The rate of heat transfer in the duct.
The pressure drop in the duct.
Answer to Problem 103P
The rate of heat transfer in the duct is
The pressure drop in the duct is
Explanation of Solution
Determine the inlet density of air.
Here, the inlet pressure of air is
Determine the cross sectional area of duct at inlet.
Here, the diameter of the duct is
Determine the inlet velocity of air.
Here, the mass flow rate of the 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 pressure drop 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
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 30 psia for
Substitute
Substitute
Thus, the rate of heat transfer in the duct is
Substitute
Thus, the pressure drop in the duct is
Want to see more full solutions like this?
Chapter 17 Solutions
Thermodynamics: An Engineering Approach
- For an ideal gas flowing through a normal shock, develop a relation for V2/V1 in terms of k, Ma1, and Ma2.arrow_forwardWhen an airplane is flying at a constant speed relative to the ground, is it correct to say that the Mach number of this airplane is also constant?arrow_forwardAir is cooled as it flows through a 30-cm-diameter duct. The inlet conditions are Ma1 = 1.2, T01 = 350 K, and P01 = 240 kPa and the exit Mach number is Ma2 = 2.0. Disregarding frictional effects, determine the rate of cooling of air.arrow_forward
- 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.arrow_forwardSolve for the ratio of the initial to final speed of sound if an air expands isentropically from 178.04 psia at 207°F to 65psia. Express your answer in 3 decimal places.arrow_forwardCompressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 600 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 150 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit, and the drop in stagnation pressure P01 − P02 during this processarrow_forward
- Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 560 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 300 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit and the drop in stagnation pressure P01 – P02 during this process. Take the properties of air to be k = 1.4, cp = 1.005 kJ/kg·K, and R = 0.287 kJ/kg·K. The Mach number at the duct exit is____ . The drop in stagnation pressure is____ kPa.arrow_forwardCarbon dioxide flows steadily through a varying cross-sectional area duct such as a nozzle shown in fig at a mass flow rate of 3.00 kg/s. The carbon dioxide enters the duct at a pressure of 1400 kPa and 200°C with a low velocity, and it expands in the nozzle to an exit pressure of 200 kPa. The duct is designed so that the flow can be approximated as isentropic. Determine the density, velocity, flow area, and Mach number at each location along the duct that corresponds to an overall pressure drop of 200 kPa.arrow_forwardIs it possible to accelerate a fluid to supersonic velocities with a velocity other than the sonic velocity at the throat? Explainarrow_forward
- how and why the stagnation enthalpy is defined? How does it differ from ordinary static enthalpyarrow_forwardThe Airbus A-340 passenger plane has a maximum takeoff weight of about 260,000 kg, a length of 64 m, a wing span of 60 m, a maximum cruising speed of 945 km/h, a seating capacity of 271 passengers, a maximum cruising altitude of 14,000 m, and a maximum range of 12,000 km. The air temperature at the crusing altitude is about −60°C. Determine the Mach number of this plane for the stated limiting conditions.arrow_forwardAir flowing at 8 psia, 480 R, and Ma1 = 2.0 is forced to undergo a compression turn of 15°. Determine the Mach number, pressure, and temperature of the air after the compression.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY