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Book Chapter

On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids

By
G. G. Stokes, M.A.
G. G. Stokes, M.A.
Fellow of Pembroke College
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Published:
January 01, 2007

Abstract

The equations of Fluid Motion commonly employed depend upon the fundamental hypothesis that the mutual action of two adjacent elements of the fluid is normal to the surface which separates them. From this assumption the equality of pressure in all directions is easily deduced, and then the equations of motion are formed according to D’Alembert’s principle. This appears to me the most natural light in which to view the subject; for the two principles of the absence of tangential action, and of the equality of pressure in all directions ought not to be assumed as independent hypotheses, as is sometimes done, inas-much as the latter is a necessary consequence of the former. The equations of motion so formed are very complicated, but yet they admit of solution in some instances, especially in the case of small oscillations. The results of the theory agree on the whole with obser-vation, so far as the time of oscillation is concerned. But there is a whole class of motions of which the common theory takes no cognizance whatever, namely, those which depend on the tangential action called into play by the sliding of one portion of a fluid along another, or of a fluid along the surface of a solid, or of a different fluid, that action in fact which performs the same part with fluids that friction does with solids.

Thus, when a ball pendulum oscillates in an indefinitely extended fluid, the common theory gives the arc of oscillation constant. Observation however shows

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Classics of Elastic Wave Theory

Michael A. Pelissier
Michael A. Pelissier
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Henning Hoeber
Henning Hoeber
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Norbert van de Coevering
Norbert van de Coevering
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Ian F. Jones
Ian F. Jones
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Society of Exploration Geophysicists
Volume
24
ISBN electronic:
9781560801931
Publication date:
January 01, 2007

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