# Swirling water while draining?

1. Dec 7, 2004

### SAZAR

What's an explanation?

(because some people (which I hear for the first time on NET) say that it doesn't have to do with that Earth rotating effect (what's it called...))

2. Dec 7, 2004

### Tide

You're thinking about the Coriolis force? That's not the explanation. I has more to do with the detailed shape of the drains and pipes.

3. Dec 8, 2004

### Coolblueflame

left right drain water

MR. TIDE is correct...and up till recently (relativly speaking) lol i too blieved this all too common misnomer ...it is indeed the dynamics of several factors in the desighn of the plumbed system... who woulda thunk it?

4. Dec 8, 2004

### SAZAR

Yes - coriolis "force" - that's what I meant, but I wasn't sure if the spelling is correct so I didn't write it...

That's what they told - the moment of force already existing in the movement of water creates swirling (not coriolis effect), and shape of object that contains water, BUT!..

...What would happen if you would have completely round container, and a hole at the exact center of it (theoretical container, perfect shape), in perfectly still conditions around it (no additional forces of any kind except those Earth makes... you know what I mean)? Then you open the hole on the bottom of it, and the water leaks out creating cone of air toward the hole. Would there be vortex or not?

-----------

It is hard for me to accept that Earth's gravity/coriolis actually does not create this swirling effect, because:
1.) I remember that when i tried to spin the water to the other direction it didn't do the work (water still wanted to go the way it goes).
2.) I think there is TOO logical explanation for it in context of gravity/coriolis effect: points on the Earth's surface spin in different speeds (because Earth does one full circle around itself in 24 hours; latitude of Earth-ball at poles is smallest, and on the equator it's at its greatest - so points on the Earth nearer to the equator travel greater distances (e.i. their speed is greater)). Now at every volume of water on Earth there is one side that is nearer to the equator, and one side that is further. The greater the distance between those two, the effect will be more obvious, but that's not the only factor - the greater the change of weight water volume loses, greater the effect (that's the other factor). It doesn't matter how small this difference of speeds is, because it's enough that there IS difference, and the weight loss would make it greater (because the force is same, and weight becomes smaller which results in greater speed!). The spinning happens because water with greater speed (nearer to the equator) is pulled toward area where the speed is smaller, so it pushes the whole lot to one direction of rotation... I think it's logical, but maybe I've forgot some other factor...

As I understand the cone of air is created because the weight quantity of water, drops at the leaking hole, so the surrounding water leaks in (with certain speed), making the effect stronger until the pit of air above the hole reaches the hole itself because the leaking becomes faster. Is it like this or something else?

5. Dec 8, 2004

### ZapperZ

Staff Emeritus
There is a difference in stating that coriolis force exist, and if it is significant enough that it affects your bathroom sink drainage. Maybe you should first of all LOOK UP the formal definition and mathematical description of the coriolis force, and make simple computation to see if it is large enough to show an affect at the scale you are thinking. We KNOW that it affects the weather pattern, but air masses are LARGE and they move very fast when compared to water draining out of a bathroom sink!

People have tried testing this, and the conclusion is that it is VERY difficult to repeat this experiment under the identical condition due to a large number of factors (how calm the water is, can the drain be "unplugged" without initiating a "seed" force, etc.). As far as I know, Tide's response is correct, and that there have been no conclusive evidence that the coriolis force plays a major role in determining and forming the direction of the vortex in water drainage.

Zz.

6. Dec 9, 2004

### SAZAR

Who's talking about bathroom sink drainage(?); I mentioned theoretical environment where conditions are perfect... did you read my second post at all...

(And why's everybody using a word "FORCE" in "CORIOLIS FORCE" when it is not some specific force; it's just an "EFFECT" produced by difference in speeds on different points of the Earth's surface?)

My point is that maybe it isn't important how small those differences in speed produced by coriolis effect are, so it is enough that there simply IS a difference...

Let's imagine huge surfaces of watter in perfect conditions (theoretical conditions)...

7. Dec 9, 2004

### ZapperZ

Staff Emeritus
.. and let's imagine that every miniscule forces in nature, no matter how weak, must also be considered.

