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I noticed that pouring tea from a cup to a plate leads to a horizontal jet of the fluid.

enter image description here

( You can click on the image to see video)

The jets were linear and extended to both the directions from its point of contact with the fluid. The speed of flow in these jets was higher than that of the radial flow*. I could reproduce the effect better using water.

  • Why do these jets form? Why doesn't the fluid just flow radially?

I know that freely falling fluids have shape oscillations, which causes the periodic elongation of its cross-section.

enter image description here

( You can click on the image to see video)

I noticed that these jets (red lines) were always orthogonal to this direction of elongation (green lines) at their point of contact. Naturally, I would expect this direction to be parallel to that of the elongation. The following video illustrates this well.

enter image description here

( You can click on the image to see video)

  • Why does the jet flow orthogonally to the plane of elongation?

*For a perfectly cylindrical stream, the cavity is circular.

enter image description here

Since an elongated cylinder is like two closely placed cylinders, shouldn't the cavities be a combination of the two circles, i.e an elongated circle? In fact, it does turn out to be an elongated circle, but the elongation is in the wrong direction.

enter image description here

This suggests that jet velocity is higher than the radial flow velocity.

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  • $\begingroup$ I've noticed that the jet hitting the horizontal plane isn't perfectly circular (cylindrical).Nor does it hit that plane at a perfectly right angle. $\endgroup$ – Gert Apr 16 at 16:57
  • $\begingroup$ Since an elongated cylinder is like two closely placed cylinders, shouldn't the cavities be a combination of the two circles, i.e an elongated circle? In fact, it does turn out to be an elongated circle, but the elongation is in the wrong direction. Could you please clarify what elongation and in which direction in the plane of the plate? What cavity? Which is the wrong direction? $\endgroup$ – lineage Apr 17 at 5:30
  • $\begingroup$ @lineage By cavity, I mean the area near the point of contact of the fluid and the plate, which has a relatively thin fluid layer. You can see this clearly in the second last image. $\endgroup$ – Krishnanand J Apr 17 at 5:40
  • $\begingroup$ by elongation do you mean the deformation of the ideally circular downpour cross-section to more like an elipsoidal or a Cassini oval? $\endgroup$ – lineage Apr 17 at 5:54
  • $\begingroup$ @lineage In the last image, as the fluid touches the plate, you can see that the stream is not perfectly cylindrical. It is stretched in a direction. I expected the cavity to stretch along the same direction as well. But it was seen that the 'cavity' stretched out perpendicular to it. $\endgroup$ – Krishnanand J Apr 17 at 5:55
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I think the elongation is caused because some of fluid (at the top) flows freely from the cup, whereas some is subject to viscous drag from the cup when pouring, and thus has lower horizontal velocity as it leaves the cup.

When the fluid hits the plate, fluid tends to flow away at right angles from the surface of the downward flow --- a perfectly cylindrical downward flow would produce a radial flow outwards from the point it hits the plate. Two such cylindrical flows next to each other would each prevent radial flow in the direction of the other. This would redirect fluid from both so that it goes perpendicular to the line between the flows.

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  • $\begingroup$ Can you please elucidate as to why the jet speed is higher than surrounding flow? This imo explains the distortion of the hydrological jump. $\endgroup$ – lineage Apr 25 at 21:24
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That's easy. Notice that the jets form between the two large vertical "pipelines" that feed the intersection with the plate. Both pipeline columns create a high stagnation pressure where they contact the plate and that pressure accelerates flow along the plate in a laminar film, outward from the foot of the pipeline. Surface tension keeps the laminar flow area thin in the vertical direction. The laminar flow of both columns intersect however, causing a further, but slight increase of (dynamic) pressure, pushing the laminar flow in at that intersection both a little upward and outward in the geometry that looks like a jet. The jet flow is confined to itself because as it moves along, the intersection line of the two laminar spreading flows keeps feeding it. Turbulence eventually dominates and the more ordered flow gets broken up.

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For a perfectly symmetric stream, you have a white hole horizon.

I quote Ulf Leonhardt's book Essential Quantum Optics, p.210: "Inside a certain ring the water surface is very smooth, but outside waves are appearing. Where the stream from the tap hits the metal, the water flows faster than the wave velocity. Then the water flows outwards and gets slower. Waves can not enter the region where the water exceeds their velocity, but they are formed at the critical radius where the water has reached the wave velocity (...) Seen from an astrophysics perspective, this resembles a white hole, an object that nothing can enter."

You can read also https://arxiv.org/pdf/1010.1701.pdf.

Other regimes are shown in http://math.mit.edu/~bush/?p=843

I guess that the asymmetry of the stream from the tap breaks this balance, and the waves (the jets) appear by the side the water from the tap is flowing at the wave velocity (or very close) when hitting the metal.

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  • $\begingroup$ the analogy to a white hole....does that explain the jet formation or the orthogonality and deformation of the circular hydraulic jump? $\endgroup$ – lineage Apr 19 at 17:22

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