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The velocities of the same fluid particle observed in two different referencesystems are two different quantities and they are not equal when the tworeference systems have translational and rotational movements relative to eachother. Thus, the velocity is variant. But, we prove that the divergences of thetwo different velocities are always equal, which implies that the divergence ofvelocity is invariant. Additionally, the strain rate tensor and the gradient oftemperature are invariant but, the vorticity and gradient of velocity arevariant. Only the invariant quantities are employed to construct theconstitutive equations used to calculate the stress tensor and heat fluxdensity, which are objective quantities and thus independent of the referencesystem. Consequently, the forms of constitutive equations keep unchanged whenthe corresponding governing equations are transformed between differentreference systems. Additionally, we prove that the stress is a second-ordertensor since its components in different reference systems satisfy thetransformation relationship.

Analysis on the Invariant Properties of Constitutive Equations of Hydrodynamics in the Transformation between Different Reference Systems