pressure transfer formula (high to low)

[microlab]

dear all

i am interested to know about whether any equation is there to find the time required to transfer pressure from a compressed container to an empty container.

i.e. a container with the volume of v1 is filled with air of say 150 PSI. another empty container is attached to it with a volume of v2. if both are connected with a tube with a diameter of x, then is it possible to calculate the time required to fill the second container with 50 PSI. off course the first container is bigger than the second one

regards

ml

 

[WimRFP]

Hello,

Depending on the connection between the two vessels it can be complicated.

In case of very thin/long tube between the vessels, it can be a laminar or turbulent flow in a pipe problem. But most formulas assume incompressible fluid. In case of large pressure drop across the pipe between the vessels, these formulas do not apply (as in your case).

Assuming that the process takes short time, you may assume adiabatic or isentropic expansion/compression. That means that after some time, your 50psi will drop due to heat exchange.

When pipe friction is low (large diameter, short connection between vessels), you may have a choked flow (flow limited by speed of sound). Looking to your pressure ratio 151psi/1psi initial, 150/50 final, you will very likely have a choked flow over the complete air transfer process.

In a choked flow, the low-pressure side doesn't influence the mass flow through the orifice as speed of sound avoids pressure disturbances to be transmitted from the low-pressure side to the high-pressure side. The mass flow from the large vessel to the small vessel depends only on the diameter of the orifice/pipe and input conditions (pressure, density, Cp/Cv ratio). When you assume your main vessel very large, you may assume that the pressure in the main vessel is constant during the filling of the small vessel. This eases the calculation or setting up a simulation model, as you have a constant mass flow during the fill period.

Best is to search for "choked flow" (for example wikipedia).

 

[microlab]

hi

thank you for the reply you must have seen the tyre filling machine
where the compressor pressure is about 150 psi
the car tyre pressure required is 32 psi(for example) the diameter of the tube from the container to the tyre is about 1 cm and about 5 meter long. if the present tyre pressure is 28 psi, then how can we calculate the time required to fill it up to 32 psi ?. can we apply any equation to find the same?

ml

 

[FvM]

In a real setup, the achieved flow can be assumed mostly defined by the tire valve pressure drop and only slightly depend on the
connection tube. It would be rather empirically determined than calculated from a "formula". If you want to calculate it though,
you have to know the exact valve geometry or at least an equivalent orifice diameter for a rough estimation.

The question sounds a lot like a homework problem. In this case, I would expect a clear specification of all conditions.

 

[WimRFP]

Hello,

I agree with FvM, the smallest cross section will be the tire (Schrader) valve, the cross section of the feed tube will be significantly larger. therefore the valve will be the limiting factor (choking will take place in the Schrader valve).

I think that you have to measure the mass flow through the valve at different pressure drop. A primitive means to do this is by discharging into a tube that has a light free moving piston. By determining volume, ambient pressure and temperature, you can determine the mass that has passed during some time.

When you have some figure for that, you need to discuss whether you accept isothermal or (for example) adiabatic conditions for the tire. It is likely that the air that discharges into the tire is below ambient temperature, so after some time the pressure in the tire will be higher.

Added after 15 minutes:

addition:
If you can measure the input mass flow (at the 150psi side), you can discharge a known amount of air in the inflated tire. From the initial and increase pressure you can guess how much air you need to fill to de desired pressure. This eliminates the need to know the valve characteristics. I don't know the spread in pressure you require to open the tire valve (there is a spring in a Schrader valve).