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# Pressuredrop duo to water freezing

## Pressuredrop duo to water freezing

(OP)
Hi,

I am working on a problem where I am tasked to calculate how much the pressure in a pipe will increase by when a portion of the water is turned to ice
For this example I am using a pipe with an 3Inch OD and the pipe has a length of 1 meter. The iceplug is placed within the pipe in the center and has a length of 3 x OD. The initial condition inside the pipe is that it is filled up with water, the pressure is around 2 bar.

I could use some tips on what formulas that could be used to solve this problem, so that I can further evaluate different pipes with different sizes, and be sure that the length of the pipe is long enough to prevent a large pressure drop.

Any help is much appreciated.

Best regards,
Arve

### RE: Pressuredrop duo to water freezing

I'm not understanding you here.

your title says Pressure drop when freezing, but the body of the post says pressure increase, but then keeps talking about a pressure drop???

Ice is less dense than water by about 9% or to put it another way, for the same mass of water it increases in volume by 9%.

So if you start with a closed volume at 2 bar and then freeze part of it the pressure will increase by quite a lot as the ice starts to form.

Is this homework?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

(OP)
Hi,

Sorry, pressureDROP is the wrong term, I guess pressure-buildup could be better?

This is not homework no. We are looking into how short a pipe could be when we freeze a portion of it, without risking the safety of anyone involved due to high pressure.

I will try to put it in a simpler question:
How do I calculate the new pressure within a pipe, when a small portion/volume of the initial water turns to ice.

### RE: Pressuredrop duo to water freezing

You need to be concerned with how much pressure is induced into the pipe wall at the center of the ice plug.
The bulk modulus gives pressure volume relations.
Free water will expand 10% in volume when changing phase to ice.
Expansion pressure is balanced with hoop stress of the pipe that is restraining the ice from expanding radially.
If the ice plug begins freezing from each end, it will expand longitudinally until enough length is developed to restrict further longitudinal expansion, at which time radial expansion will begin. If that happens, your pipe will most assuredly burst, as it will not be able to increase its volume by 10% without tearing apart.

The key to the solving the problem is finding out the bonding strength of the ice to pipe wall and that I do not know. Due to the high number of pipe bursts from frozen water pipes every winter, I'd guess it is extremely high.

### RE: Pressuredrop duo to water freezing

If we need to work on a water line that has no block valve, we have a rig we can used to freeze a short section of the line, temporarily. This allows us to do some quick and simple repairs downstream of the ice plug. We have done this many times and I have never heard of it causing a crack or leak. So, the question would be how short does the ice plug need to be? I think our inspectors have a way of determining that based on the material of the pipe and the pipe wall thickness. But, I have never seen how this is done. I would do an internet search for the tool (system, rig) that is used to deliberately freeze a line for maintenance work.

https://www.ridgid.com/us/en/sf2500-superfreeze

Johnny Pellin

### RE: Pressuredrop duo to water freezing

@op, contact a local contractor that know how? Unless you freeze a significant part of the pipe i will say small.

--- Best regards, Morten Andersen

### RE: Pressuredrop duo to water freezing

If you could assure freezing begins at the center and progresses outward each way, it should be safer.

### RE: Pressuredrop duo to water freezing

If the water is flowing while freezing then the stress on the pipe is much lower.
Also if the freezing starts at one small location and then spreads the stress isn't bad.
When you trap of volume of water and freeze it then you burst pipes.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

### RE: Pressuredrop duo to water freezing

If this is a closed system then the pressure rise will be very significant.

Freeze plugs do work on pipelines and don't burst the line, but then the pipe material is very strong. However it is the radial force which stops the plug from moving and seals the pipe.

In a simple sense start with your fixed volume of water then make up a spread sheet where the volume of water increases. As it increase the pressure will rise due to the increase in diameter of the pipe and the compression of the water. The amount of change will be whatever length of ice plug you choose divided by the total volume and then multiplied by 9%.

Try looking at this FAQ which you might be able to adapt. Just ignore the initial bit about thermal and input the changes into the change of volume part

https://www.eng-tips.com/faqs.cfm?fid=1339

Usually the way around it is to induce a small air pocket, much like you get when you put a bottle of beer in the freezer and then forget about it. Sometimes the bottle breaks, sometimes it just compresses the gas at the top of the bottle, sometimes it blows the top off.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

Your pipe will probably burst prior to reaching the maximum pressure. As LittleInch mentioned, the pressure will be significant.

Watch this demonstration by Richard Trethewey:

The pressure increases very quickly as shown in the video.

