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### Author Topic: Mathematical Analysis of an Ideal ZED  (Read 754070 times)

#### mondrasek

• Hero Member
• Posts: 1301
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #180 on: February 28, 2014, 04:34:14 PM »
No.  You are mixing circumstances of compressible and non-compressible substances.  Work is always the integral of F*ds.  If we take a capsule of fluid and subject it to 1psi or a million psi we have not done any work on that fluid.  If we apply pressure against a cross section of fluid through a distance, then we do work.  When we lift columns of fluid we can obtain the work performed and stored by solving the F*ds integral which will work out for a single column to:  E=0.5*total_weight*height = pave*volume = 0.5*density*volume*height = 0.5*density*area*height2

The energy is not stored in compression of the fluid for the simple reason that the fluid is incompressible.  The energy is stored in the gravitational potential of the raised mass.  Larry  asserted that raising some cross-section by 1' to end up with the 1+2+4 configuration "cost only 1/3" of some other configuration.  But it doesn't.  The force went from 0 to 3X what it would have raising an isolated column by 1'.  Identically, the amount of work performed was 3X that required to raise an isolated column by 1'.  The force and the energy both scaled by 3X versus the isolated column.  Had we done the exercise totally emptying the middle column, then the force would have gone from zero to 9X over a 3X stroke.  Kf would still be 3*pWater*area, and the integral would be:  0.5*3*pWater*area*(32-0) = 27*0.5*pWater*area, IE 27X the energy of raising an isolated column by 1' and 3X the energy of raising an isolated column by 3'.

No, MarkE, you are misunderstanding me.  When I said:

The Integral of Pressure * Volume is Energy,

it was in reference to the analysis of the ZED.  The Volume I was referring to is that which moves into and out of the system.  The input Volume is water.  The output Volume is that which is encompassed by the portion of the outer riser that lifts up above the original start condition height.

Sorry I did not make that more clear.  I realize you are looking at several things at once and I did not point out exactly which case I was making reference to.

#### TinselKoala

• Hero Member
• Posts: 13958
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #181 on: February 28, 2014, 05:15:31 PM »
Please do not forget that +incompressible fluids+ do not store energy in volume changes due to applied pressure.

In a spring, when you press on it with a certain force (pressure) the spring compresses (changes "volume") and thus the energy integral is valid. If you press with the same force (pressure) on a concrete block... no (or extremely little) energy is stored in compressing the concrete, its volume does not change due to your applied pressure, so the energy integral in the form you have stated it does not apply, just as the various individual ideal gas laws Boyle, Charles, Gay-Lussac and Avogadro, or indeed the full combined ideal gas law pV=nRT  do not apply to incompressible fluids.

#### LarryC

• Hero Member
• Posts: 911
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #182 on: February 28, 2014, 06:00:36 PM »
Correction, noticed that the Pod Lift values wasn't squared.

#### MarkE

• Hero Member
• Posts: 6830
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #183 on: February 28, 2014, 06:44:04 PM »
No, MarkE, you are misunderstanding me.  When I said:

The Integral of Pressure * Volume is Energy,

it was in reference to the analysis of the ZED.  The Volume I was referring to is that which moves into and out of the system.  The input Volume is water.  The output Volume is that which is encompassed by the portion of the outer riser that lifts up above the original start condition height.

Sorry I did not make that more clear.  I realize you are looking at several things at once and I did not point out exactly which case I was making reference to.
If you stick with integral of F*ds there is no room for confusion.  See for example LarryC's example of 0+3+3 columns versus 1+2+4, picking pressures or average pressures and volumes easily leads to non-physical results, whereas integrating F*ds yields the correct result every time.

#### MarkE

• Hero Member
• Posts: 6830
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #184 on: February 28, 2014, 07:35:17 PM »
Correction, noticed that the Pod Lift values wasn't squared.
Larry, the height used in a calculation is the height of a single column.  In your Stored energy calculations it looks like you took the water column height, subtracted one and then doubled it.

