Adiabatic water mixing temperature

Predict mixed temperature for two liquid-water mass flows with the same specific heat.

How this calculation works

Supply the mass flow and temperature of the warm stream and the cool stream. The model adds the mass flows and divides the sum of each flow multiplied by its temperature by that total. This is a mass-weighted temperature average because the two liquid-water streams are assigned the same constant specific heat. A stream with greater mass flow has greater influence on the final temperature; a simple arithmetic temperature average applies only to equal flows. At least one stream must flow, and the warm temperature must not be below the cool temperature. The calculation assumes adiabatic mixing without phase change or reaction. It is limited to the stated liquid-water temperature range and does not establish safe delivery temperatures or certify a thermostatic mixing valve.

Inputs and units

Warm stream mass flow (kg/s)
Warm stream temperature (°C)
Cool stream mass flow (kg/s)
Cool stream temperature (°C)

Method and formula

Tmixed = (mhot Thot+mcold Tcold)/(mhot+mcold); total mass flow = mhot+mcold.

Worked example

Example inputs

Warm stream mass flow: 1 kg/s
Warm stream temperature: 60 °C
Cool stream mass flow: 2 kg/s
Cool stream temperature: 15 °C

Calculation steps

Total water mass flow = 1 + 2 = 3 kg/s.
Mixed temperature = (1 × 60 + 2 × 15) / 3 = 30 °C.

Example results

Mixed water temperature: 30 °C
Total water mass flow: 3 kg/s

Assumptions

Same constant water specific heat for both streams; mixing has no heat loss.

Limitations

Liquid water only, 0–95 °C; no boiling, freezing, glycol mixing or chemical reactions.
Not a thermostatic-valve safety or delivery-temperature certification.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

DOE Fundamentals: Thermodynamics: Specific heat, equation 1-17; first-law energy balance