Carbon dioxide enters an adiabatic nozzle steadily at 1 MPa and 500°C with a mass flow rate of 6000 kg/h and leaves at 100 kPa and 450 m/s. The inlet area of the nozzle is 40 cm2. Determine (a) the inlet velocity and (b) the exit temperature.
(a)
The inlet velocity.
Answer to Problem 32P
The inlet velocity is
Explanation of Solution
The carbon dioxide flows through the nozzle at steady state. Hence, the inlet and exit mass flow rates are equal.
Write the formula for specific volume
Here, the gas constant of carbon dioxide is
Write the formula for mass flow rate.
Here, the cross-sectional area is
Rearrange the Equation (II) to obtain the inlet velocity
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant of carbon dioxide is,
Conclusion:
Substitute
Equation (I).
Substitute
Thus, the inlet velocity is
(b)
The exit temperature.
Answer to Problem 32P
The exit temperature is
Explanation of Solution
Write the energy rate balance equation.
Here, the rate of energy transfer in by heat, work and mass is
Here, the nozzle operates at steady state. Hence, the rate of change in internal, kinetic, potential, etc. energies becomes zero.
The rate of energy transfer in
The rate of energy transfer out
Here, the rate of heat transfer is
Here, the nozzle has one inlet and one outlet. Say inlet condition as 1 and outlet condition as 2 as follows.
Since, the nozzle is adiabatic nozzle, the heat transfer rate and work transfer rates are negligible i.e.
The Equations (V) and (VI) are reduced to as follows.
Substitute
Equation (IV).
Refer Table A-20, “Ideal-gas properties of carbon dioxide,
The enthalpy in molar basis is as follows,
Here, the molar mass of carbon dioxide is
Substitute
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The molar mass of carbon dioxide is,
Refer Table A-20, “Ideal-gas properties of carbon dioxide,
The inlet enthalpy
Write the formula of interpolation method of two variables.
Show the temperature and enthalpy values from the Table A-20 as in below table.
S.No. | x | y |
Temperature | Enthalpy | |
1 | 770 | 30644 |
2 | 773 | ? |
3 | 780 | 31154 |
Substitute
Thus, the enthalpy
Conclusion:
Substitute
Refer Table A-20, “Ideal-gas properties of carbon dioxide,
The temperature corresponding to exit enthalpy of
Show the enthalpy and temperature values from the Table A-20 as in below table.
S.No. | x | y |
Enthalpy | Temperature | |
1 | 26138 | 680 |
2 | 26422.4436 | ? |
3 | 26631 | 690 |
Substitute
Thus, the temperature corresponding to exit enthalpy of
Thus, the exit temperature is
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Chapter 5 Solutions
THERMODYNAMICS: AN ENGINEERING APPROACH
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