A method and apparatus for determining the viscosity of a non-Newtonian fluid over plural shear rates using a single capillary tube exposed to a continuously decreasing pressure differential and while minimizing the effects of surface tension of that fluid during the determination. A particular application of this method and apparatus is also provided for determining the viscosity of the blood of a living being whereby the single capillary tube initially forms a portion of a hand-held unit that obtains a portion of the circulating blood of the living being; the filled capillary tube is then ejected into an analyzer where the blood therein is exposed to the continuously decreasing pressure differential. Data is generated from the movement of the blood through the capillary tube, due to the decreasing pressure differential, and the blood viscosity is determined from that data.
