When treated sewage or industrial effluent is discharged into a river, the river dilutes it. Adjust the river flow, discharge flow and effluent concentration to see the fully-mixed downstream concentration, dilution ratio and compliance with the environmental standard update in real time, all from a mass balance.
Parameters
River flow Qr
m³/s
Flow passing upstream of the discharge. Less flow means less dilution capacity
Upstream background concentration Cr
mg/L
Pollutant concentration the river already carries before the discharge
Discharge flow Qd
m³/s
Flow of effluent released into the river from a plant or factory
Effluent concentration Cd
mg/L
Pollutant concentration in the discharged effluent (after treatment)
Environmental standard Cstd
mg/L
Upper limit to be met downstream. Above this is an exceedance
Results
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Fully-mixed concentration (mg/L)
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Dilution ratio (×)
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Concentration rise above background (mg/L)
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Max allowable discharge conc. (mg/L)
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Additional dilution needed (×)
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Standard compliance
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River plan view — pollutant plume spreading and mixing
A top-down view of a river flowing left to right. The pollutant plume spreads from the bank pipe and mixes across the channel width. Colour intensity shows concentration, and the river is shaded red if the standard is exceeded.
Mixed concentration vs river flow
Mixed concentration vs discharge concentration
Theory & Key Formulas
$$C_{mix}=\frac{Q_r C_r + Q_d C_d}{Q_r + Q_d}$$
Fully-mixed downstream concentration C_mix. Derived from a mass balance (conservation of pollutant mass), it is the flow-weighted average of the river and discharge streams. Q_r: river flow, C_r: background concentration, Q_d: discharge flow, C_d: effluent concentration.
Dilution ratio D (how many times the effluent is diluted) and the concentration rise C_rise above the upstream background. Dilution lowers the concentration but never removes the pollutant mass.
Maximum allowable discharge concentration C_d,max that would just meet the environmental standard C_std. Keeping the effluent below this value keeps the downstream water compliant.
What is River Pollutant Dilution?
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Sewage-plant water and factory effluent end up being released into a river, right? Doesn't that just pollute it?
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Good question. Effluent is indeed discharged into rivers, but the river itself does part of the pollution-control work through "dilution". The mass of pollutant in the effluent mixes into a far larger volume of flowing river water, and the concentration drops sharply. Even a factory effluent at 400 mg/L ends up much weaker downstream if the river flow is large. Raise the "River flow" slider on the left and watch the mixed concentration fall.
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How do you actually calculate the concentration after they mix? It sounds hard.
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It is surprisingly simple. You use a "mass balance" — the obvious principle that pollutant mass is neither destroyed nor created when streams mix. So the fully-mixed concentration is just the flow-weighted average of the river water and the effluent: C_mix = (Qr·Cr + Qd·Cd)/(Qr+Qd). With the default values that is (20×2.0 + 0.5×400)/20.5 = 11.7 mg/L. The large river flow pulls the result toward the river's concentration, so the effluent's 400 is heavily diluted.
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So as long as the river is big enough, you can dump any dirty effluent you like?
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That is the trap. The old saying "the solution to pollution is dilution" is only half true. Dilution lowers the CONCENTRATION, but it does not remove a single gram of the pollutant MASS. That mass is still in the river, and it accumulates downstream where many discharges combine, and re-concentrates in lakes, estuaries and bottom sediments. Relying on dilution alone is dangerous; treating the effluent properly is always the first requirement.
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Also, river flow varies a lot with the seasons. Which flow do you design for?
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This is a crucial point. A discharge permit is designed not for the annual average flow but for the "low flow" — the drought flow, the season with the least water. The smaller the river flow, the less water is available for dilution and the highest the downstream concentration becomes. A typical figure is the lowest 7-day average flow expected once in 10 years, the so-called 7Q10. Try lowering the river flow on the left to about 0.5 m³/s — the mixed concentration jumps and the verdict turns red. That is the severity of a drought.
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There is also an "Additional dilution needed" card. What is that?
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It tells you how many more times the mixed concentration must be diluted to reach the environmental standard. A value of 1.0 means you already meet it. 1.2 means "you are short by a factor of 1.2" — you need to lower the effluent concentration, cut the discharge flow, or move the outfall to a river with more flow. With the default values it is about 1.21. A small exceedance, but bringing it to 1.0 or below is the design goal.
Frequently Asked Questions
Use a mass balance — the principle that pollutant mass is conserved as it mixes. The fully-mixed downstream concentration is the flow-weighted average of the two streams: C_mix = (Qr·Cr + Qd·Cd)/(Qr + Qd), where Qr is the river flow, Cr is the upstream background concentration, Qd is the discharge flow and Cd is the effluent concentration. This tool computes C_mix and compares it with the environmental standard to report compliance.
The dilution ratio measures how many times the effluent is diluted by the river, and is given by (Qr + Qd)/Qd. For a river flow of 20 m³/s receiving a discharge of 0.5 m³/s, the dilution ratio is 20.5/0.5 = 41. Note, however, that even a large dilution ratio does not reduce the total mass of pollutant — dilution lowers the concentration but does not remove the pollutant itself.
