On Three and Two-Dimensional Disturbances of Pipe Flow

[+] Author and Article Information
Kurt Spielberg

Department of Physics, The City College, New York, N. Y.

Hans Timan

Institute of Theoretical Physics, University of Vienna, Vienna, Austria

J. Appl. Mech 27(3), 381-389 (Sep 01, 1960) (9 pages) doi:10.1115/1.3644012 History: Received August 27, 1958; Online September 16, 2011


A system of ordinary, coupled differential equations is set up for three-dimensional disturbances of Poiseuille flow in a straight pipe of circular cross section. The commonly treated equations are shown to be special cases arising from particular assumptions. It is shown that in the nonviscous, and therefore also in the general case, there exists, in contrast to the analogous problem in Cartesian co-ordinates, no transformation reducing the given problem to a two-dimensional one. A fourth-order differential equation is derived for disturbances independent of the direction of the main flow. The solutions, which are obtained, show that those two-dimensional disturbances, termed cross disturbances, decay with time and do therefore not disturb the stability of the main flow. Explicit expressions for the cross disturbances are obtained and a discussion of their nature is given.

Copyright © 1960 by ASME
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