Mathematical Analysis of an Ideal ZED

[mondrasek]

Post #733 quoted for your convenience below.  Feel free to check my work, it uses the same r3 revision of the spreadsheet that has been posted for some time.  But, I really think it is about time for you to show your work that you keep saying yields an OU result.

Sorry MarkE.  I must have missed that as well.  And your request for me to show my results is fair at this point.

I'm at home now, and do not have access to my previous calculations or CAD.  But I'd be happy to work from your drawings if you want.  If so, can you tell me exactly (or please post again) which set of diagrams your post 733 refers to?  Also, are those diagrams and calculations all correctly based off of a buoyancy Force calculated from the OD of the pod and each riser?

I am not inclined to open any of your spreadsheets.  Not that I don't think they are probably masterpieces!  I expect that they are very impressive works!  I just don't want to be influenced in my methods by anything I might read in them.  Much like how I expressed that I preferred you do your math your way and not be influenced by mine.  I hope to only share results at first and methods only if discrepancies were found while you assisted me with this double check.

To remind you, I am running no calculation in a spreadsheet except some simple summations for volume and Energy balance double and triple checks.  The spreadsheets I have are only used as a table to record the results of hand calculations.  Those calcs were all run on an old Casio calculator that I was given at my first job.  That is also at work.  But I can dust off my old TI 15C, and suffer with the switch to RPN (which I truly love).  What a marvelous piece of EE work that is!  I've had it nearly 30 years now and had to change the batteries once!  Of course, it has been turned on very little since undergrad years.

If you have a complete and accurate Stage 2 to Stage 3 drawing for me, I'll give it a go.  Or we can wait until I am back at work.  I wont press you for anything in the mean time.

Thanks,

M.

[MarkE]

Sorry MarkE.  I must have missed that as well.  And your request for me to show my results is fair at this point.

I'm at home now, and do not have access to my previous calculations or CAD.  But I'd be happy to work from your drawings if you want.  If so, can you tell me exactly (or please post again) which set of diagrams your post 733 refers to?  Also, are those diagrams and calculations all correctly based off of a buoyancy Force calculated from the OD of the pod and each riser?

I am not inclined to open any of your spreadsheets.  Not that I don't think they are probably masterpieces!  I expect that they are very impressive works!  I just don't want to be influenced in my methods by anything I might read in them.  Much like how I expressed that I preferred you do your math your way and not be influenced by mine.  I hope to only share results at first and methods only if discrepancies were found while you assisted me with this double check.

To remind you, I am running no calculation in a spreadsheet except some simple summations for volume and Energy balance double and triple checks.  The spreadsheets I have are only used as a table to record the results of hand calculations.  Those calcs were all run on an old Casio calculator that I was given at my first job.  That is also at work.  But I can dust off my old TI 15C, and suffer with the switch to RPN (which I truly love).  What a marvelous piece of EE work that is!  I've had it nearly 30 years now and had to change the batteries once!  Of course, it has been turned on very little since undergrad years.

If you have a complete and accurate Stage 2 to Stage 3 drawing for me, I'll give it a go.  Or we can wait until I am back at work.  I wont press you for anything in the mean time.

Thanks,

M.

You want the drawings with values on them, but you don't want to be influenced by those values?  What???  We agree on everything up to State 2 I think.  Show the process by which you solve for State 3.  Algebra and some descriptive text is fine.

[mondrasek]

The energy that will be required to return to State 2, is the same as the internal loss going from State 2 to State 3:  1.903mJ.

MarkE!  I just realized that you may have found it!  It takes the exact same amount of energy to return from State 3 to State 2.  But WE do not have to supply that Energy.  If we simply pull the plug at the bottom of the ZED when at State 3, the water will drain out and the system will fall through State 2 and all the way back to State 1.  WE supply zero energy to do that.  That Energy comes from GRAVITY acting on the mass of the water.

[mondrasek]

You want the drawings with values on them, but you don't want to be influenced by those values?  What???

I said I don't want to be influenced by the METHOD you used to calculate those values.  I have double checked your calculated values (by whatever method you use) with the results from my own and find they agree on the 3-layer model.  They did not on the no-pod, single layer and that is how we found some miss in your spreadsheet.  I did not look at how you originally calculated that value or what you changed it to recently.  For this reason:

Remember when we were figuring out the proper way to account for the Energy that leaves the system when the riser lifts?  I figured it could be calculated simply two different ways:

1)  As the integral of the buoyant Force * the change in the riser height
or
2)  The amount of Energy that exists in the water on top of the piston that is push up and "disappears" during the lift.

Both of those methods are correct and yield correct results.

But we have both seen that one can choose the wrong equation and get the wrong results.  If I looked at your equations, I might be influenced to do things by that method (rather than a separate and equally valid method that yields a good double check for both of us), or actually follow down the path of using the wrong method (not saying you would ever intentional use the wrong method).  So it is best to only share methods when the results are first compared and found to be in agreement or not, I think.

[MarkE]

MarkE!  I just realized that you may have found it!  It takes the exact same amount of energy to return from State 3 to State 2.  But WE do not have to supply that Energy.  If we simply pull the plug at the bottom of the ZED when at State 3, the water will drain out and the system will fall through State 2 and all the way back to State 1.  WE supply zero energy to do that.  That Energy comes from GRAVITY acting on the mass of the water.

Are you serious?  Sure, throw away a whole bunch of energy each cycle.  See how that works out efficiency wise.