Thermal Expansion of a trapped fluid with a piston and air chamber
Thermal Expansion of a trapped fluid with a piston and air chamber
(OP)
hi Folks,
I was hoping for some help in a calculation. I have a cylinder with closed ends and a floating piston in the middle. On one side of the piston I have a fluid and on the other side I have air. I will be heating up the cylinder and I would like to calculate how far the piston would travel and also what pressure would be generated. I can calculate how much air pressure will be generated by the piston moving. And I can calculate how far the piston would move due to thermal expansion. At what point would it reach an equilibrium? When the air pressure builds up enough to resist the thermal expansion of the fluid?
Can i use this equation from this post http://www.eng-tips.com/faqs.cfm?fid=1339 "By equating the change in volume of the fluid to the change in volume of the vessel one gets:αfΔT-βΔP=αvΔT+ΔPD/tE" but also add Volume of piston travel to the right side of the equation?
Any help would be appreciated.
I was hoping for some help in a calculation. I have a cylinder with closed ends and a floating piston in the middle. On one side of the piston I have a fluid and on the other side I have air. I will be heating up the cylinder and I would like to calculate how far the piston would travel and also what pressure would be generated. I can calculate how much air pressure will be generated by the piston moving. And I can calculate how far the piston would move due to thermal expansion. At what point would it reach an equilibrium? When the air pressure builds up enough to resist the thermal expansion of the fluid?
Can i use this equation from this post http://www.eng-tips.com/faqs.cfm?fid=1339 "By equating the change in volume of the fluid to the change in volume of the vessel one gets:αfΔT-βΔP=αvΔT+ΔPD/tE" but also add Volume of piston travel to the right side of the equation?
Any help would be appreciated.





RE: Thermal Expansion of a trapped fluid with a piston and air chamber
Consider how the cylinder volume will increase with temperature. This reduces effect of fluid expansion.
Ted
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
1.)If you mean liquid (a fluid can be liquid or gas) and you don't boil the liquid and, if it is almost incompressible and it expands relatively little with temperature, just calculate the pressure using the gas equation.
2.) if the liquid expansion with temperature is significant, just calculate that additional liquid volume then use the gas equation to get pressure.
"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
PV = nZRT where Z is evaluated at T the final temperature, which will be really, really hot.
"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
I think what I want to calculate is what delta V is required so that my oil only builds to 5,000psi, instead of the 10,000psi it would reach at a delta V of zero (trapped volume). I can work backwards from there to work out my air chamber volume. I'm not sure how to work out the delta V.
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
Ted
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
But I feel that is not correct. It doesn't take into account the pressure of the air chamber acting on the oil chamber. For example, in my calculation spreadsheet, if the oil expansion volume is greater than the total volume of the air chamber (piston stroke volume), then I get a negative answer for pressure. When in reality, the air pressure would ramp up to a point that it would resist the thermal expansion of the oil. This is the part that I am struggling with. I need to equate thermal expansion with compressibilty somehow.
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
Ted
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek
RE: Thermal Expansion of a trapped fluid with a piston and air chamber
A subset of this problem is treated in FAQ378-1339: Pressure increase due to thermal expansion of a trapped liquid: what you have to add is the contribution of gas compression. This one may be evaluated as follows:
P1V1/T1=P2V2/T2
where T1=293 °K and T2=414 °K
V2-V1=P1V1T2/P2T1-V1
ΔV=(P1T2/P2T1-1)V1
prex
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RE: Thermal Expansion of a trapped fluid with a piston and air chamber
(continued)
ΔV/V1=P1T2/T1(P1+ΔP)-1
and also, if Vi is the total (initial) volume (liquid plus gas),
ΔV/Vi=(P1T2/T1(P1+ΔP)-1)V1/Vi
Now this quantity may be plugged into the equation in the FAQ above equating the various contributions to the relative change in volume.
However also the contributions αfΔT and βΔP should be factored with Vf/Vi, as the liquid also doesn't occupy the full volume (Vf being the liquid initial volume).
Didn't try it, but I guess this should give a reasonable approximation. Of course the solving equation for ΔP (or in your case for ΔV, as you know the final pressure) is now more complex, due to the strongly non linear nature of the gas law. A numerical approach via Excel or another software should give the result.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads