Concept explainers
Air enters a nozzle steadily at 50 psia, 140°F, and 150 ft/s and leaves at 14.7 psia and 900 ft/s. The heat loss from the nozzle is estimated to be 6.5 Btu/lbm of air flowing. The inlet area of the nozzle is 0.1 ft2. Determine (a) the exit temperature of air and (b) the exit area of the nozzle.
(a)
The exit temperature.
Answer to Problem 26P
The exit temperature is
Explanation of Solution
Write the energy rate balance equation for one inlet and one outlet system.
Here, the rate of heat transfer is
The air flows at steady state through the nozzle. Hence, the rate of change in net energy of the system becomes zero.
Here, the heat loss from the nozzle is estimated as
There is no heat transfer at inlet i.e.
The Equations (I) reduced as follows to obtain the exit enthalpy.
Here, the heat transfer per mass flow is expressed as,
Substitute
Refer Table A-17E, “Ideal-gas properties of air”.
The inlet enthalpy
Conclusion:
Substitute
Refer Table A-17E, “Ideal-gas properties of air”.
The exit temperature
Write the formula of interpolation method of two variables.
Show the temperature and enthalpy values from the Table A-17E as in below table.
S.No. | x | y |
Enthalpy | Temperature | |
1 | 119.48 | 500 |
2 | 121.2433 | ? |
3 | 124.27 | 520 |
Substitute
Thus, the temperature corresponding to exit enthalpy of
Thus, the exit temperature is
(b)
The exit area of the nozzle.
Answer to Problem 26P
The exit area of the nozzle 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 equation of conservation of mass flow rate.
Here, the cross-sectional area is
Rearrange the Equation (V) to obtain the exit area
Conclusion:
Substitute
Thus, the exit area of the nozzle is
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Chapter 5 Solutions
Thermodynamics: An Engineering Approach
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