Mixing Mass Balance Calculator
Mixing 0.5 m³/s of effluent at 150 mg/L into a 10 m³/s river carrying 2 mg/L gives 9.04762 mg/L downstream.
9.04761904761905
Full answer, then cut to fewer decimals (not rounded):
- 9.04761904761905
- 9.0476190476190
- 9.047619047619
- 9.04761904761
- 9.0476190476
- 9.047619047
- 9.04761904
- 9.0476190
- 9.047619
- 9.04761
- 9.0476
- 9.047
- 9.04
- 9.0
- Mixed flow Q₁ + Q₂
- 10.5
- Mixed temperature (equal heat capacity)
- 20.47619048 °C
- Dilution of flow 2
- 21
Step-by-step solution
- C = (Q₁C₁ + Q₂C₂) ÷ (Q₁ + Q₂)
- C = (10 × 2 + 0.5 × 150) ÷ 10.5 = 9.047619048
Mixing Mass Balance Formula
C = (Q₁C₁ + Q₂C₂) / (Q₁ + Q₂)
flows in any consistent unit; concentrations in any consistent unit
Worked Example
A river of 10 m³/s with 2 mg/L BOD receiving 0.5 m³/s of effluent at 150 mg/L:
- C = (Q₁C₁ + Q₂C₂) ÷ (Q₁ + Q₂)
- C = (10 × 2 + 0.5 × 150) ÷ 10.5 = 9.047619048
Mixed temperature (equal heat capacity): 20.47619048 °C · Dilution of flow 2: 21
GATE tip
Conservative substances (chloride, TDS) obey this mass balance exactly; reactive ones (BOD, ammonia) only at the mixing point, after which their decay must be modelled.
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Example: Wastewater with ultimate BOD 250 mg/L and k = 0.23 per day at 20 °C, after 5 days: BOD at day 5 = 170.841 mg/L.
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Example: A river with mixed L₀ = 20 mg/L, D₀ = 1 mg/L, k_d = 0.23 and k_r = 0.46 per day: Critical (maximum) deficit D_c = 5.26316 mg/L.
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SAR = Na / √((Ca + Mg)/2)
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TH = 2.497 Ca + 4.118 Mg (mg/L as CaCO₃)
carbonate hardness = min(TH, alkalinity); non-carbonate = TH − carbonate
Example: Water with 60 mg/L calcium, 24 mg/L magnesium and 150 mg/L alkalinity: Total hardness = 248.669 mg/L as CaCO₃.
Frequently asked questions
Does this work for temperature?
Yes, for streams of similar heat capacity: the mixed temperature is the flow-weighted average, shown as a second result.
When is complete mixing a poor assumption?
Wide rivers can take many kilometres to mix across their width; close to the outfall a plume model is needed.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Mixing Mass Balance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/mass-balance-mixing-calculator/
IEEE
Scientific Converters, "Mixing Mass Balance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/mass-balance-mixing-calculator/