Power-law generalization of Newton’s formula for shear stress in a liquid in the form of a tensor rheological relation

A generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it power-law form and corresponding rheological relation written tensor form. Depending on exponent this ratio, one can come to description either laminar or turbulent flow regime. In latter case, there system differential equations with no-slip boundary condition. The proposed motion be useful, at least, obtaining preliminary, estimated characteristics before starting numerical modeling using modern turbulence models. For some values exponent, used describe behavior fluids, as well fluids small additives polymers manifestation Toms effect.