(04-28-2014, 06:35 PM)Pancakes Wrote: The coriolis acceleration points constantly to the center of sink's tied system, vector v is tangent to the circle, w is going from the southern pole to the northern pole.
As I said, the coriolis force will be pointing strictly into the center of the sink in a very strict special case: The one that the water is already cycling in a strictly circular motion (no draining happening), in one and not the other direction.
So actually that special case cant even apply to a sink where the water is pouring out in the middle, because that would mean that the movement of the water also has a component moving to the middle of this sink (which would leave the corioilis force pointing slightly away from the center). So, this special case is not only a special case, but also one that is actually not applicable to the problem of a sink being drained of water through a hole in the middle. In addition to that, you have not explained why the numbers you calculated matter, even in this (not applicable) special case.
(04-28-2014, 06:35 PM)Pancakes Wrote: What I am saying, is that the cycle itself is caused by physical aspects, rather than the rotation of the Earth. Thus the fact if you are in Britain or Australia, doesn't affect the side the water cycles since it's neglect-able to the acceleration caused by gravity.
The rotation of the earth is a physical aspect.
The fact of whether you are on the northern or southern hemisphere does affect what direction a maelstrom can take when it pours out of the hole in the middle. Only the angular velocity of the rotation caused by the coriolis force is likely to be smaller than one will notice (likely less than one rotation per day). Its likely that other factors will affect the rotatin more than the coriolis force, for example the shape of the sink, or the way the water was moving due to other reasons, for example being stirred or being poured into the sink at a ceratin direction/angle to beign with.
However, a cylindrical shaped sink with a hole in the middle, slightly tilted, is not going to hinder the coriolis force from acing. If it is, you still havent proven why, and if its true I'd still be interested to see a correct demonstration.
(04-28-2014, 06:35 PM)Pancakes Wrote: I never said it would "stop" the particle, only that it would be as strong enough as to counter Coriolis force (or acceleration rather, m does divide out if you go for forces anyway), thus the assumption of north/south and turning-side is, well, wrong, given the fact it's deprived from Coriolis acceleration.
Thing is, tilting a a bucket with a hole in the middle introdice (or counter) a rotational movement to the water. If it does, you're doing to have to show why. If it doesnt, your very hypothesis is wrong.
(04-28-2014, 06:35 PM)Pancakes Wrote: And I thought it out myself during a lecture in Dynamics about dust particles movement in a turbulence. EDIT: My teacher also confirmed this true, though he said my numbers are slightly off (I got a smaller degree, the numbers I used here were his after fixing a few things), even though I was off by a factor of 10^-2, the degree is still VERY small.
EDIT 2: What I meant with that, in summation, is that Coriolis force is so neglectable in compare to gravity. The example of the sink in an ideal system would simply create an harmonic movement, but since the particle is also having its radius changing as it slowly sinks in the sink, it gets a bigger end speed
I hope it's better explained in this way, sorry for any confusion I might've made.
Whether the coriolis force is small compared to gravity is totally irrelevant to the problem of creating a rotation, as long as gravity doesnt introduce or counter a rotation.
Its like saying that because the speed of the earth relative to some other interstellar object is small compared to the speed of a bullet relative to your body, the bullet wont kill you when it hits you. If you want to compare the numbers, you'll have to explain why your comparison matters. This, you didnt do.
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(04-28-2014, 06:35 PM)Pancakes Wrote: The coriolis acceleration points constantly to the center of sink's tied system, vector v is tangent to the circle, w is going from the southern pole to the northern pole.
As I said, the coriolis force will be pointing strictly into the center of the sink in a very strict special case: The one that the water is already cycling in a strictly circular motion (no draining happening), in one and not the other direction.
So actually that special case cant even apply to a sink where the water is pouring out in the middle, because that would mean that the movement of the water also has a component moving to the middle of this sink (which would leave the corioilis force pointing slightly away from the center). So, this special case is not only a special case, but also one that is actually not applicable to the problem of a sink being drained of water through a hole in the middle. In addition to that, you have not explained why the numbers you calculated matter, even in this (not applicable) special case.
(04-28-2014, 06:35 PM)Pancakes Wrote: What I am saying, is that the cycle itself is caused by physical aspects, rather than the rotation of the Earth. Thus the fact if you are in Britain or Australia, doesn't affect the side the water cycles since it's neglect-able to the acceleration caused by gravity.
The rotation of the earth is a physical aspect.
