engineering question: tube closed at one open at the other. 1"wide, 6 feet long. filled to the brim with water.
what angle below the hoizontal drains it the fastest?
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1)
90 degrees -- upside down would be fastest
Blackskimmmer:
are you sure? the bubbles get in the way.
Zillionaire:
nope. Depends on how stable the tube. The "stickiness" of the water and geometry of the tube determines the angle... I think.
Gotta find the optimum glug, glug frequecy, bubble size and fall rate...
Um... 45 degrees?
Zillionaire:
Start at zero go to 90
Blackskimmmer:
describe the function of angle versus time
Zillionaire:
well... If you did it really fast at the right focal point, you could generate significant cetripetal acceleration. How about infitity degrees per second?
Blackskimmmer:
that's cheating, don't make things complicated yet.
Zillionaire:
It is complicated, I would need to know the properties of water and air.
It is complicated, I would need to know the properties of water and air.
Cyclopia:
Water weighs 1 gram/cc
and is very wet.
It's a good solvent, too.
My favorite beers are about 94% water.
And I am composed mostly of water.
It's good stuff.
1.6)
Blackskimmmer:
second guess the instabilities?
tminus7:
Rayleigh-Taylor instabilities.
http://en.wikipedia.org/wiki/Rayleigh-Taylor_instability
The real reason the water falls out of the tube.
Blackskimmmer:
that article hardly made a lick'o' sense, but i like the idea that crab nebula is RT fingers. my 2nd favorite place in the universe.
well as i aint got no answers to my problem, i'll have to go out and get a tube and experiment myself.
i'll report on it.
why do you say these instablilties is why the water flows out of the tube? in the turbulent regime? or is it just what gets it initiating the flow?
tminus7:
It is what intiates the flow.
Remember the only reason we are talking about this problem at all is that the outside air pressure is pushing the water back into the closed pipe with more force than the water weight pusing out. This is the condition Of RT instability. A low density fluid, air, pushing on a high density fluid, water. The simulation picture in the wiki article, if you turn it upside down is, is exactly the OP's problem. This is for the pipe straight vertical.
One simple proof is the old playing card/ glass of water trick. Place a card over the open end of a glass of water. Hold it and invert the glass. Let go of the card and, magically, the water does not fall out! The card is a stiff solid and changes the conditions away from the RT condition. The card is not free to flow. But it shows the outside air pressure is great enough to hold the water (and card) in the glass. So gravity is insufficient to pull the water out of an inverted glass. You need RT to make it fall!
Blackskimmmer:
aha! you are assuming that the if the water leaves the tube at first without any air flowing all the way to the end first, that the water will have to leave a vacuum at the opposite end, and thus... i'm not sure i understand... ok i understand merely a bubble flowing up through the tube of water but it's flowing up because the water over it is flowing down it, bouyancy and all... i still don't understand how to make a free body diagram with the volume elements to show why things move...
argh.... physics is hard!
ok, at least with the card trick i see that if the water tries to bulge out the upsidown glass with the card, it's gotta leave a vacuum at the top.. so air pressure keeps the card horizontal..
if i replace the card with the surface of the water... (surface tension effects? argghhh).. same problem, so .. you got to get some instability hapening... wow what would a movie be of the shape of the surface of that water the first millisecond that you remove the card (without causing any eddies where it touches... yikes, how to do it clean?)
surface tension IS important. if you do the trick with a hollow glass stirir, the water doesnt come out at all! hmm... what's the cuttof diameter per given hight of column...
yikes! fluids!
2)
Zillionaire:
answer is: 0
Zillionaire:
i mean negative tan(dia/lenth)
Blackskimmmer:
curious suggestion. that's the angle of the triangle from the lip of the tube to the opposite edge.
hmmm... gonna have to try this.
InOldenDays:
Yeah, nice idea, Z.
Angular measure, though: "arctan" instead of "tan".
3)
TheRealTryanJ:
1 degree below hoizontal so it doesnt bulid vacum to prevent water from flowing.
Blackskimmmer:
that's the idea! but how do you know 3degrees isn't faster? tricky problem.
i'm gonna have to go try it later.
4)
Geoloseth:
the angle will have to change in relation to the amount of water left in the tube. In essence you tip it over and once it starts to drain you keep tipping it to the maximum angle before air gets trapped in the tube.
Blackskimmmer:
that's a second version of the question.
5)
Toober:
I'll guess. The glu-glug frequency is a function of viscosity. I'm also not convinced that the recoil due to glugging would be enough to overcome a velocity of the maximum downward angle.
BUT, assuming you want to minimize glugging. That means getting a complete layer of incoming air to the very back of the tube.
