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A third-order hydrodynamic equation with a molecular structure parameter, obtained through a projection and perturbationformalism from the Liouville equation is applied to circular and planar Poisseuille-Hagen flow. It is shown that there is noprincipal difference in the resulting parabolic velocity profiles as long as the flows remain laminar. However, a difference isnoted in the onset of turbulence in consistency with observations, showing larger stability of the parabolic velocity profilein circular pipe.