Math question?

Hi all I am building a solar pool heater and need help. I have 2inch pvc coming out of the pool pump I am wanting to go to 3/4 or 1 inch black flexible pipe. I remember from high school that 2 inch pipes don't equal a 2inch pipe. So how many 3/4 or 1inch or mixture of the two do I need. They are going to connect to a manifold and circulate on the roof and then return to the 2 inch to enter the pool. I will have T's and valves so I can shut it off when not wanted. I know my pump will handle the head pressure. Thanks in advance.

If you want a rough value is trying to maintain area, you can do it this way:

A=pi*r^2 or (pi*D^2)/4

Since pi and everything else in the equation is constant (except for r/D), double the diameter (or radius) equals 4x the area.

So four 1" pipes is roughly equal to a single 2" pipe.

If you want to find exact areas, you would look up the i.d. of the pipe(s) you are using and calculate the areas. This way is better especially if you are mixing different materials (PVC, PEX, copper, etc.) since some are IPS based and others are CTS based in how their nominal sizes are determined. In addition, wall thickness can vary between different materials. For instance, copper and CPVC are both measured based on CTS (Copper Tube Size), but a given size copper pipe has more flow area than the same size in CPVC since the copper walls are much thinner.

For something like this, you will not have to match the area, though. I suspect that your flowrate will be fairly low (normal for solar to pickup the temperature rise). Eventhough it would take 4 1" pipes to equal a 2" pipe in terms of area, you might be better off using four 3/4" lines (or less) instead.

Do you know what your pump can flow and at what level of head can it hit this flow?

I didn't do the math, but I have four 1,000' rolls of 1/2" poly on my roof. All four are parallel and manifold together at each end. Can't run it all the time because it gets the water to warm.

Four pipes equal the area of a 2" pipe, but they have twice the wall surfaces which creates back pressure, so five pipes would be a more reasonable number. BUT, the ONLY heat you will absorb with the pipes is through the wall area, so you want as much SURFACE as possible, meaning a multitude of smaller pipes will be more efficient than a couple of larger ones. In addition, the more pipes you have, the slower the velocity will be so the water will be in contact with the pipe for a longer time and thus absorb even more energy. Which is why commercial solar panels use a plethora of 3/8" or similar lines, PLUS radiation absorbing plates attached to them to give the maximum available area.