The so-called Reynolds stress may give a measure of the self-consistent flow generation in turbulent fluids and plasmas by the small-scale turbulent fluctuations. A measurement of the Reynolds stress can thus help to predict flows, e.g. shear flows in plasmas. This may assist the understanding of improved confinement scenarios such as H-mode confinement regimes. However, the determination of the Reynolds stress requires measurements of the plasma potential, a task that is difficult in general and nearly impossible in hot plasmas in large devices.In this work we investigate an alternative method, based on density measurements, to estimate the Reynolds stress, and demonstrate the validity range of this quantity, which we term the pseudo-Reynolds stress. The advantage of such a quantity is that accurate measurements of density fluctuations are much easier to obtain experimentally. Prior to the treatment of the pseudo-Reynolds stress, we present analytical and numerical results which demonstrate that the Reynolds stress in a plasma, indeed, generates a poloidal shear flow. The numerical simulations are performed both in a drift wave turbulence regime and a resistive interchange turbulence regime. Finally, the implications of misaligned probe arrays on the determination of Reynolds stresses are investigated, and alignment is found to be important but not severe.