Natural gas at 21mbar pressure in a 150mm internal diameter pipe. If there is a 60mm dia hold in the pipe how much gas will escape in 10 mins?

Any help would be great.

All of it?

It depends how long the pipe is. The volume of pipework will influence the pressure decay in the pipe and therefore the change in flowrate wrt time.

assume a constant 21mbar pressure in the pipe.

175kg.

ish.

Well notwithstanding fluid dynamics and turbulence etc:

You’ve got the type of gas and pressure inside the pipe which gives you the density. You’ve got the size of the hole which with the pressure gives you the force over the area of it. So imagine a very thin disc of gas sitting over the hole – you can work out its mass, and the force propelling it, and then how fast it will move to a point outside the pipe. Given constant pressure in the pipe calculus shoudl not be required even if you use dx or dz or whatever for your thin slices and distances to move otuside the pipe.. should cancel out I think.

There’s probably an equation for amount of gas leaving a certain sized hole tho 🙂

I don’t think the above would give a very realistic answer at all because gas escaping a hole is heavily impeded by turbulence.

Should be able to figure it from this, but I can’t figure out the discharge coefficient

molgrips – Sadly it’s a bit more complex than that. Should be able to calculate it accurately with orifice plate equations.

okay, assuming C = 1 (which might be utterly incorrect),

p1-p2 = 21mbar = 21 x 10^-3 *100000Pa=2100Pa
density = pressure/RT (R = some gas constant which I’ve forgotten, T = temp)
A = pi*(30×10^-3)^2

then total mass of gas = m(dot) * 600seconds (i.e. 10mins)

Never had to do fluid calcs myself, but there are online calcs for allsorts these days.

http://www.pipeflowcalculations.com/orifice/

C = 1 (which might be utterly incorrect),

’tis. I assumed 0.7 for a beta ratio of 0.4 (60/150), but I couldn’t be bothered iterating around the reynolds number to see if this was reasonable. Minimum would be 0.6 so not really a big deal.

R = 8314 J/kg-molK

molgrips – Sadly it’s a bit more complex than that

Oh I know.. I was just mulling it over. I know nothing about fluid dynamics 🙂 Just fancied a bit of physics instead of hunt-the-formula 🙂

So do we have a definitive answer or at least a decent estimate? I worked out several methods I found on the internet and got answers from 30kg to 300kg!

I’d just like to point out that this is an engineering question, not really maths/physics! Going on gut feeling that’s quite a low pressure differential so flow should be predominantly linear. Is there a viscosity component in the above equations? My degree suddenly seems a long time ago…

Is there a viscosity component in the above equations?

It’s a secondary effect that is built into the Reynolds number which is used to find C. The Cp/Cv ratio is built into the expansion factor which for some reason is missing from the equation that is posted.

Yeah it’s an engineering question, Physicists and Mathematicians will only over complicate the problem by getting bogged down by the fact that the “hole isn’t circular” and other relatively insignificant details.

Depends on 101 other things, to be on the safe side I’d say its whatever the normal flowrate in the pipe was before the rupture * facor (i.e. whatever the copressor at the source can pump when theres no resistance, 1.3 for a normal centrifugal pump, I’ve no idea what it is for compressors)

However……….

That seems like a very low pressure for a 6″ pipe, so hypotheticaly speeking the answer must therefore be 42.

We are only interested in modelling the problem and how it works, not the actual amount of gas 🙂

isn’t 21 mbar less than atmospheric pressure?
answer: air goes in

I assumed it was 21mbar above atmospheric

I wondered if it was a trick question…

About 53kg according our CFD package.
(Caution: Very quickly done, meshing probably a bit course).

150dia-60leak by pten2106, on Flickr

wow, that’s an impressive answer.

Takisawa wins!

not used that package, but in fluent I’d have modeled that as a pipe in a box where the hole faces a side of the box defiend as the outlet boundary, looks like you’ve modeled it as a t-piece (or is it just coming out very straight?