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.

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.