Mathematical Analysis of an Ideal ZED

[MarkE]

Mondrasek, I think that the confusion here is in how does one measure the energy of a submerged buoyant object.  For an object of constant height, the amount of force that we must apply to the object to initially submerge it changes from the value at zero submersion to the fully submerged value.  From there on the buoyant force is constant and the amount of additional work required to submerge the object further is the difference between that constant buoyant force and the constant force of gravity on the mass of the object multiplied by the change in depth.

The attached graphic will hopefully help.

[mondrasek]

Mondrasek, I think that the confusion here is in how does one measure the energy of a submerged buoyant object.  For an object of constant height, the amount of force that we must apply to the object to initially submerge it changes from the value at zero submersion to the fully submerged value.  From there on the buoyant force is constant and the amount of additional work required to submerge the object further is the difference between that constant buoyant force and the constant force of gravity on the mass of the object multiplied by the change in depth.

The attached graphic will hopefully help.

TK,

I would appreciate if you would stay on topic.  Can you please explain exactly how this post is relevant to the "Mathematical Analysis of an Ideal ZED" models so far presented?

M.

[TinselKoala]

Do you have me confused with someone else?

But look again at Mark's diagram. Do you see what he is integrating? Do you see any need for an ideal gas law in determining the work required to submerge a _sealed_ buoyant object?

Now, if you were considering a Cartesian Diver (an _unsealed_ buoyant object)  and didn't stipulate beforehand that all your fluids were incompressible, that would be a different story.

[mondrasek]

Do you have me confused with someone else?

No TK, I am just calling you out (regrettably).  Are you, or are you not, using the pseudonym of MarkE ?

But look again at Mark's diagram. Do you see what he is integrating? Do you see any need for an ideal gas law in determining the work required to submerge a _sealed_ buoyant object?

Finally!!!!!!!!!!!!!   We get to the Ideal gas law!  Which is PV=nRT.  Which for Isosthermic cases (ie. T₁=T₂) results in  Boyle's law:  PV_input=PV_output.

Now, if you were considering a Cartesian Diver (an _unsealed_ buoyant object)  and didn't stipulate beforehand that all your fluids were incompressible, that would be a different story.

Is the ZED system an "unsealed buoyant object" or not?

M.

[MarkE]

No TK, I am just calling you out (regrettably).  Are you, or are you not, using the pseudonym of MarkE ?

Finally!!!!!!!!!!!!!   We get to the Ideal gas law!  Which is PV=nRT.  Which for Isosthermic cases (ie. T₁=T₂) results in  Boyle's law:  PV_input=PV_output.

Is the ZED system an "unsealed buoyant object" or not?

M.

No Mondrasek I am not a sock puppet of TinselKoala.  And no when a gas is incompressible, the ideal gas law of which Boyle's Law, and Charle's Law are consequences do not apply.

I finally got to spending some time with your model today and have a couple of questions.  The first is that when you admit water you want to fill up the pod chamber to 60mm height.  But that will drive all of the water out of annular ring 2.  What would you like to do here?  One option is to add water in the pod chamber until AR2 gets down to 2mm above the bottom.  A second option is to prefill to a much greater height than 32.5mm.  For instance 52.4mm would leave 2mm in AR2.