Mathematical Analysis of an Ideal ZED

[mondrasek]

I have shown all the work in the spreadsheet in convenient easy to read algebraic form.  If you aren't going to bother to read and understand the work, then there is little hope for you.  Either you accept your stipulation that the system was vented in State 1 so that there was no net force up or down on the risers, or you change your problem definition.  If you accept the former, then what you have is no different than objects floating on a volume of water at the end of each:  State 1 and State 3.  State 2 added volume to the water which because of the restraint on the Russian Dolls of Ignorance was forced into AR7.  Once the restraint was released at State 3, the added fluid effectively redistributed to an equal height across the entire cross-section as required by fluid behavior.  Ergo, we poured some water into Archimedes' bath and his rubby ducky, Spanish Armada playset all rose with added water.

MarkE, the venting allowed for assembly without inducing buoyant Forces and kept internal Pressures neutral.  It is the fact that there is zero water head between the OD and ID of each riser (and no water around the pod) that determines that each element is being acted on by no buoyant Forces and therefore in equilibrium.  In your State 3 there exists positive buoyant Forces on the pod and all three risers that are yet unresolved.  How do you wish to resolve those Forces?  Or can you point out an equal and opposite Force that is neutralizing the remaining buoyant Forces?

[MarkE]

MarkE,

There is no way the system you have presented will stop in this position.

This system will continue to lift until the water level in AR7 has been drawn down below the water level in AR6 to counter the decreasing buoyant lift of the  other 2 risers and the pod.

It will be the negative buoyant condition of the 3rd riser that stops the movement, and your setup has not reached that.

The duckys are playing submarine,, and they are filled with air!

Webby do try and pay attention.  State 1 was stipulated by Mondrasek.  AR7 increases in height over the State 1 stipulated equilibrium condition just like the entire rest of the cross-section does.  That's what fluids do webby:  They flow to fill the available area.  The outer walls of the base assembly define that area.  The Russian Dolls of Ignorance configuration does not change that reality.

[MarkE]

MarkE, the venting allowed for assembly without inducing buoyant Forces and kept internal Pressures neutral.  It is the fact that there is zero water head between the OD and ID of each riser (and no water around the pod) that determines that each element is being acted on by no buoyant Forces and therefore in equilibrium.  In your State 3 there exists positive buoyant Forces on the pod and all three risers that are yet unresolved.  How do you wish to resolve those Forces?  Or can you point out an equal and opposite Force that is neutralizing the remaining buoyant Forces?

Mondrasek, again you are flat, stinking wrong.  Under the condition that you again reiterate for State 1 above, the act of adding water in State 2 is to move that condition to one where the water level rises by the added water volume divided by the cross section.  If you are going to continue to dispute basic physics then go find a suitable reference to support your absolutely incorrect argument.

[MarkE]

MarkE, your math is not in question.  But it results in a paradox, right?  If you solve to balance Energy, you end up with unbalanced Forces left over (this is what your analysis shows).  If you solve to balance the Forces, then the Energy balance is not correct.  Do you disagree?  Are there not unbalance buoyant Forces in State 3 of your analysis?

There was useful work performed that you have ignored.  The ZED in this Analysis was not allowed to rise uninhibited by a load.  We agreed on this from post 249 of this thread:

I utilized the same analysis method for the output rise as was used for the input of the water charge:  F*ds as expressed for the case of a Volume of a Fluid that is being moved by a change in Pressure that either starts or ends at zero:  P_average*V.  The riser initially will want to move with a Pressure that can be calculated from the buoyant force sum of the pod and risers.  That Pressure should drop linearly to zero as the ZED reaches equilibrium at the end of the rise.  The physical device that would restrain the initial Pressure and allow it to drop to zero while performing the rise is not important for the analysis I think.  Please let me know if you think otherwise.

You violated this first by NOT calculating the lift difference using the described method of an Energy balance.  You instead resorted to a Volume balance which is flat wrong for this open ZED.  Then you ignore that work output preformed upon the non-physical device agreed upon would provide the theoretical output F*ds as the P_average*V, or simply F_average*ds where ds is the lift distance.  So there is Work that can be performed by the change from State 2 to State 3 and you ignore that in your Analysis.

Monderasek, there is no paradox.  The behavior is all very well understood.  If you think that this is a paradox, then you must think that connecting one charged capacitor to a second uncharged capacitor is a paradox as well.  There is no more paradox here than there is to slowing down your car by applying the brakes.  Your latest incorrect assumption is that the stored energy remains constant.  You insist on this incorrect position even when the physics have been explained to you multiple times.  This whole foolish contraption is a glorified pool of fluid.  Add more fluid and it rises.  End of story.

[MarkE]

Yes MarkE do pay attention.

Where are the water heights in state 1.

Where are the water heights in end of state 2.

Where are the water heights in end of state 3.  Not back to a neutral height are they.

Nope, you are still not paying attention.  Mondrasek stipulated the neutral condition as State 1.  Now you may reasonably object to that stipulation, but then you will have to take that up with Mondrasek.  But as long as he stipulates that State 1 is as he depicted it, the result in State 3 falls out.

Now, suppose that we object to the State 1 stipulation.  Suppose that we note that the real neutral water level is in a State 0 where no risers have been inserted.  The mechanics don't change.  The "ideal ZED" remains an energy wasting piece of junk outperformed by a brick.

Water will flow and find its own level.

Tell that to Mondrasek.  He seems to think that incompressible fluids behave some other way.

There is a buoyant lift left in the risers, all of them as you have them at the end of state 3.  They all have a positive buoyant lift potential that is left,, repeat, the water still wants to move down and that will move things and make the risers go up.

Again, State 3 arises from Mondrasek's:  Wayne Travis approved stipulation of State 1.  If you object to the State 1 stipulation, and you should, then you need to ask that pair why Mondrasek stipulated State 1 as he did and why Wayne Travis approved of that stipulation.

The only avenue there is for the increase in volume needed for all of that movement is from AR7, that will get sucked down until the suction, the negative buoyant lift equals the positive buoyant lift of the other 2 risers and the pod.

Again, you need to change the stipulation of State 1.  Otherwise, we get exactly what has been shown.

Do remember that I have played with a 5 riser system, and look at some of the pics I posted of that system.

I can tell you that the system as you have it in end of state 3 WILL move up and I can tell you that the water in AR7 WILL get sucked down.

Again, that is because your experiment did not have the State 1 stipulation:  Apples and oranges.

Use your finger and follow the movement,, see that the movement can happen, see that nature will want to make that movement happen, see that that movement will happen.

You know that movement can happen because it happened for the system to go from state 1 to end of state 2.