# Why do free-falling fluids contract?

## Main Question or Discussion Point

Let's say you have a stream of water leaking out of an elevated barrel, and we ignore the effects of air resistance and assume water is incompressible.

So, the lower (and faster) the waterstream falls, the more it will contract. Sure, you say, that's because of the chemical forces between the H2O molecules. And that's pretty reasonable.

However, according to conservation of mass, if any fluid was leaking out of that tank, including ones where the forces between the molecules are very small, it should contract at the same pace as the water! Since the volume flow must be constant, Q=V*A, the further it falls the higher the velocity must become and thus the smaller the area of the stream must become - completely independent of what kind of fluid it is .

So what forces drive this contraction?

I assume the reason behind this phenomena is that the pressure in fluidstream decreases, but why? According to the Bernoulli equation, shouldn't the kinetic energy gained by the water particles be simply a result of their decreasing potential energy? Why would the pressure be converted into kinetic energy?

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## Answers and Replies

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Let's say you have a stream of water leaking out of an elevated barrel, and we ignore the effects of air resistance and assume water is incompressible. So, the lower (and faster) the waterstream falls, the more it will contract. Sure, you say, that's because of the chemical forces between the H2O molecules. And that's pretty reasonable.
reasonable and correct
- completely independent of what kind of fluid it is .
No, not quite. If there were no forces between the molecules the stream wouldn't contract. It would spray.

russ_watters
Mentor
This is a pretty common question, overlooking what should be obvious: as the water falls, it accelerates, which makes the a fixed-volume sample of it longer and therefore narrower. Simply put: it stretches.

Hydrogen bonding and aerodynamics cause both the coherent contraction of the stream as it stretches and its eventual separation into discrete drops.

ahh I see! Well, it appears I was completely off track. thanks anyway, you guys just improved my intuition in fluid mechanics! :)

Andy Resnick
Science Advisor
Education Advisor
<snip>
So what forces drive this contraction?
Could you be referring to the Rayleigh instability- the reason a stream breaks up into droplets?