You need to track the energy in each of the four water volumes as shown in this picture that I posted previously.

#### LarryC

• Hero Member
• Posts: 911
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #185 on: February 28, 2014, 08:29:02 PM »
If you stick with integral of F*ds there is no room for confusion.  See for example LarryC's example of 0+3+3 columns versus 1+2+4, picking pressures or average pressures and volumes easily leads to non-physical results, whereas integrating F*ds yields the correct result every time.

MarkE,

Yes, they both end with same stored energy, but you're not considering Power or rate of doing work.

With a pump that is rated for 1 cubic foot per minutes. Then the single column would take 3 minutes and the multiple connected columns would take 1 minute to create the same PSI in each system.

#### LarryC

• Hero Member
• Posts: 911
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #186 on: February 28, 2014, 08:41:06 PM »
Larry, the height used in a calculation is the height of a single column.  In your Stored energy calculations it looks like you took the water column height, subtracted one and then doubled it.

You need to track the energy in each of the four water volumes as shown in this picture that I posted previously.

MarkE,

In your multiple connected column example you used 4-2+1. The Zed is a multiple connected column based system, so why wouldn't it be Riser Head - Riser Gap Head + Pod Head.

Don't understand the 'doubled it' comment. I'm summing the fields and the -value is only used once.

#### TinselKoala

• Hero Member
• Posts: 13958
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #187 on: February 28, 2014, 09:09:53 PM »
Quote
Yes, they both end with same stored energy, but you're not considering Power or rate of doing work.

Power is not energy. Pressure is not energy. Flow rate is not energy.

Where are the sausages (excess energy that can be used outside the system without making the system come to a stop)?

#### MarkE

• Hero Member
• Posts: 6830
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #188 on: February 28, 2014, 10:14:43 PM »

MarkE,

In your multiple connected column example you used 4-2+1. The Zed is a multiple connected column based system, so why wouldn't it be Riser Head - Riser Gap Head + Pod Head.

Don't understand the 'doubled it' comment. I'm summing the fields and the -value is only used once.
LarryC, energy is the integral of F*ds.  The force that must be exerted to go from the 3+3 state changes from 0 to pWater*area*3ft of total head because the column in the middle counterbalances the column on the right, so it is the difference between those heads, plus the head that we develop in the left hand column that determines the net weight:  IE force that we lift each increment of distance as we pump water into the left hand column.

#### MarkE

• Hero Member
• Posts: 6830
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #189 on: February 28, 2014, 10:16:17 PM »

MarkE,

Yes, they both end with same stored energy, but you're not considering Power or rate of doing work.

With a pump that is rated for 1 cubic foot per minutes. Then the single column would take 3 minutes and the multiple connected columns would take 1 minute to create the same PSI in each system.
Larry, pressure is no measure of work or power.  I can create lots of pressure instantly without doing any work.  In column K you labeled values as Stored Energy in Ft. Lbs.  In row 8 you have a value of 329.63.  The corresponding head is 35".  The work to fill a column to 35" is:  Integral F*ds = 0.5*62.316lb/cuft*0.27816sqft*(35/12)ft2 = 73.69 ft. lbs.  You've calculated a value more than four times that.  You need to calculate energy for all four parts that the drawing identifies:

#### LibreEnergia

• Sr. Member
• Posts: 332
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #190 on: February 28, 2014, 10:29:09 PM »

"Yes, they both end with same stored energy, but you're not considering Power or rate of doing work."

This statement epitomises the misunderstanding  (or perhaps ignorance) that the majority of the over-unity community appears to be suffering. It certainly seems to pervade all threads in describing mechanical or electrical free energy devices.

Power is a 'rate of change' of work or more specifically the derivative of work with respect to time. The ONLY time you can compare 'power' from the point of view of deducing if a machine produces energy is when it transitions between two identical states in a cycle AND over the same timescale. It should be obvious from that that time falls out of the equations and you are back to considering just energy.

POWER is not ENERGY... learn and understand that, then you will begin to see how ridiculous the assertions are that devices such as the ZED can produce net energy output.

