  The curvature of the inertial or gravitational potentials defined as a
Hodge-Helmholtz decomposition of acceleration into an irrotational and a
solenoidal components, enable to federate certain domains of macroscopic
physics. After two verifications in physics, one on the calculation of the
curvatures for capillary effects and the second on the deflection of light by a
gravitational effect, the concept of curvature of the potential is applied to
the inertia. The physical analysis of each of the contributions of the
decomposition is carried out on a classic example of fluid mechanics, the
backward-facing step flow where inertia plays a preponderant role on the
recirculation length.
