  How anisotropic particles rotate and orient in a flow depends on the
hydrodynamic torque they experience. Here we compute the torque acting on a
small spheroid in a uniform flow by numerically solving the Navier-Stokes
equations. Particle shape is varied from oblate (aspect ratio $\lambda = 1/6$)
to prolate ($\lambda = 6$), and we consider low and moderate particle Reynolds
numbers (${\rm Re} \le 50$). We demonstrate that the angular dependence of the
torque, predicted theoretically for small particle Reynolds numbers remains
qualitatively correct for Reynolds numbers up to ${\rm Re} \sim 10$. The
amplitude of the torque, however, is smaller than the theoretical prediction,
the more so as ${\rm Re}$ increases. For Re larger than $10$, the flow past
oblate spheroids acquires a more complicated structure, resulting in systematic
deviations from the theoretical predictions. Overall, our numerical results
provide a justification of recent theories for the orientation statistics of
ice-crystals settling in a turbulent flow.
