Calculate length of a pipe from the volume it holds

March 22, 2007 7:37 AM

How long would a 3/4 inch inner diameter pipe need to be to hold exactly 27 gallons of water?

A co-worker tried to switch from his well to the county water utility. The feed from the street was run to the house several years ago but not turned on. They completed the hook up at the house, turned on the water at the street, and 27 gallons of water ran into the pipe then stopped. There's a blockage stoping the water, but rather than randomly dig up the yard, he'd like to pinpoint the blockage location by doing the math. I figured MeFi's math geniuses could lick this one easy.

posted by putzface_dickman to Home & Garden (33 answers total)

1 gallon is 231 cubic inches. So the answer is 231 / (pi*r*r) = 10.93 feet.
posted by RustyBrooks at 7:41 AM on March 22, 2007

Whoops, sorry, 10.93 feet is for one gallon. 27 gallons is obviously 295 feet.
posted by RustyBrooks at 7:43 AM on March 22, 2007

I figured MeFi's math geniuses could lick this one easy.

Uh...its an arithmetic problem:

Volume/(Cross-sectional Area of pipe) = Length
posted by vacapinta at 7:45 AM on March 22, 2007

The volume for a cylinder is πr²h or in this case 0.442h (assuming the internal radius is .375 inches - Rusty - looks like you used .75 as the radius).
1 gallon is 233 cubic inches
27 gallons is 6291 cubic inches.
6291 = 0.442h
6291/0.442 = h
14233 = h
which is 1186 feet. I'm thinking that it's not 3/4" pipe once it leaves the house.
posted by plinth at 7:45 AM on March 22, 2007

radius=1/2 of diameter, so 3/8.
area=pi* rad^2=.4418 square inches.

27 gal *231=6237 cubic inches.

6237/.4418=14117 inches, or 1176 feet

A 3/4 feed, over that distance, is going to drive your coworker nuts unless he has some sort of storage tank and pressure booster.

On preview, rusty, i think there's something wrong with your calculation.
posted by notsnot at 7:46 AM on March 22, 2007

It's 3/4 inch diameter. So, (231 / (pi*r*r)) * 27 = 1,117 ft
posted by deadfather at 7:47 AM on March 22, 2007

1,177. Mistyped at the end.
posted by deadfather at 7:47 AM on March 22, 2007

I get 1176.5 ft also.

I don't think that the pipe diameter given is entirely correct.
posted by bonehead at 7:47 AM on March 22, 2007

I like how many different answers there are to this very simple problem.

Also, if there's a blockage that is water tight it might also be air tight, in which case you could have compressed air in there (or maybe it would come back out the incoming end?) which would put the blockage farther on.
posted by DU at 7:51 AM on March 22, 2007

Putzface_dickman, is this out in the boonies, where such a number (roughly a quarter mile) makes sense? Referring to the uniform plumbing code, for 1000 feet, if he's got less than 45 PSI at his house (more at the main), he can't run anything at all. For 46-60 psi, again at this house, he can run a toilet, no more. Even for over 60 psi, he can only run a toilet and cold water. In that high range, a 1" line can run a small household - two toilets, a lavatory (bathroom sink) and a kitchen sink.
posted by notsnot at 7:54 AM on March 22, 2007

Also also, frink, the awesomest unit conversion tool of all time, gives the answer as 358.6 meters or 1176.5 feet.
posted by DU at 7:55 AM on March 22, 2007

Response by poster: Well, his house is 600ft from the street. He must be wrong about the diameter of the pipe. Thanks to your help he'll calculate likely distances from likely pipe diameters so that he's making a more educated use of the backhoe he'll be hiring.

This may be arithmetic, but I'd rather take 5 minutes and look like an idiot on Metafilter to relearn something than to take 45 minutes to relearn it on my own.
posted by putzface_dickman at 7:57 AM on March 22, 2007

Heh, yeah, 3/4" would be the diameter not the radius. My bad.
posted by RustyBrooks at 7:58 AM on March 22, 2007

According to my calculations and assumptions (like that air could be trapped in there, etc), I think up to 1/3 of the pipe could be filled with air. That only brings it down to 800 ft, so either I'm wrong (distinct possibility) or the data are (also easy to believe).

^ Most helpful AskMe answer ever
posted by DU at 8:02 AM on March 22, 2007

OMGDUMAS: It wouldn't bring it down at all. It would push it up to like....1800 ft.
posted by DU at 8:03 AM on March 22, 2007

Another thing to consider is that the blockage might have allowed some water past it, then locked up tight after moving a ways. The best solution will be to have the county dig up the tap (at the street) and cut it off, then blow through the house end with compressed air or water - blow the blockage back through the tap end.
posted by notsnot at 8:04 AM on March 22, 2007

Schedule 40 pipe, a likely schedule for such service, has a nominal diameter of .75 inches and an actual internal diameter of 0.824 inches.
posted by caddis at 8:10 AM on March 22, 2007

Math calcs aside, he shouldn't have to randomly dig up the yard. Dig up near the connection to the service valve and then cut the pipe there. Blow out the service pipe with an air compressor which whould hopefully relieve the blockage. Open the valve just to make sure that there isn't blockage on the other side and hook everything back up.
posted by JJ86 at 8:28 AM on March 22, 2007

The basic maths here is:
- Radius of a circle (r) = diamater / 2
- Area of a cirle = πr²

According to google, 1 US gallon = 231.000001 cubic inches, so 27 gallons = 231 * 27 = 6237 in³

Therefore:

Radius of pipe (r) = 3/8 of one inch = 0.375in
Area of pipe = π x ( 0.375 x 0.375 ) = 0.441786467

- volume of pipe = area x length

Which we can rewrite as

- volume / area = length.

