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Warren Platts
2007-Oct-23, 09:07 PM
What would be the minimum mass flux through a tube that would cause a shift from laminar to turbulent flow?

Assuming the following:
a pipe with an effective hydralic diameter of about 25 km
a substance that's about 0.7 times as dense as water, and maybe half as viscous
a Reynolds number of 3,000, or maybe 10,000

antoniseb
2007-Oct-23, 09:47 PM
What would be the minimum mass flux through a tube that would cause a shift from laminar to turbulent flow?
The fact that you know enough to give a Reynolds number suggests you have the resources to look up and compute the answer yourself. If you do that, can you post the answer here?

Saluki
2007-Oct-23, 09:56 PM
You are asking 3 questions. Which do you want to answer?

Also, what is the temperature of the fluid?

Warren Platts
2007-Oct-23, 10:04 PM
The fact that you know enough to give a Reynolds number suggests you have the resources to look up and compute the answer yourself. If you do that, can you post the answer here?
Honestly, I know just enough to be dangerous. I know Reynold's numbers have something to do with it and I've even encountered it in class, but how to do it is like my once basic competence in calculus, its gone with the wind.

Like, do Reynold's numbers change with the velocity of the fluid through the pipe?

The Wiki article says that typical Reynold's numbers (http://en.wikipedia.org/wiki/Reynolds_number) for the onset of turbulent flow in pipes range as follows:


Onset of turbulent flow ~ 2.3103 [to] 5.0104 for pipe flow

So what's the difference? If there's an order of magnitude range for Reynold's numbers, how would you pick a value for a given diameter, velocity, and viscosity?

I've been trying to figure it out on my own, but even if I succeeded, I'd still have to ask the question to make sure I did it right.

Warren Platts
2007-Oct-23, 10:08 PM
You are asking 3 questions. Which do you want to answer?

Also, what is the temperature of the fluid?
I'm asking for an estimated flow rate that would cause the "onset of turbulent flow" (as well as how sensitive this estimate is to variation in Reynold's numbers).

As for temperature--let's just say it's about 6,000 degrees Kelvin. . . . :D

Kaptain K
2007-Oct-23, 10:50 PM
If it wasn't for the absurdity of the numbers (25 Km wide pipe, 6000 K), some would think you're trying to get someone to do your homework for you.

Warren Platts
2007-Oct-23, 10:56 PM
If it wasn't for the absurdity of the numbers (25 Km wide pipe, 6000 K), some would think you're trying to get someone to do your homework for you.That's exactly what I'm up to! :D

grant hutchison
2007-Oct-23, 11:19 PM
Well, your Wiki article also gives the rule that is generally used if you want to be sure of avoiding turbulence:
For example, within circular pipes the critical Reynolds number is generally accepted to be 2300, where the Reynolds number is based on the pipe diameter and the mean velocity vs within the pipe ...Haven't you got all the data you need?
From your numbers, using the critical value for Re:

vs = 6.5x10-8m.s-1

That's the trouble with wide pipes.

So you end up moving about 22.3 tonnes a second. I have to say that choosing a pipe as wide as a city is not a good way of suppressing turbulence. :)

Edit: I posted before I saw your reply to Kaptain K, above. I don't appreciate being used to do other people's homework.

Grant Hutchison

Warren Platts
2007-Oct-23, 11:31 PM
Well, your Wiki article also gives the rule that is generally used if you want to be sure of avoiding turbulence:Haven't you got all the data you need?
From your numbers, using the critical value for Re:

vs = 6.5x10-8m.s-1

That's the trouble with wide pipes.

So you end up moving about 22.3 tonnes a second. I have to say that choosing a pipe as wide as a city is not a good way of suppressing turbulence. :)

Grant HutchisonWell, let's say you found a natural pipe with a 25km diameter, and all else you knew about it was that the flow was turbulent. So, I guess your figure would set an absolute minimum flow, but 22.3 tons per second doesn't seem like very much. That's equivalent to about 700 cubic feet per second (cfs) which is only about as much as a smallish creek.

