Air Mixing Calculator: Return Air and Outdoor Air

The state of two air streams mixed together, for example return air and fresh outdoor air before a coil.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

When two air streams mix, the enthalpy and the humidity ratio of the mixture are the mass-weighted averages of the two streams. The temperature and the relative humidity are not simple averages, which is why the calculator goes through the humidity ratio and the enthalpy and finds the temperature from them.

On a psychrometric chart the mixed state lies on the straight line between the two states, at a distance set by the ratio of the two mass flows. The calculator finds the mass flows from the volume flows and the specific volume of each stream.

If cold damp air mixes with warm humid air the straight line can pass beyond the saturation curve, and the mixture is foggy. The calculator warns when the mixed state is above 100 percent relative humidity.

Formulas used

  • W_m = \frac{\dot m_1 W_1 + \dot m_2 W_2}{\dot m_1 + \dot m_2}
  • h_m = \frac{\dot m_1 h_1 + \dot m_2 h_2}{\dot m_1 + \dot m_2}
  • T_m = \frac{h_m - 2501 W_m}{1.006 + 1.86 W_m}

Worked example

With the default numbers in the calculator above:

  1. Mass flow of dry air in each stream: 1.756 and 0.56 kg/s
  2. Humidity ratio and enthalpy of each stream: 47.81 and 71.47 kJ/kg
  3. Mixed humidity ratio (mass-weighted): 0.010467 kg/kg
  4. Mixed enthalpy (mass-weighted): 53.54 kJ/kg
  5. Mixed temperature: 26.68 °C
  6. Mixed relative humidity: 47.91 %
  7. Mixed air flow: 2000 L/s
  8. Share of stream 2 by volume: 25 %

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why not just average the temperatures?

The average of the temperatures is close when the humidity ratios are similar, but the correct method is the mass-weighted average of the enthalpy and the humidity ratio.

What percentage of outdoor air should I use?

It is set by the ventilation standard and the number of people. This calculator only finds the state of the mixture for the share you enter.

Related calculators

Further reading: ASHRAE Handbook: Fundamentals (psychrometrics); Cengel and Boles, Thermodynamics: An Engineering Approach; Moran and Shapiro, Fundamentals of Engineering Thermodynamics.

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