Development-length requirements for fully developed Laminar pipe flow of inelastic non-Newtonian liquids

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index n). Moreover at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, E et al., 2005, "The Development Lengths of Laminar Pipe and Channel Flows," J. Fluids Eng., 127, pp. 1154-1160) to account for this low Re behavior we propose a unified correlation for X-D/D, which is valid in the range 0.4 < n < 1.5 and 0 < Re < 1000.