Using the Euler-Lagrange variational principle to obtain flow relations for generalized Newtonian fluids

The Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in theflow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models, which include power law, Bingham, Herschel-Bulkley, Carreau, and Cross, are used for demonstration.