Mathematical Analysis of an Ideal ZED

[minnie]

  Yes they can and will work, if you have a transfer pump!
                                              John

[mondrasek]

The ZEDs amplify force at the expense of distance travelled, as you yourself have found and admitted freely,

Which is the basis for absolutely no conclusions.  Because I also freely admit that from what I have found, the Integral of the resultant force * distance does NOT equal that of the input.  I never said the ZEDs amply force by a relationship to a reduced distance of travel that conforms to a conservative system.

but the output work will be less than the input work, because of the inevitable losses.

This is not what the Mathematical Analysis supports.  It is your assumption and/or position, not a proven fact.

On another related note, please tell me what you think about this.  Imagine the ZED model surrounded by the "red box" I showed when analyzing your U tube joke.  There are more than the two volumes I have shown in the analysis crossing that system barrier.  Yes there is the input water, and the output riser stroke that cross the barrier.  But there is also air that leaves and enters the system through the outer annulus (outside the outer riser) that is open to the atmosphere.  So the ZED is an OPEN system, right?  Also, it is the air that crosses through this opening that allows the fluid levels to redistribute and create a resultant buoyant force that is calculating to be not equal to the force predicted by the input.

[minnie]

   I want to get this straight, you lift a weight with one side of your device, you remove the
  weight and use it, and it sinks by itself and also raises a weight on the other side of your device.
   Now if that isn't a bit of magic nothing is!
                         John.

[TinselKoala]

What about what Larry and Monderask have presented.

Any problem other than can't work.

Wayne

LOL. What other problems do you need?

You can't produce evidence to the contrary, even though you've had many years to do so. "Can't work" wins the day, then, until YOU show otherwise... but you cannot.

[TinselKoala]

Which is the basis for absolutely no conclusions.  Because I also freely admit that from what I have found, the Integral of the resultant force * distance does NOT equal that of the input.  I never said the ZEDs amply force by a relationship to a reduced distance of travel that conforms to a conservative system.

No? I could have sworn that you did, when you agreed with me here:

Of course the riser moves a much shorter linear distance than the syringe plunger, assuming a syringe with diameter smaller than the ZED's outer riser.  That is why I proposed to compare volumes.

This is not what the Mathematical Analysis supports.  It is your assumption and/or position, not a proven fact.

It is my "assumption" and position, based on thousands of years of experimentation by hundreds of thousands of scientists, engineers, and amateurs like some of us. Nobody, nowhere, has ever demonstrated otherwise. Please see the quote from Feynman re the relationship between "theory" and "experiment".

On another related note, please tell me what you think about this.  Imagine the ZED model surrounded by the "red box" I showed when analyzing your U tube joke.  There are more than the two volumes I have shown in the analysis crossing that system barrier.  Yes there is the input water, and the output riser stroke that cross the barrier.  But there is also air that leaves and enters the system through the outer annulus (outside the outer riser) that is open to the atmosphere.  So the ZED is an OPEN system, right?  Also, it is the air that crosses through this opening that allows the fluid levels to redistribute and create a resultant buoyant force that is calculating to be not equal to the force predicted by the input.

No, I don't think that is right. I considered this issue before when the "incompressible fluid" was replacing the air in the trapped chambers. The outer ringwall and the outermost layer of trapped whatever seals the rest of the system from contact with the outside air, and even in spite of that, there is nothing happening, or that can happen, in any Zed system that can change the pressure of the _outside air_. For all practical purposes its volume is infinite, so you can raise and lower your levels in the outer trapped stuff as much as you like without changing the pressure it feels from the outside air at all. Here is a place where Boyle's Law does apply: PV init = PV final, and since Vinit  and Vfinal are equal and (practically) infinite.... well, do the math.

And my U-tube isn't a joke, it's an illustration of one of the many ways that interpretation of spreadsheets can go wrong. You hit the nail on the head when you drew the red box, although there may be even simpler ways. So I have no doubt that when you draw your red box _properly_ around your system or a "real" Zed, you will also hit the same nail on the same head. No pun intended.

ETA: While we are on the subject of math, the Heron's Fountain with reservoirs of 100 mL, elevated by 20 cm,  will run for, say, a minute. How long will a Heron's Fountain with reservoirs of ten thousand liters, elevated by five meters, run? And with what pressure head?