The Faucet Question

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Fighting Lettuce
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The Faucet Question

Postby Fighting Lettuce » Mon Sep 05, 2011 10:00 pm UTC

Ok, here's a video. It's about the Coanda Effect, but that's not the point I want to talk about. Pay attention to what happens when the water is falling over the spoon. Focus on the stream just above the spoon, falling out of the faucet. Can you see the wave pattern on the surface of the stream? This can be easily verified by yourselves, putting your finger under a thin stream of water and getting it closer to the faucet, until the wave forms.

http://www.youtube.com/watch?v=Yu1zeeO9JAI&feature=player_embedded

A friend told me about this "experiment", and well, up to now, I haven't come up with anything that can explain this phenomenon. Any idea?

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Re: The Faucet Question

Postby Glass Fractal » Mon Sep 05, 2011 10:44 pm UTC

Sudden change in the speed that the water is moving, perhaps?

It happens on roads. The cars suddenly slow when they reach an accident. The braking travels backward down the road in a wave, well beyond the site of the accident.

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Re: The Faucet Question

Postby Charlie! » Mon Sep 05, 2011 10:54 pm UTC

Interesting. The waves actually just stand there!

It look like a balance between pressure waves coming out from the spoon (or my finger, when I tried it) and the restoring force of surface tension.
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Re: The Faucet Question

Postby Fighting Lettuce » Tue Sep 06, 2011 10:17 pm UTC

Glass Fractal wrote:Sudden change in the speed that the water is moving, perhaps?

It happens on roads. The cars suddenly slow when they reach an accident. The braking travels backward down the road in a wave, well beyond the site of the accident.


Mmm... I'm afraid I don't get your point :?

It look like a balance between pressure waves coming out from the spoon (or my finger, when I tried it) and the restoring force of surface tension.


Mmmm... do you think we can talk about surface tension in a stream of falling water?

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Re: The Faucet Question

Postby gmalivuk » Wed Sep 07, 2011 12:06 am UTC

Fighting Lettuce wrote:
Glass Fractal wrote:Sudden change in the speed that the water is moving, perhaps?

It happens on roads. The cars suddenly slow when they reach an accident. The braking travels backward down the road in a wave, well beyond the site of the accident.
Mmm... I'm afraid I don't get your point :?
Water molecules are the cars, the spoon is the accident, these waves are the waves of stopped/slowed cars that can extend for miles back from the actual site of said accident.

The point is that it's a fairly similar phenomenon.

Mmmm... do you think we can talk about surface tension in a stream of falling water?
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Re: The Faucet Question

Postby Charlie! » Wed Sep 07, 2011 12:27 am UTC

Fighting Lettuce wrote:
It look like a balance between pressure waves coming out from the spoon (or my finger, when I tried it) and the restoring force of surface tension.


Mmmm... do you think we can talk about surface tension in a stream of falling water?

Yes. For example, a thin stream of water will break into droplets given time. Surface tension!
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Re: The Faucet Question

Postby Fighting Lettuce » Wed Sep 07, 2011 8:07 am UTC

gmalivuk wrote:
Fighting Lettuce wrote:
Glass Fractal wrote:Sudden change in the speed that the water is moving, perhaps?

It happens on roads. The cars suddenly slow when they reach an accident. The braking travels backward down the road in a wave, well beyond the site of the accident.
Mmm... I'm afraid I don't get your point :?
Water molecules are the cars, the spoon is the accident, these waves are the waves of stopped/slowed cars that can extend for miles back from the actual site of said accident.

The point is that it's a fairly similar phenomenon.


Oh, now I understand what was he talking about! I hadn't picture the scene well. Thank you!

I agree, that seems a plausible explanation.

Charlie! wrote:Yes. For example, a thin stream of water will break into droplets given time. Surface tension!


