Compressible flow, Through a small tubing

[eightyksi]

I need to solve a problem, where a piston of one small N2 container is pushing the gas to a bigger N2 container, through a tubing 0.5". At first, the pressure of both containers is 1915 psi. Then the piston is compressing the N2 of the smaller container with a speed of 2ft/sec. We are expecting the pressure of the two container increase together. But since the tubing which connects them is so thin, 0.5", could be a design mistake, that the increase of pressure in the bigger container is going to be delayed, or less. How do we model the time history of both pressure. Which formula to use to calculate. Thanks.
And i have get the compressibility factor, which is a formula of pressure, temperature and volume. Where to find it for N2.

 

[imok2]

bolilly
For N2 compressibility factor go to this web page

http://www.burtoncorblin.com/BCTB302.pdf

Roger

 

[imok2]

bolilly, This may be of some help also

http://www.efunda.com/formulae/smc_fluids/venturi_flowmeter.cfm#calc

Roger

 

[katmar]

bolilly,

you have not really given enough information for anyone to give you a definitive answer. What does compressing at 2ft/s mean? Is this the linear velocity of the piston? Is it constant? If so, that is unusual. What is the cross sectional area of the piston?

What is the target final pressure? What are the relative volumes of the cylinders? How long is the 0.5" line? All these things would determine the route by which you would solve the problem.

At 1915 psi and ambient temperature I would neglect the compressibility of nitrogen. Assuming it is ideal is a safer assumption than some of the others you are going to have to make.

If the final pressure is not much higher than 1915 then I would assume incompressible flow (yes, incompressible flow), I would work out an average friction factor and I would make my flow formula as simple as possible. Once you have done the calcs on this simplified basis you can decide whether the situation is critical enough to demand a more rigorous solution.

The basis of all practical engineering design is to learn to know what simplifying assumptions you can make. And the only way to learn this is by doing it.

Sorry that I have more questions than answers!

regards
Katmar

 

[ShaunE]

without getting into complicated formulas, I am not surprised at the effect you are getting:

As the first vessel is compressed a flow is induced into the second vessel due to pressure difference - no problems there.

The pipe which joins the two vessels will have a resistance to flow - especially as it is relatively small also the longer it is the higher the resistance. This resistance will be seen as a back pressure, so the pressure in the first vessel will increase before the second one and may be momentarily higher than expected.

Also there is probably a refrigeration effect. As the gas is compressed the temperature will increase in vessel 1 and heat will be lost through the vessel fabric and through the pipe (does it get hot?). As the gas expands at the pipe exit into the second vessel there will be a pressure drop and a reduction in temperature, hence the second vessel will be momentarily cooled (does it get cold?)and the gas density will be increased / volume reduced and pressure will be less than expected.

However, as the vessels are joined this should all even out eventually - it is a transient effect.

In practical terms you probably need to increase the pipe diameter and keep it as short as possible. Alternatively you could put an expanded polystyrene box around vessel 2 with an access door and an internal light. - perfect beer cooler.

 

[eightyksi]

thank you everyone. Yes, the 2ft/sec is the constant linear velocity of the piston. i have not got all the configuration yet. but the volume of vessel 1 is 52,520 cubic inch, and vessel 246,300 cubic inch. the 0.5" tube, the ID is 0.4". I don't know how long it is. sorry. And i don't think the final pressure is going to get much higher than 1915psi. so maybe incompressive assumption will work. If so, can I use Bernoulli equation? And, Katmar, how to calculate the average friction factor, do they have some tables to search? And, ShaunE, in fact I don't know if vessel 1 will get hotter, and vessel 2 will get cooler. i did not have the measurement. And you are perfectly right, it is a transient effect. And my boss asked me to find out the time history of the pressure change of vessel 1 and vessel 2. I will use a common orifice solution. and try Bernoulli equation. I will let you know how it goes.