Mathematical Analysis of an Ideal ZED

[mondrasek]

No, minnie, because I genuinely believe no matter what I presented, MarkE, would take issue with it.  It is just a diversion.  Much like his convenient "errors" and insistence on arguing falsities such as the previously mentioned ID vs. OD thing.  So I am done presenting anything that MarkE wants.  If anyone genuine wants any more info or assistance, I would be happy to work on that.

The math does not lie.  And there is only one solution.  Funny enough, I learned many of the methods and equations presented in my Analysis from MarkE!  His input in other threads helped me to form the idea for this Analysis method.  And his explanations early in the thread while working with LarryC provided even more assistance, including the Energy balance sums for the columns of water.

His State 2 matches mine.  The buoyant lift Forces on the pod and risers (inside his spreadsheet) also match mine.  So I am confident with the results of my Analysis.

It would be fun to do the Feynman test and build a model to test against, but that brings in all the real world variables we have eliminated in this Ideal Analysis as well as is costly.  I don't see the point in doing that as this is an Analysis of another's idea, not something I am trying to develop.  Just something I wanted to finish exploring.  And I am presently surprised by what is to be found.

[LarryC]

Oops is right Larry.  You miscomputed the input work.  Work is the integral of F*ds.  The initial force adding your 1ft of water is zero.  But the force at the end is:  4+1-2 = 3*0.65psi/ft.  The added work is therefore the integral evaluation from 0 to 1ft of:  0.5*3*0.65psi*area/ft*z² = 0.5*3*0.65psi*area/ft*1ft², which happens to be identically the difference between the starting and ending energies of:  E_INITIAL = 2*0.5*0.65psi*area*3ft² = 18*0.5*0.65*area and E_FINAL = 0.5*0.65psi*area*(1² + 2² +4²) = 0.5*0.65psi*area*21.

MarkE,

Attached first is my example that you said had the input work wrong.


Second is a picture of the spreadsheet integration that shows the same results as the example.


Third is the actual integration spreadsheet. Where it is using P * V at each increment.


Correction: the results are the same as yours, after I correct your .65 to .43 for the psi/ft.

[MarkE]

MarkE, I'll call it a day.  I'm not in school and need not conform to any rules to pass a class.  Neither am I presenting a proof for publication in any Science Journal.  I am showing others on an Internet Forum how I Analyzed the ZED using math, CAD, and a Calculator.  If they want to share in that, they can follow the presented methodology (which includes equations) and see if they result in the same values that have been presented.  They can also decide for themselves if the conclusions drawn are supported by those methods and math.  And I offer to assist anyone who has any question along the way.

AFAIK, the only tricky part is calculating the water column heights for whatever State 3 you want to finish with.  The lift creates some internal Volumn changes that can be missed initially.  That got me two years ago and again on my first attempt more recently.  If anyone wants assistance with that I am happy to help.

Mondrasek you can blow smoke all day long if that is what suits you.  You are making it obvious that you do not want your claimed analysis checked, because you never actually present your work so that anyone can check it.  See who you can take down your garden path.

[MarkE]

Marsing, only I never asked MarkE, or anyone, to "audit" my work.  I asked if anyone would double check my work.  And that can be done by different methods.  For example, I initially calculated new Water heights for State 3 by working from the inside out comparing Volumes and moving the boundary levels previously found in State 2 in CAD.  I then double checked the work by comparing Volumes of the Air and Water in each area to those in State 1 and State 2, which is a slightly different method.  Then I triple checked the work by calculating the Energy in the Water in each state as well as introduced by the charge and seeing if those values all compared properly, a completely different and valid method.

So there are different methods, and I could show several for most steps, but I encourage others to pick their own OR follow what I did. 

Now since my methods and MarkE's both arrive at the same State 2, I see no reason to back up and "show my work" that is proven to result in identical results with MarkE.  But I did agree to "show the work" moving forward from State 2 to State 3 since that is where we diverged.  And this, I believe, I have done.  With descriptions, equations, and example calculations.

The opening post actually began like this:

All, please check the math.  I would appreciate if you can point out any mistakes in the math, assumptions, logic, and conclusions. 

Yet, Mondrasek steadfastly refuses to provide what he says he wants checked.

[Pirate88179]

Mark:

You really should consider doing youtube videos.  Your demonstration would be very educational and, even though I know from experience that making videos is hard to do well, one does get better over time.  Hell, even TK can do it. (Ducking)  Seriously, I have learned more from TK's videos than I ever learned in school.  I thank him for making them.

Give it a shot...it is obvious that you have a lot of information that you seem very willing to share.

Bill