Poiseuille flow through n-dimensional hypercircular and hyperelliptic cylinders

  • Howard Brenner
Brief Reports


Results are given for unidirectional Poiseuille flows through hypercircular and hyperellipticn-dimensional cylinders. These agree with the known solutions forn=2 and 3, corresponding, respectively, to flow between two flat parallel plates and through a circular or elliptic cylinder.


Mathematical Method Parallel Plate Poiseuille Flow Elliptic Cylinder Flat Parallel Plate 


Für geradlinige Poiseuille-Strömung durchn-dimensionale Zylinder mit hyper-kreisförmigen und hyper-elliptischen Querschnitten werden Resultate angegeben. Diese stimmen mit den bekannten Lösungenn=2 undn=3 überein, d. h. mit der Strömung zwischen zwei parallelen Platten und in Zylindern mit kreisförmigen und elliptischen Querschnitten.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Brenner,The translation and rotational motions of an n-dimensional hypersphere through a viscous fluid at small Reynolds numbers, J. Fluid Mech. (in press, 1981).Google Scholar
  2. [2]
    D. M. Y. Sommerville, An introduction to the geometry of N dimensions, Dover reprint, New York (1958).Google Scholar
  3. [3]
    J. Happel and H. Brenner,Low Reynolds number hydrodynamics, Sijthoff & Noordhoff, Alphen a. d. Rijn (1973).Google Scholar
  4. [4]
    A. Sommerfeld,Partial differential equations in physics, Academic Press, London (1964).Google Scholar
  5. [5]
    H. Bateman,Partial differential equations of mathematical physics, Dover, New York (1944).Google Scholar
  6. [6]
    M. Abramowitz and I. A. Stegun,Handbook of mathematical functions. U.S. National Bureau of Standards, Washington, D.C. (1964).Google Scholar
  7. [7]
    I-Shih Pai,Viscous flow theory. Vol. I:Laminar flow, van Nostrand, Princeton, New Jersey (1956).Google Scholar
  8. [8]
    R. Berker,Intégration des équations du mouvement d'un fluide visqueux incompressible, in: Handbuch der Physik (S. Flügge and C. Truesdell, editors), Volume VIII/2, Fluid Dynamics II, Springer-Verlag, Berlin (1963).Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • Howard Brenner
    • 1
  1. 1.Dept. of Chemical EngineeringUniversity of RochesterRochesterUSA

Personalised recommendations