Exploring the N-Prize Problem with a Space Hose Solution

[gutemine]

Cool. I'd be interested in your first take on fan speed/pressure.

Well, the first key finding was that actually the blow speed at the bottom is lower (which is logic if you limit the head to 270m/sec which is approximately the speed of sound at -90 degree of Celsius), but you need a slightly higher surpressure to keep the whole thing stable (approximately 500-1000 Pa). This helped a lot to sort out the do I feed flow speed or surpressure at the bottom question which I never could sort out when I tried to calculate from there (predicting these 2 variables at the top is much easier and logically).

Funny is that the top contributes most of the pull forces even without the diffusor, which is good for extra stability. I already assumed this (because of the v² of the friction forces, but I didn't have any idea to what extent)

I'll see if I can warp it up and add some comments and colors for the changabel fields until this evening than you can play with it yourself.

Having such a 'virtual Space Hose' where all the parameters are changeable is pretty funny, and it even gives interesting results like pressure waves on top if the surpressure is too low, or how low you can bring the hose tensions down before it fails to stay errect (approximately 100N/mm² - which is not so far away from plain PE)

As I already mentioned I'm doing also some open source software development as another hobby so as soon as I found the formulas on how to calculate the Standard Atmosphere model from the definitions it was not so diffucult to build a Spreadsheet out of it.

http://www.pdas.com/coesa.ht

Then I found another Webpage where you can calculate air viscosity for all temperatures:

http://www.lmnoeng.com/Flow/GasViscosity.htm

It took me almost 1 hour to get all 100 viscosities for the model, but I was too lazy to try to reverse engineer the math for this too :-)

From these two raw inputs you have everything needed for the pressure loss calculation at all heights, and then the fun started when putting it together.

gutemine

 

[gutemine]

One more question on the wind - I found a nice picture on this (see attachment)

Would this mean that a hose with pull from top would actually form more or less such a bent curve ?

Because I would like to include also the pull force calculation into the excel, and for this I need a better understanding of the distribution of the wind force on the lower end of the hose.

gutemine

 

[gutemine]

Damned - I still have problems with my Excel and the discrete calculation steps because now I have a circular reference.

If I go 1km down this means that the pressure on the bottom should be the one at the top + pressure loss from friction + hydrostatic pressure of the 1km of gas.

The problem is that hydrostatic pressure is dependant on the density, which is resulting from the pressure from bottom to top (if I asume that temperature is always aproximately outside temperature of the standard atmosphere) = circular reference. Now I understand why the books are saying this is a differetial equation with an integral which is only numericially solveable - if at all :-(

And if I try to overcome this by simply taking the previous density as I did until now the result is underestimating pressure, which makes the numbers look good, but then the model is invalid beyond the top few kilometers of the hose, because only there density and hence hydrostatic pressure is low enough to allow such a simplification. So calculating top to bottom was a good idea, but gives wrong results at the bottom because of the discretisation. This is also the reason why going from bottom to top produced too high numbers on top.

But problems are there to be solved, and input is welcome ;-)

gutemine

 

[ewflyer]

Is the "space hose" thread over?