| Topic: |
Science > Physics |
| User: |
"Michael Mcneil" |
| Date: |
26 Sep 2005 01:42:39 AM |
| Object: |
Zero a or zero g? |
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
This is true no matter how high the jet reaches. Bigger globules fall
apart soonest. I imagine this is due to the greater amount of air
resistance. So what holds them together all the way up?
Is it something to do with the change of direction or is it the free
fall?
--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
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| User: "Uncle Al" |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 04:55:49 PM |
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Michael Mcneil wrote:
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
This is true no matter how high the jet reaches. Bigger globules fall
apart soonest. I imagine this is due to the greater amount of air
resistance. So what holds them together all the way up?
Surface tension, 72.8 dynes/cm. It will support a double-edged razor
blade. Iron is denser than water.
Is it something to do with the change of direction or is it the free
fall?
The turbulent stream progressively fragments with flight time.
Compare this with continuous or pulsed output from a laminar flow
nozzle. It flies a remarkable distance through the air as a stable
clear slug.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Weatherlawyer" |
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| Title: Re: Zero a or zero g? |
27 Sep 2005 08:58:18 PM |
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Uncle Al wrote:
Iron is denser than water.
I just knew I should have put FOUA on the end of my OP.
I need to write it into a sig.
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| User: "Sam Wormley" |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 08:07:38 AM |
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Michael Mcneil wrote:
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
This is true no matter how high the jet reaches. Bigger globules fall
apart soonest. I imagine this is due to the greater amount of air
resistance. So what holds them together all the way up?
Is it something to do with the change of direction or is it the free
fall?
Are the globules merging with each other along there trajectory
due to hydrogen bonds?
Trajectory
http://scienceworld.wolfram.com/physics/Trajectory.html
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| User: "Autymn D. C." |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 01:49:43 PM |
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there -> their
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| User: "" |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 05:40:01 PM |
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Dhuh, thank you for pointing that important scientific fact out to all
of use.
You must be new to Usenet Newsgroup, where spelling and simple
grammatical errors are ignnored in defference to immecisvuxzzuy.
What an idiot savant you must be, simply because your post contained
absolutely no scientific or technical content.
Be gone with you, and go lurk elsewhere! :-)
Harry C.
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| User: "Andy Resnick" |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 01:06:00 PM |
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Michael Mcneil wrote:
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
Doubtful: your eye simply can't discern the individual droplets.
There's a common demo in science museums of a stream of water and a
strobe light which shows droplet formation very early in the stream.
The Rayleigh stability of a liquid jet states that the longest stable
fluid column is 2*pi*(jet radius), the source of the instability is
surface tension. The wavelength is set by surface tension, for water in
air the critical wavelength is about 1 cm. Viscosity sets the time
scale for pinching, which is fast for water. Water is about 1 cSt = 1
mm^2/s kinematic viscosity, so a 1 cm radius jet will pinch off in about
0.01 second.
This is true no matter how high the jet reaches. Bigger globules fall
apart soonest. I imagine this is due to the greater amount of air
resistance. So what holds them together all the way up?
Surface tension. For water in air it's 72 erg/cm^2. The pressure
difference across the surface of a fluid sphere is about s/r, where s is
the interfacial energy and r the radius. Large spheres are easy to
break up, small spheres will persist.
Is it something to do with the change of direction or is it the free
fall?
No. The effect of hydrostatic pressure for a (small) drop will be small
compared to the other forces, such as inertial.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "CWatters" |
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| Title: Re: Zero a or zero g? |
26 Sep 2005 01:46:27 PM |
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"Andy Resnick" <andy.resnick@op.case.edu> wrote in message
news:dh9de4$h3$1@eeyore.INS.cwru.edu...
Michael Mcneil wrote:
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
Doubtful: your eye simply can't discern the individual droplets.
There's a common demo in science museums of a stream of water and a
strobe light which shows droplet formation very early in the stream.
The Rayleigh stability of a liquid jet states that the longest stable
fluid column is 2*pi*(jet radius),
Thanks for that interesting reply. That's quite a surprise and not what I
would have expected.
