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9062 results in Discrete Mathematics, Information Theory and Coding

Page 454 of 454

  • The stability of viscous flow between rotating cylinders

  • S. Chandrasekhar
  • Journal:
    Mathematika / Volume 1 / Issue 1 / June 1954
    Published online by Cambridge University Press:
    26 February 2010, pp. 5-13
    Print publication:
    June 1954

  • As is well known the stability of viscous flow between two concentric rotating cylinders was first successfully treated both experimentally and theoretically by G. I. Taylor [1]. The mathematical problem underlying this classical investigation in hydrodynamic stability is the following:

    The hydrodynamical equations allow the stationary solution

    for the rotational velocity at a distance r from the axis of rotation, where A and B are constants related to the angular velocities Ω1 and Ω2 with which the inner and outer cylinders (of radii R1 and R2, R2 > R1) are rotated. Thus

    where

  • The Green's function of an elastic plate

  • W. R. Dean, G. Z. Harris
  • Journal:
    Mathematika / Volume 1 / Issue 1 / June 1954
    Published online by Cambridge University Press:
    26 February 2010, pp. 18-23
    Print publication:
    June 1954

  • In §§2, 3 a simple expression in finite terms is found for the small transverse displacement of a thin plane elastic plate due to a transverse force applied at an arbitrary point of the plate. The plate is clamped along, and is bounded internally by, the parabola CDE shown in Fig. 1.

Page 454 of 454