Skip to main content
SpringerLink
Log in

An eigenfunction solution of entry flow in a semi-infinite pipe at low Reynolds numbers

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

The developing flow in a semi-infinite pipe is solved for by an eigenfunction method. The results are applicable to zero and low Reynolds number flows. The eigenfunction method yields a solution which accurately predicts overshoots in the axial velocity for small axial positions. Results are presented for both uniform and non-uniform inlet conditions. The latter condition has important implications for numerical simulations of the developing flow problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

6. References

  1. J. Gillis and A. Brandt, The Numerical integration of the equations of motion of a viscous fluid. AF EOAR, SR 63–73 (1964).

  2. M. Friedmann, J. Gillis and N. Liron, Laminar flow in a pipe at low and moderate Reynolds numbers. Appl. Sci. Res. 19 (1968) 426–438.

    Google Scholar 

  3. M.H. Wagner, Developing flow in circular conduits: transition from plug flow to tube flow. J. Fluid Mech. 72 (1975) 257–268.

    Google Scholar 

  4. S. Arbarbanel, S. Bennett, A. Brandt and J. Gillis, Velocity profiles of flow at low Reynolds numbers. J. Appl. Mech. 37 (1970) 2–4.

    Google Scholar 

  5. L.C. Li and G.S.S. Ludford, The overshoot in entry flow. Arch. Mech. 32 (1980) 741–746.

    Google Scholar 

  6. J.L. Duda and J.S. Vrentas, Inviscid flow through a sudden contraction. IEC Fundam. 11 (1972) 590–593.

    Google Scholar 

  7. L.H. Benson, Velocity and thermal development in a pipe for low Reynolds number. M.S. Thesis, Clarkson College (1983).

  8. J.Y. Yoo and D.D. Joseph, Stokes flow in a trench between concentric cylinders. SIAM J. Appl. Math. 34 (1978) 247–285.

    Google Scholar 

  9. R.D. Gregory, Green's functions, bi-linear forms, and completeness of the eigenfunctions for the elastostatic strip and wedge. J. Elast. 9 (1979) 283–309.

    Google Scholar 

  10. R.D. Gregory, The semi-infinite strip x⩾0, −1⩽y⩽1; completeness of the Papkovich-Fadle eigenfunctions when φ xx (0, y), φ yy (0, y) are prescribed. J. Elast. 10 (1980) 57–80.

    Google Scholar 

  11. R.D. Gregory, The traction boundary value problem for the elastostatic semi-infinite strip; existence of solution, and completeness of the Papkovich-Fadle eigenfunctions. J. Elast. 10 (1980) 295–327.

    Google Scholar 

  12. D.D. Joseph, L.D. Sturges and W.H. Warner, Convergence of biorthogonal series of biharmonic eigenfunctions by the method of Titchmarsh. Arch. Rat. Mech. Anal. 78 (1982) 223–274.

    Google Scholar 

  13. J.P. Benthem, A Laplace transform method for the solution of semi-finite and finite strip problems in stress analysis. Quart. J. Mech. and Appl. Math. 16 (1963) 413–429.

    Google Scholar 

  14. S.A. Trogdon and D.D. Joseph, The stick-slip problem for a round jet I: large surface tension. Rheol. Acta. 19 (1980) 404–420.

    Google Scholar 

  15. S.A. Trogdon and D.D. Joseph, The stick-slip problem for a round jet II: small surface tension. Rheol. Acta. 20 (1981) 1–13.

    Google Scholar 

Download references

Author information

Author notes

  1. L. H. Benson

    Present address: Bettis Atomic Power Laboratory, 15122, Pittsburgh, PA, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Nebraska, 68588, Lincoln, NE, USA

    L. H. Benson & S. A. Trogdon

Authors
  1. L. H. Benson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Trogdon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was performed while Mr Benson was a graduate student at Clarkson College, Potsdam, NY, USA.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benson, L.H., Trogdon, S.A. An eigenfunction solution of entry flow in a semi-infinite pipe at low Reynolds numbers. Appl. Sci. Res. 42, 347–359 (1985). https://doi.org/10.1007/BF00384212

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00384212

Keywords

Search

Navigation