So, maybe I should ask the opposite question: Is there a theoretical maximum turbulent flow through a 25 km pipe with the above constraints? Like probably the flow rate should be slower than the speed of sound, shouldn't it?

grant hutchison
2007-Oct-23, 11:40 PM
... but 22.3 tons per second doesn't seem like very much.It's not. Big pipes flow turbulent at low velocities. Huge pipes flow turbulent at tiny velocities. People who specifically want to avoid turbulence use lots of little pipes, like in a Fleisch pneumotachograph (http://www.phippsbird.com/fleisch2.html).

Grant Hutchison

Warren Platts
2007-Oct-23, 11:58 PM
Edit: I posted before I saw your reply to Kaptain K, above. I don't appreciate being used to do other people's homework.

Grant Hutchison

Honestly, Dr. Hutchison, it's not for a class (I'm too old to take classes anymore), but it is homework in a sense for a problem (http://www.bautforum.com/1095721-post64.html) I'm working on for my own edification. I'd figure it out myself if I could, and I don't have a professor or GTA to turn to help me out, so you're my only hope! :)

Saluki
2007-Oct-24, 02:42 AM
The exact transition point depends on several factors, and in practice is determined by experimentation.

If you know Re, you have enough data to back-of-the-envelope Vs (and any other flow rate term you want). Fluid temperature would help nail it down since viscosity is temperature dependent. If you are trying to find transition Re, I suggest you build a 25 km diameter pipe, fill it with your fluid, and have at it. Short of that, you could set up a scale model.

neilzero
2007-Oct-24, 02:59 AM
It is possible that a 25 kilometer pipe will behave much differently than a 25 centimeter pipe, which is typical of such problems. At 6000 degrees k, the fluid will be a plasma which may flow quite different from a gas. Perhaps we also need to ask the pressure? Neil

grant hutchison
2007-Oct-24, 07:33 AM
We have the density, viscosity and characteristic length defined for us in the problem. Together with the velocity, they give us the Reynolds number via Re=lvρ/μ. So the problem is fully specified by the OP, short of testing in the real world, as Saluki says.

Grant Hutchison

Jens
2007-Oct-24, 08:16 AM
(I'm too old to take classes anymore)

I don't know if that's possible. Wasn't there a person who was over 100 who graduated from high school? :)

Warren Platts
2007-Oct-24, 11:43 AM
The exact transition point depends on several factors, and in practice is determined by experimentation.

If you know Re, you have enough data to back-of-the-envelope Vs (and any other flow rate term you want). Fluid temperature would help nail it down since viscosity is temperature dependent. If you are trying to find transition Re, I suggest you build a 25 km diameter pipe, fill it with your fluid, and have at it. Short of that, you could set up a scale model.

It is possible that a 25 kilometer pipe will behave much differently than a 25 centimeter pipe, which is typical of such problems. At 6000 degrees k, the fluid will be a plasma which may flow quite different from a gas. Perhaps we also need to ask the pressure? Neil

We have the density, viscosity and characteristic length defined for us in the problem. Together with the velocity, they give us the Reynolds number via Re=lvρ/μ. So the problem is fully specified by the OP, short of testing in the real world, as Saluki says.

Grant Hutchison
I'll lay my cards on the table: the conditions I'm interested in are those that prevail near the plasma phase transition (PPT)--if it really exists--deep within Jupiter. So the material will be mainly a molecular hydrogen/helium mixture, with perhaps a significant amount of water steam mixed in. So temp ~ 6,000o K, Pressure ~ 1 Mbar, and density around 0.7 gm/cm3.

The one observational constraint is that the flow be turbulent--but as Dr. Hutchison pointed out, the flow becomes turbulent at trivially low velocities.

So the question then becomes whether there is a "natural" maximum flow through such a pipe. But I'm beginning to understand that the natural flow through any pipe is relative to a particular pressure differential dP. That is, there is no theoretical maximum flows for pipes. I don't know what sorts of dPs would be reasonable for a 25km pipe under such conditions, but I have some ideas on how one might come up with a ballpark estimate. . . .

