In this problem a cold gas thruster is studied. The total temperature and the total pressure in the cold gas tank are ke

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In this problem a cold gas thruster is studied. The total
temperature and the total pressure in the cold gas tank are kept as
variables. We are searching for the time it will take to eject 150
kg of mass out of the tank. Use the assumptions discussed in class,
i.e, nozzle exit pressure is as same as the atmospheric pressure,
the process throughout the thruster is adiabatic, the flow in the
nozzle is isentropic, and the process in the tank is isentropic.
Use Nitrogen, R=297 J/kg.K, γ = 1.4 as the propellant gas.
Calculate the run time to eject 150 kg of mass
Initial conditions are given as:
Tank initial total pressure = 40 MPa,
Tank initial total temperature = 298.15 K,
Thruster efficiency, λ=0.98,
Patm = 997.8 Pascal,
Nozzle throat diameter = 0.5 cm,
Nozzle exit diameter = 2.5 cm,
Total pressure after the valve, total pressure of the nozzle
stagnation chamber, Pc=1.29 MPa,
Tank volume =0.3735 m3 .