A theoretical study of the spatial stability of Poiseuille flow in a rigid pipe to infinitesimal disturbances is presented. Both axisymmetric and non-axisymmetric disturbances are considered. The coupled, linear, ordinary differential equations governing the propagation of a disturbance that has a constant frequency and is imposed a t a specified location in the fluid are solved numerically for the complex eigenvalues, or wavenumbers, each of which defines a mode of propagation. A series solution for small values of the pipe radius is derived and step-by-step integration to the pipe wall is then performed. In order to ascertain the number of eigenvalues within a closed region, an eigenvalue search technique is used. Results are obtained for Reynolds numbers up to 10000. For these Reynolds numbers it is found that the pipe Poiseuille flow is spatially stable to all infinitesimal disturbances.

Two separate experiments were performed and the results were compared with theory:(1) The propagation of a short, rectangular pulse of pressure in a cylindrical tube of previously undisturbed liquid and (2) the pressure surge resulting from a step change of flow in a pipe, commonly termed "water hammer."By considering viscous shear to be frequency-dependent, good agreement between experiment and theory was found.The observation of a precursing phenomenon in a low viscosity liquid is also discussed. 174 / MARCH 1967 Transactio(is of the ASME Copyright © 1967 by ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 05/26/2015 Terms of Use: http://asme.org/terms

In this paper the first thirty-two axisymmetric modes for steady-periodic waves in viscous compressible liquids contained in rigid, impermeable, circular tubes are calculated. These results end long speculation over the effects of viscosity on guided acoustic waves. Sixteen of the modes belong to a family of rotation-dominated modes whose existence was previously unknown. The thirty-two modes were computed for a wide range of frequencies, viscosities and wave-lengths.The modes were found through the use of the method of eigenvalleys, which also led to the discovery of backward-propagating waves, an exact analytical expression for the zeroth rotational mode eigenvalue, definitive boundaries between low and intermediate frequencies and between intermediate and high frequencies, and a new type of boundary layer, called a dilatational boundary layer.

An analysis is made of the performance of narrow porous metal bearings (e.g., sintered bronze powder) which operate with a full film of lubricant. The configuration considered is that in which the bearings are pressed tightly into housings with their ends remaining open to the atmosphere. A solution for the lubricant pressure is obtained which satisfies Reynolds’ equation in the film and Laplace’s equation in the porous metal. Expressions are developed which give the Sommerfeld and Ocvirk numbers, attitude angle, and coefficient of friction as functions of eccentricity ratio, permeability parameter, and thickness-to-length ratio. The results are shown graphically for situations of practical importance.

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