Air is compressed by an adiabatic compressor from 100 kPa and 20°C to 1.8 MPa and 400°C. Air enters the compressor through a 0.15-m2 opening with a velocity of 30 m/s. It exits through a 0.08-m2 opening. Calculate the mass flow rate of air and the required power input.
The mass flow rate of air and required power input.
Answer to Problem 55P
The mass flow rate of air is
The required power input is
Explanation of Solution
Consider the air flows at steady state. Hence, the inlet and exit mass flow rates are equal.
Write the formula for mass flow rate with inlet condition.
Here, the cross sectional area is
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant of air is
Write the formula for exit velocity of the air.
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 compressor. Hence, the rate of change in net energy of the system becomes zero.
Since, the compressor is adiabatic compressor, hence neglect the heat transfer rates. And also neglect the potential energy changes. The work done is on the system (compressor) and the work done by the system is zero i.e.
The Equations (III) reduced as follows to obtain the work input.
Write the formula for change in enthalpy
Substitute
The average temperature of air is calculated as follows.
Refer Table A-2 (b), “Ideal-gas specific heats of various common gases”.
Obtain the specific heat of air at constant pressure
Write the formula of interpolation method of two variables.
Show the temperature and enthalpy values from the Table A-2 (b) as in below table.
S.No. | x | y |
Temperature | Specific heat | |
1 | 450 | 1.020 |
2 | 483 | ? |
3 | 500 | 1.029 |
Substitute
Thus, the specific heat of air at constant pressure
Conclusion:
Substitute
Thus, the mass flow rate of air is
Substitute
Substitute
Thus, the required power input is
Want to see more full solutions like this?
Chapter 5 Solutions
THERMODYNAMICS: AN ENGINEERING APPROACH
- Steam at 1000 kPa, a temperature of 300°C, and a velocity of 50 m/s. The steam leaves the turbine at a pressure of 150 kPa and a velocity of 200 m/s. Determine the work per kg of steam flowing through the turbine, assuming the process to be reversible and adiabatic.arrow_forwardArgon gas enters an adiabatic compressor at 14 psia and 75F with a velocity of 60 ft/s, and it exits at 200 psia and 240 ft/s. If the isentropic efficiency of the compressor is 87 percent, determine (a) the exit temperature of the argon and (b) the work input to the compressor.arrow_forwardSteam enters a turbine steadily at a flow rate of 1 kg/s at 7 MPa and 500 degrees and exits as saturated steam at 40 kPa. If there is a heat loss of 10 kW from the turbine, what will be the power produced by the turbine?arrow_forward
- Air enters the compressor of a gas turbine plant at ambient conditions of 100 kPa and 25 ⁰C with a low velocity and exits at 1 MPa and 347 ⁰C with a velocity of 90 m/s. The compression process is adiabatic, and the power input is 271. Determine the mass flowrate of the air through the compressor.arrow_forwardNitrogen gas is compressed from 80 kPa and 27°C to 480 kPa by a 10-kW compressor. Determine the mass flow rate of nitrogen through the compressor, assuming the compression process to be isentropic.arrow_forwardSteam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 2.7 kg/s and leaves at 20 kPa. If the power output of the turbine is 2.5 MW, determine the temperature of the steam at the turbine exit. Neglect kinetic energy changesarrow_forward
- Air is expanded in an adiabatic turbine of 85 percent isentropic efficiency from an inlet state of 2200 kPa and 300C to an outlet pressure of 200 kPa. Calculate the outlet temperature of air and the work produced by this turbine per unit mass of air.arrow_forwardSteam enters an adiabatic turbine steadily at 7 MPa, 500°C, and 45 m/s and leaves at 100 kPa and 75 m/s. If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine the mass flow rate of steam through the turbine.arrow_forwardRefrigerant-134a at 140 kPa and –10°C is compressed by an adiabatic 1.3-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies, determine the volume flow rate of the refrigerant at the compressor inlet in L/min.arrow_forward
- Refrigerant-134a at 140 kPa and –10°C is compressed by an adiabatic 1.3-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies, determine the isentropic efficiency of the compressor.arrow_forwardRefrigerant-134a enters an adiabatic compressor as saturated vapor at 30 psia at a rate of 20 ft3 /min and exits at 70 psia pressure. If the isentropic efficiency of the compressor is 80 percent, determine the second-law efficiency of the compressor. Assume the surroundings to be at 75°F.arrow_forwardAir is compressed by an adiabatic compressor from 100 kPa and 12°C to a pressure of 800 kPa at a steady rate of 0.2 kg/s. If the isentropic efficiency of the compressor is 80 percent, determine the required power input to the compressor.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