How Can Air Velocity Be Calculated at a Nozzle's End Over Time?

[scientist0523]

Hi,

This is not homework, it's for myself. I'm trying to understand it for me only.

I have a piston that is translating in a cylinder and pushing/sucking air through a nozzle.
It's much comparable to a bicycle pump.
The piston is moving with non-linear (exponential) velocity until it slams against the cylinder wall.

I need a formula to find the air velocity at the end of the nozzle in function of time.

I have tried using Bernoulli's principle, but it does not apply because we are dealing with a compressible flow. And I'm not sure how pressure builds up, as the airflow through the nozzle 'negates' the pressure buildup
Also the volume and position (even velocity?) of the air particles in the cylinder change in time, so that means it's an unsteady flow?
I have looked at the unsteady flow equation but I can't seem to understand it either.

Help is appreciated.

 

[RTW69]

This is not a trivial problem. I would model as a tire pump. Try this link.

http://hep.princeton.edu/~mcdonald/examples/tirepump.pdf

 

[scientist0523]

Thank you very much for this link!
I knew it wasn't easy, but this will help me a lot.

EDIT: as useful as it may be, I'm not looking to pump the air into a tire, but to pump it in the environment with P=atm and so no pressure builds up as it's volume is infinitely big.

 

[scientist0523]

Anyone with more insight of fluid dynamics?