The Development Lengths of Laminar Pipe and Channel Flows

The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as $L∕D=C0+C1Re$ and for $Re→0$ one obtains $C0=0.619$⁠, whereas for $Re→∞$ one obtains $C1=0.0567$⁠. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for $Re→0$ and $Re→∞$⁠. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: $L∕D=C0′+C1′$⁠; Re, where $C0′=0.631$ and $C1′=0.044$⁠. Finally, correlations are given to express $L∕D$ analytically for the entire Re range for both laminar pipe and channel flows.