# Expansion pressure of water in a closed system

1. Mar 15, 2006

### laca4677

If you take a quart of water and take it from 60 degrees farenheit to
-35 degrees farenheit not allowing for expansion, what is the average
delta psi/degree and the delta pressure total?

2. Mar 15, 2006

### Staff: Mentor

This seems to be a homework problem, which belongs either in Introductory Physics or Other Sciences or perhaps the Engineering Homework section.

The water is being cooled. The pressure of the closed system will depend on the change of density of the water, such that at fixed mass, as the water cools it relieves pressure on the container as it contracts, but around 4°C it begins to expand again.
http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/waterdens.html#c2

Determine the density of water with respect to its inital temperature of 60°F (15.6°C).

3. Mar 16, 2006

### laca4677

This is actually not a homework problem. Someone at the office decided to hand this off to me and I was having some problems solving it and I this is what I ended up with. I was unsure about the bulk modulus and coefficient of expansion due to the density changes during the cooling and phase changes of water. I ended up using a few different formulas, but this was definately easier with hydraulic oil then with water (NO real big change in density or a phase change).

Thanks for any and all help.

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4. Mar 16, 2006

### laca4677

Let me expand on the application. We are trying to show the pressure difference between using hydraulic oil and water when you are doing a service job on drill pipe with pressure. They set a freeze plug in a section of the pipe using dry ice so that they can replace a valve in a line that still has pressure on it.

5. Mar 16, 2006

### Q_Goest

I believe the density of ice is lowest at it's freezing point, so as you continue to lower the temperature it only gets slightly more dense. If this is true, you can calculate the worst case (highest pressure / highest pipe stress) being the frozen plug at roughly 32 F.

Considering the pipe to be rigid though is overly conservative in the sense it will give you an extrordinarily high pressure if you're only considering the bulk modulus of the ice. I think you'll have to consider the expansion of the pipe as well.

Regardless of that calculation though, it seems what you're proposing, plugging a water line by freezing the water, is very doable and not uncommon. Carbon dioxide might not be the best thing to use, but should work. I'd worry about phase changes of the CO2 (liquid to a solid especially) and the possibility of plugging your CO2 line. Liquid nitrogen would be a great way to do it. For example, this company on the internet uses LN2 for all sorts of pipe and all sorts of liquids.

I'd suggest testing the application a few times on a similar piece of pipe prior to attempting on an actual process pipe. You could easily set up an identical section of pipe filled with pressurized water or other fluid and freeze a plug for an extended period of time. Inspection and testing of the material would determine if there was any permanent affect on the pipe. This would also allow you to test your apparatus and procedures prior to attempting it on an actual process line.

Last edited by a moderator: May 2, 2017
6. Mar 16, 2006

### laca4677

We already do this in practical applications. The reason that we use dry ice is because it is readily available in most countries in the world. This is not usually something that they plan on having to do it is when something fails in the system and needs to be replaced.

7. Mar 16, 2006

### Bystander

Still not clear what you're after here, but quick rule of thumb and easy way to remember it for the water to ice phase change is that the one atmosphere freezing point is 273.15 K, the triple point is 273.16 K (vapor pressure is near zero); (delta P)/(delta T) is one atm./0.01 K, so you're looking at 100atm/K, 10 MPa/K, 2900 psi/K, 1500 psi/F, pick your units. If you've been tasked with demonstrating to customers that there is no danger of damaging plumbing with the method, you're out of luck. If two plugs form either side of a liquid volume, you're going to burst every pipe every time. If the freezing method yields growth of a single plug from a single cold spot, or applies the cryogen to high spots in the flow line, you're okay.

8. Mar 20, 2006

### laca4677

Single plug/Single Freeze Point

The plug is in metal pipe, and we are freezing a single plug from a single cold point. What I am trying to show is that the pressure increase will not damage the plumbing. The pressure gain due to temperature of a single quart of varying fluids not being allowed to expand due to the pipe restricting expansion will not exceed pressure maximums. If anyone would like to discuss this please send me an E-mail at laca4677@yahoo.com.

9. Mar 20, 2006

### Bystander

What you'll have to demonstrate is that the plug volume is a small enough fraction of the total system volume that the ice expansion can be accommodated by compressibility in the unfrozen part of the system. If the system volume is one quart, and you freeze it completely with dry ice, you've got to confine 3500 to 4000 atmospheres. One quart in ten, P max is 500 - 1000 atm. One in twenty, 250 - 500. (10 ppm estimated compressibility --- you'll have to look up the actual number)