A make-up air system providing near neutral dehumidified air to the building. Calculate the following and make sure that all answers are in SI units.
P = 1 atm
T1 = 80 F
Relative Humidity of 70%
T2 = 40 F
T3 = 60 F
I. Mass flow rate of dry air entering
II. Mass flow rate of condensate
III. Volumetric flow rate of condensate
IV. Dew point temperature at T3
V. Rate of heat transfer to the chilled water coil
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To calculate the requested values, we will use the psychrometric chart and the following formulas:
I. Mass flow rate of dry air entering:
We can assume that the relative humidity is constant throughout the process. From the psychrometric chart, we can find the saturated vapor pressure (Pv1) at T1 and the saturated vapor pressure (Pv2) at T2.
Pv1 = 0.3809 * 10^(7.5 * T1 / (T1 + 237.3)) = 0.3809 * 10^(7.5 * 80 / (80 + 237.3)) = 3.321 kPa
Pv2 = 0.3809 * 10^(7.5 * T2 / (T2 + 237.3)) = 0.3809 * 10^(7.5 * 40 / (40 + 237.3)) = 0.6369 kPa
The mass flow rate of dry air (M_dot) can be calculated using the formula:
M_dot = (P - Pv1) / ((R_a/M_a) * T1) = (P - Pv1) / ((287.1 / 0.02897) * (T1 + 273.15))
Plugging the values, we get:
M_dot = (101.325 - 3.321) / ((287.1 / 0.02897) * (80 + 273.15)) = 1.917 kg/s (approx.)
II. Mass flow rate of condensate:
The mass flow rate of condensate (M_c) is given by:
M_c = (Pv1 - Pv2) / ((R_v/M_v) * (T2 - T3))
Plugging the values, we get:
M_c = (3.321 - 0.6369) / ((461.5 / 0.018) * (40 - 60)) = 0.001213 kg/s (approx.)
III. Volumetric flow rate of condensate:
The volumetric flow rate of condensate (V_c) can be calculated using:
V_c = M_c / ρ_v
Where ρ_v is the density of condensate, which can be assumed as 1000 kg/m³.
V_c = 0.001213 / 1000 = 1.213 x 10^(-6) m³/s (approx.)
IV. Dew point temperature at T3:
The dew point temperature (T_dp) at T3 can be determined by finding the intersection of the constant relative humidity line at 70% and the temperature line at T3 on the psychrometric chart.
From the chart, we can estimate that the dew point temperature at T3 is approximately 52°F.
V. Rate of heat transfer to the chilled water coil:
The rate of heat transfer (Q) to the chilled water coil can be calculated using the formula:
Q = M_dot * (h1 - h2)
Where h1 is the enthalpy at T1 and h2 is the enthalpy at T2. From the psychrometric chart, we can find the enthalpy values.
h1 = 30 Btu/lb
h2 = 16 Btu/lb
The conversion factor from Btu to J is 1055.06 J/Btu.
Q = (1.917 kg/s) * (30 - 16) Btu/lb * (1055.06 J/Btu) / (2.20462 lb/kg) = 25006.75 J/s (approx.)
Q = 25.00675 kW (approx.)
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