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jdg812
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As water is pulled into an opening by gravity, it begins to spin. Why does it spin?
DaveC426913 said:Because angular momentum from the initial state of the water is preserved. It's the same thing that a skater uses to start in an open, slow spin and pull their arms into go into a closed tight spin.
That's corect, but that was an answer to a different question.mr. vodka said:Angular momentum for a spinning object is mass times velocity times radius. As momentum is preserved and as the radius decreases (because of the water going out), the velocity must increase.
i probably think that in this case what is decreased is the fluid mass, so it start to spinn faster... L=mvr. that's it.jdg812 said:That's corect, but that was an answer to a different question.
Consider the numerical exapmle.
R = 30 cm, r = 3 cm.
Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec
A minute later, BOTH of the speeds, the speed far from the funnel and the speed close to funnel becomes much larger,
for example
v(R) = 12 cm/sec, v(r) = 120 cm/sec
The question is:
Why a minute later the speed at the distance 30 cm from funnel increased from 1 cm/sec to 12 cm/sec? Why a minute later the speed at the distance 3 cm from funnel increased from 10 cm/sec to 120 cm/sec?
There is a large bath, about 100 gallons of water and a small hole, about 1 inch diameter. A minute later there is still about 95 galons of water. Decrease of the mass of water is only 5%, but increase of rotation speed of the whole funnel is about 1200%.Marco_84 said:i probably think that in this case what is decreased is the fluid mass, so it start to spinn faster... L=mvr. that's it.
I feel like I've been hustled. Your OP belied the depth of your knowledge on the subject.jdg812 said:...
Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec
But I don't think the whole volume participates at that point. Due to inertia and friction I imagine you can consider the dynamics of a smaller volume of only a few gallons surrounding the drain.jdg812 said:There is a large bath, about 100 gallons of water and a small hole, about 1 inch diameter. A minute later there is still about 95 galons of water. Decrease of the mass of water is only 5%, but increase of rotation speed of the whole funnel is about 1200%.
I am not sure about gravity, but the tub, actually bottom of it near the hole, exert friction. So it should reduce the angular momentum. But actually, the angular momentum increases a minute after beginning of the process.DaleSpam said:In the case of water down a drain angular momentum is not precisely conserved. The tub (and maybe gravity?) does exert torque on the water.
Yes. There are two mechanisms of the speed increase as the water approaching the hole. The first one is that water goes closer to vertical ax, momentum conservation and so on... The second one is that water goes to a lower level, PE => KE and so on... But the question was not about speed increase as the water approaching the hole, but about increase of the speed of the funnel as whole a minute after beginning the process.DaleSpam said:[nitpick]In addition to the conservation of angular momentum there is also conservation of energy. As the water moves down into the drain there is some loss of PE. By conservation of energy you can also get an overall increase in KE in the tub depending on the KE of the water going down the drain. [nitpick]Of course, accounting for energy lost to viscous heating etc.[/nitpick]
I am not satisfied with my knowledge of the subject... what I actually want is to find any effective measures against tornadoes and tropical storms that are too annoying in my lovely Florida. But in order to find something, I need deep understanding of rotation phenomena.DaveC426913 said:... the depth of your knowledge on the subject.
You cannot consider part of the water in isolation to the rest. Viscous forces "connect" the water approaching the hole to the rest of the water in the funnel. The viscous forces are small, but not negligible. That is why, as you observed, it takes a rather large amount of time.jdg812 said:But the question was not about speed increase as the water approaching the hole, but about increase of the speed of the funnel as whole a minute after beginning the process.
Consider only FIVE gallons of water surrounding the drain.DaveC426913 said:But I don't think the whole volume participates at that point. Due to inertia and friction I imagine you can consider the dynamics of a smaller volume of only a few gallons surrounding the drain.
That is exactly what I was thinking about, but I needed an independent opinion... thanksDaleSpam said:You cannot consider part of the water in isolation to the rest. Viscous forces "connect" the water approaching the hole to the rest of the water in the funnel. The viscous forces are small, but not negligible. That is why, as you observed, it takes a rather large amount of time.
The five gallons of water surrounding the drain is a very poor system to choose. It is not an isolated system and the boundaries and interactions are very difficult to define. You are much better off considering all of the water in the tub. That makes the boundaries much easier to define as well as the interactions with the surroundings.jdg812 said:Consider only FIVE gallons of water surrounding the drain.
At t = 0 (or t = 10 sec), the funnel spins slowly.
Different initial conditions.jdg812 said:Why behavior of the next five gallons, which forms quickly spinning funnel is different from behavior of the first five gallons, which formed slowly spinning funnel?
You are absolutely right!DaleSpam said:The five gallons of water surrounding the drain is a very poor system to choose. It is not an isolated system and the boundaries and interactions are very difficult to define. You are much better off considering all of the water in the tub. That makes the boundaries much easier to define as well as the interactions with the surroundings.
And different boundary conditions!DaleSpam said:Different initial conditions.
