Mathematical Analysis of an Ideal ZED

[MarkE]

Your demonstration clearly shows that in a system with more than one buoyant object (where the objects are in interfering contact with each other) it is the SUM of the buoyant Forces that must equal ZERO for the system to be in equilibrium.  The negative buoyant Force in your bottle due to the negative water Head is exactly balanced by the positive buoyant Forces due to the positive water Head on each pontoon straw.

Good, I am glad you accept that.  Now, look back at State 1 and apply the same principle.

Checking for a balanced buoyant Force condition in the State 3 state is the first step I have show.  Both on your State 3 where it was not zero (it was a negative value showing your State 3 would need to sink to find equilibrium) and my own State 3 where it was also not zero (it was a positive value showing my State 3 would need to RISE to find equilibrium).

We both sought to find zero net up force in State 3.  We used different methods.  The question is whether either method was in fact correct.  I know that it was stupid me for conceding a point I shouldn't have that State 1 is in equilibrium, because as these demonstrations prove, it is not.  The same logic that you assert: that the ring walls are supported from below by the buoyant force of the water beneath them in State 2 and State 3, is also true in State 1.  We had to do real work to first sink the riser assembly, and then we had to continue to apply force to keep it down, or more accurately:  to keep the water in the annular rings 2 through 7 up above the relaxed level of 22mm to the elevated level of 32.5mm.  That represents additional stored energy in State 1 that is available to attempt to lift the risers above their most submerged depth at 1mm above the base.  This in turn should cause you to question what the hell it was that you did in your calculations to arrive at the conclusion that the energy added in State 2 is the only energy that tries to escape by pushing up the risers.  They would go up from State 1 as shown in this demonstration. 

We can figure out what I did wrong in my calculations because I have shown all of my work.  We cannot figure out what you have done wrong until you show yours. 

[MarkE]

Just to help a little bit here.

Would it not be better to use a one way valve in the bottom of the little bottle,, that is what you have made with your vent.

Then you *could* just use the old method of a lever, a bucket on a string and a weight on the other end of the lever,, since that is all you have made.

The pontoons are what is lifting the thing, no interaction with them so there is no correlation to the ZED.

For purposes of the demonstration the tape is completely adequate.  All that we need to know is:

1) What is the equilibrium condition with the vent open?  We have that in the full up picture.
2) What is the condition, equilibrium or non-equilibrium when in the down position and the water levels have equalized due to the open vent?

The pontoons do not do any lifting.  All of the lifting is done by the water.  The pontoons reduce the lift due to their non-zero density.  The pontoons are a close approximation to the massless risers specified for the "ideal ZED".  Had the combination of the pontoons and the water bottle been truly massless then the relaxed up position would be floating on the surface of the water, instead of partially submerged.  In this respect the demonstration is more like a real ZED than the "ideal ZED" because any real ZED's risers have materials with an SG > 1.0.  If they are hollowed out, those air bubbles would act like the soda straw pontoons.

[mondrasek]

Good, I am glad you accept that.  Now, look back at State 1 and apply the same principle.

Nope.  Our air is assumed incompressible.

We both sought to find zero net up force in State 3.  We used different methods.  The question is whether either method was in fact correct.  I know that it was stupid me for conceding a point I shouldn't have that State 1 is in equilibrium, because as these demonstrations prove, it is not.  The same logic that you assert: that the ring walls are supported from below by the buoyant force of the water beneath them in State 2 and State 3, is also true in State 1.  We had to do real work to first sink the riser assembly, and then we had to continue to apply force to keep it down, or more accurately:  to keep the water in the annular rings 2 through 7 up above the relaxed level of 22mm to the elevated level of 32.5mm.  That represents additional stored energy in State 1 that is available to attempt to lift the risers above their most submerged depth at 1mm above the base.  This in turn should cause you to question what the hell it was that you did in your calculations to arrive at the conclusion that the energy added in State 2 is the only energy that tries to escape by pushing up the risers.  They would go up from State 1 as shown in this demonstration. 

We can figure out what I did wrong in my calculations because I have shown all of my work.  We cannot figure out what you have done wrong until you show yours.

You have cleverly played with your system until the VACUUM you are inducing in the air inside the bottle is balancing the buoyancy Forces from your pontoons.  If anyone cares to make something similar they will find that they cannot achieve the identical water inside and outside that you show by the methods you describe.  Do you know why?  I do.

[Marsing]

hi..  mondrasek

it seem that you asked someone to repair your car or something without touching it, with closed eyes, is there something that you hide inside?
as PC is your toy and you are also VBA programmer, how could it be so difficult for you to learn only a bit of excel ?,
there is no doubt that you know exactly a help button in excel and you know google is a huge library. I'm sure you will not regret exploring excel features.  say goodbye to calculator    

[MarkE]

Nope.  Our air is assumed incompressible.

You have cleverly played with your system until the VACUUM you are inducing in the air inside the bottle is balancing the buoyancy Forces from your pontoons.  If anyone cares to make something similar they will find that they cannot achieve the identical water inside and outside that you show by the methods you describe.  Do you know why?  I do.

There you go Mr. I won't show my work insinuating that I have done something underhanded.  I haven't.  There is nothing here that I "played with".  I added pontoons until the net assembly had an SG well under 1.0.  The risers you stiplulated have an SG of 0.  So let's do some free body diagrams, shall we?  The up relaxed picture with the vent open is slightly submerged.  Fb_up = Fg.

Any of the cases even with the vent open require an additional force to overcome Fb_down.

Fb_down > Fb_up, Ftotal down > Fg.  The weight provides the extra force.

This extra force is not only self-evident in the sealed assembly's ability to draw water up such that:

Fb_middle = Fg + Fg_water_updraw

So go ahead and build this thing.  Show me that I've gamed it somehow.  And then eat crow, because you won't be able to show that I have gamed anything.  These experiments like all the work I have presented are completely transparent.