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7 October, 20:57

Two airstreams are mixed steadily and adiabatically. The first stream enters at 35°C and 30 percent relative humidity at a rate of 15 m3/min, while the second stream enters at 12°C and 90 percent relative humidity at a rate of 25 m3/min. Assuming that the mixing process occurs at a pressure of 90 kPa, determine the specific humidity, the relative humidity, the dry-bulb temperature, and the volume flow rate of the mixture. Use data from the tables.

a) The specific humidity is __kg H2O/kg dry air.

b) The relative humidity is __ %.

c) The dry-bulb temperature is __ °C.

d) The volume flow rate of the mixture is __m3/min.

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  1. 7 October, 22:27
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    a) The specific humidity is _0.00881_kg H2O/kg dry air.

    b) The relative humidity is _59.8_ %.

    c) The dry-bulb temperature is _20.2_ °C.

    d) The volume flow rate of the mixture is _39.77_m3/min

    Explanation:

    First let determine the enthalpy h1 and absolute humidity W1 from the psychometric chart using temperature T1 = 35°C and relative humidity Q1 = 30%

    h1 = 62.2kJ/kg

    V1 = 0.89m³/kg

    W1 = 0.01054

    The volume flow rate V'1 = 15m³/min, the mass flow rate m'1 is,

    m'1 = V'1/v1 = 15/0.89 = 16.85kg/min

    Also, From temperature T2 = 12°C and relative humidity Q2 = 90% and volume flow rate V'2 = 25m³/min

    h2 = 31.9kJ/kg

    V2 = 0.82m³/kg

    W2 = 0.00785

    the mass flow rate m'2is,

    m'2 = V'2/v2 = 25/0.82 = 30.49kg/min

    To get the absolute humidity W3 and the enthalpy h3,

    m'1/m'2 = (W2-W3) / (W3-W1)

    16.85/30.49 = (0.00785-W3) / (W3-0.01054)

    0.5526 (W3-0.01054) = (0.00785-W3)

    0.5526W3 - 0.00582 = 0.00785-W3

    0.5526W3 + W3 = 0.00785 + 0.00582

    1.5526W3 = 0.01367

    W3 = 0.01367/1.5526 = 0.00881

    absolute humidity W3 = 0.00881

    m'1/m'2 = (h2-h3) / (h3-h1)

    16.85/30.49 = (31.9 - h3) / (h3 - 62.2)

    0.5526 (h3 - 62.2) = (31.9 - h3)

    0.5526h3 - 34.37 = 31.9 - h3

    0.5526h3 + h3 = 31.9 + 34.37

    1.5526h3 = 66.27

    h3 = 66.27/1.5526 = 42.68kJ/kg

    enthalpy h3 = 42.68kJ/kg

    Use W3 and h3 to determine temperature T3, relative humidity Q3 and and specific volume V3 all through psychometric chart

    T3 = 20.2°C

    Q3 = 59.8%

    V3 = 0.84m³/kg

    By last of mass conversations, we can determine m3,

    m3 = m1 + m2

    m3 = 16.85 + 30.49 = 47.34kg/min

    Then, the volume flow rate V'3 can be found by,

    V'3 = m3*V3

    V'3 = 47.34*0.84 = 39.77m³/min.

    volume flow rate V'3 = 39.77m³/min.
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