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Flow-Weighted Blending Concentration

Also known as blending two streams · flow weighted average concentration · mixed stream concentration · blend calculation · two source blending · flow proportioned blending · combined stream concentration · mass balance blending

C=Q1C1+Q2C2Q1+Q2C = \frac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}

Worked example: 300 L/min at 12 mg/L with 700 L/min at 2 mg/L → 5 mg/L — press Try an example to run it live, then adjust anything.

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See also
Mixing Two Solutions (C₁V₁ + C₂V₂ = C_f V_f) — The same mass balance for two BATCHES rather than two streams — volumes in a tank instead of flows in a pipe.Hydraulic Detention Time — Blending is only complete after the streams have actually mixed, and this is how long the junction chamber gives them.BOD Mass Loading — The other everyday use of the same balance: concentration times flow is a mass loading, and mass is what actually adds.

Learning zone

Two streams meet, the masses add, and the concentration that comes out is the flow-weighted average of the two that went in. Three hundred litres a minute at 12 mg/L joining seven hundred at 2 mg/L gives (300×12+700×2)/1000=5(300 \times 12 + 700 \times 2)/1000 = 5 mg/L. Run backwards it becomes the lever rule and answers the question a utility actually asks: to bring a 1400 mg/L TDS well down to a 500 mg/L target using 250 mg/L surface water takes 3.6 parts of surface water to one of well — the flows split in inverse proportion to the distances from the target.

The two limits on this arithmetic matter more than the arithmetic. First, it requires a conservative quantity — one that is simply carried along, neither reacting, settling, degassing nor precipitating on mixing. Chloride, sulphate, sodium and total dissolved solids behave; alkalinity, hardness, dissolved oxygen, chlorine residual and anything biological do not, and a hard water blended with an alkaline one can start depositing calcium carbonate on contact, landing below what this predicts. pH is the sharpest case of all, because it is a logarithm and cannot be flow-averaged at all — average the hydrogen ion concentrations instead. Second, blending is not treatment. It lowers a contaminant by dilution and lowers nothing else, regulators generally judge it at the consumer's tap rather than at the mixing chamber, and the ratio has to hold at every flow the plant runs rather than only at the design one. A blend that meets a limit on an average day and fails during the morning peak has failed.

Flow-Weighted Blending Concentration
C=Q1C1+Q2C2Q1+Q2C = \frac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}
Where
  • CC= Blended concentration (mg/L)
  • Q1Q_1= Flow of stream 1 (L/min)
  • C1C_1= Concentration of stream 1 (mg/L)
  • Q2Q_2= Flow of stream 2 (L/min)
  • C2C_2= Concentration of stream 2 (mg/L)
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