The fact of whether you are on the northern or southern hemisphere does affect what direction a maelstrom can take when it pours out of the hole in the middle. Only the angular velocity of the rotation caused by the coriolis force is likely to be smaller than one will notice (likely less than one rotation per day). Its likely that other factors will affect the rotatin more than the coriolis force, for example the shape of the sink, or the way the water was moving due to other reasons, for example being stirred or being poured into the sink at a ceratin direction/angle to beign with.
However, a cylindrical shaped sink with a hole in the middle, slightly tilted, is not going to hinder the coriolis force from acing. If it is, you still havent proven why, and if its true I'd still be interested to see a correct demonstration.
(04-28-2014, 06:35 PM)Pancakes Wrote: I never said it would "stop" the particle, only that it would be as strong enough as to counter Coriolis force (or acceleration rather, m does divide out if you go for forces anyway), thus the assumption of north/south and turning-side is, well, wrong, given the fact it's deprived from Coriolis acceleration.
Thing is, tilting a a bucket with a hole in the middle introdice (or counter) a rotational movement to the water. If it does, you're doing to have to show why. If it doesnt, your very hypothesis is wrong.
(04-28-2014, 06:35 PM)Pancakes Wrote: And I thought it out myself during a lecture in Dynamics about dust particles movement in a turbulence. EDIT: My teacher also confirmed this true, though he said my numbers are slightly off (I got a smaller degree, the numbers I used here were his after fixing a few things), even though I was off by a factor of 10^-2, the degree is still VERY small.
EDIT 2: What I meant with that, in summation, is that Coriolis force is so neglectable in compare to gravity. The example of the sink in an ideal system would simply create an harmonic movement, but since the particle is also having its radius changing as it slowly sinks in the sink, it gets a bigger end speed
I hope it's better explained in this way, sorry for any confusion I might've made.
Whether the coriolis force is small compared to gravity is totally irrelevant to the problem of creating a rotation, as long as gravity doesnt introduce or counter a rotation.
Its like saying that because the speed of the earth relative to some other interstellar object is small compared to the speed of a bullet relative to your body, the bullet wont kill you when it hits you. If you want to compare the numbers, you'll have to explain why your comparison matters. This, you didnt do.
Fair enough, I guess.
The movement towards the center of the water is very slow, far slower than the angular speed (at least in the outer rim, which would determine the rotation direction) which is why I neglected it when doing the calculation for the rotation direction, should've mentioned that.
The numbers are comparison of accelerations. In the example I gave out, it simply shows out that Coriolis acceleration cannot be the reason for the rotation direction.
Note that rotation will always happen due to a turbulent nature of the sink, which happens due to other physical reasons, though these reasons such as water compression\pressure comparison (I might be using a slightly incorrect terms in English, so in a case I do, I beg your pardon) wouldn't determine the direction in which it would rotate.
Anyway back to the numbers, if we would choose a point in time and place on the outer rim, we could show, that by mere gravity reasons, that point, that very exact point, would be rotating to the other side, this would actually create an harmonic movement, and not an angular one. I think I did miss something very crucial in my calculations now that I think about it - what would need to be the angle to stop the rotation IF, it would only deprive from Coriolis acceleration. This I might do tomorrow should I have the time, but I wager the degree would still be lower than 0.1.
TL;DR, the comparison of the numbers show out that it cannot be that the rotation is caused by Coriolis acceleration, since it just needs a tiny bit of an angle to fling it out of the angular movement zone into the harmonic one, which isn't even a rotation in this case.
DISCLAIMER - it's 2 AM here, I will go over what I've written in this post tomorrow to fix any bullcrap I might've accidentally written, so don't take it all as your sacred truth.
(04-29-2014, 12:12 AM)Pancakes Wrote: The movement towards the center of the water is very slow, far slower than the angular speed (at least in the outer rim, which would determine the rotation direction) which is why I neglected it when doing the calculation for the rotation direction, should've mentioned that.
That, and you should also explain why you expect the water to turn in such a way that the coriolis force points in wards and not outwards.
(04-29-2014, 12:12 AM)Pancakes Wrote: The numbers are comparison of accelerations. In the example I gave out, it simply shows out that Coriolis acceleration cannot be the reason for the rotation direction.
So you gave an example where you (allegedly, I'm not convinced you did show what) showed that the coriolis force cannot be the reason for the rotation. That, in itself, does not show that the coriolis force will not cause the water to turn in a certain direction while draining. It would just show that a certain rotation that you postulated was not caused by the coriolis force. What do you expect you are proving there? (if you actually proved anything)
(04-29-2014, 12:12 AM)Pancakes Wrote: Note that rotation will always happen due to a turbulent nature of the sink, which happens due to other physical reasons, though these reasons such as water compression\pressure comparison (I might be using a slightly incorrect terms in English, so in a case I do, I beg your pardon) wouldn't determine the direction in which it would rotate.
