Air is heated as it flows subsonically through a duct. When the amount of heat transfer reaches 67 kJ/kg, the flow is observed to be choked, and the velocity and the static pressure are measured to be 680 m/s and 270 kPa. Disregarding frictional losses, determine the velocity, static temperature, and static pressure at the duct inlet.
The static temperature in the duct.
The static pressure in the duct.
The velocity in the duct.
Answer to Problem 100P
The static temperature in the duct is
The static pressure in the duct is
The velocity in the duct is
Explanation of Solution
Determine the speed of sound at the exit.
The exit velocity of the air flow in the device is
Determine the relation of ideal gas speed of sound at the exit.
Here, the specific heat ratio of air is
Determine the exit stagnation temperature of air.
Here, the exit static temperature of ideal gas is
Determine the inlet stagnation temperature from energy equation.
Here, the heat transfer to the duct is
Determine the stagnation temperature ratio at the inlet.
Here, the maximum value of stagnation temperature 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 velocity in the duct.
Here, the ratio of Rayleigh flow for inlet velocity is
Conclusion:
From the Table A-2, “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 1 for
Substitute 1.400 for k,
Substitute
Substitute
Substitute
Refer to Table A-34, “Rayleigh flow function for an ideal gas with k=1.4”, to obtain the value inlet Mach number 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 ratio of stagnation temperature at
S. No |
ratio of stagnation temperature |
Mach number |
1 | ||
2 | ||
3 |
Calculate inlet Mach number at
Substitute
From above calculation the inlet Mach number at
Repeat the Equation (IX), to obtain the value of inlet ratio of temperature, pressure, and velocity at 0.7778 inlet Mach number as:
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 1151 K for
Thus, the static temperature in the duct is
Substitute 270 kPa for
Thus, the static pressure in the duct is
Substitute
Thus, the velocity in the duct is
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Chapter 17 Solutions
Thermodynamics: An Engineering Approach
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