Mmm... yes, but there you are referring to the surface tension of individual droplets, not to the surface of the whole stream, aren't you? I don't know, I always thought that a moving fluid doesn't develop surface tension, at least not so much as one that remains still. In fact, I was told that the water of the pool in springboard jumps was kept at movement just because that reason. Was I so wrong? :|

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Re: The Faucet Question

Postby Charlie! » Wed Sep 07, 2011 8:58 am UTC

Fighting Lettuce wrote:Mmm... yes, but there you are referring to the surface tension of individual droplets, not to the surface of the whole stream, aren't you? I don't know, I always thought that a moving fluid doesn't develop surface tension, at least not so much as one that remains still. In fact, I was told that the water of the pool in springboard jumps was kept at movement just because that reason. Was I so wrong? :|

Yup, you were :P I think Mythbusters did this one before, actually - it makes no difference.
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Re: The Faucet Question

Postby Zamfir » Wed Sep 07, 2011 10:48 am UTC

Fighting Lettuce wrote:
Oh, now I understand what was he talking about! I hadn't picture the scene well. Thank you!

I agree, that seems a plausible explanation.

Yeah. What you're looking at is the surface-tension wave equivalent of a supersonic boom. Supersonic shocks are the result when a flow passes a body at more than the speed at which pressure waves travel upwards. Or a body moves through a non-moving fluid.

At subsonic speeds the pressure waves pass the "information" about the disturbance forward. But in supersonic flow the incoming flow splits in a region that is unaware of the disturbance, and a region near the disturbance that does adapt to the disturbance. With a jump in pressure in between. For more complicated geometries you get a whole system of flow regions that stays fixed around the body, with (friction-smoothed) shocks and wave fans in between.

In the faucet case above, you see something similar happening. This time with the pressure waves replaced by tension waves on the surface of the flow. Those waves have a much lower wave velocity then pressure waves, so the flow from the faucet is "supersonic" with respect to surface-tension waves. You get a shock pattern around a disturbance. But instead of pressure shocks, you get (smoothed) shocks in the width of the flow.

A npther similar case are the waves generated by a ship. In that case the relevant waves are gravity surface waves. Those are a different phenomenon from surface-tension waves, with a different travel velocity. Most ships travel supersonically with respect to that velocity, so they create a surface wave pattern round them, roughly like a jet fighter does with pressure waves.

For cars, the "wave velocity "is the reaction chain of braking . It looks a bit like flow phenomenon, but there are real differences too.

Some pictures, compare them to your hand in a faucet flow:
Image
Ship generating a wavey pattern behind its bow wave. I am not sure why ships sometimes cause this wavey pattern, while supersonic aircraft only generate a "bow wave" without a wavey pattern behind it. Might be Kelvin-Helmholtz instability. A vaguely analogous case for surface tension is Rayleigh instability, which could be the driver behind the specific wavey pattern you have observed. Rayleigh instability is what causes a stream to break into discrete drops, and a weak version of it might turn the bow shock around your hand into a wavey pattern.

Image
Duck doing the same. Is cute.

Image
Supersonic flow in a channel, meeting a disturbance. See how the shocks "reflect"on the edges of the channel, and on each other? I am not sure, but something similar may happen with tension waves as they travel around the faucet flow and meet each other at the other side. That might be another explanation of the particular waviness. Note that the black-white wave pattern in the picture is an artifact of the imaging method, only the sharper regions are real flow phenomena.
Last edited by Zamfir on Wed Sep 07, 2011 11:08 am UTC, edited 1 time in total.

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Re: The Faucet Question

Postby Fighting Lettuce » Wed Sep 07, 2011 11:07 am UTC

And why is this wave significant just when the finger is really close to the faucet?

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Re: The Faucet Question

Postby Tass » Wed Sep 07, 2011 11:24 am UTC

Fighting Lettuce wrote:And why is this wave significant just when the finger is really close to the faucet?


Because the streams velocity increases the longer it has fallen. You have to generate the waves at a point were they can outrun the stream, so to speak, and be able to travel upwards.

By the way surface tension is not something water "develops"* it is always 72.8 mN/m. This value is insignificant on human scales, but play a large role from the millimeter scale and down.