#### LarryC

• Hero Member
• Posts: 911
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #191 on: February 28, 2014, 11:56:04 PM »
Larry, pressure is no measure of work or power.  I can create lots of pressure instantly without doing any work.  In column K you labeled values as Stored Energy in Ft. Lbs.  In row 8 you have a value of 329.63.  The corresponding head is 35".  The work to fill a column to 35" is:  Integral F*ds = 0.5*62.316lb/cuft*0.27816sqft*(35/12)ft2 = 73.69 ft. lbs.  You've calculated a value more than four times that.  You need to calculate energy for all four parts that the drawing identifies:

I am calculating energy for all four parts, you need to learn to use the Trace Dependents and Trace Precedents button. The 35 in J8 is not used anywhere, it is a visual double check for me to make sure I set the newly added Inner and Outer riser water ht correctly so they equal the original riser heads in column C. The Inner and Outer riser water ht is used in the store energy calculation.

Never said pressure is a measure of work or power.  You would have known, I was talking about the multiple connected columns is the basis for the Zed design as I have stated many time. The PSI is used in the Risers the same as in a pneumatic cylinder and does create Work during the stroke. Getting the PSI up and down with less input volume is key to increased Power.
In the spreadsheet the volume input to get to Ready to Stroke is 22 for the Zed and 81.02 for the Archimedes and the Output Ft Lbs is 33.55% greater for the Zed. Based on the fact that it would take much longer for a pump to ready the Archimedes than for the Zed, the Zed will cycle faster. Cycle faster increases Work done over time or Power.

Misleading statements caused Librenergia to take it out context and put his big foot in his mouth, when I know just as much about work and power as most of you and apparently with better comprehension, since most of you cannot understand how the Zed works.

#### MarkE

• Hero Member
• Posts: 6830
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #192 on: March 01, 2014, 12:03:29 AM »
Larry, I have gone through at least four spreadsheets now and none of them appear to calculate the all the energy values correctly and use those values to generate a balance.  I tell you what:  Rather than asking me to second guess what you are doing, why don't you add a couple of notes in your spreadsheet that say what you are using for what purpose, and where you draw your conclusions.

#### LibreEnergia

• Sr. Member
• Posts: 332
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #193 on: March 01, 2014, 12:12:57 AM »

Misleading statements caused Librenergia to take it out context and put his big foot in his mouth, when I know just as much about work and power as most of you and apparently with better comprehension, since most of you cannot understand how the Zed works.

Sorry. ..You have only confirmed my hypothesis.

It matters not one bit that a Zed compared with Archimedes might have different power characteristics. When you move from identical starting states to identical ending energy states only the change in energy is important, not how long it takes to transition between those two states

Consider the two statements

1. How much energy would it take to raise the Titanic from the bottom of the sea, vs
2. 'How much power would it take' to raise it.

The answer to 1 is a fixed amount irrespective of time. , The answer to 2 is 'any amount of power you happen to have available.

The ZED is no different to that scenario. Stop using power considerations to explain why the ZED 'works'. It just doesn't. Any person with even  modicum of understanding of physics or engineering understands  why.

#### LarryC

• Hero Member
• Posts: 911
##### Re: Mathematical Analysis of an Ideal ZED
« Reply #194 on: March 01, 2014, 12:39:36 AM »
Sorry. ..You have only confirmed my hypothesis.

It matters not one bit that a Zed compared with Archimedes might have different power characteristics. When you move from identical starting states to identical ending energy states only the change in energy is important, not how long it takes to transition between those two states

Consider the two statements

1. How much energy would it take to raise the Titanic from the bottom of the sea, vs
2. 'How much power would it take' to raise it.

The answer to 1 is a fixed amount irrespective of time. , The answer to 2 is 'any amount of power you happen to have available.

The ZED is no different to that scenario. Stop using power considerations to explain why the ZED 'works'. It just doesn't. Any person with even  modicum of understanding of physics or engineering understands  why.