Air/Water Balance in Pipe

[Hemyu]

Condition:

1. 8" ID pipe is filled with air at atm
2. Pipe section is 4' long
3. Leaky valve allows water to enter section
4. Flow rate of water unknown
5. Water pressure is 100 psi

Assumption:

Water fills section until it can no longer compress the volume of air that was inside the section

Unknown:

Temperature, but pipe was underground.

Requirement:

1. To determine the pressure of the compressed air (I figure it to be 100 psi at equilibrium)
2. The amount of energy stored in the compressed air
3. Where in the section the air would be (I figure the air to occupy the top portion of the section as it is lighter)
4. A reference to support theory that when pressurized air escapes from a small opening (opening due to cutting into pipe), the rapid escape of air releases a great amount of energy and would shatter a plastic pipe

Thank you kindly in advance.

 

[BigInch]

Volume of air remaining will be V1 * (15+100)/15
Volume of water is total volume minus that.

Longitudinal tension in the pipe will be 100 psi * pi * 4^2
Stress concentrations at each end of the cut will exceed the allowable stress causing it to rip continuously.

"I am sure it can be done. I've seen it on the internet." BigInch's favorite client.

"Being GREEN isn't easy." Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.live.com

 

[rconner]

While you have perhaps not yet provided quite enough information for most rigorous analysis of the issues per all your “requirements” 1-3, a search of these forums and the web would reveal many past discussions on the energy of compressed gases in pipelines, and also air or gas over water issues (see e.g. with regard to the former robsalv’s
7 Jun 05 22:14 post on the thread at

http://eng-tips.com/viewthread.cfm?qid=122175

, and the standard reference he cites). [See also the letter of Mr. Jack Roach of Colonial Engineering etc. at the OSHA site

http://www.osha.gov/dts/hib/hib_data/hib19880520.html

.]
As to your “requirement” 4, plastic pipes in general do not have much fracture toughness, nor do they have a very large flaw nor “critical crack (or damage) length” (both of sufficient size/length can cause a crack to disastrously propagate) as has been taught by BigInch. Much more information could be found with a good search engine and such keywords. Your scenario however sounds eerily familiar however to an incident I saw reported several years ago in a utility in New York, where a worker was actually killed while attempting to first cut into a particular type of plastic pipe while under pressure (obviously inadvisably!), and many other workers in many other locations have been injured and scared witless while attempting to purposefully wet tap (in and of itself a rather common practice, though in these cases with unintended explosive consequences) into the same type of pipe while pressurized. Maybe there is often a good bit of energy (and maybe even some air) present even in a good many even common water pipelines, that should be respected?
While fingers can be (and are) pointed all over the place whenever something bad happens, I noticed the near 30 year old paper at the site

http://www.stormingmedia.us/79/7915/A791503.html

also includes the following interesting statement from some MIT folks, “…brittle fracture properties of plastics may be of practical importance in choosing between different materials…”

 

[cloa]

Obviously 1. 100 psi is the worst case scenario but your leaky valve is going repress a good deal of the water's pressure- its not the same as an open pipe. If you knew the valve type and some idea of its failure mechanism then someone might have some idea of hydrodraulic drag equivalent to that water leak or it would be in a handbook. There is probably going be the maximum possible gas dissolved in the water if its a spray so that has be allowed for. Flow rate if continous after inital release of water is probably irrelevant.

 

[rconner]

Of course the information "leaky valve" in and of itself isn't very specific, and in practical application could mean a lot of different things. Is the valve just allowing a seep or dribble of water past, is there a 2x4 wedged in the disc or gate etc., or did a worker snap the stem fully off some time before trying to close it from the full open position, but turning the operating nut in the wrong direction? The latter couple scenarios might not "repress" the flow/pressure much! ;>)