Mathematical Analysis of an Ideal ZED

[MarkE]

Hi MarkE,


Liked what you did with the drawing, but has a few minor issues, I'll respond later on that post.


You're too fast, so I'll also respond to your ~8% later.


But wanted to address your integration concerns as it is key to the process.
The Left avg. psi at E13 is the average pod psi from the end of equalization to the start of ready to stroke.
The Right avg. psi at H13 using the same technique. So left 3.233, right 3.992. Now when adding water to the right along you would multiply that average psi times the volume to get the input cost.


But, if at the same time we are allowing water to flow out the left at its average PSI, it is returning energy to the Right. This return of energy reduces the input energy applied to the transfer by the average pressure differential between the two units. So the Average PSI Differential shown at I13 is the average pressure required to transfer the fluid. I can show this process in a little different format if it would help.


In your pinhole example, if you had two columns of water with one having 25% less water and you had a small tube connected to the pinhole in each column. Would the water flow out as fast as your one column example or would the speed be reduced by 75%? Its all about the pressure differential.


Larry   

Larry, if I have a capsule of water and lift that capsule from one height to another then I can just multiply the weight by the distance moved and I am done because the gravitational force on that capsule is constant.  But if what I do is change the height of a column by pumping water in or letting water out then I need to perform the integration. 

Let's suppose that we have two water towers each 1 sq meter in area, and 2m high.  First, let's fill each to 1m height:

Fstart = 0
Fend = 9789N
F/z = 9789N/m
Integral of:  (kf*z dz) = 0.5*kf*z^2
zstart = 0
zend = 1m

0.5*9789N/m*1m^2 - 0 = 4894.5J
We have that in each of two columns, so the total energy stored is:  2*4894.5J = 9789J

Now, let's pump the water back out of one column into the other, emptying the one and filling the other:

Fstart = 9789N
Fend = 19578N  Filled
Fend = 0 Emptied
Kf/z = 9789N/m

work added to column filled = 0.5*9789N/m*(Hend^2 - Hstart^2) = 0.5*9789N/m*(2^2-1^2) = 3*4894.5J
work removed from column emptied = 0.5*9789N/m*(Hend -Hstart) = 0.5*9789N/m*(0^2-1^2) = -4894.5J
net work performed: 9789J

So, we had 2*4894.5J = 9789J in the two columns combined at the start, we added 3*4894.5J to the column that we took up to 2m, and we removed 4894.5J from the column that we emptied.  We have the same total volume of water, but we doubled the stored energy, and we added every Joule of that extra energy from the outside. 

The converse of this is that when we equalize a column filled to a higher level with a column filled to a lower level, we lose energy to heat.  The worst case is where we take a column filled to 2H and equalize it with an empty column so that we now have 2 each of 1H.   This is the exact complement of the fill exercise that I just described and it loses half the stored energy:  That energy is lost forever: kaput, toodleoosky, goodbye Charlie. 

Your spreadsheet appears to be calculating energy by a series of linear adds and subtracts based on average pressure.  That yields incorrect results.  Integration is necessary.

[MarkE]

MarkE,


Thanks for continuing, like your analysis technique.


Few minor issues in the drawing. The Riser Head bottom arrow should be even with the water height in the next column to the left. I have .48150 for D5 Riser Gap and the arrows are pointing at the pod water, should move to the right one column for the Riser gap.


Larry

Larry, OK I fixed that.  Because the stipulation is equal cross-section area in each column, I changed the formulas to derive the diameters with the areas fixed at 51circular inches, IE 51*pi/4.  Consequently, the formulas are:

Riser area = (26^2 + 51 )*pi/4  = 570.9844647900
Vessel area = (26^2 + 2*51)*pi/4  = 611.0397711233
Riser diameter = (26^2 + 51 )^0.5 = 26.96293752543
Annular clearance = (26.96293752543 - 26)/2 = .4814687627128
Riser diameter = (26^2 + 2*51 )^0.5 = 27.89265136196

The precision of these numbers are not particularly significant once we defined the annular cavities to all have the same 51 circular inch areas and perform our calculations based on that stipulated area rather than calculated area. 

[MileHigh]

Quote from Wayne:

I am sorry MH - you should ask Monderask or Larry to explain.

Quote from MarkE to Larry:

Your spreadsheet appears to be calculating energy by a series of linear adds and subtracts based on average pressure.  That yields incorrect results.  Integration is necessary.

Webby, Mondrasek, Larry:

It's wake up time.  Can't you see what's happening?  You guys are trying your best but you aren't technical and you are simply wrong.  Wayne is using you and stroking you and trying to pretend that you guys know what you are doing but you clearly don't know what you are doing.  Wayne is using you to create the pretense that you are right for his own reasons.  The reason is to create the general impression that you guys 'get it' and his system is real.

You are lucky to have guys like MarkE and TK to give you guidance.  If they work out the whole sequence with you then you will be lucky to get that amount of hand-holding.

Be clear that I have nothing against you guys.  You are simply being used by Wayne for his own nefarious purposes.

To Wayne:

I am sorry MH - you should ask Monderask or Larry to explain.

Not so.  If MarkE and TK do a full cycle with your "explainers," holding their hands all the way then you will be exposed for the cynical manipulator you desperately try to be in order to keep your gravy train flowing.

The whole thing is reprehensible.  The Hammer of Justice, I can hear the knocking in the distance.

MileHigh

[MarkE]

MileHigh, it could be a long time before you see any satisfaction wrt to Wayne Travis.  It's the odd burned investor or investors who can become real nightmares for even experienced sharpies.  When a burned investor has the resources and the intent to get satisfaction, they have been known take sharpies down a long, dark, and painful road.  Such cases are rare, but they do happen.

[MileHigh]

Mark:

Yes I know many times they get away with it.  It's unfortunate.  How many people may have sunk their life savings into Wayne?  I don't know if we will ever know.

MileHigh