Mathematical Analysis of an Ideal ZED

[MarkE]

MarkE, I agree with all of it except for your statement #5.  And that is because I have done the math and did not find those expected results for this unique construction (ZED).  I would fully have expected your statement to hold true due to my training and experience (and knowledge of history).  But I could not find the classical expected result to present itself.  And so I did, and still do, ask for a double check of the analysis of this 3-layer ZED model.

Mondrasek, take two columns and connect them with a pipe at the bottom.  For the moment we will use identical cross-sections only for simplicity of the illustration.  Now, fill each of the columns to a height H1 and calculate the stored energy:

1) E = 2*0.5*pFluid*area*(H1² - 02) = pFluid*area*H1²

Next, move some amount of fluid from the right hand column: C2, to the left hand column C1 such that C1 increases by H2, and C2 decreases by H2:

2) Eadded_or_removed = integral F*ds.
Estored = integral F*ds column left ending + integral F*ds column right ending
K1 = pFluid*area
Estored = 0.5*K1*((H1+H2)² - H12) + 0.5*K1*((H1-H2)² - H1²) = 0.5*K1*((H1+H2)² - (H1-H2)²) = 4*0.5*K1*H2

Fstart = 0, because the columns are balanced.
Fend = Weight_left - weight_right = 2*pFluid*area*H2 = 4*K1*H2
Kf = 4*K1*H2/H2
Eadded = 0.5*Kf*(H2² - 0²) = 4*0.5*K1*H2

Ergo, in order to introduce a difference in height, we must apply 2*pFluid*area*Height change.  IOW, we did the work of lifting two volumes of the fluid each volume the change in height times the column area.  The exact reverse happens when we move a pair of connected columns towards equalization:  We lose internal potential energy identically equal to the sum of the weights times the distances: H2 moved.  Ergo, equalization loses stored energy.  Ergo equalization is lossy.  Ergo statement #5 is true.  QED.

This means that it is unequivocal that the State2 to State3 transition loses energy making the overall process lossy.  Now, someone could hypothesize that if we added a payload weight and lifted it that could produce some sort of net gain.  However, the incremental process amounts to lifting a weight.  All prior evidence is that gravity is conservative, and therefore lifting and lowering weights (neglecting losses) is also conservative.  Therefore adding a payload weight to the problem does not change the underlying conservative physics.

So tell me what you think.  Because as far as I can tell we are past establishing that the ZED is a loser, and are now down to giving you a solution for the ending heights of each of the columns.

[MarkE]

MarkE,


Where is it broken now? You've proved that our Engineering calculations that you been saying were wrong, are correct, as they match your Integral F*ds calculations.

LarryC you obviously have not been paying attention.  But since you now agree that the algebraic reduction is correct, feel free to try and justify that those equations represent the physics.  If you succeed you fail, because by your own words they do not yield even close to unity.  And if you fail you establish that for all your claimed expertise you still have not modeled the system correctly.

[mrwayne]

Engineers "jumped to your conclusion".  You are a hoot.  The seemingly effortless way that you continue to shamelessly keep suggesting that you have something behind your tattered curtain is really awesome.

Thanks Mark,

I have warned you that our system is counter intuitive - and you are trusting your intuitive - and it is good - Not the best I have seen - you get lock jaw when you trust in what you already know - is making you blind.

Richard is one of the best - and when he found what he thought was a dead end - he said - How did you get around "this" and he learned the system very quickly.

Jumping to conclusions is a big mistake........... and I believe - that is why our system eluded the world.

The Math will reveal the truth, Keep up the good work.

.....................................

You do not need me - you are on the right path to either conclusion.

Wayne

[MarkE]

Thanks Mark,

I have warned you that our system is counter intuitive - and you are trusting your intuitive - and it is good - Not the best I have seen - you get lock jaw when you trust in what you already know - is making you blind.

Richard is one of the best - and when he found what he thought was a dead end - he said - How did you get around "this" and he learned the system very quickly.

Jumping to conclusions is a big mistake........... and I believe - that is why our system eluded the world.

The Math will reveal the truth, Keep up the good work.

.....................................

You do not need me - you are on the right path to either conclusion.

Wayne

Wayne Travis, it's awesome that you misrepresent so freely.  Your claims of excess energy and breaches of conservative behavior by gravity are in fact completely unevidenced falsehoods.  You choose to ignore what has already been proven.  That's a big sign of scienter.

No, I don't need you.  You have nothing to offer but lies.

[mrwayne]

Wayne Travis you do not speak for me.  Larry's spreadsheet remains broken.  The analysis above shows that there is no gain to be had with the serpentine piston.  As soon as we release the device, we lose energy that we paid.  There is no sign of over unity.  There are only losses.

Right you are - my bad for the inclusion..

You have a one track mind - what you think the end is going to be..........

Get to the end of the Math - show the errors - everyone is appreciative.

The end is a three layer dual ZED system - Net Energy.

The new end of discussion will be; What is the Difference between a Non conservative Net Energy system and O/U.

That difference is what required our engineers to rethink of the black box.

We let people call it what they understand - for now.

Wayne