OF COURSE, there is a coriolis "force" acting on any volume of water. OF COURSE this is present in the most ideal situation. This has NEVER been the issue. But if you are trying to propose something, it must then have the possibility of being experimentally tested! If not, this is an exercise in futility, so why bother in the first place? You spent all that time writing down lines and lines of arguments on why it must be present (you could just look up a mechanics textbook and see this has already been treated there), and yet, if you do not have a clue on how it can be tested, what have you accomplished?

Now since we all here have agreed that, in the REAL case: (i) the effect of the coriolis force at this scale is miniscule (simple back-of-the-envelope calculation); (ii) it HAS been tested and no conclusive evidence of the coriolis force affecting water at this scale, then what exactly is there more to be said? Are you trying to convince us that coriolis force exist? And exists in a volume of water being ideally drained? Is this new?

Zz.

8. Dec 9, 2004

### DaveC426913

Yes, the Coriolis Force has an effect on very large systems - no doubt about it. It influences the direction of hurricanes afterall, most of which rotate in the same direction. We know its the Coriolis Force because this direction is reversed south of the equator.

Note that not all hurricanes are determined by the Coriolis Force; a certain fraction of hurricanes overcome the weak force and spin in the opposite direction.

9. Dec 9, 2004

### Clausius2

I have been waiting for the responses here because I'm not sure which is the truth with this stuff. I have heard people (someone) talking about pipe and drainage system geometry. Well it is true that experimentally it has an important effect, due to the fact that the drainage geometry information is propagated to the fluid in its movement if it is at low Mach Number.

If you want a theoretical model, you must employ Navier-Stokes equations.

1st case) I assume total symmetry in the entire solution domain, so the movement can be considered three dimensional but axilsymmetric. The equations that govern the movement are:

$$\frac{\partial u_z}{\partial z}+\frac{1}{r}\frac{\partial r u_r}{\partial r}=0$$ assuming incompressible flow.

$$u_r\frac{\partial u_r}{\partial r}+u_z\frac{\partial u_r}{\partial z}=-\frac{\partial P}{\partial r}+\nu\Big(\frac{\partial}{\partial r}(\frac{1}{r}\frac{\partial (ru_r)}{\partial r}) +\frac{\partial^2 u_r}{\partial z^2}\Big)$$

$$u_r\frac{\partial u_z}{\partial r}+u_z\frac{\partial u_z}{\partial z}=-\frac{\partial P}{\partial z}+\nu\Big(\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial u_z}{\partial r}) +\frac{\partial^2 u_z}{\partial z^2}\Big)$$

Take a look at this. No tangential (\theta) movement is implemented with this equations under assumption of total axilsymmetry. It is the "simplest" model for calculating the steady discharge process. As you have pointed, we could take into account the coriolis force. To do that we have to view the event from a non-inertial reference frame (the Earth). Let's compare its order of magnitude with convection forces:

$$\frac{O(Coriolis)}{O(Convective)}=\frac{\rho\omega v}{\rho v^2/D}=\frac{\omega D}{v}$$

where $$\omega=\frac{2\pi rad}{24 hours}=\frac{2\pi}{86400} rad/s$$ is the velocity of rotation of the Earth.
D is the diameter of the hole and v is the characteristic velocity of discharge. A further analysis will give you $$v\approx \sqrt{gH}$$ where H is the height of the water level.

In fact you can check that:

$$Fr=\frac{\omega D}{v}<<<1$$ for the most cases. Fr is a modified Froude Number of the flow.

To sum up: we have checked that coriolis force is an effect of secondary order in this kind of flows, and in particular at this scales (D). For large turbulent scales, like hurricans or tornadoes, this modified Froude Number is of the order 1, so that the effect of the Coriolis force has to be considered. At the flow you have considered, the eventual vorticity probably is provoked by means of the propagation of small perturbations in the flow. That propagation is helded at experimental flow, due to theoretically unexpected boundaries (rugosity) and unsteady effects. I don't really think it is due to Coriolis force, and I have proved my opinion.

