Time to compress fluid in cylinder
Time to compress fluid in cylinder
(OP)
I have an application where I need to determine the time needed to compress a gas in a piston cylinder arrangement a given distance (ie. the time for the piston to travel x inches). Would anyone happen to know the methodology and equations used to find this?





RE: Time to compress fluid in cylinder
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"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
On the other hand, the amount of hp required to meet your time requirements is a fluids question that some us might be able to help with if that is part of your question.
David
RE: Time to compress fluid in cylinder
RE: Time to compress fluid in cylinder
RE: Time to compress fluid in cylinder
Time (movement) of the piston is strictly geometrical - as noted above. The gas WILL COMPRESS as the piston moves, it has no choice.
if you have a gas-driving-a-piston, then the time to fill the upper piston will depend on its valve's characteristics, the length and diameter and umber of bends in connecting piping, and the relative sizes of the piston and initial gas flow.
Give us a drawing of your piston's driving mechanism - Your replies, unfortunately, are not yet clear to those of us reading them.
RE: Time to compress fluid in cylinder
RE: Time to compress fluid in cylinder
israelkk you're saying the same thing as everyone else. Once you write the dV/dt function, you know the time it takes and all you have to do (with an ideal gas) is to use V1 P1/V2 to get the pressure P2.
If you have the power available to reach P2, its just a matter of driver rpm and geometry.
BTW BYX are you a student? This doesn't sound like a real-world question.
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
Bottom line is that you are not going to do gas compression with a spring.
David
RE: Time to compress fluid in cylinder
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
In actuality, the gas would heat up as it is compressed, which would throw the results off some. It's been a while since I took thermodynamics, though, and I'd have to hunt up how to figure that heating, or even if it is a specific amount.
RE: Time to compress fluid in cylinder
T(out)=T(in)*(K(out)/P(in)^((k-1)/k)
all temperatures and pressures are in absolute units. "k" is the ratio of specific heats.
David
RE: Time to compress fluid in cylinder
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
David
RE: Time to compress fluid in cylinder
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
P2 = (P1V1)/(V2)
P2 = F2/A
F2/A = {P1V1)/(V2)
F2 = (m of piston)*(acceleration of piston) = m*a
(m*a)=(P1*V1*A)/(V2)
a = P1*V1*A/(V2*m)
(dU/dt) = P1*V1*A/(V2*m)
dU = int(P1*V1*A/(V2*m) dt)
U = (P1*V1*A*t)/(V2*m)
(dx/dt) = (P1*V1*A*t)/(V2*m)
x = int((P1*V1*A*t)/(V2*m)dt)
x = (P1V1A*t^2)/(2*V2*m)
t = sqrt[(x*2*V2*m)/(P1*V1*A)]
this does NOT take into account friction from the piston walls, compressibility, temperature, etc. etc.
-Mike
RE: Time to compress fluid in cylinder
F2 = m * a is an instaneous force, yet P1, V1 and V2 are descrete values at two different times t0 and t1.
Even if you let F2 be the average force and a be the average accelaration, you must know the amount of time passed between having V1 and V2.
Bringing us back to, if you know the length of time between t0 and t1, why are you trying to solve for it? Which BTW I don't think you ever do.
U seems to be a bit of a red herring.
But getting back to the problem, here's velocity again in the form of dx/dt. This integral must be evaluated over dt, so oops, if we don't know t0 and t1, how can we integrate?
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"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
-Mike
RE: Time to compress fluid in cylinder
I would run the calculations across a row in a spreadsheet with dt in the first column. Next columns, put pressure, temperature, piston pressure load, piston spring load, calculate acceleration, calculate velocity, calculate position, calculate new fluid properties, etc...
This is essentially the Simpson rule, though you'll find you can often do some averaging, so you essentially turn the integration into a trapazoidal rule.
Make a bunch of graphs that show the location of the piston, velocity, etc...
Make dt a variable, then change it, making it smaller. You should find that for too large a value of dt, the piston location and velocity are completely eratic. As you make the dt variable smaller and smaller, the graphs all stop changing. You're done.
I'd be interested in seeing how others approach this problem.
RE: Time to compress fluid in cylinder
Using spreadsheet for numerical integration is limited to the maximum number of cells in a columns. A problem such that may need more integration steps than the number of cells in a columns.
RE: Time to compress fluid in cylinder
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Time to compress fluid in cylinder
put a fork in this thread
-Mike