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How to calculate pressure increase in a closed liquid filled cylinder?
Posted: 22 Mar 02 (Edited 16 Oct 03)
You have to find the expansion coefficeint of the diesel oil. Normally there will be a linear coefficent. Then it should be fairly easy to calculate the volume expansion, then you have to find the liquid compressibility, that would enable you to calculate the pressure rise when you assue a constant volume.
You need a databook for those two constants.
A general equation would look something like this:
expansion coeeficient: a (ft3/deg F)
Compressibility: b (ft3/psi)
at constant volume: dP (psi) = a*dT/b
Now finding the physical data could be difficult. For diesel this is a methode:
I checked google (www.google.com) a great search engine.
I found a chevron datapage: http://www.chevron.com/prodserv/fuels/bulletin/diesel/L...
Here the linear thermal expansion coefficient is 0.00046 /deg F
The compressability is however more difficult. I took the first reference that i could find (not quite sure its diesel no. 2 but it is diesel). The value i found at this link http://www.amesim.com/de/pdf/fuel_113.pdf is approx 1/15000 bar = 1/217500 psi
A 50 def F temp increase should therefore lead to a increase in pressure of 0.00046*50*217500 psi=5000 psi pressure increase (the correspond OK with Butelja's rule of thumb where 1 def F means 60-70 psi increase since .00046*217500 equals 100 psi/deg F).
For water (in US units):
At 550 °F, the specific volume of the liquid is 0.0218 ft^3/lb. At 600 °F, the specific volume of the liquid is 0.0236 ft^3/lb. This is an increase in volume of 8.257% for a 50 °F temperature change. To compress the water by 8.257% (to keep constant volume) would require a pressure increase of (300,000 psi)*(8.257%) = ~25,000 psi. Dividing this by the 50 °F temperature change gives ~500 PSI/°F.
These are rough numbers. The compressibility of water will be nonlinear for large pressure changes. Container thermal expansion and compliance will tend to slightly lower the numbers. At lower temperatures (~100 °F), the numbers work out closer to ~100 psi/°F. Hydrocarbons in schedule 40 carbon steel pipe are ~70 psi/°F.
PS: Try a seach engine like GOOGLE if you are looking for physical properties. I used the search terms "expansion coeeficient diesel" and "bulk modulus diesel" to find these sites
You should also take a look at
The have a lot of info and many good links
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