Uhm, yeah what you said there does not make any sense in english. You may want to reformulate it. Turbulent nature of the sink? Do you mean that the water will probably already have some sort of movement relative to the sink before the draining starts? I already said that in order to demonstrate anything, we'd have to assume that there was no such movemment, because the coriolis force would be too small to change the movement significantly. Only water compression/pressure has nothing to do with that, and does not cause a rotation.
(04-29-2014, 12:12 AM)Pancakes Wrote: Anyway back to the numbers, if we would choose a point in time and place on the outer rim, we could show, that by mere gravity reasons, that point, that very exact point, would be rotating to the other side, this would actually create an harmonic movement, and not an angular one. I think I did miss something very crucial in my calculations now that I think about it - what would need to be the angle to stop the rotation IF, it would only deprive from Coriolis acceleration. This I might do tomorrow should I have the time, but I wager the degree would still be lower than 0.1.
not sure what you mean with harmonic movenent. You mean a movement without a rotation? Yeah, thats what gravity does. One of the characteristics of a gravity, or an electiracal fiels is that its rotation is 0 (rotation here meaning the operator "rot", I guess you should be able to know what that is). It doesnt cause rotation, so it doesnt hinder rotation, so it wont hinder rotation caused by corioilis force.
(04-29-2014, 12:12 AM)Pancakes Wrote: TL;DR, the comparison of the numbers show out that it cannot be that the rotation is caused by Coriolis acceleration, since it just needs a tiny bit of an angle to fling it out of the angular movement zone into the harmonic one, which isn't even a rotation in this case.
The mistake that you seem to have made is that you picked a certain location with a certain speed and a certain direction, where the slant angle that you chose would do exactly what you want it too: work against the coriolis force. But the equation you set up is valid for exactly 1 infintesimally small point in the sink, and not valid anywhere else, because the speed, direction, and slant angle relative to the direction will be different. And even for that infinitessimally small point, since the sink is symetrical, there is another infinitessimally small point at the other side of the hole where exactly the oposite of what you calculated happens: the slant and gravity work in the same direction as the coriolis force, and not in the oposite one. So what you calculated is 100% irrelevant.
(04-29-2014, 12:12 AM)Pancakes Wrote: DISCLAIMER - it's 2 AM here, I will go over what I've written in this post tomorrow to fix any bullcrap I might've accidentally written, so don't take it all as your sacred truth.
I think you were a little over-eager in thinking that your reasoning was correct, just because you came to a conclusion that you expected.
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Re-read what I've written and yeah. I used incorrect English terms. Since water in this amount, and the forces that work on it, we can relate to it as steady flow of an ideal, non-compressionable, liquid (I hope thats more correct), and while you are right about amplify and hinder, there is the possibility for the water to not rotate at all, if we look on the gravity-coriolis comparison, it would do movement as such you can see in this thing old clocks have which escapes my mind. Harmonic.
I don't mean to disprove here the fact there is rotation, just the fact that it is caused by Coriolis acceleration, rather than geometrical reasons. And the misbelief that it has a predetermined cycling side.
The numbers I've show are very relevant, since they show how insignificant Coriolis acceleration is in the system. Even a nearly perfect plumber would do the job with a deviation degree of ~5 degrees. That just shows how insignificant Coriolis acceleration is, when you have gravity that plays in.
EDIT: Not to mention the fact that if you look at local geometry, a simple local field tolerance that at a sink would be like, what? +-0.5 mm? That alone would yield a local deviation that is creating a force far bigger than Coriolis. What I've shown is just Geometry vs spinning systems derived forces
(04-29-2014, 08:30 AM)Pancakes Wrote: Re-read what I've written and yeah. I used incorrect English terms. Since water in this amount, and the forces that work on it, we can relate to it as steady flow of an ideal, non-compressionable, liquid (I hope thats more correct), and while you are right about amplify and hinder, there is the possibility for the water to not rotate at all, if we look on the gravity-coriolis comparison, it would do movement as such you can see in this thing old clocks have which escapes my mind. Harmonic.
???
With old clocks you mean pendulum, a harmonic oscillation? Yeah there is the posiblity that the water doesnt rotate, but how does this have anything to do with what you claimed you were demonstrating?