Hope that helps.

Last edited: Dec 9, 2004
10. Dec 14, 2004

### LURCH

Now that I did not know. I thought all hurricanes and cyclones obeyed the Coriolis directions, and only a few smaller storms varied.

11. Dec 15, 2004

### DaveC426913

Good point. Don't take my statement as gospel.

Googling the terms turns up definitions for oppositely-rotating storms, cyclone and anti-cyclone. It seems to suggest that they each have a different cause (pressure/temperature). I guess that's not the same as suggesting some hurricanes actually run counter to Coriolis. Hurricanes are cyclonic.

http://www.atl.ec.gc.ca/weather/hurricane/hurricanes9.html

http://hurricanetrack.com/hgloss.html [Broken]

Last edited by a moderator: May 1, 2017
12. Dec 17, 2004

### ObsessiveMathsFreak

The reason for the confusion surrounding this matter is of course the Simpsons episode where Lisa convinces Bart that water will always drain counterclockwise in the northern hemisphere due to the coriolis effect. Bart can even be seen trying( and failing) to make the water drain in the opposite direction by sloshing it with his hand. This is later achieved in the episode in the US Austrailian embassy, where engineers have installed a large and complicated gyroscopic contraption on all the embassy toilets to make them spin "The american way"(Leading to a tearful rendition by Homer of the national anthym).

It is true that the Coriolis effect is present in draining water, however it is negligable! Water will not drain only counterclockwise in the northern hemisphere! In reality, its spin is dictated by the shape of the container and other initial conditions. Barts hand would in fact have cause the water to drain in the opposite direction and a simple change in he shape of the cistern outlets on th etoilets would have saved the US taxpayer such great expense! :E

Your sink will most likely drain in a random direction. If you left a large bathtub still for a number of hours and then openen a tiny drain at the bottom, then perhaps coriolis "forces" will be effective. However in reality this effect is confined to very large fluidic disturbances over large time scales. i.e. Cyclones and anticyclones. Oceeans are also effected, and one might presume that perhaps magma flows are effected, but that last one was a guess on my part.

13. Dec 18, 2004

### Clausius2

To add something more, maybe the flow is no longer laminar, it will be fully turbulent:

-Water height=10cm
$$v=\sqrt{gH}\approx 1m/s$$

-Hole Diameter=D=1 cm

$$Re=\frac{\rho v D}{\mu}=\frac{\1000\cdot 1\cdot 10^{-2}}{1.12\cdot10^{3}}=8958$$

The flow is turbulent, so it will have a lot of small variations which surely provoke instabilities and eventually the presence of great vorticity in axis direction.

Another idea: Imagine a reservoir filled with water. Suddenly, a hole is practised on one side, so the water flows out through the hole. Hence the gravity is perpendicular to flow. Do you think just in the hole section is it going to be any swirl or not? And do you think that swirl is caused by Coriolis?.

I don't think so. That swirl will be enhanced by turbulence if the hole is enough large. If not the flow remains laminar and surely axilsymmetric if and only if the hole diameter is small campared with the reservoir characteristic lenght.

14. Dec 20, 2004

### abertram28

"It is true that the Coriolis effect is present in draining water, however it is negligable!

"Your sink will most likely drain in a random direction!"

these two statements are in opposition. if your sink does drain in a truly random direction resulting from minute changes in initial condiditions and a near random result is the outcome, then any systemic and continuous force would have a great impact on the general solution. if the coriolis effect is actually present then it would definately dicatate that on a noticeable level the drain would have a directional preference.

you have all said it yourself many times. the coriolis effect IS present. then you go on to say that if there were no initial conditions, the water would drain non-preferentially. so, since the coriolis effect is always in the same direction, it would skew all initial conditions toward a preferred spin.

im not understanding how it can be totally random if very systemic forces are at work. my toilet ALWAYS flushes the same way. and no matter what i do, spinning the water in the sink always results in failure to change the drainage direction, and there is little in the way of non-symetrical pipe design that could effect it. water doesnt even reach the non-symetrical parts before the spin is initiated. someone just tell me why the coriolis effect doesnt apply when the size of the object is "small" and i will be happy.

