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Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a temperature of 800K pressure of 200kPa and a velocity of 50m/s .It leaves nozzle at a temperature of 650K and a pressure of 100kPa .Heat loss at a constant rate of 25kW takes place from the nozzle to the surroundings. Assume air to behave as an ideal gas with constant Cp value of 1.005kJ/kgK and neglecting potential energy changes the exit velocity of air in m/s is?
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Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a tem...
Given:
- Air flow rate (m_dot) = 1 kg/s
- Initial temperature (T1) = 800 K
- Initial pressure (P1) = 200 kPa
- Initial velocity (V1) = 50 m/s
- Final temperature (T2) = 650 K
- Final pressure (P2) = 100 kPa
- Heat loss rate (Q_dot) = 25 kW
- Specific heat capacity at constant pressure (Cp) = 1.005 kJ/kgK
Assumptions:
- Air behaves as an ideal gas
- Neglecting potential energy changes
The enthalpy change (ΔH) of the air can be calculated using the specific heat capacity at constant pressure (Cp) and the change in temperature (ΔT).
ΔH = Cp * ΔT
ΔT = T2 - T1
Substituting the given values:
ΔT = 650 K - 800 K = -150 K
ΔH = 1.005 kJ/kgK * (-150 K) = -150.75 kJ/kg
The work done (W_dot) by the air can be calculated using the enthalpy change (ΔH) and the mass flow rate (m_dot).
W_dot = m_dot * ΔH
W_dot = 1 kg/s * (-150.75 kJ/kg) = -150.75 kW
The heat loss (Q_dot) from the nozzle to the surroundings is given as 25 kW.
Q_dot = -25 kW (negative sign indicates heat loss)
The change in kinetic energy (ΔKE) of the air can be calculated using the initial and final velocities (V1 and V2).
ΔKE = (1/2) * m_dot * (V2^2 - V1^2)
Let V2 be the unknown final velocity.
Substituting the given values:
1/2 * 1 kg/s * (V2^2 - 50^2) = -150.75 kW - 25 kW
V2^2 - 2500 = -175.75
V2^2 = -175.75 + 2500
V2^2 = 2324.25
V2 = sqrt(2324.25) ≈ 48.2 m/s
The exit velocity of the air from the nozzle is approximately 48.2 m/s.
- Air flow rate (m_dot) = 1 kg/s
- Initial temperature (T1) = 800 K
- Initial pressure (P1) = 200 kPa
- Initial velocity (V1) = 50 m/s
- Final temperature (T2) = 650 K
- Final pressure (P2) = 100 kPa
- Heat loss rate (Q_dot) = 25 kW
- Specific heat capacity at constant pressure (Cp) = 1.005 kJ/kgK
Assumptions:
- Air behaves as an ideal gas
- Neglecting potential energy changes
Step 1: Calculation of Enthalpy Change
The enthalpy change (ΔH) of the air can be calculated using the specific heat capacity at constant pressure (Cp) and the change in temperature (ΔT).
ΔH = Cp * ΔT
ΔT = T2 - T1
Substituting the given values:
ΔT = 650 K - 800 K = -150 K
ΔH = 1.005 kJ/kgK * (-150 K) = -150.75 kJ/kg
Step 2: Calculation of Work Done
The work done (W_dot) by the air can be calculated using the enthalpy change (ΔH) and the mass flow rate (m_dot).
W_dot = m_dot * ΔH
W_dot = 1 kg/s * (-150.75 kJ/kg) = -150.75 kW
Step 3: Calculation of Heat Loss
The heat loss (Q_dot) from the nozzle to the surroundings is given as 25 kW.
Q_dot = -25 kW (negative sign indicates heat loss)
Step 4: Calculation of Change in Kinetic Energy
The change in kinetic energy (ΔKE) of the air can be calculated using the initial and final velocities (V1 and V2).
ΔKE = (1/2) * m_dot * (V2^2 - V1^2)
Let V2 be the unknown final velocity.
Substituting the given values:
1/2 * 1 kg/s * (V2^2 - 50^2) = -150.75 kW - 25 kW
V2^2 - 2500 = -175.75
V2^2 = -175.75 + 2500
V2^2 = 2324.25
V2 = sqrt(2324.25) ≈ 48.2 m/s
Step 5: Answer
The exit velocity of the air from the nozzle is approximately 48.2 m/s.
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Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a tem...
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Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a temperature of 800K pressure of 200kPa and a velocity of 50m/s .It leaves nozzle at a temperature of 650K and a pressure of 100kPa .Heat loss at a constant rate of 25kW takes place from the nozzle to the surroundings. Assume air to behave as an ideal gas with constant Cp value of 1.005kJ/kgK and neglecting potential energy changes the exit velocity of air in m/s is?
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Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a temperature of 800K pressure of 200kPa and a velocity of 50m/s .It leaves nozzle at a temperature of 650K and a pressure of 100kPa .Heat loss at a constant rate of 25kW takes place from the nozzle to the surroundings. Assume air to behave as an ideal gas with constant Cp value of 1.005kJ/kgK and neglecting potential energy changes the exit velocity of air in m/s is? 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 at a flow rate of 1kg/s enters the nozzle of a jet engine at a temperature of 800K pressure of 200kPa and a velocity of 50m/s .It leaves nozzle at a temperature of 650K and a pressure of 100kPa .Heat loss at a constant rate of 25kW takes place from the nozzle to the surroundings. Assume air to behave as an ideal gas with constant Cp value of 1.005kJ/kgK and neglecting potential energy changes the exit velocity of air in m/s is? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air at a flow rate of 1kg/s enters the nozzle of a jet engine at a temperature of 800K pressure of 200kPa and a velocity of 50m/s .It leaves nozzle at a temperature of 650K and a pressure of 100kPa .Heat loss at a constant rate of 25kW takes place from the nozzle to the surroundings. Assume air to behave as an ideal gas with constant Cp value of 1.005kJ/kgK and neglecting potential energy changes the exit velocity of air in m/s is?.
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