Mixed air temperature calculator

How the mixed air is calculated

Outdoor air and return air that meet in a mixing box leave as one stream, and the dry air, the water vapor and the energy all carry over. ASHRAE writes the balance by mass of dry air, so each CFM is first turned into pounds of dry air with the specific volume of its own stream. The mixed humidity ratio and enthalpy are the mass-weighted values, and the dry-bulb comes back out of the enthalpy equation. With no humidity readings the page weights each dry-bulb by the dry air from absolute temperature, and it shows the plain CFM average beside that. The second form works backward from three thermometer readings to the outdoor air percent.

Dry air in each stream

m = 60 x CFM / v (lb of dry air per hour, v in ft3 per lb of dry air)The specific volume comes from the psychrometric engine, for that stream's own dry-bulb and humidity at the elevation entered. In the default case the 4,238 CFM of outdoor air has v = 12.65 and carries 20,109 lb/h of dry air. The 13,243 CFM of return air has v = 13.74 and carries 57,827 lb/h.

Mass and energy balance

W3 = (m1 W1 + m2 W2) / (m1 + m2) and h3 = (m1 h1 + m2 h2) / (m1 + m2)ASHRAE's three mixing equations are the enthalpy, dry air and moisture balances, and eliminating the mass of the mix gives its Eq. 45. On the psychrometric chart the mix sits on the straight line between the two streams, dividing it in the ratio of their dry air masses. The default case gives a humidity ratio of 0.00823 lb/lb and an enthalpy of 25.13 BTU/lb.

Mixed dry-bulb with humidity

t3 = (h3 - 1061 W3) / (0.240 + 0.444 W3)This is the enthalpy equation, h = 0.240 t + W (1061 + 0.444 t), solved for t. The result is 67.3 °F. Example 4 in the 2001 ASHRAE chapter reads 67.1 °F off the chart with a ruler, so the book value is good to a few tenths of a degree.

Mixed dry-bulb with no humidity

t3 = (m1' t1 + m2' t2) / (m1' + m2'), m' = CFM / (t + 459.67)Dry air at one pressure has a mass proportional to CFM over absolute temperature, which is why cold air counts for more than its CFM. For the default temperatures that gives 67.3 °F, within 0.01 °F of the full balance. The plain CFM average, (CFM1 t1 + CFM2 t2) / (CFM1 + CFM2), gives 67.8 °F.

Mixed RH, wet-bulb and dew point

RH from W3 and the saturated W at t3, then the full state from the engineThe balance gives the humidity ratio, and the ratio of vapor pressures turns it into RH, 58.0 percent here. From there the engine returns the wet-bulb, 58.2 °F, and the dew point, 52.1 °F. Averaging the two RH figures directly would give 55.0 percent, which is not the mix.

Past saturation

RH from the balance above 100 percent means fog, so find saturated air at the same enthalpyA mix that lands above the saturation curve forms fog. The page then finds the saturated air at the enthalpy of the mix, which is warmer than the dry-bulb before the fog because condensing water gives up heat, and reports the water that drops out. Liquid water's own enthalpy is left out. 5,000 CFM of saturated 10 °F outdoor air with the same flow of 80 °F, 70 percent RH return air gives 134.7 percent RH by the balance.

Percent outdoor air from three temperatures

OA % = (RAT - MAT) / (RAT - OAT) x 100This follows from the dry-bulb balance with equal specific heats. It is the same ratio as (MAT - RAT) / (OAT - RAT) with both signs flipped. The Example 4 temperatures, 39.2 °F, 77 °F and 67.1 °F, give 26.2 percent. Next to the 25.8 percent that the book's dry air masses give, the thermometer method lands within half a point when the readings are clean.

How much a reading error can move it

error in points = 200 x reading error / |RAT - OAT|Differentiating the formula with respect to the three temperatures gives partial derivatives whose absolute values add up to 2 / |RAT - OAT|. A 1 °F error on each reading therefore moves the answer by up to 5.3 points at 37.8 °F of difference and 33.3 points at 6.0 °F. PNNL calls the method meaningful only above 5 °F of difference and Falke says it works best at 10 °F or more, which is why the page refuses under the first and warns under the second.

Worked examples from the ASHRAE Handbook

The default case is Example 4 in the 2001 ASHRAE Fundamentals chapter on psychrometrics, converted from SI. Read off the chart with a ruler, the book gives 67.1 °F dry-bulb and 58.3 °F wet-bulb, and it puts 25.8 percent of the dry air outdoors. This page gives 67.3 °F, 58.2 °F and 25.8 percent, and the mixed air is at 58.0 percent RH with a dew point of 52.1 °F. The outdoor air is 24.2 percent of the CFM and 25.8 percent of the dry air, because the cold outdoor air is the denser of the two.

The table below shows how far the plain CFM average sits from the dry-air weights when the return air is at 75 °F and 30 percent of the CFM comes from outdoors. That gap is small on a mild day and reaches a degree or more when it is cold. With humidity entered the page uses the full mass and energy balance, and the table is the case with no humidity.

Eight cases below run through the same functions the form uses. First comes the ASHRAE example, and the second takes the humidity away to show what the dry-bulb alone gives, 67.3 °F against 67.3 °F. In the sixth row, cold saturated outdoor air meets humid return air and passes the saturation line, so it fogs. The last two rows are the percent form, one on the Example 4 temperatures and one on an economizer check with temperatures chosen for the page and the airflow of the Contracting Business article, where 50.0 percent of 2,000 CFM is 1,000 CFM of outside air.

