Copepods can perceive moving predators and prey by means of the hydrodynamical disturbances these generate. We formulate a simplified, general model of the fluid disturbance generated by a plankter that is moving or generating a feeding current and we estimate the magnitude and attenuation of the different components of the fluid disturbance. We use this model to argue that prey perception depends on the absolute magnitude of the fluid velocity generated by the moving prey, while predator perception depends on the magnitude of one or several of the components of the fluid velocity gradients (deformation rate, vorticity, acceleration) generated by the predator. On the assumption that hydrodynamic disturbances are perceived through the mechanical bending of sensory setae, we estimate the magnitude of the signal strength due to each of the fluid disturbance components. We then derive equations for reaction distances as a function of threshold signal strength and the size and velocity of the prey or predator. We provide a conceptual framework for quantifying threshold signal strengths and, hence, perception distances. The model is illustrated by several examples, and we demonstrate, for example, (1) how larval fish behaviour is adapted to allow their undetected approach up to the strike distance of their copepod prey, (2) that prey velocity is much more significant for prey encounter rates than traditionally assumed, even for cruising predators, (3) that prey perception is strongly biased towards large and rapidly swimming/sinking prey particles, and (4) that the model can accommodate the 3 orders of magnitude variation in clearance rates observed in the copepod Oithona similis feeding on motile protists and sinking particles. We finally discuss the implications of hydromechanical predator and prey perception to trophic interactions and vertical particle fluxes, and suggest important research questions that may be addressed.