Onset of Turbulence in Planar and Circular Pipe

L. Jirkovsky, L. Bo-ot


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.

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