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. ;)
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...