# Explanation for breaking up of a stream of water into droplets

Water falling from a tap eventually breaks into droplets at a particular distance from the tap. The distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. What is the valid explanation for this phenomenon?

My own line of reasoning is as follows : let $D$ be the critical distance measured from the tap, i.e. the distance at which the water breaks into droplets. At a distance $d<D$ the flow can be assumed to be streamlined to a good approximation; in which case the cross-sectional area of the stream goes on steadily decreasing down the flow. Due to this, the surface energy per unit volume associated with the surface of the water should go on increasing with the distance from the tap until it reaches a point where it becomes greater than/equal to the surface energy of the same volume of water as a water drop. At this distance, by minimisation of potential energy the water should break into droplets to minimise the surface energy. Let's say this happens when the cross section of the flow reaches a threshold value $A$. Now if the volume flux is low; it would mean that the cross sectional area at the tap is itself low. Due to that, the threshold area $A$ would be attained at a lesser distance from the tap. This probably explains the observation that the distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. Am I right? Please correct/add to my explanation.

$D = k_{1}\left (\frac{F^{2}\rho _{w}}{A\gamma_{s}} \right )^{k_{2}}$