Calculating pinhole leak rates through a pipe under pressue 3

[kcjBoiler]

I'm a little embaressed by the fact that I don't know how to do this, but as they say, "if you don't use it you lose it"

I have a pinhole leak in a 12" pipe that is pressurized at around 300 psi and has a gas flow of approximtely 300,000 lbs/hr. I just need to come up with a conservative estimate as to how much is leaking out of the pinhole. Are there any plug and chug calculations that I could use to get me within +/- 10%?

This seems pretty straight forward, and was wondering if someone with more experience could help.

Many thanks.

 

[sailoday28]

mbeychok (Chemical)
Welcome back!
The first of your referenced equations must use stagnation conditions to be correct. Also, what is meant by real density?
The first equation is approximate, only if the upstream Mach numbers are low.
If the agencies that you reference, use other than stagnation conditions, they are misapplying choked flow equations.

 

[dcasto]

Finally, give us an exactly round, tappered pinhole and its diameter +/-.001%. At some point, all the equations don't matter because of all the unknowns.

 

[mbeychok]

.
dcasto:

Bravo! I am giving you a second star for being a voice of sanity. Not every problem requires a Ph.D. thesis.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[kcjBoiler]

Thank you all for your in-depth analysis, and I'm also glad I could come up with an interesting problem.

I ended up using an equation from Chemical Process Safety Fundamentals by Daniel Crowl (4-40), and double checking my results with dcastos's and mbeychok's equations, and was close enough. I was also fortunate enough to be able to see the leak for myself and visualize my answer to see if it made sense.

I know that these are probably not to most accurate answers, but I was told to be conservative and use "engineering judgment".

Thanks again!

 

[rconner]

This is probably my stupid question, and you have certainly gotten some in depth responses. To sort of verify all this comprehensive work that has been done and to obtain a meaningful answer(as I did not initially realize you had access to the leak), I was just curious if you could weigh a large rubber balloon on a sensitive balance, then hold it over the leak for a length of time e.g. measured with a stop watch (I would assume the gas @ 300 psi might blow same up, though without building a lot of backstop pressure), then weigh the balloon again to determine roughly how much agas escaped over that time period?