Calculators › Industrial systems: air, pumps, fans, heat recovery Recovery and bypass mixing temperature calculator
Recovery and bypass mixing temperature
Mix streams of the same air with equal density and heat capacity, no phase change and no additional heat gain; the outlet temperature is airflow-weighted, not an unweighted average.
Units IP (US) SI (metric)
T out = Q recovery × T recovery + Q bypass × T bypass Q recovery + Q bypass T_{\text{out}} = \frac{Q_{\text{recovery}} \times T_{\text{recovery}} + Q_{\text{bypass}} \times T_{\text{bypass}}}{Q_{\text{recovery}} + Q_{\text{bypass}}} T out = Q recovery + Q bypass Q recovery × T recovery + Q bypass × T bypass T out = Q recovery × T recovery + Q bypass × T bypass Q recovery + Q bypass T_{\text{out}} = \frac{Q_{\text{recovery}} \times T_{\text{recovery}} + Q_{\text{bypass}} \times T_{\text{bypass}}}{Q_{\text{recovery}} + Q_{\text{bypass}}} T out = Q recovery + Q bypass Q recovery × T recovery + Q bypass × T bypass
Calculator
Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.
Worked example
Given
Q recovery Q_{\text{recovery}} Q recovery 5,000 cfm T recovery T_{\text{recovery}} T recovery 68 °F Q bypass Q_{\text{bypass}} Q bypass 2,500 cfm T bypass T_{\text{bypass}} T bypass 32 °F T out = 5000 × 68 + 2500 × 32 5000 + 2500 = 56 T_{\text{out}} = \frac{5000 \times 68 + 2500 \times 32}{5000 + 2500} = 56 T out = 5000 + 2500 5000 × 68 + 2500 × 32 = 56
Given
Q recovery Q_{\text{recovery}} Q recovery 3,000 L/s T recovery T_{\text{recovery}} T recovery 24 °C Q bypass Q_{\text{bypass}} Q bypass 1,000 L/s T bypass T_{\text{bypass}} T bypass 4 °C T out = 3000 × 24 + 1000 × 4 3000 + 1000 = 19 T_{\text{out}} = \frac{3000 \times 24 + 1000 \times 4}{3000 + 1000} = 19 T out = 3000 + 1000 3000 × 24 + 1000 × 4 = 19
Symbols and units
Symbol Meaning Unit
T out T_{\text{out}} T out mixed outlet temperature °F Q recovery Q_{\text{recovery}} Q recovery recovery-branch airflow cfm T recovery T_{\text{recovery}} T recovery recovery-branch temperature °F Q bypass Q_{\text{bypass}} Q bypass bypass-branch airflow cfm T bypass T_{\text{bypass}} T bypass bypass-branch temperature °F
Symbol Meaning Unit
T out T_{\text{out}} T out mixed outlet temperature °C Q recovery Q_{\text{recovery}} Q recovery recovery-branch airflow L/s T recovery T_{\text{recovery}} T recovery recovery-branch temperature °C Q bypass Q_{\text{bypass}} Q bypass bypass-branch airflow L/s T bypass T_{\text{bypass}} T bypass bypass-branch temperature °C
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