Generalization of the Poiseuille law based on the constitutive rheological relation for polymeric liquids

The method of perturbations of the small parameter determining the anisotropy of the properties of linear polymers is used to determine the velocity profile and rate for steady flow in a round tube. It is shown that for the four-parameter rheological model considered, the stress state of the Poiseuille flow along with the tangential shear stress is characterized by the first and second differences of normal stresses.