Concept explainers
Air is heated as it flows through a 6 in × 6 in square duct with negligible friction. At the inlet, air is at T1 = 700 R, P1 = 80 psia, and V1 = 260 ft/s. Determine the rate at which heat must be transferred to the air to choke the flow at the duct exit, and the entropy change of air during this process.
The rate of heat transfer in the duct.
The entropy change in the duct.
Answer to Problem 108P
The rate of heat transfer in the duct is
The entropy change in the duct is
Explanation of Solution
Determine the inlet density of air.
Here, the inlet pressure of air is
Determine the mass flow rate of the duct.
Here, the inlet velocity of air is
Determine the inlet stagnation temperature of air.
Here, the inlet static temperature of ideal gas is
Determine the relation of ideal gas speed of sound at the inlet.
Here, the specific heat ratio of air is
Determine the speed of sound at the inlet.
The inlet velocity of the air flow in the device is
Determine the static temperature in the duct.
Here, the ratio of Rayleigh flow for inlet temperature is
Determine the static pressure in the duct.
Here, the ratio of Rayleigh flow for inlet pressure is
Determine the stagnation temperature in the duct.
Here, the ratio of Rayleigh flow for exit stagnation temperature is
Determine the rate of heat transfer of the duct.
Determine the entropy change of the duct.
Conclusion:
From the Table A-2E, “Ideal-gas specific heats of various common gases” to obtain value of universal gas constant, specific heat of pressure, and the specific heat ratio of air at
Substitute
Substitute
Substitute
Substitute 1.4 for k,
Substitute
Refer to Table A-34, “Rayleigh flow function for an ideal gas with k=1.4”, to obtain the value ratio of static temperature, pressure, and stagnation temperature at
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is ratio of stagnation temperature and Mach number.
Show the Mach number at
S. No |
Mach number |
ratio of stagnation temperature |
1 | ||
2 | ||
3 |
Calculate ratio of static temperature, pressure, and stagnation temperature at
Substitute
From above calculation the ratio of stagnation temperature at
Repeat the Equation (XII), to obtain the value of inlet ratio of static temperature and pressure at
From the Table A-34, “Rayleigh flow function for an ideal gas with k=1.4”, to obtain the value of the outlet ratio of temperature, pressure, and velocity at 1 outlet Mach number as:
Substitute
Substitute 80 psia for
Substitute
Substitute
Thus, the rate of heat transfer in the duct is
Substitute
Thus, the entropy change in the duct is
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Chapter 17 Solutions
Thermodynamics: An Engineering Approach
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