If I were able to come up with such a dP, then it should be able to come up with some back-of-the-envelope average velocities? At which point Reynold's numbers cease to be relevant?

Warren Platts
2007-Oct-24, 01:22 PM
OK, let's just go with a 10% pressure drop of about 0.1 Mbar. So the static pressure surrounding the pipe is 1 Mbar, and the interior pressure on the inside is 0.9 Mbar.

What would be the mass flux through the opening?

Would the Navier-Stokes equation be relevant here?

What about sensitivity to Reynolds numbers?

tusenfem
2007-Oct-24, 01:37 PM
Warren, I think you better read through chapter 9 (and maybe 10) of Frank Shu's "The physics of astrophysics, Vol II: Gas Dynamics" which deals with viscous shear flows and turbulence.

You are asking halfway impossible questions to be answered here on the board. And the problem is not correctly posed in your last message. To get an airflow in your pipe you have to have a driver. Now pressure difference is not enough, because there is already a steady state pressure difference in the pipe (which is Jupiter's red spot).
Now, I don't see what you want to do with the pressure drop across the boundary of the pipe. That would mean that you are looking at a circulation that is radially away from the center of the pipe. But your initial problem is an uprising in the pipe.

So, read up on gas dynamics, that would be a start. Navier-Stokes (see Wiki (http://en.wikipedia.org/wiki/Navier_Stokes) which I have not checked on correctness), when applied correctly could be a good start to figure things out.

Warren Platts
2007-Oct-24, 02:09 PM
Warren, I think you better read through chapter 9 (and maybe 10) of Frank Shu's "The physics of astrophysics, Vol II: Gas Dynamics" which deals with viscous shear flows and turbulence.

You are asking halfway impossible questions to be answered here on the board. And the problem is not correctly posed in your last message. To get an airflow in your pipe you have to have a driver. Now pressure difference is not enough, because there is already a steady state pressure difference in the pipe (which is Jupiter's red spot).
Now, I don't see what you want to do with the pressure drop across the boundary of the pipe. That would mean that you are looking at a circulation that is radially away from the center of the pipe. But your initial problem is an uprising in the pipe.

So, read up on gas dynamics, that would be a start. Navier-Stokes (see Wiki (http://en.wikipedia.org/wiki/Navier_Stokes) which I have not checked on correctness), when applied correctly could be a good start to figure things out.

Ugh! :wall: I don't have time to earn a degree in fluid mechanics! My die has been cast. I'm reconciled to the fact that I'll probably never die as a millionaire, and I'll probably never die a fluid mechanics expert. . . . :boohoo:

That's why I'm begging for help!

As for drivers, its just like a vacuum cleaner. There's the static pressure outside of your vacuum hose (1 Mbar in this case) and the pressure measured on the inside of the hose (0.9 Mbar in this case). That should be enough to get something going I would think.

John Mendenhall
2007-Oct-24, 02:42 PM
Ugh! :wall: My die has been cast. I'm reconciled to the fact that I'll probably never die as a millionaire, and I'll probably never die a fluid mechanics expert. . . . :boohoo:

And when you're finished with the Jovian gas pipe, then there're terrestial volcanic pipes, and lava tubes, and Kimberlite pipes, and mantle plumes, and . . . :doh:

I still like your GRS idea.

grant hutchison
2007-Oct-24, 03:44 PM
The difficulty (well, a difficulty) is that as soon as flow is turbulent, it has a strong interaction with the pipe. That interaction is represented by jigger factors in the flow equation, which are usually established experimentally.
So then we need to know what your pipe's made of, how rigid it is, how rough or smooth its inner surface is, what forces it might apply to the fluid running through it ... We're suddenly a very long way from Poiseuille's simple little equation for laminar flow.
Not that I'm claiming I could provide an answer if you provided such information about your "pipe" ... I'm just pointing out why people are being apparently reluctant to spit out a simple answer for you.

Grant Hutchison

tusenfem
2007-Oct-25, 07:23 AM
Ugh! I don't have time to earn a degree in fluid mechanics!

