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Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r?

On one hand, if the rate at which water flows through the ring were greater than the flow rate of the faucet, wouldn't that violate conservation of mass?

On the other hand, shouldn't water be traveling faster through the lower hoop, so it should have a higher flow rate?

I've asked some people about this, and I've been told that the water column will inevitably become thinner as it falls such that the flow rate through the hoop will be the same as r. Is this true?

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    $\begingroup$ Yes, it is true. What other possibility is there? $\endgroup$
    – Chet Miller
    Commented Oct 5, 2023 at 22:06
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    $\begingroup$ you can imagine it still as a changing tube , when they get accelerated due to gravity , velocity increases , hence its area decreases. $\endgroup$
    – Razz
    Commented Oct 6, 2023 at 1:51

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If measured in liters/minute, the falling stream of water conserves mass so its flow rate remains constant (there's nowhere else for the water to disappear to).

The velocity of the falling stream increases with distance from the origin because gravity is accelerating it. the stream responds by necking down and becoming progressively thinner as it speeds up.

The end of this process occurs when surface tension disassembles the stream into a string of individual droplets. These will speed up until they achieve terminal velocity.

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