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When a streamlined flow of water flows down through an ordinary tap, it's cross-sectional area decreases according to eq. of continuity due to atmospheric pressure. If the same apparatus were to be arranged in a vacuum, would the cross-sectional area of the flow decrease? And if yes, which force pushes it inwards?

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  • $\begingroup$ Presumably the argument is that in a vaccum the water stream could remain the same radius and voids could form within it. I suspect surface tension would prevent this but I don't know enough about the subject to risk an answer. $\endgroup$ – John Rennie Mar 8 '16 at 10:41
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It would be difficult to begin with to set up such an apparatus to produce a stream of water because for a flow of water from a nozzle there would need to be a pressure difference. As such the water would instantly vaporize once exposed to the vaccuum. So technically, the cross-sectional area of a stream of water would expand to fill the vaccuum it is contained in.

While mass is obviously conserved even in a vaccuum, the continuity equation is undefined in a vaccuum because it is based on a continuum assumption which does not hold when the mean free path of particles is too large (which is the case in a vaccuum)

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Equation of continuity is basically mass conservation. It can write more simply in case of incompressibility, but it can still be written with varying densities.

BTW interstellar medium and nebula can be considered as fluids, at the appropriate scale of time and space.

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  • $\begingroup$ You seem to be using a different continuity equation for your answer than Apoorv is for his question. $\endgroup$ – Asher Mar 8 '16 at 14:17

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