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Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the space which surrounds the pipe. But (in absence of gravity) the water stream will not be constant anymore. There will be formed waterdrops around this water stream. Why?

I think that such a process can be modeled by stochastic differential equations. The probability of having a water stream $\Omega$ decaying in a set of $N$ different waterdrops $\Omega_i$ indexed with $i \in \mathbb N$ and $\Omega = \cup_{i=1}^N\Omega_i$ may be denoted as $w(\Omega \mapsto\{\Omega_i|i\in\{1,...,N\}\})$. Is it possible to compute such a probability? Are there models for water sprinkling existing?

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Surface tension at the air-liquid interface of the water stream will tend to minimize the interaction energy by decreasing the interfacial area. The shape which has the lowest interfacial area per unit volume is a sphere (droplet). You may also be interested in the Plateau-Rayleigh instability which deals with the formation of droplets from a stream.

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