Find mixed flow, concentration, and mass loading for steady-state stream mixing. Optionally include completely mixed first-order decay.
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Worked examples
These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.
Example 1
SI river + outfall: 10 m³/s at 5 mg/L + 1 m³/s at 50 mg/L
Given
streams
1.flowrate 10 m^3/sconcentration 5 mg/L
2.flowrate 1 m^3/sconcentration 50 mg/L
Assumptions
Steady state with complete mixing at the confluence; the constituent is conservative during mixing (no reaction, settling or volatilization).
Solution steps
The mg/L ≡ g/m³ identity
A liter is a thousandth of a cubic meter and a milligram is a thousandth of a gram, so the factors cancel: concentrations in mg/L ARE g/m³. Multiplying m³/s by mg/L therefore gives g/s directly — no conversion factor needed.
1 mg/L = 1 g/m³
Flow balance
Water volume is conserved: flows simply add.
Qmix = ΣQi
Qmix = 10 m^3/s + 1 m^3/s = 11 m^3/s
= 11 m^3/s
Conservative mass balance
Constituent mass is conserved, so the mixed concentration is the flow-weighted average of the stream concentrations.
US wastewater blend: 8 MGD at 2 mg/L + 2 MGD at 25 mg/L
Given
streams
1.flowrate 8 MGDconcentration 2 mg/L
2.flowrate 2 MGDconcentration 25 mg/L
Assumptions
Steady state with complete mixing at the confluence; the constituent is conservative during mixing (no reaction, settling or volatilization).
Solution steps
The mg/L ≡ g/m³ identity
A liter is a thousandth of a cubic meter and a milligram is a thousandth of a gram, so the factors cancel: concentrations in mg/L ARE g/m³. Multiplying m³/s by mg/L therefore gives g/s directly — no conversion factor needed.
1 mg/L = 1 g/m³
Flow balance
Water volume is conserved: flows simply add.
Qmix = ΣQi
Qmix = 8 mgd + 2 mgd = 10 mgd
= 10 mgd
Conservative mass balance
Constituent mass is conserved, so the mixed concentration is the flow-weighted average of the stream concentrations.
Q·C is a mass flux: (m³/s)·(g/m³) = g/s, reported in kg/day — the units regulators and design guides use.
ṁi = Qi·Ci
per stream: 60.57 kg/day; 189.3 kg/day; total = 249.8 kg/day
= 249.8
Handbook form check
The familiar US form lb/day = 8.34 · Q(MGD) · C(mg/L) hides the conversion 1 MGD · 1 mg/L = 8.345 lb/day; the small difference from the exact value is that rounded 8.34.
ṁ(lb/day) ≈ 8.34 · Q(MGD) · C(mg/L)
shortcut: 550.4 lb/day vs exact 550.8 lb/day
Results
Mixed flow rate Qmix
10mgd
Mixed (flow-weighted) concentration Cmix
6.6mg/L
Mass loading of stream 1 (kg/day)
60.57
Mass loading of stream 2 (kg/day)
189.3
Total mass loading (kg/day)
249.8
Where this answer was checked
source
Conservative mass balance with US flows (NCEES FE Reference Handbook) — Cmix in MGD·mg/L units; loadings via 1 MGD = 3785.411784 m³/day
mixing then CSTR decay: Cmix = 40 mg/L, k = 0.5/day, θ = 2 day → 20 mg/L
Given
streams
1.flowrate 0.3 m^3/sconcentration 20 mg/L
2.flowrate 0.1 m^3/sconcentration 100 mg/L
first order decay
rate 0.5 1/daydetention time 2 day
Assumptions
Steady state with complete mixing at the confluence; the constituent is conservative during mixing (no reaction, settling or volatilization).
Decay is applied as a steady-state completely-mixed (CSTR) reactor after mixing; a plug-flow reach would decay further, to C·e^(−kθ).
Solution steps
The mg/L ≡ g/m³ identity
A liter is a thousandth of a cubic meter and a milligram is a thousandth of a gram, so the factors cancel: concentrations in mg/L ARE g/m³. Multiplying m³/s by mg/L therefore gives g/s directly — no conversion factor needed.
1 mg/L = 1 g/m³
Flow balance
Water volume is conserved: flows simply add.
Qmix = ΣQi
Qmix = 0.3 m^3/s + 0.1 m^3/s = 0.4 m^3/s
= 0.4 m^3/s
Conservative mass balance
Constituent mass is conserved, so the mixed concentration is the flow-weighted average of the stream concentrations.