Controlling the physicochemical properties of nanoparticles in fluids directly impacts on their liquid phase processing and applications in nanofluidics, thermal engineering, biomedicine and printed electronics. In this work, the temperature dependent viscosity of various aqueous nanofluids containing carbon nanotubes (CNTs) or graphene oxide (GO), i.e. 1D and 2D nanoparticles with extreme aspect ratios, is analyzed by empirical and predictive physical models. The focus is to understand how the nanoparticle shape, concentration, motion degrees and surface chemistry affect the viscosity of diluted dispersions. To this end, experimental results from capillary viscosimeters are first examined in terms of the energy of viscous flow and the maximum packing fraction applying the Maron–Pierce model. Next, a comparison of the experimental data with predictive physical models is carried out in terms of nanoparticle characteristics that affect the viscosity of the fluid, mostly their aspect ratio. The analysis of intrinsic viscosity data leads to a general understanding of motion modes for carbon nanoparticles, including those with extreme aspect ratios, in a flowing liquid. The resulting universal curve might be extended to the prediction of the viscosity for any kind of 1D and 2D nanoparticles in dilute suspensions.