While draining a good amount of water into my sink a vortex formed. I’ve watched dishwater in industrial sized sinks drain, and often swirled the water to coax a vortex. Sometimes it would break contact with the drain due to what seemed like a limitation on it’s depth.
Is there a limiting factor with vortexes in water?
As we await the chemists and physicists, I submit viscosity and surface tension will make an appearance.
It would also be interesting to see if pressure came into play at such a small level.
Not exactly a vortex, but the Corryvreckan, the third largest whirlpool in the world is off the coast of Scotland. A dummy was thrown into it with a depth gauge. The gauge was marked as reaching a depth of 262 when it was recovered.
262… What?
I would expect the more you were able to swirl the water, the deeper the vortex could go. But also, that adding turbulence while swirling the water could make it break up at a shorter depth. That might have been the limiting factor.
Now, are we talking about the funnel shaped air pocket or the entire column of water? I mean, just to get it out of the way, the North Pacific Gyre is probably too big, right?
Hmmm, I’d bet that cavitation plays a major role here, good point.
The former. Unless I’m grossly misguided, a Gyre is a horizontal flow similar to the jet stream, whereas the vortex I’m asking about is vertical. I will clarify my question in my next post.
Ok, so a vortex or whirlpool can occur in nature, and has limiting factors. My question is based on a massive sink on Earth that drains water. Hypothetically of course.
Is fluid friction a thing? When I’ve made a vortex in an industrial sink it was easy to get the water to spin, but the contact of the vortex (the air part) with the drain would falter. This implied suction to me, but that can’t be if there’s still water at the bottom.
Could it be that this vortex has angular momentum fighting against the minimal pressure of the tub of water?
Yeah, I figured that’s what you meant. Just to throw my two cents in, I’ll suggest that muddy water, being heavier, will throw out a bigger vortex than say, potable water.
Also, the speed of the current increases by how far away the water is from the river banks.
I was really hoping to get a scientific answer or theory about this.
Bump.
I believe you are asking about the plug hole vortex. Here’s the fluid dynamics for it.
The height is given by equation 2.13 on page 44.
That’s interesting, but it’s only approximate, since it implies an infinite depth.
Muddy water will have a higher density (owing to the suspended silt in the water) but will also give the water a higher dynamic viscosity. Which factor dominates would depend on the relative measures of those two factors.
The short answer to the question of the o.p. is that yes, there is a maximum depth that a columnar vortex (henceforth referred to as a spout) can sustain. However, determining that length that can practically be sustained is complex and approximate in practice.
The governing relationship here is what fluid dynamicists call the Reynolds number, Re, which is a dimensionless number of the flow that is essentially the ratio between inertial forces (e.g. those due to the density of the fluid) and viscous forces (due to internal shear within the fluid) along with the characteristic length of the fluid and kinematic velocity of the flow. This depends not only on the properties of the fluid but also the geometry of the boundary and any baffles or other influences on the continuity of the flow. Flows with low Re tend to flow in a very laminar (non-turbulent) fashion and for a given rotational rate can support a longer, more stable spout which will remain attached to the drain. A higher Reynolds number (Re > 2300) flow will tend to detach and ‘wander’ around because of instabilities in the flow.
The actual mechanics of what is going on with the draining fluid forming a rotating spout bears some discussion. For simplicity, we’ll talk about a relatively narrow basin with a cylindrical section (which we’ll call the rotational volume) and a drain located at the symmetry axis. Furthermore, we’ll assume a purely Newtonian fluid (one in which the viscous forces are proportional to the rate of local dislocation at every point in the fluid) with an irrotational outer boundary (i.e. the fluid at the walls and floor of the basin are constrained not to move). Once we open the drain plug, rotation of the fluid is due to conservation of angular momentum; that is, as the fluid flows toward the central axis (as it has to in order to reach the drain) the rate of rotation increases in order that inertia is conserved. Although it is often asserted that this is due to the Coriolis effects of the Earth’s rotation, in truth the initial conditions of the fluid (i.e. rotations imparted when you pull the drain plug up) and imperfections in the shape and misalignment of the rotation axis to the basin axis will dominate. Even with perfect symmetry you will always end up with some amount of rotation, though with a very low Re flow and a large drain aperture it may not be visible.
So, essentially what is happening is that the fluid at the basin boundaries is not moving at all, and the flow at the free boundaries (i.e. the top surface and the inside of the spout) will move as fast as it needs to in order to maintain conservation of angular momentum, with the rate of rotation in the radial direction varying linearly. As the flow near the basin flood is constrained from motion in two directions, the spout tends to form an asymptotic curve about the axis (assuming the drain can be treated as a point) the shape of which is governed by the ratio of radial acceleration versus the downward acceleration due to gravity. Note that ambient pressure and surface tension at the free boundary plays no part in this; as long as there is no significant differential between the free surface and the drain, the ambient pressure makes no difference in terms of flow behavior. Ultimately, the maximum length is determined by having a Re at the drain that is <2300. In theory, pure water with no dissolved air should be able to sustain spouts with a very long depth to diameter of the rotational volume.
Now, the real world is more complex than this highly idealized scenario. For one, for a real sink or basin the effective rotational diameter is much, much smaller than the dimensions of the basin owing to nonlinearities in the real viscosity of a fluid; that is, only a narrow cylinder of the body of water is participating in the rotation and there is no clear boundary. Another factor is often the geometry of the drain itself; if not perfectly symmetric it will cause instabilities in the flow which will propagate back up the spout or cause the flow to detach. Yet another consideration is that water typically has a significant amount of dissolved air, which will be drawn out at the tip of the spout into a true vortex (where pressure is significantly below ambient) which will result in cavitation and cause the spout to detach. So the maximum depth of the spout compared to the diameter of the rotational region is always significantly less simple theory would predict.
In predicting of real world flows, empirical rules and/or observational data is typically employed in order to characterize the type of flow phenomena which dominate (often referred to as the “flow regime”). Even with the use of direct, high fidelity numerical simulation, e.g. the various methods of computational fluid dynamics, such methods are employed to validate simulations because of the wide variability in behavior and contributing phenomena.
Stranger
Fantastic. Thank You!
Metres, apparently.
Nice to have you back Stranger.
Was he gone? Okay, that was a dumb question given your reply. Glad to see he is back. I’ve been absent long enough to have not noticed that he was away.