Put in our numbers:

6237 / 0.441786467 = 14117.682 inches long, or 1176.4735 feet
posted by gaby at 10:08 AM on March 22, 2007

DU: how did you get frink to figure that out?
posted by tayknight at 10:18 AM on March 22, 2007

Sometimes the meter (and part of the supply?) is smaller than the actual length of the supply pipe, so you may want to assume 1":

[http://www.irrigationtutorials.com/sprinkler03.htm]

Try to find a size stamped on the meter. If you can't find a size, ask your water company or just assume the meter is the next size SMALLER than the pipe running to the house. It is common for the meter to be one size smaller than the pipe. Standard water meter sizes are: 5/8", 3/4", 1", 1 1/2".

Perhaps you can check the house side and see if it looks like the house side supply looks larger?
posted by RikiTikiTavi at 11:11 AM on March 22, 2007

Frink one liner: 27 gallons/(pi * ((.75 inch)/2)^2) -> ft

I ♥ frink
posted by DU at 11:23 AM on March 22, 2007

Google will also calculate and do conversions for you. Just paste in:

27 gallons/(pi * ((3/4 inch)/2) squared) in feet
posted by JackFlash at 12:00 PM on March 22, 2007

Depends on the temperature of the water.
posted by Joe Invisible at 12:17 PM on March 22, 2007

If caddis is correct and it's schedule 40 with an actual ID of 0.824" that comes out to 975 feet for 27 gallons.

If RikiTikiTavi is right and the supply pipe is 1" (reducing to 3/4 to the meter) then the length is 662 feet.

I think your friend needs more information but honestly I think he's up for quite a bit of digging.
posted by 6550 at 12:48 PM on March 22, 2007

Your friend needs to contact a plumber... unless he enjoys random digging in his yard. Plumbers have tools and years of training/experience (and will hire and supervise the backhoe portion).

Just because 27 gallons went in doesn't mean the blockage is that far in. There's air in the system and the blockage is probably the combined distance of 27 gallons plus the now pressurized air.

According to my plumber friend, 'town' water pressure is usually around 135psi (if I recall correctly) during the day and goes up/spikes at night (less demand). And most lines going from the curb to the house are 1". Or at least that's the code around these parts (Western NY).
posted by jdfan at 1:19 PM on March 22, 2007

Depends on the temperature of the water

No, it doesn't. If he were asking what length of pipe would hold a given mass of water, it would (slightly), but that's not what he asked.
posted by DevilsAdvocate at 3:38 PM on March 22, 2007

Okay, algebraic gymnastics.

If you do find out the actual diameter of the pipe, and all your previous assumptions are correct (no air, no leakage, etc) then here's the formula to figure out the distance with all the conversions built in and everything:

Distance in feet = 661.77 divided by the square of the diameter in inches.
D=661.77 / (diameter^2)

This is accurate to within .01ft of the best of the above calculations (by notsnot, bonehead, DU, gaby).
posted by lostburner at 5:03 PM on March 22, 2007

I think everyone is overlooking the obvious with all these precise calculations. How the hell is all the water from the blockage going to get out of a faucet? I would be impressed if you could entirely empty a pipe with a majority of the water lower than the head....

That's why I get paid the big bucks as an engineer, fellas. The problem as written is insoluble unless you know the depth of the water main. I'm guessing that the problem is most likely not in his water service but is in the main.
posted by JJ86 at 6:56 PM on March 22, 2007

that's a joke right jj?
the problem is insoluble because the volume of water exceeds the pipe volume so the original assumption is wrong
however, your head is not appreciating head, so i suggest you just go get some instead
posted by caddis at 7:05 PM on March 22, 2007

Well that too, obviously....

I just think it's funny that the MeFi collective genius is barking up the wrong tree trying to equate the 27 gallons to the length of pipe.
posted by JJ86 at 7:11 PM on March 22, 2007

Here's a little hint to help the calculators.
posted by JJ86 at 7:32 PM on March 22, 2007

Response by poster: So, the plumber surmised that the obstruction was another shutoff valve. They adjusted their assumption about the diameter of the pipe. From the calculation supplied decided that it was closer to the house than to the street. They dug from the house out a few feet, found a shutoff valve. It broke when they tried to open it, so it's being replaced today. I didn't learn what the final diameter of the pipe was, but did hear that the plumber from the water utility determined that the water pressure in the house will be 80 psi once he's connected. That's up from 60psi from the well.

The curious among you could probably determine the exact distance (It's roughly 600ft) from the street to the house as well as the diameter of the pipe.

Thanks for the help.
posted by putzface_dickman at 5:01 AM on March 23, 2007