The Development Lengths of Laminar Pipe and Channel Flows

Abstract

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.

Computational study on non-asymptotic behavior of developing turbulent pipe flow

“…(6) at Re=557 is 31.62. Therefore, the present predictions show a good consensus with the results presented by Durst et al [16]. Contour plot of mean axial velocity field is given in Fig.…”

Single-Phase Heat Transfer and Pressure Drop of the Cooling of Water inside Smooth Tubes for Transitional Flow with Different Inlet Geometries (RP-1280)

“…This was done by using the bellmouth inlet in combination with an extra length of tubing that had the same diameter as the test section. The length of the tubing was determined by Durst et al (2005), which required a minimum length of 120-tube diameters. To ensure this minimum was met, the length of the inlet was chosen as 160-tube diameters.…”

Electrokinetic development length of electroviscous flow through a contraction

“…The development length of laminar flow in pipes and channels without electrokinetic effects has been well defined (Durst et al, 2005). The development length of electroosmotic flow in a microchannel has also been investigated (Yang et al, 2001(Yang et al, , 2005.…”