Calculating the hydrodynamic entry length of a cicular pipe.

[wildturkey101]

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?

[FredGarvin]

I don't think you're going to find a derivation for that. IIRC those are correlations from a lot of experimentation.

[wildturkey101]

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. ;)