Mixed Air Enthalpy Calculator: Formula and Example

A mixed air enthalpy calculator estimates the enthalpy of air after two airstreams combine, using each stream’s temperature, relative humidity, and dry-air mass flow rate. Enter those values at the same pressure and the calculator returns the mixed-air enthalpy, temperature, and humidity ratio; the result assumes the streams mix without heat exchange or condensation.

Formula

For each inlet stream, first estimate water-vapor pressure from dry-bulb temperature and relative humidity, then calculate humidity ratio and moist-air enthalpy. The calculator uses the following approximate psychrometric equations at standard atmospheric pressure:

Saturation vapor pressure: p_ws = 0.6112 exp(17.67T/(T + 243.5)) kPa, where T is in °C.
Actual vapor pressure: p_w = (RH/100)p_ws, where RH is relative humidity in percent.
Humidity ratio: W = 0.62198p_w/(P − p_w) kg water/kg dry air, with P = 101.325 kPa.
Specific enthalpy: h = 1.006T + W(2501 + 1.86T) kJ/kg dry air.
Mixed enthalpy: h_mix = (ṁ₁h₁ + ṁ₂h₂)/(ṁ₁ + ṁ₂).

Here, ṁ is dry-air mass flow in kg/s, T is dry-bulb temperature in °C, RH is relative humidity, and W is humidity ratio. The calculator then averages the inlet humidity ratios by dry-air mass flow and solves the enthalpy equation for mixed dry-bulb temperature. The constants 1.006 and 1.86 are approximate specific heats of dry air and water vapor in kJ/(kg·°C); 2501 kJ/kg is the approximate latent heat reference used by this common HVAC equation.

Worked Example

Using the defaults, both dry-air flows are 1 kg/s. At 20 °C and 50% RH, saturation vapor pressure is approximately 2.338 kPa and actual vapor pressure is 1.169 kPa. Thus W₁ ≈ 0.00726 kg/kg and h₁ ≈ 38.55 kJ/kg dry air. At 5 °C and 80% RH, saturation pressure is approximately 0.872 kPa and actual vapor pressure is 0.698 kPa, giving W₂ ≈ 0.00432 kg/kg and h₂ ≈ 15.91 kJ/kg dry air.

The flow-weighted enthalpy is (1 × 38.55 + 1 × 15.91)/(1 + 1) ≈ 27.23 kJ/kg dry air. The flow-weighted humidity ratio is (0.00726 + 0.00432)/2 ≈ 0.00579 kg/kg. Substituting into the enthalpy equation gives a mixed dry-bulb temperature of approximately 12.7 °C. The displayed result rounds enthalpy to 27.23 kJ/kg dry air.

Assumptions

Both streams are at the same standard atmospheric pressure, 101.325 kPa.
Air is treated as a moist-air mixture, and the stated flow rates are dry-air mass flows, not total moist-air flows or volumetric flows.
Mixing is adiabatic, with no heat transfer to surroundings, fan heat, or energy addition.
No water condenses or evaporates during mixing. If the calculated state is supersaturated, a real system may condense moisture and the simple result is not physically complete.
The psychrometric equations and heat-capacity values are approximations; use a psychrometric chart or more detailed model when higher precision or unusual pressure is important.

When to Use a Mixed-Air Enthalpy Calculator

HVAC designers and operators use mixed-air calculations to estimate the condition of air where return air and outdoor air meet upstream of a coil. Enthalpy includes both sensible heat associated with temperature and latent energy associated with water vapor, so it can compare air-conditioning loads more usefully than temperature alone. The same method applies to any two air streams when their flow rates and inlet states are known.

For example, an outdoor stream may be cooler but much more humid than return air. A temperature-only average could suggest a lower cooling burden while missing the added moisture that the cooling coil must remove. Enthalpy helps reveal that difference, although the downstream coil load also depends on the final target state and equipment performance.

For more than two streams, extend the weighted-average formula: add each stream’s dry-air mass flow multiplied by its enthalpy, then divide by total dry-air mass flow. Do the same for humidity ratio. If only volume flow is available, convert it to dry-air mass flow using the appropriate density at each stream’s conditions; using volume flow directly as a mass weighting can introduce error.

How to Interpret the Results

Mixed enthalpy is an energy content per kilogram of dry air, not a heat-transfer rate. To estimate a rate of energy transport relative to a reference state, multiply the dry-air mass flow by an enthalpy difference: Q̇ = ṁ(h_out − h_in). The result is in kJ/s, equivalent to kW, when mass flow is kg/s and enthalpy is kJ/kg.

