A compressible gas of nitrogen is contained in a tank and is discharged thorough a small convergent nozzle. The pressure at the exit is maintained at \(p_{2}\).

Find the instantaneous discharge rate assuming that the temperature and pressure in the tank are \(p_{1}\) and \(T_{1}\). The nozzle diameter is \(d_{0}\).

Develop a model for the change of mass of gas in the tank as a function of time.