Reciprocal relationships in viscous hydrodynamics

W. E. Olmstead*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Reciprocal relationships are derived for the basic physical problem of a rigid body which translates with constant velocity through a viscous incompressible fluid of infinite extent. In addition to this basic situation, further allowances are made for rotational, magnetic, and thermal effects, as well as a restricted type of time dependence. The reciprocal relationships involve the net fluid force exerted on the moving body and the net heat flux through its surface. The most interesting result concerns invariance of the drag when the body motion is reversed, independent of any symmetry. The principle of reciprocity is shown to stem from the various linearizations {Mathematical expression} of the nonlinear inertial terms in the Navier-Stokes equations. Even some very sophisticated choices of {Mathematical expression} still lead to reciprocity. The crucial point is whether {Mathematical expression} posses a certain reversibility property.

Original languageEnglish (US)
Pages (from-to)289-300
Number of pages12
JournalActa Mechanica
Issue number4
StatePublished - Dec 1975

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering


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