Onset of Turbulence in Planar and Circular Pipe - Jirkovsky, L.; Bo-ot, L. (Science Diliman: A Journal of Pure and Applied Sciences; Vol 15 No 1 (2003), 2007)
A third-order hydrodynamic equation with a molecular structure parameter, obtained through a projection and perturbation formalism from the Liouville equation is applied to circular and planar Poisseuille-Hagen flow. It is shown that there is no principal difference in the resulting parabolic velocity profiles as long as the flows remain laminar. However, a difference is noted in the onset of turbulence in consistency with observations, showing larger stability of the parabolic velocity profile in circular pipe.