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Gas tank discharging

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Old   September 5, 2015, 04:49
Default Gas tank discharging
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I think the gas tank discharging were highly studied. But I am still confused when I count the number of equations and the number of unknowns.
Problem: Having known pressure and temperature of gas into the tank find their variation versus time if the tank discharges in atmosphere through a small hole.
1. Mass conservation (continuity equation)
2. Momentum conservation( Euler or Bernoulli equation)
3. Energy conservation
4. Gas state equation
3 parameters inside the tank: pressure temperature and density
3 parameters at the hole; velocity, temperature and density
1. the pressure at hole is assumed to be equal with atmospheric pressure
2. The state equation is counted twice; inside the tank and at the hole

Conclusion; 5 equation and 6 unknowns
Could you tell me what I am misiing?
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Old   July 12, 2016, 13:32
Default Equation for the discharge from the orifice
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I think you are missing the equation which correlates the orifice (hole) discharge rate to the tank pressure.
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compressible flow, discharge coefficient, discharging, one dimensional flow

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