The lower the river flow, the less water is available for dilution and the higher the downstream concentration becomes. Designing for the annual average flow would cause exceedances during droughts. The design condition for a discharge permit is therefore the low flow, often specified as the lowest 7-day average flow expected once in 10 years (7Q10). Lower the river-flow slider in this tool to feel how severe drought conditions are.
Only half true. The old saying that the solution to pollution is dilution lowers the concentration but does not remove a single gram of pollutant mass. That mass stays in the river, accumulates downstream where many discharges combine, and can concentrate again in lakes, estuaries and sediments. This tool addresses the concentration just after mixing; in practice biodegradation, settling and accumulation must also be assessed.
Real-World Applications
Discharge planning for sewage treatment plants: A city's sewage treatment plant ultimately releases its treated effluent into a river. To meet the discharge permit, the concentrations of BOD, COD, total nitrogen and total phosphorus in the treated water must be combined with the receiving river's flow and background concentration to predict the fully-mixed downstream concentration and show it stays below the environmental standard. The mass-balance calculation in this tool is directly usable for that first estimate.
Permit applications for industrial effluent: Industrial discharges from food, chemical or plating plants are submitted for a discharge permit to the municipality or river authority. The "maximum allowable discharge concentration" is the key figure in the review, and effluent above it must receive further treatment before release. Where several facilities discharge to the same river, they are managed under a total-load framework that accounts for downstream accumulation.
Impact assessment of spills and abnormal discharges: When a tank rupture or a treatment-plant failure releases highly concentrated effluent for a short time, the flow and discharge rate quickly give an estimate of the concentration reaching a downstream intake or ecosystem. The dilution ratio and mixed concentration support the first-response decision on whether a water intake must be stopped.
Pre-study for environmental assessment and numerical models: Before building one- or two-dimensional water-quality models (full simulations solving the advection-diffusion equation), a complete-mix model like this tool gives a first read on the approximate downstream concentration. If a detailed model differs from this estimate by an order of magnitude, it is a sanity check pointing to an input error in flow or load.
Common Misconceptions and Pitfalls
The biggest misconception is "dilution makes pollution disappear". As this tool shows, dilution lowers the concentration but does not reduce the total mass (load) of pollutant at all — the dangerous half of the old maxim "the solution to pollution is dilution". The mass stays in the river, the concentration rises again downstream where many discharges combine, and it settles and re-concentrates in slow-moving lakes, estuaries and bottom sediments. Nutrients lead to downstream eutrophication; heavy metals lead to sediment contamination and bioaccumulation. Dilution only buys time; the fundamental measure is reducing the mass itself through effluent treatment.
Next, "it is fine to design for the annual average flow". The design condition for a discharge permit must be the low flow (drought flow) with the least dilution capacity, not the average flow. As the mixed concentration in this tool jumps when you lower the river flow, the downstream concentration is highest exactly when the flow is smallest. A typical design flow is the lowest 7-day average flow expected once in 10 years (7Q10). Calculating with the average flow and feeling safe means exceeding the standard during every drought season.
Finally, "complete mixing can be assumed immediately". The formula in this tool gives the concentration after the effluent has mixed uniformly across the full channel width. In reality, just downstream of the outfall the effluent forms a narrow plume along the bank, and the river travels hundreds of metres to several kilometres before complete mixing is reached. Within that mixing zone the local concentration near the bank is far higher than the fully-mixed value calculated here. If a water intake or a water body to be protected lies near the outfall, do not judge by the fully-mixed concentration alone — separately assess the mixing length and the local concentration.
How to Use
Enter river flow rate (m³/s) and background pollutant concentration (mg/L) using the river flow and concentration sliders
Set discharge flow rate (m³/s) and effluent pollutant concentration (mg/L) using the discharge parameters
The simulator calculates fully-mixed concentration, dilution ratio, and compliance against standard limits—adjust discharge concentration downward or increase river flow to achieve regulatory compliance
Worked Example
River carries 5 m³/s with 2 mg/L background BOD. Industrial wastewater discharges 0.5 m³/s at 80 mg/L. Total flow becomes 5.5 m³/s; fully-mixed concentration = (5×2 + 0.5×80)/5.5 = 9.1 mg/L. Dilution ratio = 80/9.1 = 8.8×. If the standard permits 6 mg/L, additional dilution of 1.52× is required (either reduce discharge to 53 mg/L or increase river flow to 7.7 m³/s).
Practical Notes
Seasonal river flow variation critically affects dilution capacity; summer low-flow periods (2 m³/s) demand stricter pre-treatment than spring floods (15 m³/s)
Account for tributary inflow and stratification in large rivers—fully-mixed assumption underestimates impact if vertical/lateral mixing is incomplete within 1–2 km
Heavy metals and persistent organics require treatment to below 5 mg/L regardless of dilution; use this simulator for biodegradable BOD, nitrogen, and acute toxins only