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?