AbstractAn analysis based on steady uniform laminar flow of a non‐Newtonian fluid in a tube is presented which predicts Newtonian flow behaviour in the limits of zero and infinite shear, respectively. It is shown that an upper limiting viscosity occurs in the limit of infinite shear for a fluid with or without a yield stress, whereas a lower limiting viscosity is obtained for a fluid without a yield stress in the limit of zero shear. For a fluid with a yield stress, an infinite viscosity is found in the limit as the shear stress approaches the yield stres