We derive a metric to assess the reliability of linear constitutive relations that describe nonequilibrium hydrodynamic transport. The derivation of the metric utilizes the first-order perturbation to equilibrium Maxwellian velocity density function in the Chapman-Enskog expansion. The metric is defined as the contribution to macroscopic quantities from those regions of phase-space volume wherein the first-order perturbation becomes unphysical. The volume of these subregions of phase-space and, therefore, the corresponding contribution to macroscopic quantities increases with the strength of nonequilibrium (equivalently, the gradients of physical observables). Physical interpretation and performance of the metric are examined for a nonreactive sonic boundary layer flow. The metric provides the first apriori estimate of uncertainties on physical observables computed from the Navier-Stokes equations. The assigned uncertainties can be propagated in the flow field to assess the applicability of the Navier-Stokes equations for flows with strong nonequilibrium and/or rarefied gas physics.

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• Compressible flows
• High-speed flow
• Kinetic theory
• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics