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A complete thermal fluid dynamics analysis of a sprinkler droplet following its path from the sprinkler nozzle to the ground is made difficult by the high nonlinearity of the differential equations describing the phenomenon. This fact, caused by a great inter-dependence between the parameters that play a role in the process, is partially overcome in this paper by representing the process in terms of force balance to which a few simplifying hypotheses are applied. The goal of this approach is to make the description entirely analytical thus avoiding any empiricisms that could limit the generality of the study. The model realised is able to provide reliable kinematic data, which prove to match significantly with data available in literature, especially for higher Reynolds numbers. The paper also shows an application of the model to the computation of the aerial evaporation of a water droplet: quantitatively, this part of the study is able to provide an upper limit of the friction-induced phenomenon only, however qualitatively the consequent analysis of the results opens a new window on the full understanding of the aerial evaporation of sprinkler water, highlighting the possible role played by certain environmental parameters, such as air friction and air temperature. This latter analysis also involved careful experimental activity, which is also presented herein.

Theoretical and experimental analysis on the thermal fluid dynamics of water droplets in irrigation