The velocity of the oxygen at nozzle exit by treating the oxygen as an ideal gas and using enthalpy departure charts.
Answer to Problem 77P
The exit velocity of the nozzle by treating the oxygen as an ideal gas is
The exit velocity of the nozzle by using enthalpy departure charts is
Explanation of Solution
Write the general formula energy balance equation for closed system.
Here, rate of energy transfer into the system is
At the steady state, the rate of change of net energy of the system is zero.
Since the inlet velocity is negligible and the Equation (I) is rewritten as follows for the nozzle.
Here, inlet velocity is
Write the formula for change in entropy equation
Here, universal gas constant is
Write the change in enthalpy equation per mole basis.
Here, Ideal enthalpy at final state is
Write the formula for change in enthalpy equation in mass basis.
Here, molar mass is
Calculate the reduced temperature
Here, critical temperature is
Calculate the reduced pressure
Here, critical pressure is
Calculate the reduced temperature
Here, critical temperature is
Calculate the reduced pressure
Here, critical pressure is
Write the formula for change in enthalpy
Here, change in enthalpy of ideal gas is
Refer Table A-19E, “Ideal properties of oxygen”.
The inlet enthalpy
Refer table A-1E, “Molar mass, gas constant and critical properties table”.
The molar mass of oxygen is
The critical temperature of oxygen is
The critical pressure of oxygen is
The gas constant of oxygen is
Conclusion:
Substitute
Refer Table A-19E, “Ideal properties of oxygen”.
The exit enthalpy
Substitute
Substitute
Equation (V).
Substitute
Thus, exit velocity of the nozzle by treating the oxygen as an ideal gas is
Substitute 1060 R for
Substitute
Refer the table A-15E, “Nelson-Obert generalized compressibility chart”.
Obtain the enthalpy departure factor
Substitute 802 R for
Substitute
Refer the table A-15E, “Nelson-Obert generalized compressibility chart”.
Obtain the enthalpy departure factor
Substitute
Substitute
Thus, the exit velocity of the nozzle by using enthalpy departure charts is
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Chapter 12 Solutions
Thermodynamics: An Engineering Approach
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