More plumbing math

In my preceding post "Rain barrel design using two bunghole system":

The cross-section of a two-inch pipe is 3.14 square inches (if you're doing the math, remember the radius of a 2-inch diameter pipe is 1 inch).  The cross-section of a 3/4 inch pipe is 0.44 square inches.  If you have a 2-inch bottom pipe then it can feed 7 or 8 pipes with a 3/4 inch diameter.

 I'm actually going to be feeding my closed barrel system through the 1.5 inch overflow from an upright rain barrel.  The cross section of a 1.5 inch pipe is 1.76 square inches.  I'll have four barrels, being fed through 3/4 inch diameter pipe.  Each of the 4 pipes has a cross-section of 0.44 inches, for a total of 1.76 square inches.  Perfect in theory, but this will not be theory.  There will be losses such as friction, but this isn't rocket science, even if it might be rocket fuel tank science.

I am aware that I'm playing with engineering when things won't be perfect.  Usually a rainstorm causes a downspout to have a lot of falling water mixed with air, and it is not completely full of water.  Feeding a 2x3 inch downspout into a 3-inch diameter pipe adds much more capacity than is usually needed.  The overflow needs to be able to handle what the 2x3 inch is delivering, and how quickly the barrels can take the water will determine how much of a sudden cloudburst it can catch.

We're dealing with a situation where hundreds of gallons will arrive as quickly as an inch of rain can fall.    If the water tends to arrive as an all-day trickle, then the plumbing only needs to deal with a trickle.  You have to design the plumbing to deal with the amount of water that you're willing to catch or lose.  A little planning can reduce the amount of water that will be lost through the overflow.