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18 September, 08:01

2.73 A fan within an insulated duct delivers moist air at the duct exit at 358C, 50% relative humidity, and a volumetric flow rate of 0.4 m3 / s. At steady state, the power input to the fan is 1.7 kW. The pressure in the duct is nearly 1 atm throughout. Using the psychrometric chart, determine the temperature, in 8C, and relative humidity at the duct inlet.

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  1. 18 September, 08:43
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    Temperature at 8C = 32 °C * 8 = 256

    Relative humidity is = 60% * 8 of 256°C accordingly.

    Explanation:

    Considering the volumetric flow rate = 0.4 m³/s

    Moist air delivered (Temperature T1 = 358 C)

    With Relative humidity at duct outlet = 50%

    Power input at steady rate = 1.7 KW

    Pressure in the duct = 1 atmosphere

    Temperature at 8C = ?

    Relative humidity at the duct inlet = ?

    Recalling that the value for specific enthalpy and specific volume is

    Specific Enthalpy = h1 = 81 kj/kilogram of dry air

    and Specific Volume = v1 = 0.9 m³/kg

    Now, recalling the formula for mass flow rate,

    We have, m = Volumetric flow rate / Specific volume

    Therefore, 0.4 m³/s : 0.9 m³/kg

    = 0.44 kilogram / second

    Recalling the enthalpy at inlet,

    we have, h2 = h1 - p/m

    Where h1 = Specific enthalpy

    p = power input at steady rate

    m = calculated mass flow rate

    Now, if we substitute the values into the equation,

    we have h2 = 81 kj/kilogram of dry air - 1.7 KW / 0.44 kilogram / second

    h2 = 77.175 kj / kilogram of dry air.

    Therefore, the properties of air at constant absolute humidity and specific enthalpy is 77.175 kj/kg.

    Temperature at 8C = 32 °C * 8 = 256

    Relative humidity is = 60% * 8 of 256°C accordingly.
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