*According to these variable, ı need to know some equations or solution methods.
This is not a simple problem - I'm not going to look up all the formulas, but here's the solution method I've used.
First, if P1 is more than twice P2, you get a break because flow will achieve sonic velocity in the valve throat, so the velocity of the gas will be the speed of sound at the narrowest part of the orifice.
Speed of sound is a function of density, which is a function of pressure. So you work it out as an integral from P1 down to 2*P2.
Or, you can use a spreadsheet. Figure P1 causes mass flow dm out of the orifice for time dT, then figure a new P1 based on the mass left in the pipe. Then do it again.
Then, when the pressure in the pipe = 2*P2, use a standard pressure drop calculation for flow through the valve & pipe. Flow will then be a fuction of the square root of pressure & either integrate or use the spreadsheet to step through it.
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