Why Does Water Flow Narrower from a Faucet at the Bottom?

[valeska_dmell]

Hello everyone.
Que: Is there a reason for water flowing from a faucet to be narrower at the bottom then the top?? Like a physics reasoning?

 

[turbo]

If the water comes out under modest pressure, it will accelerate as it falls toward the sink. The total mass passing any particular point along the stream per second will remain constant. Is that a good enough pair of hints?

 

[valeska_dmell]

Would it be that though the mass is the same as you said the velocity of the water flowing will be different at different points and hence it necks down?

 

[russ_watters]

Yes.

 

[Prologue]

I don't find that reasoning appealing. What happens to a ball of water in space as it falls to the earth? Does it spaghettify? The answer is 'yes', but not very much. I doubt the difference in a few inches will change g enough to have a significant effect.

I would lean toward surface tension forces along with the water being attached to the faucet. If there were no surface tension forces and no faucet, just a falling ball of water, then the water would not neck down. If there was a just a glob of falling water (with surface tension) it wouldn't neck down. But combine the two and you get necking down. Think of a water droplet that is just barely hanging on to the end of the faucet, not actually falling but coming close to falling off. It too necks down. It does this because in that configuration the g forces balance the surface tension forces. Extend that to the water falling down and then you get necking down. The water is pushed out and falls but is still attracted to the water behind it, also, now it is in a sort of cylindrical shape. Then the attraction of the water to itself squeezes it down into a skinnier cylinder as it falls.

There still is a problem though, after a while the water tube turns into a bunch of droplets. But again, look back at the 'static' water droplet case. After a certain point, the droplet weighs too much and the water on top can't hold it up anymore. So the sides collapse in and now you have a free falling droplet. So, after a point, the flowing tube has the same effect. The stuff is so skinny that the force pulling it up is less that the force trying to pull in cylindrically, so it collapses, forms droplets and breaks away from the pack.

The combination of the falling water's attraction to the water already in the faucet, and the falling water's attraction to itself give the necking down effect.

I know that equal mass flow argument is still correct (because it is a continuous tube), but it isn't all that revealing to me. Some questions are taken for granted like: Why is it a continuous tube? But, of course, you can almost always take a theorem and form an axiom or the flip flop of that, so whatever works.