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Thermodynamics of Varying Stations

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Air flows through the converging-diverging nozzle. The conditions at the inlet side are at standard atmospheric conditions, while the density and the temperature at station B is 0.060 lbm/ft3 and 30.5 degree Fahrenheit. Also, the density at station C is 0.050 lbm/ft3, with the velocity at station A recorded to be at 380 ft/s. Determine the following, assuming ideal gas conditions and isentropic process:

a) Mass Flow of air
b) The velocity of stations B and C
c) The pressure at station B and C
d) The changes in internal energy, enthalpy, kinetic energy and potential energies.

Draw a diagram of the converging-diverging nozzle, where the diameter at station
A=5 in, B=2 in, and the diameter at station C=6 in.

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Solution Preview

Please see the attachment for the full breakdown of the solutions of the thermodynamics affecting varying stations.

Converging-diverging nozzle

First off all, I have to specify that I prefer to work in SI units. I don't think that it is a problem to convert the SI units in English-American ones.

a) The inlet conditions are the standard atmospheric conditions, which means
From here, we can get the density at inlet station, by applying the ideal gas law:
where R = the gas constant (in our case, this is the air thermodynamic constant).
The general formula for computing the gas constant is the following:
where  = the universal gas constant, which is  = 8.314 kJ/kmol.K
M = the molecular weight of the gas, which is M = 29 kg/kmol (for air)

As a result, the air constant will be:

Solution Summary

The answer addresses the mass flow of air, velocity and pressure of varying stations, and the changes in energy.