incompressible flow in circular pipes. Participants explore various approaches, formulae, and historical context related to this fluid mechanics problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant seeks a method to calculate the entry region length as a function of Reynolds number and pipe diameter, noting the existence of several formulae that provide a ratio of entry length to diameter and Reynolds number.
  • Another participant suggests that the formulae are likely correlations derived from experimental data rather than derived analytically.
  • A different participant mentions that analytic solutions are feasible but expresses difficulty with the mathematical complexity involved, referencing Boussinesq's classic approximation from 1892.
  • One participant requests a similar derivation for 2D channel flow, indicating interest in a related but distinct problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the availability of a derivation for the entry length; some believe it is based on empirical correlations while others reference historical analytical solutions. The discussion remains unresolved regarding the derivation methods.

Contextual Notes

There is a lack of accessible literature detailing the derivation of the entry length, and participants note the challenge of finding historical sources. The discussion also highlights the potential differences in approaches for circular pipe flow versus 2D channel flow.

wildturkey101
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Does anyone know how to calculate the entry region length of laminar incompressible flow in a pipe? There are several formulae available which give a ratio of the (entry length)/(pipe diameter)/(Reynolds number) = 0.02-0.06.

I'm not looking for the final solution, but rather the approach used in order to calculate the entry region as a function of Reynolds number and pipe diameter, and so far have been unsuccessful.

It's a classic problem originally handled by Boussinesq, but I can't seem to find any literature sources that actually go through the derivation. All the fluids books I've looked at just give the final expression:

X_entry length = 0.05*Reynolds*Diameter.


Any help?
 
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I don't think you're going to find a derivation for that. IIRC those are correlations from a lot of experimentation.
 
Analytic solutions are possible, but I've just been bogged down in the mathematics...

Boussinesq first solved it analytically back in 1892 to give the classic approximation for laminar flow of (X/D)/Re=(1/20) ... No one seems so keep 19th century French fluid mechanic journals on file anymore. ;)
 
I'm looking for the same solution for 2D channel flow. Can someone help me? I need the derivation
 

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