(04-29-2014, 08:30 AM)Pancakes Wrote: I don't mean to disprove here the fact there is rotation, just the fact that it is caused by Coriolis acceleration, rather than geometrical reasons. And the misbelief that it has a predetermined cycling side.
The numbers I've show are very relevant, since they show how insignificant Coriolis acceleration is in the system. Even a nearly perfect plumber would do the job with a deviation degree of ~5 degrees. That just shows how insignificant Coriolis acceleration is, when you have gravity that plays in.
EDIT: Not to mention the fact that if you look at local geometry, a simple local field tolerance that at a sink would be like, what? +-0.5 mm? That alone would yield a local deviation that is creating a force far bigger than Coriolis. What I've shown is just Geometry vs spinning systems derived forces
I think the "misbelief" that you are refering to is that when a sink drains water, a slight clockwise or counterclock wise rotation will be induced depending if you're north or south, because of the coriolis force. Thats not a misbelief. That actually happens. The rotation induced is just so small that:
a) you would never even notice it in your regular sink
b) it will be super-imposed by other rotations that were happening in the sink which will likely be much larger, for example through stirring or the water entering the sink in a certain angle at the edge of it, which makes the water rotate much faster than anything the coriolis acceleration would do.
c) a special shape of the sink (for example a spiral shape) would cause the water to rotate faster in either direction while draining out.
However, what you you have calculated has absolutely no relevance to that what so ever.
First of all, the slant angle of the bottom of the sink, as long as the bottom is flat and not in some special space like a spiral, will not affect any rotational movement, except maybe in the special case that the water in the sink is very very shallow so that it just runs off the floor and goes into one side of hte sink. If the water is not shallow and not running off on the floor of the sink, there actually IS no acceleration happening because of the slanted floor. Take a glass of water. Tilt it slightly. Is the water in the glass being continously accelerated while its tilted? Nope. If the water is not shallow, water above a certain distance from the floor of the sink will not be affected by what the floor looks like, except through turbulent exchange of momentum maybe, so your calculation is actually irrelevant to almost the entirety of the content of the sink. In any case, your calculation is not representative enough to say that the coriolis-induced rotation wont happen, without more information on the shape and size of the sink.
Bottom line is.... the only thing you proved is that the coriolis acceleration roughly corresponds to the acceleration of water running off a surface at a certain angle. However, this does NOT mean that coriolis-force induced rotation doesnt happen unless the bottom of the sink is flatter than that angle.
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Yeah, for obvious reasons it can. But comparing the 2 forces in the way that he did alone doesnt really prove it, as long as you dont introduce additional conditions on shape and size of the sink, and initial movement of the water.
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(04-30-2014, 10:19 AM)Faxe Wrote: Yeah, for obvious reasons it can. But comparing the 2 forces in the way that he did alone doesnt really prove it, as long as you dont introduce additional conditions on shape and size of the sink, and initial movement of the water.
Yes it does. These things are manufactured like what, with a tolerance field of +-0.5 mm?
The local deviation you would get, would create a bigger force that combined with geometry (the curve) would determine the rotation being clockwise or counter-clockwise.
And the misbelief I talked about isn't a "slight rotation" I know that actually happens and I never claimed otherwise. What I claimed that the water have an overall rotation side that is completely dependent on which part of the globe you are at. Which it isn't.
You still fail to understand that what I've calculated is just 2 forces that act in order to show how one is completely irrelevant to the system that is being talked about.
I don't see how this I failed to demonstrate.
I calculated geometry vs Coriolis, and shown how far stronger geometry is, to a point coriolis is neglectable. Completely neglectable.
EDIT: And just to repeat it once more - completely neglectable
You know I think I explained it already in a way that you should be able to understand if you wanted to.
I'll try again.
Your weighing of the coriolis force against the acceleration through gravity caused by a slant is not representative for the problem of the entire sink. It is only representative for a tiny small area in the sink, which is on the surface.The coriolis force acts everywhere where the water is moving, in the whole volume. And even looking only at the surface, you would have to integrate over the whole surface and prove that the effects of the slants or irregularities in the sink have an effect that creates rotation in the integral. The gravity/slant effects may just as well cancel themselves completely in the integral.
To correctly prove if its negligible or not, you would have to integrate over the whole sink. Which depends on the shape, size, water viscosity, time it takes to drain it completely. The larger the sink and the more time it takes to drain it, the larger the effect of the coriolis force will be. That is not reflected in your calculation at all.
You are correct in saying that the coriolis force is negligible in the average sink. But your calculation alone did not prove it.
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