Expert: Paul Soderman - 7/1/2011

Question
Hi Paul
Hope you can help I have a sealed stainless pipe of volume 0,001 cubic metres filled with petrol at 1 Bar atmospheric pressure and 10 degrees C.What temperature would I require to raise the pressure to 140 Bar to break the burst disc. My problem is I dont believe the gas laws apply to liquid? but I could be wrong.
Thanks for taking the time I appreciate it.

Answer
Steve - No, you are correct.  The gas laws do not apply to liquids.  But a liquid trapped in a sealed container and heated will try to expand as will the container.  But the volume change is small so the pressure goes up quickly.  The basic equation is:

del T = del p (B + D/(tE))/(alpha f - alpha V),  where

del T = the temperature change
del p = the pressure change
B = compressibility factor of fluid = 1/Ef where Ef = bulk modulus of elasticity of fluid
D = diameter of container
t = wall thickness of container
E = elastic modulus of container
alpha f = volumetric coefficient of thermal expansion of fluid
alpha v = volumetric coefficient of thermal expansion of container

Fun isn't it.  See a sample calculation for water at http://www.eng-tips.com/faqs.cfm?fid=1339

For your case (and you better check my numbers) I used:
del p = 139 bar = 139x10^5 Pa
Ef = 1.3x10^9 Pa   gasoline
E = 2x10^11 Pa  steel
D/t = 10 assuming a heavy steel container
alpha f = 1x10^-3 per deg C gasoline
alpha v = 36x10^-6 per deg C steel

And if my arithmetic is good, I get an increase of 11.8 deg C as the temperature rise needed to reach your burst pressure. It should burst at 21.8 deg C. This changes if you have any gas in the container or if D/t is different. Hope this is good.  Don't bet the farm on this without checking the equation and numbers carefully.
Paul