Mixed temperature and humidity ratio describe the state together. Relative humidity is not directly averaged: it depends on the resulting temperature and vapor pressure. A mixed humidity ratio can be converted to vapor pressure and then relative humidity only after the mixed temperature and pressure are known. This is why averaging the two RH percentages is generally wrong.

Common Errors and Limits

Mixing up flow bases: use dry-air mass flow for the equations. If a source provides total moist-air mass flow, account for its water-vapor content before applying this dry-air formulation.
Entering volumetric flow as mass flow: m³/s and kg/s are not interchangeable. Air density varies with temperature, humidity, and pressure.
Using the wrong pressure: the calculator assumes 101.325 kPa. At altitude, calculate with local barometric pressure; saturation vapor pressure still depends primarily on temperature, but humidity ratio depends on total pressure.
Confusing relative humidity and humidity ratio: RH is a temperature-dependent percentage, while W is a water-vapor-to-dry-air mass ratio. Do not average RH values.
Ignoring condensation: if the computed mixture would be above saturation, liquid water may form. A model must then account for condensation and latent heat rather than treating the mixture as unchanged moist air.

Small rounding differences are normal because psychrometric constants and saturation-pressure fits vary slightly among references. For equipment selection, control settings, or compliance calculations, verify the state with the pressure and psychrometric method specified for that application.

Frequently Asked Questions

What does mixed air enthalpy mean?
It is the flow-weighted energy content of two or more moist-air streams after mixing, expressed here per kilogram of dry air. It accounts for both air temperature and moisture content.

Can I average the temperatures of two air streams?
Only as a rough estimate when the streams have equal dry-air flow and similar moisture content. For unequal flows or different humidity, calculate enthalpy and humidity ratio using dry-air mass-flow weighting.

Should relative humidity be averaged?
No. Relative humidity is not a conserved mixing quantity. Average humidity ratio by dry-air mass flow, then determine relative humidity from the resulting temperature, pressure, and vapor content.

What if I know airflow in CFM or m³/s?
Convert volume flow to dry-air mass flow using air density at the relevant stream’s temperature, humidity, and pressure. The calculator’s flow inputs are kg/s, so entering a volumetric value without conversion gives an invalid result.

Does this calculator include a cooling coil?
No. It predicts the state immediately after ideal mixing. A coil adds or removes heat and often removes moisture, so its outlet condition requires a separate process calculation and equipment information.

Formula used

in t1 | Stream 1 dry-bulb temperature | °C | 20 | -273.15
in rh1 | Stream 1 relative humidity | % | 50 | 0 | 100
in f1 | Stream 1 dry-air mass flow | kg/s | 1 | 0
in t2 | Stream 2 dry-bulb temperature | °C | 5 | -273.15
in rh2 | Stream 2 relative humidity | % | 80 | 0 | 100
in f2 | Stream 2 dry-air mass flow | kg/s | 1 | 0
out h | Mixed-air enthalpy | kJ/kg dry air | (f1*(1.006*t1+0.62198*(rh1/100*0.6112*exp(17.67*t1/(t1+243.5)))/(101.325-rh1/100*0.6112*exp(17.67*t1/(t1+243.5)))*(2501+1.86*t1))+f2*(1.006*t2+0.62198*(rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))/(101.325-rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))*(2501+1.86*t2)))/(f1+f2) | 2
out tm | Mixed-air dry-bulb temperature | °C | (h-2501*((f1*(0.62198*(rh1/100*0.6112*exp(17.67*t1/(t1+243.5)))/(101.325-rh1/100*0.6112*exp(17.67*t1/(t1+243.5))))+f2*(0.62198*(rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))/(101.325-rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))))/(f1+f2)))/(1.006+1.86*((f1*(0.62198*(rh1/100*0.6112*exp(17.67*t1/(t1+243.5)))/(101.325-rh1/100*0.6112*exp(17.67*t1/(t1+243.5))))+f2*(0.62198*(rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))/(101.325-rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))))/(f1+f2))) | 2
out w | Mixed-air humidity ratio | kg water/kg dry air | (f1*(0.62198*(rh1/100*0.6112*exp(17.67*t1/(t1+243.5)))/(101.325-rh1/100*0.6112*exp(17.67*t1/(t1+243.5))))+f2*(0.62198*(rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))/(101.325-rh2/100*exp(17.67*t2/(t2+243.5))*0+101.325-rh2/100*0.6112*exp(17.67*t2/(t2+243.5)))))/(f1+f2) | 5

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.