### RE: Pressuredrop duo to water freezing

(OP)
Thanks for the responses

LittleInch, I tried to work with the equation you presented, but does this not apply for temperature change as the complete volume changes temperature? You said I could ignore the thermal part, but I struggle to use this formula.

I tried however to focus on the fixed volume (Script of attempt below), and tried to but together a script in matlab where the input is ID, OD and length of the pipe.
I read that it takes 220 bar to compress 1% of the total volume of water. So what I did is I calculated the volume added from the 9% extra (VolumeIceCube*0.09) when the water turns to ice. I then calculated the actual required volume it has to compress by dividing the change in volume by the total volume (VolumeRequiredCompression). I used the relationship and timed it with the 220 bar and ended up with a pressure of 59.4 bar. If I reduce the length of the pipe from 1000mm to 100mm the required pressure goes up to 594 bar.

I expect that there are flaws that I struggle to see here.. Any tips?

SCRIPT:
{
OD = 76.2
ID = 75
L = 1000

r = ID/2
A = pi * r^2

InitialWaterVolume = A * L

VolumeIceCube = A * 30

VolumeRequiredCompression = deltaV / InitialWaterVolume * 100

PressureRequiredToCompress = 220/1 * VolumeRequiredCompression = 59.4 BAR
}

Best regards,
Arve

### RE: Pressuredrop duo to water freezing

At a fairly basic level that looks pretty good. It doesn't allow for the expansion of the pipe under pressure so the pressure rise will be a bit less but only maybe by 10 to 20% difference.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

LittleInch: how could you be so careless as to leave a bottle of beer in the freezer, that is an unforgivable sin.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

### RE: Pressuredrop duo to water freezing

I know - fortunately I've usually remembered just in time before it actually explodes and is just icy "slush" with a solid core in the middle.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

Actually I missed the fact that this looks like very thin tubing (OD-ID = 0.6mm thick?)

this is too thin and your ice plug will almost certainly break the pipe.

I don't think even my copper pipe is that thin and it's like 15mm OD.

So this will fail.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

There appears to be a misconception in this thread that it is the ice that applies a force to the pipe and causes it to burst. This is not correct. The expansion of freezing water in a sealed volume causes the water pressure to increase and it is the hydrostatic pressure that causes pipes to burst, often in places where there is no ice.

### RE: Pressuredrop duo to water freezing

Not sure about that. There is definetly some additional hoop stress going on which is how freeze plugs work. More than a couple of D long you're going to get some lock up and extra internal pressure.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pressuredrop duo to water freezing

A piece of string with weights on each end for tension will cut through a block of ice just due to the contact pressure of the string causing a rise in melting point. It is in instances where the ice traps a pocket of water that then progressively freezes that you have pressure increases. Ice freezes in the shape of its container but it does not expand once frozen. It is the water that expands when it freezes.

For example, if you freeze a vertical pipe that is open at the top, from the bottom, there will be no pressure increase when it is fully frozen. However, if it freezes at the top first, the trapped water below will burst the pipe as it freezes. In a cold environment there is a natural tendency for water to freeze from the top down, because the density of water is at a maximum at 4C.

If ice expanded after freezer it would slough off of surfaces due to this expansion. But we know that ice adheres to most surfaces very tightly. It is this adhesion that keeps ice plugs in place.

### RE: Pressuredrop duo to water freezing

#### Quote (Compositepro (Chemical))

A piece of string with weights on each end for tension will cut through a block of ice just due to the contact pressure of the string causing a rise in melting point. It is in instances where the ice traps a pocket of water that then progressively freezes that you have pressure increases. Ice freezes in the shape of its container but it does not expand once frozen. It is the water that expands when it freezes.

For example, if you freeze a vertical pipe that is open at the top, from the bottom, there will be no pressure increase when it is fully frozen. However, if it freezes at the top first, the trapped water below will burst the pipe as it freezes. In a cold environment there is a natural tendency for water to freeze from the top down, because the density of water is at a maximum at 4C.

If ice expanded after freezer it would slough off of surfaces due to this expansion. But we know that ice adheres to most surfaces very tightly. It is this adhesion that keeps ice plugs in place.

Here are some pictures of frozen piping. The client insisted on keeping this outside piping on standby until the last minute with winter rapidly approaching. In addition to your scenario, there may be instances when the entire pipe freezes causing expansion. I had a project some years ago when the equipment was not operating (and blocked in) and a very quickly moving severe freeze occurred. As you can see from the pictures, the entire pipe froze which split almost the entire PVC pipe. The third picture shows the entire pipe split and fell off leaving an ice core.

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