As for drivers, its just like a vacuum cleaner. There's the static pressure outside of your vacuum hose (1 Mbar in this case) and the pressure measured on the inside of the hose (0.9 Mbar in this case). That should be enough to get something going I would think.

Well, you don't have to get a degree, but some basic knowledge does not hurt anyone.

You are confused about the driver. Let's just go directly to the GRS, because that is what you want to model. Now, indeed there is a pressure difference between the bottom of the "pipe" and the top, and this is because of gravity and that pressure difference cannot create a flow.

The flow that you want needs an extra driver. Then you say, let's have a greater pressure outside the "pipe" then inside of it. Well, as there are no solid boundaries in the GRS, this would mean that the gas/plasma would just flow and equilibrate. Also, is that truly the flow that you want?

As far as I understand, you want an upward flow in the "pipe". This can only happen when, e.g. you heat up the gas at the bottom and start up a convection flow. Even with a solid pipe, an underpressure of the surroundings (and, BTW where is that under pressure, I guess at the bottom of the "pipe") will let gas/plasma flow into it at the bottom till there is equilibrium.

Please, reconsider everything, and then come up with a model that describes what you actually want, then after we get that working, we might start to consider turbulent/laminar flow etc.

Warren Platts
2007-Oct-25, 11:08 AM
Well, you don't have to get a degree, but some basic knowledge does not hurt anyone.

You are confused about the driver. Let's just go directly to the GRS, because that is what you want to model. Now, indeed there is a pressure difference between the bottom of the "pipe" and the top, and this is because of gravity and that pressure difference cannot create a flow.

The flow that you want needs an extra driver. Then you say, let's have a greater pressure outside the "pipe" then inside of it. Well, as there are no solid boundaries in the GRS, this would mean that the gas/plasma would just flow and equilibrate. Also, is that truly the flow that you want?

As far as I understand, you want an upward flow in the "pipe". This can only happen when, e.g. you heat up the gas at the bottom and start up a convection flow. Even with a solid pipe, an underpressure of the surroundings (and, BTW where is that under pressure, I guess at the bottom of the "pipe") will let gas/plasma flow into it at the bottom till there is equilibrium.

Please, reconsider everything, and then come up with a model that describes what you actually want, then after we get that working, we might start to consider turbulent/laminar flow etc.Believe me, I have answers for all your points. But lest I be accused of discussing an ATM topic outside of ATM, let me say that the question here is a hypothetical "science-fiction" question regarding mainstream hydrodynamics given the conditions that prevail in gas giant planets in this solar system and elsewhere. Therefore, for the purposes of this thread, assume the pipe is made of solid diamond. If you have a point to be made about the GRS, then please make in the ATM thread on that topic (http://www.bautforum.com/against-mainstream/65704-great-red-spot-low-pressure-system.html). :)

Warren Platts
2007-Oct-25, 11:52 AM
Well, your Wiki article also gives the rule that is generally used if you want to be sure of avoiding turbulence:Haven't you got all the data you need?
From your numbers, using the critical value for Re:

vs = 6.5x10-8m.s-1

That's the trouble with wide pipes.

So you end up moving about 22.3 tonnes a second. I have to say that choosing a pipe as wide as a city is not a good way of suppressing turbulence. :)

Grant Hutchison
Dr. Hutchison,

I found the following numbers from Guillot, Stevenson, Hubbard, and Saumon's (2004, "The interior and of Jupiter", table 3.4, in Bagenal et al.'s Jupiter)

Reynolds number (Re) = 1011
Rosby number (Ro) = 10 -4
Ekman number (E) = 10 -15

I guess high Re implies a turbulent regime; the low Rosby number implies "convective motions will be mostly confined to a plane perpendicular to the axis of rotation" (whatever that means--I'm having trouble visualizing that); and the Ekman number describes "the relative magnitude of viscous and Coriolis forces. It is extremely low, indicating that frictional forces are largely negligible for large scale motions in the planet." (p. 45)

So, I was wondering if these new numbers would affect your initial calculations much.

grant hutchison
2007-Oct-25, 01:38 PM
So, I was wondering if these new numbers would affect your initial calculations much.'Fraid not. Ekman and Rossby are ratios that are relevant to the Coriolis deflection of a fluid flow in a rotating system (eg a planet), so they're not a help with your mysterious pipe.
The quoted Reynolds number just shows that fluid motion is going to be turbulent down to small scales in whatever regime is being described by your reference.

