chem geek
Though there is no vacuum in the panels, I don't count the static head since it does cancel each other out up and down (it's just that one shouldn't go negative in the panels).
If there is no vacuum, they can't cancel each other out. You're still adding the static head; you're just doing it on the return side.
Think about this:
There is a pipe that rises 23 feet vertically out of the water, turns 90 degrees and runs 10 feet horizontally, and then turns 90 degrees back down 10 feet to the water. No vacuum relief. Once the pipe is full of water, the pressure in the top horizontal pipe is -10 psi (gauge) and the pressure at water level is zero psi (gauge) (static before moving the water). In this case, the rise and fall cancel each other out because the falling water "pulls" the rising water by the suction created from the water falling.
However, if you put a vacuum relief at the top, there cannot be a vacuum, and the pressure at water level has to be +10 psi static when the pump pushes the water to the roof. Since the water falling back down cannot "pull" the rising water, its potential energy can only be used for the return trip to the pool. If the return trip generates only 3 psi of head loss, you lose the other 7 psi.
You only get back the potential energy if the return trip generates at least 10 psi, or more. In this case, you have to add an extra 7 psi to close the vacuum relief valve. Therefore, you do get to 10 psi, but only by adding 7 psi of extra restriction. You're still losing the 7 psi. Further, you don't need to add the 7 psi restriction. You can just allow the vacuum valve to stay open and suck in air.
To calculate the head loss for an open loop vs. a closed loop, you have to add the height of the panels, but you can subtract the head loss due to the dynamic head created from the panels to the pool (up to the amount of static head).
In your case, the rise and fall do cancel, but only due to the creation of additional head loss in the return from the panels to the pool due to the addition of some type of restriction. The math comes out the same, but I think that it's an important conceptual point to understand that the rise and fall do not cancel each other out in the same way that they do in a closed loop system.
chem geek
The height of the top of the highest solar panel may be more than 15 feet, possibly closer to 20 feet, though I'll have to measure that. So that's 6.5 to 8.6 PSI required in losses from the top of the panel to the returns, probably with a flow restrictor in there somewhere.
This is where you are adding the height of the panels.
chem geek
If I add that to what it takes to get to that highest point I get around (2.7 + 2.2/2 + .9 + either 6.5 or 8.6) = 11.2 to 13.3
You are adding the height (6.5 or 8.6 psi) to the dynamic head caused by the water going to the panels + the dynamic head caused by the water going through the panels
Allen G Myerson
Your total head would be 6.5 psi static to get up to the panels + the dynamic head caused by the water going to the panels + the dynamic head caused by the water going through the panels + the pressure at the vacuum breaker (which should be close to zero).
You can add the height going up or coming down, either way, it's still adding the same thing.
You do get some of the potential energy back from the water falling, but it is limited to the dynamic head loss from the panels to the pool, which should be much less than the height, which is why you need to add extra restriction if you want to close the vacuum relief valve, which you don't necessarily need to do.