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TECHNICAL PAPERS

The Development Lengths of Laminar Pipe and Channel Flows

[+] Author and Article Information
F. Durst, B. Ünsal, O. A. Bayoumi

Institute of Fluid Mechanics,  Friedrich Alexander Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany

S. Ray1

Institute of Fluid Mechanics,  Friedrich Alexander Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany

1

On leave from the Department of Mechanical Engineering, Jadavpur University, Kolkata- 700 032, India.

J. Fluids Eng 127(6), 1154-1160 (Jun 02, 2005) (7 pages) doi:10.1115/1.2063088 History: Received August 16, 2004; Revised June 02, 2005

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 LD=C0+C1Re and for Re0 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 Re0 and Re. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: LD=C0+C1; Re, where C0=0.631 and C1=0.044. Finally, correlations are given to express LD analytically for the entire Re range for both laminar pipe and channel flows.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

The constants C relationship between the Reynolds number and the ratio of development length and pipe diameter

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Figure 2

Axial development of velocities at different radial positions for Re=1, 10, 100, and 1000

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Figure 3

Variation of constant C with Reynolds number of the pipe flow

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Figure 4

Numerical results for L∕D plotted to deduce C0 and C1 in the L∕D relationship

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Figure 5

Predicted development length results and comparison with the convection diffusion relationship in Eq. 14 for laminar pipe flow

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Figure 6

Predicted development length results and comparison with convection diffusion relationship for laminar channel flow

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Figure 7

Axial development of velocity profile for Re=10

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Figure 8

Change of local skin friction factor through the entrance region of the pipe

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