@Jandell: Then you can go beat your head against a brick wall. It will have just about the same effect.

Brian, you have yet to explain how, at the bottom of the continuous descending column of tanks, you can bring one tank to an abrupt halt, in order for its weight to keep moving, while not also bringing all the other tanks, which are following it without gaps, also to an abrupt halt.  You have also not explained how, if the water pressure at, say, 30 feet is small enough to be able to be overcome by the momentum of the falling weight, yet the pressure at or near the surface is great enough to push the expander back in. There is no mechanical advantage from your pulley system. The chain of tanks must be moving as fast at the top as it is at the bottom, have you considered that? How do you deal with the momentum of your weight, at the TOP? It's going in the wrong direction.
You see, until you clear up your misconceptions about how things actually work, trying to make an exact mathematical analysis is like, well, beating your head against a brick wall.

But don't let me stop you, I'm the Evil Skeptic after all, and I get my jollies from seeing people waste their time. Just go build the thing. Oh, wait, you have no building skills or materials. Well, then use a spreadsheet to analyze the system properly. No, wait, you have limited math skills.  Well, then, you could seek advice from those who have those skills--but clearly you don't have to take it.

Brian,

I thought of a simple experiment that you may be able to try to show the effects of the drag of water on your system.  It approximates your concept of the tanks falling in a continuous column.  Find yourself a small wheel with a solid rim, ie. no spokes.  You want the wheel and rim to be smooth so that any cross section taken through the center is equal to any other.  These are common on children's push and ride toys as well as some strollers and wagons.  When you spin this type of wheel it approximates your continuous column, since there are no gaps between sections in the wheel and the only place water resistance can exist is on the sides.  So spin this wheel in air and note how much it runs.  The only resistance is the friction from the bearings and air resistance.  Then dunk the wheel underwater and spin it again.  You will see that it does not spin much at all.  This will show how much drag water has on an object moving through it, even if falling or rising in a continuous column.  It may lead you to understand that your falling and rising tanks could only move very slowly, thus eliminating the momentum you envision being built up to do the work of expanding your tanks.

Also, a complete mathematical analysis of your system would be not only very laborious, but still not conclusive.  With fluids you have to deal with turbulence, something very hard to model.  This is one of the reasons that weather modeling is so difficult and imprecise.  Back in the day the first super computers were used to solve the complex equations governing turbulence in a fluid and it's effects on drag.  Now a modern computer could likely model simple systems in near real time, but only to a gross approximation.  This is the reason that real wind tunnel testing exists:  the math and complexity of trying to model every molecule of a fluid and all the forces governing it's interactions are beyond what we can do even with the fastest computers.  But approximations do exist and lead those of us who have studied or worked in the field to know certain phenomenon will certainly exist, like drag.  I personally cannot calculate exactly how much drag there will be, but can tell you with certainty that it will be significant.  The above recommended experiment will show that.

Thanks,

M.

M.
If it took 2 weeks for the tanks to fall this machine would still work.
But the faster the tanks fall the better it will work.

Jandell made a statement that using high school math and science it would be easy to prove  this machine won’t work, so what’s the proof ?

Figure it out for yourself.  Your lack of understanding of basic physics and math does not have to be a permanent condition.

M.
When you calculate how fast the tanks will fall make sure you consider water temperature.
Hot water moves easier than cold.

Try this simple test.
Fill a bucket full of water, get a glass, put enough weight in the glass so that it almost sinks. Put the glass in the bucket. Spin the glass. Notice how long the glass spins.

And now take the same glass (without water inside) and tie a thread around it so you can suspend it from a tall beam in air.  This is an imperfect example because the thread will also resist twisting but that is insignificant.  Spin your glass now.  See how it does not appear to slow down for a much much much greater time?

Your glass in water experiment shows exactly what I was explaining.  The glass refuses to spin FAST.  It slows quite quickly.  It spins SLOWLY for a long time, just as your tanks will only fall and rise slowly.

No speed equals no momentum.  Please tell us how your device works without your assumed momentum?  You have stated that it will work just fine.  How?  We can show you the math for the "no momentum" case.  You need to understand that momentum will play an insignificant part in the expansion of the tanks for us to continue.  Can you understand this yet?

M.

M.
When the tank gets to the bottom the 63 lb lead weight is still at the top of the tank.
The weight will fall about 11 inches. When a 63 lb weight falls 11 inches it can do enough work to increase the displacement of the tank by about 5 lbs.  At a depth of 10 ft.

I thought of another high tech test. No wobble in this one.
Fill a bucket full of water, the bucket has to be smooth inside. With a stick get the water spinning inside the bucket as fast as you can, than drop the stick into the bucket, watch the stick spin. Notice how long it spins. If you use hot water it will spin longer.

Brian,

Previously we have discussed that the 63lb weight cannot expand your tank if the expansion area is equal to the cross section of your tank (1' x 1' x 1').  It can only expand a piston with ~14 sq inches (not 144 sq inches).  I have asked repeatedly for you to show a design of a tank with only a 14 sq. in. piston on each side and the weight in the middle.  The purpose is to show you one cannot be made.  You continue to avoid doing any of the work to teach yourself what you are missing.

I have to ask:  Is your purpose here to try and win an argument/debate, or to learn the truth about your concept?  If it is the former, I will gladly stop trying to help you learn and admit defeat for your arguments.  You can then include me with the others that have "failed to prove" that your idea will not work.  But if you wish to learn the truth then get off your ass and show the design!

You are avoiding doing any of the experiments/exercises we have suggested that should show you the flaws in your concept.  Instead you have repeated statements time and again that have been shown to more knowledgeable persons to be false.  You repeat these false statements as proof that your concept will work.  Repeating a falsehood over and over does not make it true.

Show us the design of a tank that can expand only ~14 sq. in. pistons on each side.  This exercise is designed to help YOU understand.

Also, my glass did not wobble noticeably (better glass or spin, who knows or cares?).  It did however slow quite rapidly due to the known effect of the drag from the surrounding water.  The water adhered to the sides of the glass in a relationship including the constant known as the Reynolds number for that surface.  While I might have used a glass with a surface who's Reynolds number was more advantageous to your arguments, there is no known surface that will let it reach a terminal velocity approaching 50% of what it could reach in air.  5%, maybe, but that is only and educated guess.

M.

I will post Jendells numbers as soon as I get them.

M.
Go to my website and check out GRAVITY MACHINE # 1
It will help if you print out the drawings.

M.
Gravity Machine # 1 is the best answer I can give you.
You asked for a different design, Gravity Machine # 1 is a different design.
I am not side stepping your question, I am answering your question.
At my website http://bsandler.com click on the tab at the top of the page marked Gravity Machine # 1