Viscosity and action

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Abstract

Hamilton's principle is used to show that for the laminar flow of a given volume of liquid through a tube the product of the energy dissipated and the time is a minimum. This condition requires a parabolic velocity distribution in laminar flow through tubes. It is also shown that the non-turbulent flow of a fluid showing shear dependence is not laminar, and that it resembles in many fundamental respects the turbulent flow of a Newtonian liquid. These results follow from the recognition of apparent viscosity as a direct measure of the action per unit volume associated with a given change in the configuration of the elements of which the fluid may be imagined to consist.