Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy functionals with a single parameter q. These reduce to the extensive Boltzmann-Gibbs form for q = 1, but a remarkable number of statistical and thermodynamic properties have been shown to be q-invariant - that is, valid for any q. In this paper, we address the question of whether or not the value of q for a given viscous, incompressible fluid can be ascertained solely by measurement of the fluid's hydrodynamic properties. We find that the hydrodynamic equations expressing conservation of mass and momentum are q-invariant, but the conservation of energy is not. Moreover, we find that ratios of transport coefficients may also be q-dependent. These dependences may therefore be exploited to measure q experimentally.