Fluids used in many chemical and petroleum industrial processes are often described as complex systems that exhibit non-Newtonian character. Due to the complex nature of non-Newtonian fluids, universally accepted flow equations are unavailable. This paper uses the Carreau and modified power law-Cross (MPL-Cross) rheological models to derive pressure drop-flow rate relationships under laminar flow condition. The aim is to develop simple but effective equations that enable accurate estimation of pressure drop for flow in any pipe size using viscometric data. The new relationships compare favourably with experimental data. Furthermore, new Reynolds number and generalized Reynolds number expressions have been defined.