Why does water spin in funnel?

jdg812

As water is pulled into an opening by gravity, it begins to spin. Why does it spin?

DaveC426913

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 in to go into a closed tight spin.

jdg812

Thanks DaveC426913,

Actually, there are two regimes of spinning with two different speeds of spinning: immediately after opening a hole in the bath and about a minute later.

Immediately after opening the hole, conservation of angular momentum already works and one may see very slow spinning far from hole and faster spinning close to hole.

A minute later, the spinning becomes many times faster than in the very beginning. So, what is the reason of the fast spinning? Or what is the reason of increasing of the speed of spinning a minute later?

nonequilibrium

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.

jdg812

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?

Marco_84

i probably think that in this case what is decreased is the fluid mass, so it start to spinn faster... L=mvr. thats it.

DaleSpam

[nitpick]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.[/nitpick]Accounting for that amount of torque the rest of what has been said about angular momentum is correct.

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]

jdg812

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%.

DaveC426913

I feel like I've been hustled. Your OP belied the depth of your knowledge on the subject.

DaveC426913

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

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.

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.

jdg812

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.

So, I am not satisfied with the hurricanes in Florida and not satisfied with the present knowledge of the subject...

DaleSpam

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

Consider only FIVE gallons of water surrounding the drain.
At t = 0 (or t = 10 sec), the funnel spins slowly.

At t = 1 min, the first five gallons are gone. There are another five gallons of water surrounding the drain. The funnel spins quickly. 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?

jdg812

That is exactly what I was thinking about, but I needed an independent opinion... thanks

DaleSpam

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.Different initial conditions.

jdg812

You are absolutely right!

And different boundary conditions!