So, place the tube at zero degrees horizontal, and draw a line from the lower open lip back to the upper closed lip. (you can figure it out from the dimensions you gave).I'm guessing that that is the minimum tipping angle for non-glugging.
6)
Blackskimmmer:
Ok, here is the report on my preliminary experiments:
well, i didn't get a tube yet, so i used two bottles:
I) louza bottle 1.5" wide mouth, 12" high, 3"wide bottom walls fairly streight
horizontal: 9sec
10sec
it starts off fast and then the last bits dribble out
30deg? about 2 sec, some glugging
45deg: 2sec? some glugging
2.5sec
vertical: 1.5sec
II)beer bottle: 3/4"opening, 4" of 1" neck, 10" tall, 2" at base
horizontal: 20sec, glugging, doesn't empty all the way slows to a dribble etc..
20deg? close to making the line from upper lip to rear bottom end horizontal: 11sec
11sec
45deg: 10sec fairly periodic glugging
9 sec
vertical: 8.5sec nonperiodic glugging? the glugging caused my hand to shake
8.5sec
7.5 sec
8.5sec
dynamic: 10sec
10sec
8 sec starting vertical and going more horizontal at end
10sec
9sec
dynamic maintaining NO glugging: 16sec
18sec
dynamic vertical then horiz then final vertical spill: 9sec
9sec
none of the measurements are precise. to the nearest second because how well could i time when i released the water with my palm? i used my computers clock with seconds. windows XP and IBM thinkpad.
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Blackskimmmer:
wow, i haven't done a physics exp in a while
alot of work!
analysis: while the glugging close to vertical is pretty bad, the speed of emptying between glugs and the speed of emptying at the end (less glugs) seems to more than make up for it.
would be interesting to time precisely the vertical emptying times maybe 100 times and see what kind of distribution i get.
would be interesting to analyse the periodicity of the gluging at various angles.
curious that dynamically changing the angle i couldn't get much better timing!
this is fun. it would be interesting to get a good long cylinder and a stand with a clamp and measure the angle (arcsin(height of rear end/len) more accurately. the longer the tube, the less imprecise my timings will be due to my impreciese "shutter" opening!
Toober:
To standardize:
When I had done similar experiments with students, we used PVC pipe closed-off with a PVC valve that you can cheaply purchase (>$8?) at Home Depot. The experiments we had done were pressure vs. height vs. velocity experiments, but only at 90-degrees vertical.
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Someday, I'd like to get back to Newtonian experiments.
Blackskimmmer:
yes, i hope to get around to finding some tubing, should be fun.
i suppose if i had glass tubing i could do things like time how long a bubble takes to rise to the top. i recall an exhibit on davinci and one of the things he messed with was the chaotic motion of bubbles...
Toober:
He described bubbles, but only as a part of turbulence (as I recall from my readings).
Blackskimmmer:
this stuff, from:
http://www.esam.northwestern.edu/~miksis/
Computation of Moving Boundary Problems in Fluid Dynamics
Rising gas bubbles play an important role in many physical and biological processes, such as the dynamics of multiphase flows, cavitation processes, and the flow of bubbles in the bloodstream. The rise of gas bubbles and the observation of a path instability has been documented since the time of Leonardo Da Vinci, but questions related to the origin of this instability still exist. CatherineNorman thesis topic was concerned with the development of a level-set numerical method to study the dynamics of rising bubbles. She considered both bubbles rising under an inclined plane and bubble free rising. She considered both cases were there was a film of liquid between the bubble and the plane and classes where there was a three-phase contact line. Hecode allowed for adaptive meshing and she developed a full second-order method.
On the right is a numerical calculation using the level-set code of C. Normann. Here we see a three-dimensional gasbubble rising from rest. The bubble initially rising along the center-line and flattens in the direction it is moving. With increasing distance, a spiraling path instability occurs. Because the bubble is rising inside of a finite channel, the spiraling instability eventually becomes a zig-zag instability where the bubble move back and forth in a center-plane normal to two of the faces.
References
* C.Norman and M.J. Miksis, "Dynamics of a Gas Bubble in an Inclined Channel at Finite Reynolds Number", Phys. Fluids, 17(2), 022102, 2005.
* C.Norman and M.J. Miksis, "Gas Bubble with a Moving Contact Line Rising in an Inclined Channel at Finite Reynolds Number", Physica D, 209, 191-204, 2005.
* C.E. Norman, "A level-set numerical method to determine the dynamics of gas bubbles in inclined channels", Ph.D. Thesis, Northwestern University, June 2005.
another description with davinci quote:
http://ct-cr4.chem.uva.nl/single_bubble/nature.pdf
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