(Ek is an estimate of the ratio of viscous to fictitious (=Coriolis) forces; Ro is the ratio of inertial to fictitious; Re is the ratio of inertial to viscous. This implies, as you can see from your example, that Re = Ro/Ek. If you have any two of these numbers, you know the third.)

Grant Hutchison

tusenfem
2007-Oct-25, 02:09 PM
Believe me, I have answers for all your points. But lest I be accused of discussing an ATM topic outside of ATM, let me say that the question here is a hypothetical "science-fiction" question regarding mainstream hydrodynamics given the conditions that prevail in gas giant planets in this solar system and elsewhere. Therefore, for the purposes of this thread, assume the pipe is made of solid diamond. If you have a point to be made about the GRS, then please make in the ATM thread on that topic (http://www.bautforum.com/against-mainstream/65704-great-red-spot-low-pressure-system.html). :)

So we have a solid pipe, which extends from the "bottom" of J to the "top" of J.
At the bottom you have in the pipe a 10% lower pressure than outside of the pipe.
In the pipe you will have a pressure gradient created by gravity from the top to the bottom
The pressure difference at the bottom (however you created that) will want to equilibrate with the pressure outside the pipe, unless you have closed it off.
It will equilibrate by "sucking in" gas from the surroundings, coming to pressure equilibrium.
We do not know what you envision in the rest of the pipe, with respect to pressure. It at the top also a 10% difference or is there the same pressure as outside the pipe?
The inflowing gas will move into the pipe, how far depends on how the pressure in the pipe varies and what the pressure at the top is.
Unless you put a heating source at the bottom I do not see how you can get a continuous flow in your pipe. And then there has to be a down flow region too in the neighbourhood.

The whole problem changes of course when you decide that the pipe is surrounded by a homogeneous medium. Here I mean, that there is no pressure gradient along the pipe and at the top as well as at the bottom there is an outside pressure of 1 Mbar and an inside pressure of 0.9 Mbar.

So, stop looking at all kinds of numbers that you might find in books and or on the web, and start putting up the problem in the correct way. I am sure if you put it all correctly together you can easily use the fluid transport equations to get an estimate of the flow in the pipe. Navier-Stokes even has a nice "grad P" term on the right hand side.

If you do not present the problem in a sensible way, you cannot expect us to give you any answers, other than putting our own ideas into the problem, which may not coincide with what you have in mind.

Warren Platts
2007-Oct-25, 02:37 PM
Guys,

Don't worry about it anymore. I've figured out a simple work-around.

Dr. Hutchison,

Thanks for your last post. I've never had relations among the dimensionless numbers explained to me so clearly or concisely. :clap:

tusenfem,

I'm beginning to wonder if you're purposely trying to get me in trouble with the moderators around here. :mad: There is an answer to your question regarding an energy source (latent heat ;)), but that's ATM territory and so I've already posted the answer to your question in the ATM thread. I know you know where that thread is because you've posted there.

grant hutchison
2007-Oct-25, 06:28 PM
Dr. Hutchison,

Thanks for your last post. I've never had relations among the dimensionless numbers explained to me so clearly or concisely.Well ...

There's clarity, there's concision and there's accuracy. And we can have any two we like. :)

In this case, I supressed the slightly messy reality that Ekman comes in several flavours, all doing the same job and summarizing the same ratio, but only one of which fits precisely into that balanced equation with Rossby and Reynolds.

Grant Hutchison

tusenfem
2007-Oct-26, 09:30 AM
tusenfem,

I'm beginning to wonder if you're purposely trying to get me in trouble with the moderators around here. There is an answer to your question regarding an energy source (latent heat), but that's ATM territory and so I've already posted the answer to your question in the ATM thread. I know you know where that thread is because you've posted there.

