Mathematical Analysis of an Ideal ZED

[MarkE]

I am not much of a spreadsheet person,, but the annotations help with following what you are doing,, that was after I realized that those were not the named ranges,, just notes.

Then I used my calculator to follow the formulas,, that helped me in understanding "HOW" the formulas should be used,, I am a hands on learner for the most part.

Do you realize that all the actual formulas use named ranges?  The named ranges are but for the audit items in column B.  The names are in column A. 

[MarkE]

I see that and that makes it so that I have to keep moving all around.

I found that there is an error in one of the A columns, the formula calls for a ST_2 but in the A column it is ST_3 but the formula still gets the information,, so I assumed that the A column was just notation.

A 126

The names are supposed to be self evident.  The whole point is to not need to jump around, but read it as though it were written out on paper.  In some cases the names refer to things that happen during the transition between states.  I can rename those to the form STn_STn+1 to make that more obvious.

[MarkE]

Hi MarkE,

While I am at it,, I do have an issue with the pressure under the pod.

B 107

I do not think it impacts much but that actual pressure would be

1719.31171611pa



But it looks like you are using the head value for lift consideration.

A126 ST2_AR6_Hdel_pmm is the water height in mm in AR6 for each mm that the risers go up.  I can rename this ST2_ST3_AR6_Hchg_mm_per_mm if that will make it more readable.

B107 looks wrong to me too.  It's missing the multiplier factor:  (1+AR1area/AR2area + AR1area/AR3area ... AR1area/AR7area).  I get 1719.304806Pa using 9.80665 for G₀ and 998.2N/m3 for pWater.

[MarkE]

I can get what you are referring to,, then I go and find it to stick into my calculator,, and all the parts that go along with it,, that is what I meant.

So I see what you are calling and in what sequence, but for me to stick it into my calculator for practice I must go and look at each of the cells.

I think that you can make your life a lot easier by just inserting a column or columns some place and putting your formulas in those cells.  Then you will have everything written down for yourself without having to worry about keystroke errors or trying to remember what you have done.

[LarryC]

Well, under special circumstances one can get the right answer for energy using P_AVE*V.  The single column is such a case, and we can see that in Larry's example, provided that we pick the right P_AVE.

What we cannot do to get the right answer is use P_AVE obtained across multiple columns.
If we set K1 = pWater*G₀ then
In the [0,3,3] left hand case of Larry's example we would incorrectly calculate an internal energy of,

P_AVE is: K1*(0+3+3/3) = K1*2. 
V is Area*(3+3) = Area*6
P_AVE*V = K1*Area*12

The correct answer can be found by adding the energies of each column, and for that the individual P_AVE*V gives the right answer:

0.5*K1*Area*(0 + 3*3 + 3*3) = K1*9

Larry chose to calculate the energy added to get to the [1,2,4] case by calculating the average pressure in the left hand column and multiplying that by the volume in the left hand column.  And for those circumstances he got the right answer.  His analogy to a 3ft high column needs a bit of work, because while that gives the correct pressure, it yields the wrong volume and represents three times as much energy as was added.

MarkE,

All column energies are accounted.


The End Col 1 PSI in the spreadsheet is 1.30. The PSI for  Col's 1, 12" of water is .43. The 1.30 is calculated as Col 1 PSI - Col 2 PSI + Col 3 PSI = .43 - .87 + 1.73 = 1.30 after rounding. Col 2 is subtracted from Col 3 to give the water head pressure.


Pavg*V works for all cases from 1 to infinity number of columns or risers.