Converting PSI Pressure Loss in a Pipe to Fluid Loss Rate

[CWPeltzer]

TL;DR

Pipe Testing

Summary: Pipe Testing

I need some help on how to calculate PSI loss to gallons per hour?

We will be testing this 8" PVC line at 150 PSI for 4 hours. If the test gauge drops 10 PSI per hour, what is the formula to determine the gallons per hour lost?

Thank you for your help.

 

[berkeman]

Welcome to the PF.

How long is the pipe? You are not replenishing the water in the pipe while running this test? So the leaked water is replaced by air that bubbles in via the leak?

 

[CWPeltzer]

Welcome to the PF.

How long is the pipe? You are not replenishing the water in the pipe while running this test? So the leaked water is replaced by air that bubbles in via the leak?

500' long with roughly 60 offset fittings. no we will not be adding water through test.

Thank you for the help

 

[Chestermiller]

Are you aware of the property known as bulk compressibility? If so, how is it defined? Could you analyze this if the pipe did not get any smaller in total volume?

 

[jrmichler]

When you pump the water into the pipe, you are compressing:
1) The water, as @Chestermiller pointed out, and
2) Stretching the pipe, mostly increasing the diameter, and
3) Compressing any air bubbles trapped inside. With 500 feet of pipe and 60 fittings, I can guarantee there will be air bubbles.

It will take about 1300 gallons of water to fill that pipe, plus more water to pressurize it. I suggest filling the pipe until it is full, but not pressurized. Then measure the amount of water to pressurize it. One way is by pumping the water in through a water meter. Record the total amount every 10 PSI or so, and plot the results to get a graph of volume vs pressure. Draw a smooth line through the appropriate data points, and you will know exactly how much water per 1 or 10 PSI pressure drop. Here is one possible meter: https://www.mcmaster.com/4119k41. They also have other water meters.

The PVC might creep a little the first or second time you run the test, so repeat the test if the results are marginal. If the apparent leak rate decreases with successive tests, blame it on creep and/or trapped air bubbles dissolving into the water.

 

[JBA]

Do you have a pass/fail leak criteria for your pipe system; and, if so, who is determining this criteria i.e. is it your's internally or is it a customer's specification.

 

[Chestermiller]

Assuming negligible change in pipe volume and no dissolved air, for a water bulk modulus of 320000 psi, a 10 psi decrease corresponds to about 5 oz on 1300 gallons.

 

[JBA]

Using std 8" sch 40 PVC pipe dimensions; and, PVC material physical data from the below reference, I calculate about 0.65 Gal / 10 psi will be expelled due to pipe diametrical and longitudinal contraction while reducing the test pressure from 150 to 0 psig with an initial 1300 gallon pipe filled volume at 0 psig.

https://www.usplastic.com/knowledgebase/article.aspx?contentkey=557

 

[Dullard]

Temperature changes will probably swamp your data. A 10 PSI decrease could be a 5 oz leak, or it could be a 0.2C temp decrease.

 

[Chestermiller]

Temperature changes will probably swamp your data. A 10 PSI decrease could be a 5 oz leak, or it could be a 0.2C temp decrease.

@JBA showed that the pipe contraction swamps the liquid water expansion, and that the actual water loss for a 10 psi decrease will be more like 85 oz. And this is only for a 10 psi change.

 

[berkeman]

So what y'all are saying are that this is an ill-advised (and poorly designed) test. Can you make suggestions to the OP for a better test? The pipe is kind of long, but if it were shorter, they could maybe drain the water out afterward and compare that to the initial volume to find the leaked volume?

And to @CWPeltzer -- Who defined/required this test? Do they understand these pretty severe limitations? Do they just want to know if the fittings will leak?