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21 September, 12:02

Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10°C, and 100 m/s, and it receives heat as it flows through it. Nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s.

a) Determine the Mach number of the nitrogen at the inlet and the amount of heat received if the exit Mach number is 0.51.

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  1. 21 September, 15:02
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    A) Mach number at Inlet; M1 = 0.292

    B) amount of heat received; Q_in = 105.59 KJ/kg

    Explanation:

    A) The formula for the speed of nitrogen at the inlet is;

    C1 = √kRT1

    Where;

    k is a constant = 1.4

    R is the gas constant of nitrogen R = 296.8 J/kg. K

    T1 is the temperature at inlet = 10°C = 10 + 273 K = 283K

    Thus;

    C1 = √ (1.4 * 296.8 * 283)

    C1 = 342.9 m/s

    Formula for mach number at inlet is;

    M1 = V1/C1

    We are given V1 = 100 m/s

    Thus; M1 = 100/342.9

    M1 = 0.292

    B) We are given mach number at exit; M2 = 0.51

    Also; V2 = 200 m/s

    Thus; M2 = V2/C2

    C2 = V2/M2 = 200/0.51

    C2 = 392.16 m/s

    Now, we know that;

    C2 = √kRT2

    So, 392.16 = √ (1.4 * 296.8 * T2)

    392.16² = 415.52*T2

    T2 = 392.16²/415.52

    T2 = 370.11 K

    Now formula for steady flow balance equation is;

    Q_in = = cp (T2 - T1) + [ (v2) ² - (v1) ²]/2

    Where Q_in is the amount of heat energy received and cp is the specific heat of nitrogen, = 1.040 KJ/kg. K

    Plugging in the relevant values;

    Q_in = 1.04 (370.11 - 283) + [ (200) ² - (100) ²]/2] (1KJ/Kg/1000m²/s²)

    Q_in = 90.59 + 15

    Q_in = 105.59 KJ/Kg
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