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When one turns on the tap in the kitchen, a circle is observable in the water flowing in the sink. The circle is the boundary between laminar and turbulent flow of the water (maybe this is the wrong terminology?). On the inside the height of the water is lower than on the outside. I'm sure that you have seen it many times, if not you can try it out yourself.

I found out by experiment that the effect is most likely independent of the curvature of the sink, as it works in strongly curved bathroom sinks as well as in flat kitchen sinks.

Why is there a circle, why not a gradual change and what is happening qualitatively and/or quantitatively in this system?

As I have not found a satisfying answer to this problem yet, every time I turn on a tap, I am reminded of my own ignorance. It is really annoying.

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Turns out that the hydraulic jump is far more intriguing than one might expect. It allows you to construct an analog model of a white hole in a kitchen sink - arxiv.org/abs/physics/0508215 !! –  user346 Apr 10 '11 at 4:46
    
Similar Question –  JoeHobbit Apr 10 '11 at 14:07
    
@user2843: an answer that just contains a link isn't much help to the community here, and besides, pointing out a similar question is best done as a comment. I converted this one for you. –  David Z Apr 10 '11 at 21:03
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1 Answer

up vote 8 down vote accepted

You are observing a hydraulic jump.

The Wikipedia article is very good, so I won't try to out-do it.

In brief summary, when the water starts running out from the place where it hits the sink, the same flux is spread out over a larger and larger circumference as you move out. This means the flow gets shallower and moves more slowly as you move further out.

If a wave propagates in this flow, its wave speed depends on the height of the water. Its speed relative to the flow also depends on the flow speed. So the propagation of wave changes as we move further out as the flow underneath the wave changes.

The wave itself changes the height of the water - the water is deep at the peak of the wave and shallow at a trough. Different parts of the wave moves at different speeds. This is clearly a non-linear phenomenon. Similar to waves crashing at the beach, eventually the propagating wave crashes over on itself. This causes a "hydraulic jump". The main effects are

  1. The speed of the flow goes down.
  2. The height of the water increases, converting some kinetic energy to potential.
  3. Some energy is lost to heat through turbulence.

The physics of water in your sink is not very easy - since the flow is so shallow, surface tension has considerable importance. You can learn more details in the Wikipedia article linked above.

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Thank you for your answer and the link. There are a couple of points which are still not clear to me. I still do not see the physical reason why the transition is so abrupt. Or is this the not very easy part? Furthermore why are you writing about a moving wave in your answer. Isn't the wave standing still? –  Johannes Apr 10 '11 at 20:05
    
There is an abrupt transition because there is a certain depth of the water where the wave starts breaking. The hydraulic jump is standing still, but it itself is not a wave. There are waves traveling radially outward from the place where the water hits the sink. Those waves all break at the same point. –  Mark Eichenlaub Apr 10 '11 at 21:09
    
Why do these waves (I presume they are differing in wavelength and amplitude) break all at the same point? And why should there be waves at all if the water is flowing in the sink at a constant rate? –  Johannes Apr 10 '11 at 22:34
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Roughly speaking, the water flow isn't smooth, but the not-smoothness is roughly constant. You'll really just have to read the article and links therein for more detail, sorry. –  Mark Eichenlaub Apr 10 '11 at 22:59
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Regarding the location of the jump, I think it's quite relevant that over a jump the Froude number transitions from supercritical (>1) to subcritical (<1). The Froude number is kinda analogous to the Mach number, with similar implications for wave propagation - in supercritical flow, waves cannot propagate upstream (i.e. towards the center), in subcritical flow, they can. So waves travelling inwards all have to terminate at the jump. This again plays towards the "white hole" analogy already mentioned somewhere else here. –  Christoph Jun 9 '11 at 20:49
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