# Hot Water Delivery Calculations

Does anyone know of a formula for calculating how much time it would take to clear out a specific length/diameter plumbing supply line for a given system pressure? My interest is related to hot water delivery. I’ve not exhausted a search, but thought someone here might have the answer.

I’m laying out my plumbing system and this information would be a great asset for planning.

Thank you, Daniel

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## Replies

The pressure doesn’t really matter much if you know the delivery volume per unit time of the fixture on the end. If you know that, then all you need to calculate is the contained volume of water within the pipe. Divide that volume by the fixture’s delivery volume per unit time to get the “how long to empty the pipe” number.

Volume contained within the pipe is pi times the radius of the pipe squared, multiply that by the length of the pipe. It’s lots easier to work in metric units, so I would just convert everything to metric and then back at the end if you need to.

An example, assuming a 1” pipe (2.54cm):

Radius is half the diameter, so 1.27cm. Square that and you get 1.61cm. Multiply that by pi (3.14) to get the area of the end of the pipe. That gives just over 5 square centimeters.

Let’s assume the pipe is 50 feet long. That converts to 50*(12 inches per foot)*(2.54cm per inch) = 1,524cm. Multiple that by the area we already calculated to get about 7,624 cubic centimeters of volume.

The metric system makes the next part really easy: a cubic centimeter is a milliliter, and there are 1,000 milliliters in one liter. That means our pipe contains 7.624 liters of water.

If your faucet delivers 12 liters per minute, you need just over 38 seconds to empty the pipe.

The “convert it all to metric first” trick also makes it easy to work out the pressure at the bottom of a pipe due to gravity. Just take that volume you calculated and remember that one liter of water weighs one kilogram. It’s easy to then use the area of the pipe to convert to PSI if needed.

Bill

Thanks! This will be big help for me.

Daniel

Be careful about the size - for example, PEX, where 1" tubing isn't 1" inside.

Also note that if there is a lack of "plug flow" then it takes longer than you would normally calculate.

edit:

https://www.garykleinassociates.com/PDFs/15%20-%20Efficient%20Hot-Water%20Piping-JLC.pdf

Plug flow?

Yeah, rather annoyingly, pex pipe isn't 1" inside or out.

Such is the way of all things pipe — nothing about a typical pipe is actually described by the “nominal size”. There are handy tables on the internet with actual dimensions though, just remember that the actual dimensions for “1 inch pipe” vary with the type of pipe (PEX, schedule 40, schedule 80, etc.)