Water droplets analysis: the classical and quantum hydrodynamic frameworks

The design of a sprinkler irrigation system is always associated with a full understanding of the kinematics of the droplets during their aerial path. Resolving this problem involves both theoretical and experimental considerations. Among the theoretical studies the classical mechanical approach, based on the Newton’s law, offers a useful tool to describe the trajectories of water droplets from the sprinkler nozzle to the ground. The problem becomes even more complicated when not just a single droplet alone is assessed but a multi-droplet system is accounted for. In addition to the interparameter dependencies, it is also observed an inter-droplet reciprocal repulsion, mainly due to electrical interactions between the hydrogen and the oxygen atoms of the different water molecules. An alternative to traditional classical procedures, to analyse water droplet dynamics in sprinkler irrigation, has been recently proposed in the form of a quantum approach. In this context, the whole classic-quantum and single-droplet versus multi-droplet alternatives need to be discussed and pinpointed and these are the main aims of the present paper which focuses on the theoretical part of the issue, thus highlighting the new perspectives of a deeper comprehension in the spray flow related phenomena. On the whole, the new approach leads to the concept of quantum trajectory in analogy to the well-established concept of classical trajectory and allows to recast the classical fluid dynamnic equations into the so-called quantum equations.