Check Valve Switch flow calculation

Hi,

I have a check valve (air) that I would like to compute the air flow at which the check valve is activated. It is used to maintain a safe level of vacuum in a system. The valve is normally closed (no air flow) and it is open when the pressure on both sides is equal (vacuum). The spring constant is known so are the diameter on both inlet/outlet orifices. I have no instruments to establish the flow so I would like to solve it mathematically. Any reference, examples will be greatly appreciated.

Please help.

I didn't find the right solution from the Internet.

References:

https://www.engineersedge.com/engineering-forum/showthread.php/5206-Check-Valve-Switch-flow-calculation

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Thanks