I have heard that a segment of piping in one of our plant was frozen with the hydrotest water in it.  Although it is not related to my area of responsibility, I was thinking how I could calculate the pressure exerted by the expanded water in the solid phase.  It's been a long time since 1st year university and I don't even have my 3-phases of matter book anymore.  Can anyone point me to a source that can show me how I can calculate the pressure excerted by the ice on the pipe?/>ball vave< Meanwhile, I'd try to search the web and when I get home, I'd search my Mark's handbook.

Determine if pipe is restrained longitudinally.
Determine if pipe was open to atmosphere or sealed off as it froze (ie, some of the expansion takes place before the water freezes).
Calculate mass of water in a unit length of pipe.
Calculate equivalent volume of ice this represents.
Find bulk modulus of ice.
Assume different pressures.  Calculate reduction in ice volume due to the pressure, and increase in pipe volume due to the pressure until you get a match- considering longitudinal expansion also if not restrained.
First pressure to guess would be the one corresponding to yield point of pipe.  If the final answer is above this pressure, you probably won't have a good idea of how the pipe behaved.

I can see how a line might start freezing at one point, and build up more and more pressure as it froze down the line, if it was closed off at the far end.

I did this analysis a few decades ago, looking at using a freeze plug to isolate for a new tee.  As I recall, the start of the freeze had some ability to move laterally (the line was water-full and vented) and pressure was pretty constant.  Increasing the length of either of the freeze plugs toward the other one quickly used up that small movement.  Once the plugs were fixed in place (by the length of the freeze) then any additional freezing on the trapped side resulted in amazingly high pressures very rapidly.  The numbers I recall were on the order of dozens of bar per gram of additional ice.

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