GATE 2009 AEROSPACE ENGINEERING (Q 21-30)

  1. An ideal axial compressor is driven by an ideal turbine across which the total temperature ratio is 0.667. If the total temperature at turbine inlet is T0 = 1500 K and specific heat of gas cp= 1 kJ/kg/K, the power drawn by the compressor per unit mass flow rate of air is approximately,
    1. 300 kW/kg/s
    2. 1000 kW/kg/s
    3. 600 kW/kg/s
    4. 500 kW/kg/s

    Answer:- 500 kW/kg/s

    The units of the cp are wrong. It should be 1 kJ/kgK.

    For ideal axial compressor and turbine system,

    Power required by the compressor = Power extracted by the turbine

    = cp(T01-T02) (T01 = Turbine inlet temperature T02 = Turbine exit temperature)

    = cp*T01[1-(T02/T01)]

    = 1*1500(1-0.667)

    = 499.5 kW/kg/s ~ 500kW/kg/s

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