In metallic samples of small enough size and sufficiently strong momentum-conserving scattering, the viscosity of the electron gas can become the dominant process governing transport. In this regime, momentum is a long-lived quantity whose evolution is described by an emergent hydrodynamical theory. Furthermore, breaking time-reversal symmetry leads to the appearance of an odd component to the viscosity called the Hall viscosity, which has attracted considerable attention recently due to its quantized nature in gapped systems but still eludes experimental confirmation. Based on microscopic calculations, we discuss how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields.The semiclassical theory of electronic conduction, based on relaxation of total momentum by impurities, phonons and umklapp scattering, occupies a central place in condensed matter physics. It is therefore of particular interest to study the cases for which it fails. One case that has attracted much interest is the possibility of a hydrodynamic regime, where transport is dominated by viscous effects . One needs a large separation of scales between momentum-relaxing and momentum-conserving scattering in order to see these effects. This was recently achieved in graphene [23,24] and PdCoO 2 [25,26].Interest in such a hydrodynamic regime also emanated from a conjectured bound on diffusion constants for the hydrodynamics of strongly interacting quantum systems [27,28]. Even though the physics described in this work is semiclassical and probably still quite far from these quantum-mechanical bounds, the observations that we hope to stimulate would constitute an important first step towards the understanding of emergent hydrodynamical regimes in electronic systems.A further motivation for the work is that reaching a viscous regime for a charged fluid enables one to break time-reversal symmetry by adding a magnetic field and hence to study a non-dissipative component to the viscosity tensor called the Hall viscosity. The recent interest in this Hall viscosity emanates from the fact that it is topologically quantized in gapped systems [29]. In order to study this effect experimentally, in analogy with the Hall conductivity, the first step would obviously be to measure the classical Hall viscosity. We show in this letter how this measurement could be done by describing specific size effects from Hall viscosity in transport in restricted 2D channels under transverse magnetic fields. This paper is organized as follows. We start by assuming a perfect hydrodynamic regime and calculate ρ xx and ρ xy . We show that the 1/W 2 component of ρ xy is proportional to the Hall viscosity, thereby providing a way of measuring it. In order to have realistic predictions to compare with experiments, one should also take into account other, non-viscous effects that can lead to a sizedependent resistivity. We thus perform a kinetic Boltzmann calculation in which t...