Fluid Mechanics: Open Access

Reynolds Number and Spacetime Curvature

Abstract

Franck Delplace

The reference length or scale length used in Reynolds number definition is of considerable importance. A quick review of Reynolds number definitions used in batch and continuous flow systems showed that this reference scale can be theoretical or conventional. Using curvature quantity coming from general relativity theory, we showed that Reynolds number could be seen as the ratio of two curvatures. This result could give interesting information for the design of high performances exchangers. Moreover, the use of curvature allowed establishing a relationship between momentum diffusivity and velocity gradient tensor. Applied to general relativity equation, we showed a strong link between gravity theory and hydrodynamics.