The flow of many liquids, for example, solutions, polymer melts, and concentrated dispersions, may differ considerably from Newtonian fluids. Knowledge of the rheology of non-Newtonian fluids is essential in the design of processing machinery and pipelines. However, the multiplicity of rheological systems and the complexity of the behavior of the fluids render it impossible to quote laws of general validity that describe the flow and rheological characteristics under any given condition. Recourse must therefore be taken to a description of the rheological behavior under the conditions that relate to those in practice. A case in question is the flow through pipes of non-Newtonian fluids, many of which are very viscous. It concerns hydrodynamically developed laminar flow and is the subject to which the analytical methods discussed here have been restricted.