Standards and data sources

• 2001 ASHRAE Fundamentals Handbook (SI), Chapter 6 Psychrometrics, Adiabatic Mixing of Two Moist Airstreams - mixing equations by mass of dry air, the straight-line result on the chart, and Example 4. The page opens on that example converted to IP units, 4,238 CFM at 39.2 °F and 35.6 °F wet-bulb with 13,243 CFM at 77 °F and 50 percent RH. Its chart readings are 67.1 °F dry-bulb and 58.3 °F wet-bulb, and this page gives 67.3 °F and 58.2 °F. Tests allow half a degree against the book. Later editions carry the same section in Chapter 1.
• ASHRAE Handbook - Fundamentals (2021), Ch. 1 Psychrometrics - the humidity ratio, specific volume, enthalpy and wet-bulb equations (Eq. 22, 26, 32, 35 and 37) and the standard atmosphere that the psychrometric engine behind this page uses for the state of each stream and of the mix.
• Rob Falke, Measuring Fresh Air With a Thermometer, Contracting Business, 2008 - a field check from outside air, return air and mixed air temperatures. The article says the formula does not give good results when indoor and outdoor conditions are nearly the same, that it works best with 10 degrees or more of difference, and that smaller differences call for readings to a tenth of a degree. Its example puts 1,000 CFM of outside air in a 2,000 CFM system at 50.0 percent, which the tests reproduce.
• PNNL, Building Re-tuning, AHU Minimum Outdoor-Air Operation (PNNL-SA-88958) - the outdoor air fraction as (MAT - RAT) / (OAT - RAT) and the caution that it is only meaningful when the outdoor air temperature differs from the return air temperature by a margin of about 5 °F either way. This page refuses under that margin.

Limitations of this calculator

• Steady state and well mixed. The page treats the two streams as blended completely, and a real mixing box can leave layers. A reading taken in a layer is one stream's temperature, not the mix.
• Each CFM is for its own stream. The page treats each figure as measured in the air of that stream. A CFM read at the coil, after mixing, is a third figure, and with humidity entered the page shows the mixed airflow at the conditions of the mix.
• Without humidity the answer is an estimate. Dry-air weights from absolute temperature land within 0.01 °F of the full balance for the default case, and moisture moves it a little more in wet air. The plain CFM average sits 0.5 °F from the full balance there, and 3.6 °F away with outdoor air at -10 °F and return air at 75 °F.
• Nothing between the readings is modeled. A fan, a heater, a coil or a long duct run between the mixing point and the sensor changes the temperature, and the page cannot see it. The percent form in particular fails when the mixed-air sensor sits after a fan.
• The temperature method needs room between OAT and RAT. This page refuses a difference under 5 °F, following PNNL, and warns under 10 °F, following Falke. Those two figures are rules of thumb from the trade literature, not limits from a code.
• A fogged mix is an estimate. The page finds saturated air at the enthalpy of the mix and leaves out the enthalpy of the liquid water, so the temperature after the fog is close but not exact. Real fog also depends on how the streams meet.
• Humidity comes from the project's psychrometric engine, which uses the Magnus-Tetens saturation curve, within about 0.5 °F of Hyland-Wexler in the HVAC range. Dry-bulb range is -40 to 150 °F, relative humidity from 1 percent, and elevation from -500 to 12,000 ft.
• Outdoor air percent does not say whether a space is ventilated enough. The ventilation rate comes from a standard such as ASHRAE 62.2 or 62.1, and a measured airflow is the proof.
• This is a planning and field-check estimate. A licensed contractor, the equipment manufacturer's instructions and the authority having jurisdiction decide the installation, and the page makes no claim of code compliance.

Common mixed air mistakes

1. Averaging the dry-bulbs by CFM on a cold day. The plain CFM average ignores that cold air is denser. With 4,000 CFM at -10 °F and 6,000 CFM at 75 °F it gives 41.0 °F, while the dry-air weights give 37.4 °F, 3.6 °F lower. The gap shrinks on mild days and grows with the spread.
2. Averaging relative humidity or wet-bulb. Humidity mixes in humidity ratio and enthalpy, not in RH. Weighting the two RH figures of the default case by CFM gives 55.0 percent, and the mix is at 58.0 percent. RH depends on temperature, so a straight average of it carries no meaning.
3. Reading the mixed air after the fan. A sensor behind the supply fan reads the mix plus the heat of the motor and the fan. With OAT at 40 °F and RAT at 75 °F, a true mix of 55 °F is 57.1 percent outdoor air, and a sensor that reads 58 °F makes it 48.6. That is 8.6 points of outdoor air lost to heat that is not in the mix.
4. Trusting a reading with OAT close to RAT. With OAT and RAT only 6.0 °F apart, a 1 °F error in each reading can move the answer by 33.3 points, against 5.3 points when they are 37.8 °F apart. A result of 50.0 percent from such a day tells almost nothing. Wait for a day with 10 °F or more of difference, or measure the airflows.
5. Taking a damper position for the outdoor air percent. A damper at 20 percent open is not 20 percent outdoor air. Linkage slop, leakage past the blades, fan speed and the pressure in the mixing box all move the real fraction. The temperature check or an airflow measurement shows what the unit is doing.
6. Ignoring fog when cold and humid air meets warm return air. 5,000 CFM of saturated 10 °F outdoor air with the same flow of 80 °F, 70 percent RH return air gives 134.7 percent RH by the balance. Water drops out, about 45.7 lb/h, and the air after the fog is at 47.0 °F, not the 42.6 °F the dry-bulb balance alone gives.

Common questions about mixed air

Related calculators

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Used on the same job

• Dew point calculator Check the dew point of the mix against the surface temperatures it meets.
• Condensate drain calculator Water off the coil from the mixed air that enters it.
• Dehumidifier size calculator The moisture that ventilation air brings in, in pints a day.