*Well maybe on the picosecond time scale. If a piece of water was shattered (yes on this timescale it could be) it would take some time for the molecules to rearrange themselves, but this would minimize the free energy, so the surface tension would decrease with time towards the equilibrium value of 72.8mN/m. Of course surfactants like soap can also reduce surface tension. If a pool stands and collects impurities from the air the surface tension might change over time, but once again it would be a decrease not an increase. In any case neither of these things are relevant in the case of a running faucet, so disregard this entire footnote.

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Re: The Faucet Question

Postby Zamfir » Wed Sep 07, 2011 11:27 am UTC

On rereading my post above, I think it needs a warning: it's not an explanation. It's more a direction to look in, with pictures of other phenomena that exhibit the same effect of being unmoving in a moving flow. I do not not know for sure what causes your exact phenomenon of little waves above a finger.

Fighting Lettuce wrote:And why is this wave significant just when the finger is really close to the faucet?

Hmm, I had to find a good faucet to see it better. As I can see it, the waves don't happen if you keep my finger very close to the faucet, then become clearer as I move my finger lower, then disappear again when my finger is too low. That suggests some kind of goldilocks effect, where the flow velocity has to have a particular ratio to the wave velocity. The water accelerates as it falls down, and at some point it has the right ratio.

Pure speculation: that goldilocks ratio might be 1. So the waves above your fingers happen when the flow velocity is roughly the same as the wave velocity. If your finger is too high, tension waves travel upwards faster than the flow and disappear. If your finger is too low, they cannot travel upwards at all, and all interesting stuff happens behind the finger. Near 1 you get this special build up, perhaps. Just as aircraft encounter special flow phenomena when they travel close to Mach 1 (which they therefore try to avoid).
Last edited by Zamfir on Wed Sep 07, 2011 11:45 am UTC, edited 2 times in total.

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Re: The Faucet Question

Postby Tass » Wed Sep 07, 2011 11:42 am UTC

Zamfir wrote:On rereading my post above, I think it needs a warning: it's not an explanation. It's more a direction to look in, with pictures of other phenomena that exhibit the same effect of being unmoving in a moving flow. I do not not know for sure what causes your exact phenomenon of little waves above a finger.

Fighting Lettuce wrote:And why is this wave significant just when the finger is really close to the faucet?

Hmm, I had to find a good faucet to see it better. As I can see it, the waves don't happen if you keep my finger very close to the faucet, then become clearer as I move my finger lower, then disappear again when my finger is too low. That suggests some kind of goldilocks effect, where the flow velocity has to have a particular ratio to the wave velocity. The water accelerates as it falls down, and at some point it has the right ratio.

Pure speculation: that goldilocks ratio might be 1. So the waves above your fingers happen when the flow velocity is roughly the same as the wave velocity. If your finger is too high, tension waves travel upwards faster than the flow and disappear. If your finger is too low, they cannot travel upwards at all, and all interesting stuff happens behind the finger. Near 1 you get this special build up, perhaps. Just as aircraft encounter special flow phenomena when they travel close to Mach 1 (which they therefore try to avoid).


My intuition tells me the same.

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Re: The Faucet Question

Postby Zamfir » Wed Sep 07, 2011 11:46 am UTC

This book chapter on flow instabilities shows the phenomenon, I think. Look at picture 3. It references "Hydrodynamic and hydromagnetic stability" by Chandrasekar, the black hole guy, for a theoretical treatment. But I can't find access to that book.

The way it is described (buckling of a capillary jet approaching an obstacle) suggests a close relation to the normal Rayleigh instability in an undisturbed flow.

That chapter is fun overall, actually

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Re: The Faucet Question

Postby jmorgan3 » Thu Sep 08, 2011 6:14 am UTC

Zamfir wrote:Ship generating a wavey pattern behind its bow wave. I am not sure why ships sometimes cause this wavey pattern, while supersonic aircraft only generate a "bow wave" without a wavey pattern behind it.

I think it's because gravity and surface tension waves in liquids are dispersive, while pressure waves in air are non-(or weakly-)dispersive. In a boat's wake, the waves behind the boat, perpendicular to its direction of travel, are the exact wavelength such that they propagate at the speed of the boat. Sound waves can't do that.
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