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Help on fluid pressure in a contianer
2

Help on fluid pressure in a contianer

Help on fluid pressure in a contianer

(OP)
I have a few question on pressure in the head space.
The container is 256cc. If the container is filled with water
of 225cc,
1)what is the pressure in the head space at room temperature. If the temperature is increased to 250F what willbe the new pressure in the head space?
2) How many cc's must he bottle expand to net 5 psi in bottle at 250F?
thank you in advance

RE: Help on fluid pressure in a contianer

Use the coefficient of thermal expansion for water to find the change in volume with change in temperature. From that, you can calculate the pressure change in the head space.

To answer 1 and 2, you must know either the pressure at room temperature or at 250F, then you can calculate the other.

You will also need to know the wall thickness of the bottle and Young's modulus for the bottle's material in order to calculate the change in bottle volume from a change of pressure within.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Help on fluid pressure in a contianer

(OP)
Thanks for your reply.
Regarding the first question, can I calculate the pressure in the head space at room temperature, with given volume. The content inside is water. This is the condition without thermal expansion. What formual's to use is it PV=nRT?? tahnks,

RE: Help on fluid pressure in a contianer

kdsilv1

Would you mind explaining a little more about the use of this container/bottle/tank?  What codes are you building this to?  What materials are being used?

Looking at your last question, I'm a little concerned that you expect your bottle to expand due to an increase in pressure -- does the system not have a relief valve on it?  Are you sure the material will actually expand versus rupturing?

In regard to your question about figuring out the initial pressure, I don't believe you can just consider the air as an ideal gas.  A lot would depend upon the conditions under which the bottle was filled as to how much water vapor would be in the air.  Can you describe how the bottle will be filled, and what initial conditions will be present -- is this a field application, where things could rapidly change or is this a laboratory situation where things are very controlled?  Is this a cover gas applied afterwards or an air pocket left during filling?

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

RE: Help on fluid pressure in a contianer

(OP)
VPL, thanks for your reply.
The process is similar to retort. The jar is filled with faucet water then closure/cap is applied. The jar is filled with 225 cc of water. The head space is 30 cc (air pocket left after filling). I would like to calculate the initial head space pressure and room temperature. The jar is made of Polypropylene but very rigid (assume rigid structure for inital pressure). The closure is also polypropylene.
If the temperature is increased to 250F, the bottle expands and wuold like to know the pressure at 250F.
Thanks.

RE: Help on fluid pressure in a contianer

kdsilv1

Being somewhat blunt, this isn't a homework problem, is it?

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

RE: Help on fluid pressure in a contianer

(OP)
NO, I work for a company. I have to find the pressure and apply it in Finite element analysis software. Without knowing the pressure it is difficult to approach...

RE: Help on fluid pressure in a contianer

Forgot to say that you will also need the thermal expansion coefficient of the bottle.
---------------------------------------------
The air expands according to V = nRT/P

The water expands according to it's thermal expansion coefficient and compresses according to its bulk modulus property, to which the net volume change will be the algebraic sum of both.

The air volume plus the water volume will equal the bottle volume, as the bottle expands in accordance with its thermal expansion coefficient and its internal pressure (if the bottle is basically circular, an approximation can be made using a hoop stress formula and the tangential strain calculated by dividing hoop stress by its Young's modulus).

Develop an expression for the total change in volume of the water and air and set that equal to the volume of the bottle: solve for the pressure.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Help on fluid pressure in a contianer

Based on what you've described, the initial pressure should be your local atmospheric pressure. The process for filling the bottle would not cause an increase in pressure.

In going to 250°F, don't forget that the water could go through a phase change.  The presence of an air pocket would provide room for some water to flash to steam.  At that point, I would not use the ideal gas law for the steam/water mixture.  FYI, for saturated steam, the saturation pressure at 250°F is about 15 psig. However, the actual pressure is likely to be somewhat below that as there isn't sufficient air space for all the water to turn to steam.

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

RE: Help on fluid pressure in a contianer

(OP)
Good point about the saturated steam and corresponding pressure. So according to VPL, it doesnt matter if I fill 15ml or 200ml the initial pressure in the head space is atmospheric pressure??
I guess the information provided by you people should help me approach the problem to some extent.

RE: Help on fluid pressure in a contianer

The saturation pressure for water at 250 F is roughly 15.2 psig.  This is the partial pressure of the water vapor above the water.  Add to this the pressure contribution (partial pressure) of the air.  Use ideal gas law to determine.  Final pressure is the sum of these two partial pressures.

Note that if the container is polypropylene, the allowable stress is going to decrease, possibly quite dramatically (I didn't look it up).  Anyway, you shouldn't need FEA to do this, just conventional pressure vessel formulas, and a knowledge of stress allowable for the material at this temperature.  

To ensure your analysis is conservative, I'd suggest not considering how much the container might expand.  That expansion is never taken into account by vessel codes.    

RE: Help on fluid pressure in a contianer

I'm a little confused by this discussion.  I know that if I take a vessel that is liquid-full, pressure will increase about 100 psi/degree F through thermal expansion.  So increasing temperature in that vessel would get me to (assuming a starting point of 60F) 19,000 psi (assuming the vessel doesn't break).

Now if there is adequate space for an equilibrium between the water and the saturated steam going from 60F to 250F will give me about 15 psig.

I'm fine with all that.  Now here is where I get confused.  If there isn't enough space for the steam/water to reach equilibrium then what controls?  I guess as long as there is some compressible fluid for the water to expand into it is compression arithmetic, but if the expansion compresses the gases beyond 15 psig then the steam will condense and the only thing that matters is the thermal expansion coeeficient of the water.  What am I missing?

David

RE: Help on fluid pressure in a contianer


Assuming the container is rigid, the situation is similar to that of a pressure cooker.

Liquid water expands by ~6% from 60 to 250oF.
The vapor space would therefore contract by 0.06×225 =13.5 cc, becoming 17.5 cc.

Vapor pressure of water at 250oF is 2.031 ata.
The air pressure is calculated from PV=nRT considered an ideal gas, where V= 17.5 cc.

Both pressures are added, as iainuts indicated, following Dalton's law of pressure additions.

RE: Help on fluid pressure in a contianer

(OP)
Thank you all for the suggestions.
We are using 265 F instead of 250 F
I may approach this way, find the change in volume by using delta V = B* Vi* (delta T)
where B is thermal expansion coefficient at 50F (10C) which is 0.000088/C
Vi = 225ml and delta T = 265-50F or 130-10C

Take the pressure at 265 F from steam tables, which is 39 psi then use P1V1 (vapour) = P2V2 (air) and find pressure P2
Any suggestions.

RE: Help on fluid pressure in a contianer


kdsilv1

• Liquid water expansion coefficients change much between 50 anf 265oF. Therefore, I suggest you use the tabulated specific volumes for water.

• The formula P1V1 = P2V2 is only valid when V1 and V2 are specific volumes. Otherwise the correct equivalence is P1V1/n1 = P2V2/n2

RE: Help on fluid pressure in a contianer

I would go with iainuts approach. Use ideal gas law to calculate the pressure change of the air. Use the steam tables to calulate the vapour pressure change of the water. Add to get the final pressure in the container.

If you need more precision, calculate the volume change of the water using the change in density from room temperature to 250°F. Same goes for the container using the coefficient of thermal expansion.

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