Discharge of Gases or Vapours from Vessels

A leak with diameter of 0.1 m (leak cross section area 7.85 x 10 m ) occurs in a vessel with a volume of V = 10 m. The vessel is filled with m = 300 kg of ethylene (boiling point — 103.7 °C) at a temperature of T = 290 K. Determine the mass flow rate rii(t) as a function of time. 

In the first place we check whether the pressure ratio is smaller than critical not. According to Eq. (7.22) we have 

The pressure in the vessel is obtained from the equation of state for gases (7.10) 

Since w Wcrit, the discharge is critical. Critical discharge ends at a pressure of 1.76 bar. The storage density of the ethylene is 

The initial mass flow rate is obtained from Eq. (7.23) 

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