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| User: "Weatherlawyer" |
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| Title: Re: Zero a or zero g? |
27 Sep 2005 09:02:15 PM |
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Andy Resnick wrote:
Michael Mcneil wrote:
Watching a fountain throw a jet of water an hundred feet or so, straight
up in the air, it struck me that the globules don't begin to fall apart
until after they have reached the zenith.
Doubtful: your eye simply can't discern the individual droplets.
There's a common demo in science museums of a stream of water and a
strobe light which shows droplet formation very early in the stream.
The Rayleigh stability of a liquid jet states that the longest stable
fluid column is 2*pi*(jet radius), the source of the instability is
surface tension. The wavelength is set by surface tension, for water in
air the critical wavelength is about 1 cm. Viscosity sets the time
scale for pinching, which is fast for water. Water is about 1 cSt = 1
mm^2/s kinematic viscosity, so a 1 cm radius jet will pinch off in about
0.01 second.
This is true no matter how high the jet reaches. Bigger globules fall
apart soonest. I imagine this is due to the greater amount of air
resistance. So what holds them together all the way up?
Surface tension. For water in air it's 72 erg/cm^2. The pressure
difference across the surface of a fluid sphere is about s/r, where s is
the interfacial energy and r the radius. Large spheres are easy to
break up, small spheres will persist.
Is it something to do with the change of direction or is it the free
fall?
No. The effect of hydrostatic pressure for a (small) drop will be small
compared to the other forces, such as inertial.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
Thanks, Doc., any chance of a translation?
I noticed that the stuff 1cm or smaller lasted all the way down.
Can you go over the bit about jet diameters once more.
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| User: "Andy Resnick" |
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| Title: Re: Zero a or zero g? |
28 Sep 2005 12:24:00 PM |
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Weatherlawyer wrote:
<snip>
Thanks, Doc., any chance of a translation?
Sure- where should I start?
I noticed that the stuff 1cm or smaller lasted all the way down.
Right- a fluid sphere is an (approximately) equilibrium shape, so as
long as nothing collides with it, it should persist indefinitely.
Can you go over the bit about jet diameters once more.
Basically, what was done was a stability analysis of a cylindrical fluid
jet. Without getting into any math, it can be shown that an infinitely
long cylindrical jet will lose it's shape most quickly to axial
disturbances of wavelength 2*pi*(jet radius)- I think I mis-spoke
earlier. What this means is that if I make a fluid column, either
dynamically, by squirting fluid out of an orifice or statically, by
making something called a "liquid bridge", The longest right-circular
cylinder of fluid I would ever see is 2*pi*(column radius) long, and
that's when there is no density difference (i.e. pressure difference)
between the fluid column and surrounding bath. And no fluid flow, either.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "Weatherlawyer" |
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| Title: Re: Zero a or zero g? |
28 Sep 2005 04:40:13 PM |
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Andy Resnick wrote:
Weatherlawyer wrote:
I noticed that the stuff 1cm or smaller lasted all the way down.
Right- a fluid sphere is an (approximately) equilibrium shape, so as
long as nothing collides with it, it should persist indefinitely.
How is this related to the durability of smaller droplets? It was easy
to see the large globes were decaying due to the flow of air around
them. I would have said that stability is a function of the turbulence
engendered by diameter.
Or something like that. A droplet will try to form or be forced into a
shape that forms a slipstream. At a certain size in whatever gas
densities the drop can keep its shape. Above that, it breaks apart.
Can you go over the bit about jet diameters once more.
Basically, what was done was a stability analysis of a cylindrical fluid
jet. Without getting into any math, it can be shown that an infinitely
long cylindrical jet will lose it's shape most quickly to axial
disturbances of wavelength 2*pi*(jet radius)- I think I mis-spoke
earlier.
What this means is that if I make a fluid column, either
dynamically, by squirting fluid out of an orifice or statically, by
making something called a "liquid bridge", The longest right-circular
cylinder of fluid I would ever see is 2*pi*(column radius) long, and
that's when there is no density difference (i.e. pressure difference)
between the fluid column and surrounding bath. And no fluid flow, either.
Again you lost me.
right-circular cylinder of fluid?
