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Pipe freeze analysis

Pipe freeze analysis

Pipe freeze analysis

(OP)
When water pipes freeze, how do you analysis the forces and pipe stresses from the phase change?

Anyone have links to online reports or analysis?

RE: Pipe freeze analysis

If you assume a closed end pipe, the change in specific volume of water between +1 and 0ºC must be accomodated by pipe radial expansion.  Stress = E * strain.  Calculate the change in circumference/or * iginal_circumference.  That strain divided by the Young's modulus of the pipe material will give you the stress in the expanded condition.

at 1ºC Water density is 999.9 kg/m3  SVw = 0.0010001
at 0ºC Ice has a density of 917.0 kg/m3. SVi = 0.0010905
pi D^2/4 / pi/D = ratio of volume to circumference

That's about a 10% increase in volume.  The stress generated in a pipe icreasing in diameter. The pipe is getting a little smaller too as it decreases circumference by 0.000012 mm/mm-Cº

When you do the math you'll find out its enough to rupture most pipes.

http://virtualpipeline.spaces.msn.com

RE: Pipe freeze analysis

As water expands upon cooling from 4C to 0C, I recommend using the densities or specific volumes at these temperatures.
Regards

RE: Pipe freeze analysis

Sailo, all significant expansion takes place between 0ºC and 0ºC

at 4ºC the SG of water is 1.000
at 1ºC the SG of water is 0.999
at 0ºC the SG of water is 0.999(8)
at 0ºC the SG of ice is 0.917

Water specific volume differences between 0 and 4 degrees probably isn't going to hurt the pipe, but the phase change does.  You won't notice any difference in the calculations if you use either 4 or 0, as its during the phase change that 99% of the density difference between water in the liquid phase and ice in the solid phases takes place, which explains why ice floats.

To be technically correct, the initial temperature should be taken as the temperature at which the container is sealed, not 4ºC.

http://virtualpipeline.spaces.msn.com

RE: Pipe freeze analysis

Until the water freezes, expansion can push the water back into the delivery system unless the backflow is blocked.  Once the water freezes it can not flow back.  Biginch says it best to be concerned right at phase change.

Ted

RE: Pipe freeze analysis

You can do the calculations directly on an area expansion basis if the pipe is totally longitudinally restrained and use 2 x the linear temperature coefficient of expansion, on a voumetric basis where the pipe is free to expand (or contract) longitudinally use 3 x TCExp.

http://virtualpipeline.spaces.msn.com

RE: Pipe freeze analysis

Do bear in mind that the pressure of the liquid water trapped between an ice "plug" and a dead end (valve, etc) (or between two ice "plugs", as sometimes happens) may well be much higher than the pressure that would occur purely due to the entire pipe contents freezing as described in the previous posts.

Brian

RE: Pipe freeze analysis

Depends on if the plug is allowed to grow longitudinally during expansion or not.  If expansion is not restricted longitudinally, the resulting pressure would most likely be determined by the hydraulics of the pipeline at the time.  If ice expansion is restriced longitudinally, the stress could reach hundreds of times the hydraulic pressure.  10% of E is 300,000 psi on a 1" wall thickness.

http://virtualpipeline.spaces.msn.com

RE: Pipe freeze analysis

BigInch, You are correct-I neglected the key statement of change of phase.
  I tried websites-with no success- to find compressive stress (pressure) vs density for ice. Knowing that piping/equipment can/do fail under freezing conditions, it still should be of interest to find effect of ice stress during freezing. While I'm not a structual/civil engineer, the effect should make a good technical paper.
Regards

RE: Pipe freeze analysis

I can still clearly see in my mind the effects of ice expansion while growing up in the NE USA.  The milk man (ya we had a "bread man" too) would leave the milk at 5am in a box on the steps up to the house.  Many times the bottle exploded, although some times just the cap was pushed off.  I also remember that my neighbor's engine block exploded in 1961.  I thought it was rather spectacular at the time.

Sailo,
Search for the "bulk modulus" of ice, for which I found the value of 2E9 N/m2, strangely enough being used in conjunction with estimating the stress in a freezing engine block, here

http://physics.ucf.edu/~khondaker/TeachingMaterial/PHY%202048%20L32_spring%2007.pdf

http://virtualpipeline.spaces.msn.com

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