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Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.?
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Air enters an insulated diffuser operating at steady state with the pr...
Air Flow in an Insulated Diffuser
Given:
- Inlet pressure (P1) = 0.7 bar
- Inlet temperature (T1) = 5.7 °C
- Inlet velocity (V1) = 200 m/s
- Exit pressure (P2) = 1 bar
- Exit flow area (A2) = 1.2 times the inlet flow area (A1)
- Specific heat capacity at constant pressure (CP) = 1.005 kJ/kg·K
- Gas constant (R) = 0.287 kJ/kg·K
Assumptions:
- Steady-state operation
- Negligible potential energy effects
Solution:
Step 1: Convert units
- Convert the inlet pressure from bar to Pa: P1 = 0.7 * 10^5 Pa
- Convert the inlet temperature from °C to K: T1 = 5.7 + 273.15 K
Step 2: Calculate properties at the inlet
- Calculate the specific gas constant (R): R = CP - CP / γ
- Calculate the gas constant for air (R): R = 0.287 kJ/kg·K
- Calculate the specific heat capacity at constant volume (CV): CV = CP - R
- Calculate the specific heat ratio (γ): γ = CP / CV
- Calculate the density at the inlet (ρ1): ρ1 = P1 / (R * T1)
- Calculate the mass flow rate (m): m = ρ1 * A1 * V1
Step 3: Apply the conservation equations
- Apply the mass flow rate equation: m = ρ2 * A2 * V2
- Rearrange the equation to solve for the exit velocity (V2): V2 = (m) / (ρ2 * A2)
Step 4: Calculate properties at the exit
- Calculate the density at the exit (ρ2): ρ2 = (m) / (A2 * V2)
- Calculate the exit temperature (T2): T2 = T1 + (V1^2 - V2^2) / (2 * CP)
- Calculate the exit velocity (V2): V2 = (m) / (ρ2 * A2)
Step 5: Calculate the exit temperature and velocity
- Substitute the values into the equations:
- V2 = (m) / (ρ2 * A2)
- ρ2 = (m) / (A2 * V2)
- T2 = T1 + (V1^2 - V2^2) / (2 * CP)
Step 6: Evaluate the equations
- Substitute the known values into the equations and solve for the unknowns:
- A2 = 1.2 * A1
- V1 = 200 m/s
- P1 = 0.7 bar
- T1 = 5.7 °C
- CP = 1.005 kJ/kg·K
- R = 0.287 kJ/kg·K
Step 7:
Given:
- Inlet pressure (P1) = 0.7 bar
- Inlet temperature (T1) = 5.7 °C
- Inlet velocity (V1) = 200 m/s
- Exit pressure (P2) = 1 bar
- Exit flow area (A2) = 1.2 times the inlet flow area (A1)
- Specific heat capacity at constant pressure (CP) = 1.005 kJ/kg·K
- Gas constant (R) = 0.287 kJ/kg·K
Assumptions:
- Steady-state operation
- Negligible potential energy effects
Solution:
Step 1: Convert units
- Convert the inlet pressure from bar to Pa: P1 = 0.7 * 10^5 Pa
- Convert the inlet temperature from °C to K: T1 = 5.7 + 273.15 K
Step 2: Calculate properties at the inlet
- Calculate the specific gas constant (R): R = CP - CP / γ
- Calculate the gas constant for air (R): R = 0.287 kJ/kg·K
- Calculate the specific heat capacity at constant volume (CV): CV = CP - R
- Calculate the specific heat ratio (γ): γ = CP / CV
- Calculate the density at the inlet (ρ1): ρ1 = P1 / (R * T1)
- Calculate the mass flow rate (m): m = ρ1 * A1 * V1
Step 3: Apply the conservation equations
- Apply the mass flow rate equation: m = ρ2 * A2 * V2
- Rearrange the equation to solve for the exit velocity (V2): V2 = (m) / (ρ2 * A2)
Step 4: Calculate properties at the exit
- Calculate the density at the exit (ρ2): ρ2 = (m) / (A2 * V2)
- Calculate the exit temperature (T2): T2 = T1 + (V1^2 - V2^2) / (2 * CP)
- Calculate the exit velocity (V2): V2 = (m) / (ρ2 * A2)
Step 5: Calculate the exit temperature and velocity
- Substitute the values into the equations:
- V2 = (m) / (ρ2 * A2)
- ρ2 = (m) / (A2 * V2)
- T2 = T1 + (V1^2 - V2^2) / (2 * CP)
Step 6: Evaluate the equations
- Substitute the known values into the equations and solve for the unknowns:
- A2 = 1.2 * A1
- V1 = 200 m/s
- P1 = 0.7 bar
- T1 = 5.7 °C
- CP = 1.005 kJ/kg·K
- R = 0.287 kJ/kg·K
Step 7:
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Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.?
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Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.?.
Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.?.
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Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.?, a detailed solution for Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? has been provided alongside types of Air enters an insulated diffuser operating at steady state with the pressure of 0.7 bar a temperature of 5.7 degree Celsius and a velocity of 200 metre per second at the the exit the pressure is 1 bar the exit flow area is 20% greater than the the inlet flow area potential energy effects can be neglected. Determine the air exit temperature and the velocity take CP 1.005 kilo joule per kg Kelvin and R 0.287 kilo joule per kg Kelvin.? theory, EduRev gives you an
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