Mathematical Analysis of an Ideal ZED

[mondrasek]

I object to this improper claim that buoyancy forces are "turned on".  Force builds from zero linearly and incrementally as water pumped in is forced around the obstacles in its path.  There is no "on" state or contrary "off" state.

MarkE, you can object to this description of "turned on" as it is not an instantaneous change between a state of 0 or 1.  But it is the vernacular used by the majority of the population.  I was only trying to point this out.

Ever "turn on" a CRT device and wait for the picture to appear as the tube "warms up?"  Same thing.  "Turn on" does not have to mean instantaneously.  There is a delay in the on and off state of every device, no matter how high the switching frequency.

Forces don't resolve.  Acceleration stops when net force reaches zero.

Yes, acceleration stops in this single ZED system when all the buoyancy Forces sum to zero.  If they are left at any other value then those Forces are: a) unresolved (my term), or b) (please tell me how to properly express this condition here).

[MarkE]

MarkE, you can object to this description of "turned on" as it is not an instantaneous change between a state of 0 or 1.  But it is the vernacular used by the majority of the population.  I was only trying to point this out.

I challenge you to show where this idea of "turned on" is accepted in industry or academia.  It is a bull shit suggestion by our own HER/Zydro.  It is part of their misdirection.

Ever "turn on" a CRT device and wait for the picture to appear as the tube "warms up?"  Same thing.  "Turn on" does not have to mean instantaneously.  There is a delay in the on and off state of every device, no matter how high the switching frequency.

No it is not.   The buoyant force builds linearly from zero as water is pumped in.  It has no time dependency.  It has no state dependency.  More displacement = more force.

Yes, acceleration stops in this single ZED system when all the buoyancy Forces sum to zero.  If they are left at any other value then those Forces are: a) unresolved (my term), or b) (please tell me how to properly express this condition here).

Unbalanced forces mean net force.  Newton's Second Law still applies:  F = mA.  This example like your two riser and three riser before it is fundamentally lossy.  You start by supplying work to create State 1.  Then you add work, ideally without loss adding potential energy to get to State 2.  Then without extracting any useful work, you lose more than 2/3 of the potential energy you added to get to State 2 by going to State 3.   So, this scheme is less efficient than a brick.  And yet it is the "ideal ZED".  That means that real ZEDs with real friction can only underperform this machine that is already less efficient than a brick.  The best ZED is therefore no ZED at all.  HER/Zydro's claims to extra energy by using pods and risers are by your example of the ideal device: completely refuted. 

Now, what I want to know is that having last night looked back at the hydro differential thread and having seen that among others Kan Shi explained all of this almost two years ago while you were engaged, why do you still resist what you obviously have the capacity to understand?

[MarkE]

I tried not to misrepresent anything.

Actually MarkE,, you need to take that up with TK, he says he is the one to first use that term, and he demonstrated that the virtual water provided the same change in scale reading as the real water.

Still, it only took a small volume of real fluid to make that big change.

I highly doubt that TK being the learned person he is ever claimed to be the discoverer of Archimedes' paradox.  I am quite confident that he explained the paradox, which really isn't a paradox at all when one thinks about it carefully.  We covered this before when we discussed Grimer's cement volume derivations.

[mondrasek]

Newton's Second Law still applies:  F = mA.

Yes it does.  And lets look at that relationship.

F = mA

m is mass.  Mass is a property of a physical material that does not change for the accepted IDEAL conditions of a constant temperature and obvious absence of a state of matter change.  Therefore m is a CONSTANT.

A is acceleration.  In this case it is the acceleration due to gravity.  It is also a CONSTANT.

So the Force (F) in F = mA is a mathematical fact which the calculation of cannot be disputed.  It is the product of two CONSTANTS (and yes, TK, one is a vector so the result is a vector).

So, what is Energy?  It is a resultant of the prior mathematical fact that is Force.  It is F*ds (where ds is distance).

F is Force which is the product of two constants.

ds is distance which is another calculable (or measurable) physical fact and therefore a CONSTANT.

Ergo, you must solve for Force before you calculate the Energy.  And regardless of the outcome of that Energy value, it must be correct.

In your first attempt at this Analysis you solved first for Energy Balance.  This was erroneous and resulted in a physical State 3 that could not actually exist due to "unresolved" Forces in the system that did not sum to zero.

[MarkE]

MarkE,

Why would you NOT extract the useful work that can be extracted, sure if I run my car and don't go anywhere I will get ZERO MPG.

Common sense would say that if you can extract with no other effects then maybe you should, what part of this is it that you do not understand.

Webby, you are stuck on the same potential transfer problem that seems will vex you forever. 

For each um of upward movement we can calculate the net force on the riser.  It goes from its maximum starting value to zero.  It does so as a linear function.  Therefore we can express the force as:  F = F0 - K2*Z.  (K2 because I do not wish to confuse this constant with the pi/4*pwater*G0 K1 I often use.)  In other words the system operates like a cocked spring.  And now comes the problem with the ZED:  It is the way that the spring is utilized that is fundamental to the energy loss.  The potential energy stored in this "spring" is transferred into other potential energy in a direct process.  As a result, the process always suffers from the tyranny that:  N*(X/N)² = X/N.  The only way to break even is to restrict N to 1.0, which means that you cannot redistribute potential energy from one store to another by any direct transfer mechanism without loss.  Gears, levers, pulleys, or in this case the riser, IE anything that translates static force and distance to another static force and distance constitutes making N greater than zero, and you lose: period.  In the case of the ZED, the less upward movement of the riser, the better.  The optimum is zero.