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9 January, 00:22

Air, modeled as an ideal gas, is compresses at steady state from 1 bar, 300 K, to 5 bar, 500K, with 150 kW of power input. Heat transfer occurs at a rate of 20 kW fom the air to cooling water circulating in a water jacket enclosing the compressor. Neglecting kinetic energy and potential energy effects, determine the mass flow rate of the air, in kg/s.

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  1. 9 January, 00:32
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    0.64 Kg/s

    Explanation:

    Given

    -Fluid: Air

    -Inlet 1:

    Pressure P1 = 1 bar

    Temperature T2 = 300 K

    -Exit 2:

    Pressure P2 = 5 bar

    Temperature T2 = 500 K

    -Power input to compressor W = - 150 KW

    -The rate of heat transfer from the air to cooling water circulating in a water jacket enclosing the compressor Q = - 20 KW

    Required:

    -Mass flow rate m [kg/s]

    Assumption:

    -Constant average values

    -Steady flow

    -Kinetic energy effects are ignored

    -Potential energy effects are ignored

    -Ideal gas.

    Solution:

    Energy equation could be defined by.

    Q - W=m[ (h2-h1) + (V_2^2-V_1^2/2) + g (Z_2-Z_1) ]

    As kinetic and potential energy are ignored.

    Q - W=m (h2-h1)

    Specific enthalpy for air at P1 = 1 bar and T2 = 300 K from table

    h1 = 300.1 KJ/Kg

    Specific enthalpy for air at P2 = 5 bar and T2 = 500 K from table

    h2 = 503.2 KJ/Kg

    The mass flow rate could be calculated as following.

    m = Q - W / (h2-h1)

    = 0.64 Kg/s
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