No, I am just trying to get you to define your problem correctly. The background may be GRS but that is beside the point. There is nothing ATM going on here, and I am not forcing you to go there or trying to get you banned. I am sure the moderators will have no problem with setting up a hypothetical model (like you did) and then work through the Navier-Stokes equations.

Just regular, mainstream science will not be able to answer your question if you do not pose it correctly, therefore the questions for clarification.

to the moderators:
I am sure you will give Warren the possibility to describe his model that he wants to have investigated, such that we can do a calculation finally of the mass flow through this pipe.
Thanks for your leniency.
Martin

Warren Platts
2007-Oct-26, 01:31 PM
No, I am just trying to get you to define your problem correctly. The background may be GRS but that is beside the point. There is nothing ATM going on here, and I am not forcing you to go there or trying to get you banned. I am sure the moderators will have no problem with setting up a hypothetical model (like you did) and then work through the Navier-Stokes equations.

Just regular, mainstream science will not be able to answer your question if you do not pose it correctly, therefore the questions for clarification.

to the moderators:
I am sure you will give Warren the possibility to describe his model that he wants to have investigated, such that we can do a calculation finally of the mass flow through this pipe.
Thanks for your leniency.
Martin

OK, well then let's just say we know for other reasons that the total molar flux is 1017 moles of an ideal gas per second. So according to the ideal gas law (PV = nRT), we can solve for volume (V = nRT/P) per second since we know P (1 Mbar = 1011 Pascals[Newtons per meter2]), n (1017 moles), R (the gas constant--8.314 Newton-meters per mole per degree Kelvin), and the temperature (6,000o K).

1017 mol 8.314 N m 6 X 103 K m2
_____________________________ ~ 5 X 1010 cubic meters per second

s mol K 1011 N


if I did my math(s?) correctly and all the units canceled the way they're supposed to.

Assuming a density of 0.7 grams per cubic centimeter (which by happy coincidence is the same as 0.7 metric tons per cubic meter), that works out to 3.5 X 1010 metric tons per second.

The area of a 25 km circle is about 500 square kilomters or about 5 X 108 m2. Therefore, if the total flow is 5 X 1010 m3/s, then the average velocity would be 100 meters per second. (This is an interesting result since I had assumed an average velocity of 50 m/s at the top of the 10,000 km funnel shaped "pipe" in order to estimate the molar flux.)

We can go a little further and calculate the kinetic energy contained in a 1 meter-thick slice out of the 25 km diameter pipe (mv2/2). One such slice would have a total volume of 5 X 108 m3, and hence 3.5 X 108 tons or 3.5 X 1011 kg. And the velocity squared would be 104 m2 per s2. Multiplying and dividing by 2 yields ~ 1015 Joules, and converting that to an energy rate or power, 1015 Watts

I think I did that last part wrong. Since the column is moving at 100 m/s, then to figure out the power of the column, I would have to consider the mass of a 100 m slice, rather than a 1 m slice. Correct? So that would boost the power to 1017 Watts, or about pi X 106 quads per year--about 30,000 times the annual energy demand of the US (http://www.cmu.edu/all/Lecture711.pdf)--which seems more reasonable.

So the question now becomes: Are these hypothetical flows reasonable, given the modern understanding of hydrodynamics? Because of the high Reynolds number, the flow will be turbulent, but because of the low Ekman number, friction is neglible, and the low Rosby number means the flow might take on a corkscrew pattern.

Speaking of happy coincidences: I've noticed that there are 2.2 miles per hour in 1 meter per second, and there are also 2.2 pounds per kilogram. Coincidence, or a reflection of underlying unity???

tusenfem
2007-Oct-29, 10:13 AM
Okay, I guess your math is okay.
However this does not mean a thing, I asked for a description of the pipe that you envision. You start with an assumed 1017 moles/sec flow and transform it to some other unit m3/sec.