until then, this thread is as much BS and hype as every other site, IMO. dont get me wrong, PF rocks, but someone please rescue all of us...

btw, i have read the articles about this effect and much of the >mis<information. i do understand that the relative magnitude of the force is smaller... but we werent comparing it to any force in particular at the beginning... right? and the statement about randomness and relationship between cause and effect was made in very poor context. my initial remarks about the use of those statements remains unchanged. coriolis DOES dictate the tendancy to rotate one direction or the other given that identical initial conditions have no tendancy. that is what those two quotes and my remarks show.. in an ideal condition like the original poster suggested, coriolis does dictate. however small it might be, it is not random, and most initial conditions could be attributed to nearly random circumstances. one thing you could not have would be a pipe system or hole/bucket system that favored one spin. it is obvious that some forces are larger than coriolis, but which ones, why, and when?

Last edited: Dec 20, 2004
15. Dec 20, 2004

### ZapperZ

Staff Emeritus
The gravitational force from Alpha Centauri is unbelievably small here on earth, but it IS present. Does that mean where Alpha Centauri is at any given instant can be detected and affect the dynamics of our weather system? Let's get REAL now. If we don't even consider the effects of gravity on a beam of electrons, what possible effects can you see from a "non-zero" gravitational effects from Alpha Centauri?

Now, all you need to do is find an order-of-magnitude calculation of how big the coriolis force is for a typical volume of water in a sink moving with that kind of speed. Then figure out if any possible initial condition is enough to wipe this out. Just because something is "non-zero", it doesn't mean it is significant enough to affect the dynamics of the system. You are more than welcome to conduct your own experiment. I'm sure Am. J. Phys. or Eur. J. Phys. would be more than happy to publish your result if you can actually detect the coriolis force at this scale, especially when all of the other attempts to find its effect inconclusive.

Zz.

16. Dec 20, 2004

### Janitor

Sinks are waaaaaayyyyyy too small for the Coriolis effect to matter. Same for somewhat bigger things like dust devils and tornadoes.

17. Dec 21, 2004

### Sneaksuit

If you drilled a hole exactly in the center of a container there would be no swirl no matter what the shape and size of the container as long as the top is open to the atmosphere. There is never a swirl in a seperatory funnel...the level of the liquid lowers evenly on a horizontal plane unless you have the stopper on, in which case sometimes a swirl can occur and the air comes up from the bottom.

18. Dec 21, 2004

### da_willem

http://math.ucr.edu/home/baez/physics/General/bathtub.html

19. Dec 21, 2004

### Clausius2

Sometimes I feel myself ignored in this forum. Is it not clear enough the mathematical demostration I made above?. Despites how one can fundament his arguments, always there are people who seem to ignore the comments.

I have demostrated Coriolis doesn't apply when the size of the object is small, so you're happy yet.

The movement in your toilet is not random at all. I have said before that turbulence is not random at all. The swirl cause can rest over a million of causes. But the cause of Coriolis effect is negligible. Why don't you jot down in the list the effect of centrifugal force experimented by the earth spinning around the sun or the entire galaxy, the possible conductivity of the water and its influence in the movement via MagnetoHidroDinamics equations?. We would show you all that effects are negligible compared with these others:

-The proper geometry of the outlet.
-Microscopic wall rugosity.
-Initial conditions.
-Reynolds Number.

All those effects are responsible of turbulence, which is to my understanding the principal cause of swirling. It is not an external instability, but internal instability cause by the influence of viscous effects at first sight not forecasted by us. Sure you're water toilet spins always in the same direction: you have the same geometry, same initial conditions, same walls.

DO not try to compare the flow with an idealized flow. Any mathematical model written via Navier Stokes would have to consider the two first effects put above. That's nearly impossible. It has been possible only recently via Direct Numerical Simulation. So that, pay more attention to the proper regimen flow instead of imagining forces which are negligible at this scale compared with the turbulent stresses.