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A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 15 kW. The inlet and Outlet velocities of air are 100 m/s and 150 m/s respectively. Find the exit air temperature, Assuming adiabatic conditions . Take Cp of air is 1.005 KJ / kg-k .?
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A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 1...
Problem Statement


A blower handles 1 kg/s of air at 20 degree Celsius and consumes a power of 15 kW. The inlet and outlet velocities of air are 100 m/s and 150 m/s, respectively. Find the exit air temperature, assuming adiabatic conditions. Take Cp of air is 1.005 KJ/kg-K.

Solution


Assumptions


  • Adiabatic conditions

  • Steady-state operation

  • Negligible changes in potential energy

  • Negligible changes in kinetic energy



Calculations


  • Mass flow rate (m) = 1 kg/s

  • Inlet temperature (T1) = 20 degree Celsius = 293 K

  • Inlet velocity (V1) = 100 m/s

  • Outlet velocity (V2) = 150 m/s

  • Power consumed (W) = 15 kW

  • Specific heat capacity (Cp) = 1.005 KJ/kg-K

  • Assuming adiabatic conditions, the heat transfer (Q) is zero

  • The change in enthalpy (ΔH) of the air can be calculated using the following formula:

    ΔH = W/m = Cp * (T2 - T1)

    where T2 is the exit temperature of the air.

  • Substituting the given values:

    ΔH = 15,000 / 1 = 15,000 J/s

    Cp = 1.005 KJ/kg-K

    T1 = 293 K

    ΔH = Cp * (T2 - T1)

    15,000 = 1.005 * (T2 - 293)

    T2 = 307.96 K



Results

The exit air temperature is 307.96 K or 34.81 degree Celsius.

Explanation


This problem is related to the thermodynamics of a blower. The blower takes in a certain mass of air at a given temperature and velocity, and expels it at a higher velocity and an unknown temperature. The problem assumes adiabatic conditions, which means that there is no heat transfer between the air and its surroundings. Therefore, the energy balance of the air can be expressed as the change in enthalpy. Enthalpy is a measure of the total energy of a system, and it includes the internal energy, pressure, and volume. The change in enthalpy of the air is equal to the work done by the blower. The specific heat capacity (Cp) of air is required to calculate the change in enthalpy. Cp is a measure of the heat required to raise the temperature of a unit mass of a substance by one degree Celsius. Finally, the exit temperature of the air can be calculated using the change in enthalpy and the Cp
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A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 1...
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A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 15 kW. The inlet and Outlet velocities of air are 100 m/s and 150 m/s respectively. Find the exit air temperature, Assuming adiabatic conditions . Take Cp of air is 1.005 KJ / kg-k .?
Question Description
A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 15 kW. The inlet and Outlet velocities of air are 100 m/s and 150 m/s respectively. Find the exit air temperature, Assuming adiabatic conditions . Take Cp of air is 1.005 KJ / kg-k .? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 15 kW. The inlet and Outlet velocities of air are 100 m/s and 150 m/s respectively. Find the exit air temperature, Assuming adiabatic conditions . Take Cp of air is 1.005 KJ / kg-k .? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Blower Handles 1 kg/s of Air at 20 Degree C and Consume a power of 15 kW. The inlet and Outlet velocities of air are 100 m/s and 150 m/s respectively. Find the exit air temperature, Assuming adiabatic conditions . Take Cp of air is 1.005 KJ / kg-k .?.
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