What exactly do you mean? The coefficient of viscosity decreases or the viscous resistance as a global phenomenon decreases at constant coefficient of viscosity?ank_gl said:as the rotation progresses, the viscous resistance decreases
I believe that answer to the question why does it rotate at all?, is the same as the answer to the question "why it rotates faster and faster as the rotation progresses?".ank_gl said:but one thing that kicks me is the fact, it rotates. why does it rotate at all?? i have a large tank, full of water, i punch a hole in it, water, a lil after, drops below forming a vortex. why does it happen?? i asked this question, all through my course, but didnt get any answer OR i am ultra stupid;))
I don’t think that precise measurements are possible in hydrodynamics. Deviations about 1% from the law 1/r may 'save' the model. It takes about 1 minute to develop stationary fast spinning funnel. For that time liquid makes several hundreds turns around center of vortex. So, the process of acceleration of the whole thing is comparatively slow. The torque required for such slow acceleration may cause deviations of about 1% or less from exact 1/r law.DaleSpam said:The Wikipedia page (http://en.wikipedia.org/wiki/Vortex) mentions that for a free vortex "The tangential velocity v varies inversely as the distance r from the center of rotation, so the angular momentum, rv, is constant".
Yes.DaleSpam said:The viscous shear forces should exert a net torque in the opposite direction.
Me too...DaleSpam said:I can't see how gravity would exert a torque about a vertical axis.
I believe the torque is within 1% of experimentally measured 1/r law.DaleSpam said:Where's the torque?
First, you should remove drain plug at all and close the hole by your business card. Then wait 5 minutes until the water is in rest. After that remove business card using piece of wire (a long needle would be the best), moving it ALONG the bottom of the bath. After such non-disturbing opening of the hole, you should get the funnel WITHOUT spinning for a minute or more.DaleSpam said:EDIT: I cannot reproduce the "points far away start spinning faster" thing in my sink even though anecdotally I think I have seen such occurences. The drain plug may be interfering. The situation you described above, was that just hypothetical, or have you done such an experiment?
Yes, that is like Cheshire Cat smile...DaleSpam said:Well, if there is no external torque in the right direction then the only way possible for the "far away" fluid to gain angular momentum is if the fluid going down the drain has less angular momentum per unit mass than the rest of the fluid. In the ideal irrotational vortex the angular momentum is uniform throughout the fluid, so you would get no such effect. However, I don't know the derivation of the irrotational vortex equations, it could be that they are assuming no viscosity. If so then it would make sense that the innermost fluid would have the highest shear rates and therefore rotate slightly slower than the inviscid limit and therefore have less angular momentum than the bulk of the fluid.
DaleSpam said:... and I can't see how gravity would exert a torque about a vertical axis.
Where's the torque?
If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?YellowTaxi said:Try Focault's pendulum - coriolis effect.
The effect is due to the rotation of the Earth on its axis (of rotation...). We always subconciously assume Earth is staionary when it simply isn't.
And it's caused by moving in toward that axis (ever so slightly with Focault pendulum as it falls), and likewise opposite effect when it swings away away from the Earth's axis. It's like trying to keep a straight line as you walk inwards towards the centre of a roundabout or carousel. The fact you're already rotating throws you to one side of the line that you're trying keep.
You could also demonstrate the effect by dropping something verticlly from 100m at the equator. I think it should hit the ground about 1mm to one side.
So basically I think there wouldn't be any torque if you were on a planet that doesn't spin.
The reason the vortex speeds up is probably the positive feedback effect that somebody earlier mentioned. ie it's because all the particles in the water are connected by intermolecular forces :-) and obviously a larger effect from surface tension. -So what happens at the center has a knock on effect on the water further out. Especially true for the water on the surface where moleculr forces are stronger..
my 2cents
Integral said:If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?
Integral said:If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?
meeeee5 said:hey guys, i was just wondering if any of this angular rotation would occur if the Earth was not moving? because without a rotational 'nudge', the water would not begin to spin. this fact seems to be neglected here?
Water spins in a funnel due to a phenomenon called the Coriolis effect. This effect is caused by the rotation of the Earth, which causes objects in motion to appear to curve. In the case of water in a funnel, the rotation of the Earth causes the water to curve as it flows down the funnel, creating a spinning motion.
Yes, the direction of the water spin in a funnel is dependent on the hemisphere you are in. In the Northern Hemisphere, the water will spin counterclockwise, while in the Southern Hemisphere, it will spin clockwise. This is due to the direction of the Earth's rotation and the Coriolis effect.
Yes, the Coriolis effect can affect any fluid in motion, not just water. This includes air, oil, and other liquids. Any fluid that is moving in a curved path, such as in a circular motion, will experience the Coriolis effect.
The size of the funnel and the amount of water can affect the spinning motion to some extent. A larger funnel and a larger amount of water may result in a stronger spinning motion, but the Coriolis effect will still be present regardless of the size or amount of water.
Yes, the Coriolis effect can be seen in other natural phenomena, such as hurricanes, tornadoes, and ocean currents. It is also responsible for the rotation of the Earth's weather patterns and the formation of large-scale atmospheric systems.