The fact that you get almost the same value 100 vs. 50 m/s is not a surprise, because somehow (we don't know how) you came up with the mole/sec value based on 50 m/s then transformed them in a circle and found 100 m/s.

Warren Platts
2007-Oct-30, 01:07 AM
Okay, I guess your math is okay.
However this does not mean a thing, I asked for a description of the pipe that you envision. You start with an assumed 1017 moles/sec flow and transform it to some other unit m3/sec.
Actually, my friend, I did not do the math correctly. If we start with 1017 moles/sec and assume a typical molar weight of 2.5 gm/mole (86% H2, 13.6% He, and a few molecules of heavier stuff), that works out to 2.5 X 1014 kg/s. To cram that much mass into the volume I calculated (5 X 1010 m3/s, corrected) would result in a density of 5 gm per cm3--that's way too high. Therefore, something is wrong.

What I think is wrong is that the ideal gas laws depart from reality at those temperatures and pressures for hydrogen/helium mixture. That is, the mixture "stiffens" and becomes less compressible as the pressure increases.

So the way to calculate the volume flow is from the given density (0.7 gm/cm3) and given mass (2.5 * 1014 kg): that works out to 3.6 X 1011 m3 per second. Such a mass flux is the equvalent of 10,000 Gulf Streams.

Which brings me to my other mistake, when I came up with two different velocities for the top and the bottom of the pipe.

If
the mass flux is the same at the top and the bottom, and
energy is conserved (kinetic energy power is the same for top and bottom, and
the width of the column is allowed to expand adiabatically so that the inside of the pipe is isobaric with respect to the outside medium, and
the outside is a similar mixture of molecular hydrogen and helium,
then the velocity at the top and bottom should be the same (because K.E. = 1/2 mv2).

Anyone can feel free to correct me if I'm wrong there.

So, the new power estimate would be (1/2) * 2.5 X 1014 * 502 m2 s-2 = 3 X 1017 J/s (watts) or about ten million quads per year (about 20,000 times more than human world energy consumption (http://carto.eu.org/article2489.html))

THEREFORE:

A 25-km wide pipe could not accomodate the flow given the mass, density, and velocity constraints. The opening at the bottom would have to be bigger.

The area of the opening is given by the volume flow divided by the average velocity of the flow: 3.6 X 1011 m3 / 50 m/s = 7.2 X 109 m2.

If the opening was round, that would work out to a 100 km pipe diameter! :D

tusenfem
2007-Oct-30, 07:38 AM
maybe what is wrong is that you still have not defined the problem correctly here on the board. I seem to fail to see what you want to calculate.

A pipe with a mass flux, okay (you chose for some reason the value you chose)
If nothing happens to the pipe then flow in is flow out.
If nothing happens in the pipe, except flow, you can use the gas law.

But now you suddenly say that the pipe is to expand to remain isobaric with the outside medium?

I give up, first describe fully what you want to do, this does not work.

mugaliens
2007-Oct-31, 12:16 PM
You are asking 3 questions. Which do you want to answer?

Also, what is the temperature of the fluid?

And the material out of which the pipe is made? PVC and steel have different characteristics, though that holds true much more for a 1/2" pipe than a 25 km diameter pipe!

Suppose you let us know more about who's supposed to build such a pipe and why...

Warren Platts
2007-Oct-31, 05:03 PM
And the material out of which the pipe is made? PVC and steel have different characteristics, though that holds true much more for a 1/2" pipe than a 25 km diameter pipe!

Suppose you let us know more about who's supposed to build such a pipe and why...I'll let you know just as soon as the Patent Office gets back to me! :D

Wakenaam
2007-Oct-31, 05:32 PM
Are the conditions on Jupiter close to the assumptions for the basic fluid dynamic equations? Newtonian vs Non-Newt, gravity difference, compressibility etc?

Warren Platts
2007-Oct-31, 06:12 PM
Are the conditions on Jupiter close to the assumptions for the basic fluid dynamic equations? Newtonian vs Non-Newt, gravity difference, compressibility etc?I think so, but I'm not 100% sure.