Onset of turbulence in planar and circular pipe

Abstract

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 Poiseuille-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.