2*pi*(column radius) long? That's some 6" on a 2" diameter pipe? The
column reached 40 or 50 metres at a guess.
And it remained substantially intact all the way up. It was as soon as
it started back down that it fell apart, forming globules. However the
fountain was timed so that it switched off at the same time the column
got to the 40 or so metres. Thus it fell back unopposed.
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| User: "Andy Resnick" |
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| Title: Re: Zero a or zero g? |
29 Sep 2005 10:21:54 AM |
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Weatherlawyer wrote:
Andy Resnick wrote:
Right- a fluid sphere is an (approximately) equilibrium shape, so as
long as nothing collides with it, it should persist indefinitely.
How is this related to the durability of smaller droplets? It was easy
to see the large globes were decaying due to the flow of air around
them. I would have said that stability is a function of the turbulence
engendered by diameter.
Ok... Let's start with the Laplace relation Dp = -sk. Dp is the
pressure difference across the interface, s is the interfacial energy
(72 erg/cm^2 for water and air), and k is the surface curvature, and can
be written as (1/R1 + 1/R2), where R1 and R2 are the principal radii of
the surface. For a sphere, R1 = R2, so the Laplace relation is Dp =
-2s/R, where R is the radius of the droplet. So, we can see that the
smaller the drop, the larger the pressure difference across the interface.
So what? Well, the pressure difference can be interpreted as an
indicator of how stable the interface is. The tiny bubbles in beer are
very stable because of this large pressure difference. Emulsions are
stable for this reason also. Now for large water globules, the interial
force generally easily smashes up the sphere, but there can be
exceptions, if the experimenter is sufficiently careful:
http://spaceflight.nasa.gov/station/crew/exp6/spacechronicles.html
Don is a rare creature- and a really nice guy.
<snip>
What this means is that if I make a fluid column, either
dynamically, by squirting fluid out of an orifice or statically, by
making something called a "liquid bridge", The longest right-circular
cylinder of fluid I would ever see is 2*pi*(column radius) long, and
that's when there is no density difference (i.e. pressure difference)
between the fluid column and surrounding bath. And no fluid flow, either.
Again you lost me.
right-circular cylinder of fluid?
2*pi*(column radius) long? That's some 6" on a 2" diameter pipe? The
column reached 40 or 50 metres at a guess.
And it remained substantially intact all the way up. It was as soon as
it started back down that it fell apart, forming globules. However the
fountain was timed so that it switched off at the same time the column
got to the 40 or so metres. Thus it fell back unopposed.
Ok, let's analyze your observations. You have a 5 cm diameter circular
jet issuing from a nozzle at an exit velocity of about 3 m/s (for a 50
meter high column).
Water has a kinematic viscosity of about 1 cS = 1 mm^2/s
http://astrowww.phys.uvic.ca/~tatum/classmechs/class20.pdf
And the growth rate of the critical disturbance u=s/(vpr), where s is
the interfacial energy, v the kinematic viscosity, p the density, and r
the jet radius, is about 300/s:
http://www.iop.org/EJ/article/1367-2630/5/1/359/nj3159.html
Donnelly, R. J.; Glaberson, W. "Experiments on the capillary instability
of a liquid jet". Proc. Roy. Soc. (London), Sec. A (1966), 290(1423), 547-56
So the critical disturbance will exponentially grow and propogate 2.5 cm
in t = [ln(2.5/e0)/300] s where e0 is the amplitude of the initial
perturbation. Let's assume the perturbation amplitude is very small, say
0.01 mm: an irregularity in the orifice, for example. Then, t = 0.026
seconds, during which the fluid moves 8 cm.
So, how can we square this with your claim that the jet is maintained
for most of the height?
I claim that the jet is not maintained, simply that your eye cannot
follow the disturbance as the water moves:
http://www.answers.com/main/content/wp/en/thumb/5/59/250px-Brooklyn-museum-splash-fountains1302p-nobather.jpg
is a good picture showing the column break-up. As you can see, it
happens fairly early.
Now, I have seen dancing fountains that are single tubes of water:
http://www.atlanticfountains.com/laminar_leaper.htm
But I'm not sure how the orifice is designed- clearly, there is
attention paid to the design.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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