Mixing of two air streams (adiabatic)

v_{1} = \frac{0.287042 (t_{1} + 273.15) (1 + 1.607858 \frac{W_{1}}{1000})}{p}

v_{2} = \frac{0.287042 (t_{2} + 273.15) (1 + 1.607858 \frac{W_{2}}{1000})}{p}

m_{1} = \frac{{\dot{V}}_{1}}{v_{1}}

m_{2} = \frac{{\dot{V}}_{2}}{v_{2}}

W_{3} = \frac{m_{1} W_{1} + m_{2} W_{2}}{m_{1} + m_{2}}

h_{1} = 1.006 t_{1} + \frac{W_{1}}{1000} (2501 + 1.86 t_{1})

h_{2} = 1.006 t_{2} + \frac{W_{2}}{1000} (2501 + 1.86 t_{2})

h_{3} = \frac{m_{1} h_{1} + m_{2} h_{2}}{m_{1} + m_{2}}

t_{3} = \frac{h_{3} - 2.501 W_{3}}{1.006 + 0.00186 W_{3}}

where
$v₁, v₂$: specific volume of each stream (m³/kg dry air)
$t₁, t₂$: dry-bulb temperature of each stream (°C)
$W₁, W₂$: moisture content of each stream (g/kg)
$p$: atmospheric pressure (kPa)
$m₁, m₂$: dry-air mass flow of each stream (kg/s)
$V̇₁, V̇₂$: air volume flow of each stream (m³/s)
$W₃$: mixed moisture content (g/kg)
$h₁, h₂$: specific enthalpy of each stream (kJ/kg)
$h₃$: mixed specific enthalpy (kJ/kg)
$t₃$: mixed dry-bulb temperature (°C)

Explain this equation

Finds the condition of air after two streams mix, such as return air and fresh air in an AHU mixing box. Use it to set the coil entering condition.

v₁ and v₂ are specific volumes, the cubic metres each kilogram of dry air occupies, which depend on temperature, moisture and pressure. Dividing each volume flow by its specific volume gives the dry-air mass flows m₁ and m₂. W₃ and h₃ are mass-weighted averages of moisture content and enthalpy. t₃ is worked back from h₃ and W₃.

Mixing conserves dry air, water and energy, so moisture and enthalpy average by mass. Temperature is recovered by rearranging the enthalpy equation.

Sense check: 75 % return at 22 °C with 25 % fresh at −2 °C gives about 15.6 °C, close to the simple volume-weighted 16 °C.

Watch out: never average relative humidities, and check the mixed point is not beyond saturation.

Finds the condition of air leaving a mixing box, from the flow, temperature and moisture content of the two streams. Typical use: return air mixed with fresh air ahead of an AHU coil.

Enter your values to see the result.

Good to know

Each volume flow is turned into a mass flow of dry air using its specific volume v (m³/kg), because the mix is weighted by mass, not volume. Moisture content and enthalpy are then mass-weighted averages, and the mixed temperature is worked back from the mixed enthalpy. Weighting temperatures simply by volume flow is usually within a few tenths of a degree.

Common mistake

Mixing relative humidities. RH does not average; always mix moisture content and enthalpy.

Limits

Adiabatic mixing at constant pressure. If the mixed point lies beyond saturation (cold fresh air with humid return air), fog forms and the real state differs; check the mixed RH.

Sources

Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.

Mixing of two air streams (adiabatic)

Good to know

Common mistake

Limits

Sources

Mixing of two air streams (adiabatic)

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