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Mixing Humid Air

Reference data and engineering information about mixing humid air for air psychrometrics applications.

mixinghumidair

Overview

Engineering reference data for Mixing Humid Air in air psychrometrics.

Key Formulas

Humidity Ratio

ω=0.622PvPa\omega = 0.622 \frac{P_v}{P_a}

Mass of water vapor per mass of dry air.

Relative Humidity

ϕ=PvPvs×100%\phi = \frac{P_v}{P_{vs}} \times 100\%

Ratio of actual to saturation vapor pressure.

Wet Bulb Temperature

Twb=Tdb−Pvs−PvγT_{wb} = T_{db} - \frac{P_{vs} - P_v}{\gamma}

Temperature measured by wet-bulb thermometer.

Enthalpy of Moist Air

h=cpT+ωhgh = c_p T + \omega h_g

Sensible + latent heat per unit mass of dry air.

Variables

SymbolDescriptionUnit
ω\omegaHumidity ratiokg/kg
ϕ\phiRelative humidity%
PvP_vVapor pressurePa
PvsP_{vs}Saturation vapor pressurePa
TdbT_{db}Dry bulb temperature°C
TwbT_{wb}Wet bulb temperature°C

Examples

Example 1: Mixing Point Above the Saturation Line (No Fog)

1 kg of air at 25 °C and 50% relative humidity (C) is mixed with 1 kg of air at -5 °C and 80% relative humidity (A).

From the Mollier diagram:

  • For state (C): Specific humidity (x_C) = 0.0097 kg/kg, Enthalpy (h_C) = 50 kJ/kg
  • For state (A): Specific humidity (x_A) = 0.002 kg/kg, Enthalpy (h_A) = 0 kJ/kg

Calculating the mixed state (B):

Humidity Ratio: xB=QAxA+QCxCQA+QC=(1 kg)(0.002)+(1 kg)(0.0097)1+1=0.00585 kg/kgx_B = \frac{Q_A x_A + Q_C x_C}{Q_A + Q_C} = \frac{(1 \text{ kg})(0.002) + (1 \text{ kg})(0.0097)}{1 + 1} = 0.00585 \text{ kg/kg}

Enthalpy: hB=QAhA+QChCQA+QC=(1 kg)(0)+(1 kg)(50)1+1=25 kJ/kgh_B = \frac{Q_A h_A + Q_C h_C}{Q_A + Q_C} = \frac{(1 \text{ kg})(0) + (1 \text{ kg})(50)}{1 + 1} = 25 \text{ kJ/kg}

Temperature (for sensible mixing): tB=QAtA+QCtCQA+QC=(1 kg)(−5)+(1 kg)(25)1+1=10 °Ct_B = \frac{Q_A t_A + Q_C t_C}{Q_A + Q_C} = \frac{(1 \text{ kg})(-5) + (1 \text{ kg})(25)}{1 + 1} = 10 \text{ °C}

Based on these values and the Mollier diagram, the relative humidity at the mixing point is approximately 80%.

Example 2: Mixing Point Below the Saturation Line (Fog Formation)

1 kg of air at 25 °C and 90% relative humidity (C) is mixed with 1 kg of air at -5 °C and 80% relative humidity (A).

From the Mollier diagram:

  • For state (C): Specific humidity (x_C) = 0.018 kg/kg, Enthalpy (h_C) = 70 kJ/kg
  • For state (A): Specific humidity (x_A) = 0.002 kg/kg, Enthalpy (h_A) = 0 kJ/kg

Calculating the mixture properties: Enthalpy of the mixture: hB=(1 kg)(0)+(1 kg)(70)1+1=35 kJ/kgh_B = \frac{(1 \text{ kg})(0) + (1 \text{ kg})(70)}{1 + 1} = 35 \text{ kJ/kg}

Humidity ratio of the mixture (including potential fog): xB=(1 kg)(0.002)+(1 kg)(0.018)1+1=0.01 kg/kgx_B = \frac{(1 \text{ kg})(0.002) + (1 \text{ kg})(0.018)}{1 + 1} = 0.01 \text{ kg/kg}

Interpreting the Mollier Diagram: The calculated point (h_B = 35 kJ/kg, x_B = 0.01 kg/kg) lies below the saturation line. This indicates fog will form.

  1. The actual final temperature is found where the constant enthalpy line (35 kJ/kg) intersects the saturation curve: ~12.7 °C.
  2. The specific humidity at this saturated state is approximately 0.0089 kg/kg.
  3. The condensed moisture is the difference: xcondensed=xB−xsat=0.01−0.0089=0.0011 kg/kg (of water droplets)x_{condensed} = x_B - x_{sat} = 0.01 - 0.0089 = 0.0011 \text{ kg/kg (of water droplets)}

Important Notes

Volume vs. Mass in Calculations: The provided formulas use air volume (Q). While using mass is more accurate, for common HVAC and ventilation conditions, volume-based calculations are sufficient. Caution: This volume approximation may not be valid for high-temperature industrial processes (e.g., industrial dryers) where air density changes significantly.

Detecting Fog Formation: A mixing point results in fog or condensation if its state point on the psychrometric chart or Mollier diagram lies below the saturation line. In this case, the final air mixture is saturated, and the excess moisture appears as suspended droplets (fog) or condensation.

References

Source: engineeringtoolbox.com