Formula & Calculator
Stack Emission Rate
Calculates the mass emission rate of a pollutant from an industrial stack based on its concentration and exhaust gas flow rate.
Interpretation
E = C × Q. The pollutant emission rate from a stack, where C is concentration and Q is flow rate. Used for emissions inventory and regulatory reporting.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E | Emission rate | g/s |
| C | Pollutant concentration in stack gas | g/m3 |
| Q | Stack gas volumetric flow rate | m3/s |
What it means
The stack emission rate is the mass of pollutant emitted per unit time (e.g., kg/h). It is calculated by multiplying the pollutant concentration (C) in the exhaust gas by the volumetric flow rate (Q) of the gas stream. This is a fundamental calculation for air pollution control. It is used to determine compliance with emission limits, to design control equipment, and to estimate the contribution of a source to ambient air concentrations. The concentration can be measured continuously or via periodic sampling. Example: A stack has a flow rate of 100,000 m³/h and a measured concentration of SO₂ of 0.5 g/m³. The emission rate is E = 0.5 × 100,000 = 50,000 g/h = 50 kg/h. This would be compared to the permitted limit and may require additional control measures.
Worked example
Stack Emission Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C | 0.05 g/m³ |
| Q | 20 m³/s |
| Parameter | Value |
|---|---|
| C | 0.1 g/m³ |
| Q | 15 m³/s |
Common mistakes
- Concentration C: The pollutant concentration in the stack gas – e.g., µg/m³.
- Flow rate Q: The volumetric flow rate of the stack gas – in m³/s or m³/h.
- Units: E = C × Q – ensure units are consistent (e.g., µg/s, kg/day).
- Reference conditions: Flow and concentration are often corrected to standard conditions (e.g., dry, 0°C, 1 atm).
- Sampling: Concentration may vary over time – use average values for emission calculations.
Applications
Stack emission rate is the product of pollutant concentration (C) and volumetric flow rate (Q) of the flue gas, providing the mass of pollutant emitted per unit time (e.g., kg/hr). This is a fundamental calculation for industrial emission inventories, permit compliance, and design of pollution control equipment. Environmental engineers use it to estimate annual emissions, to determine the efficiency of control devices (e.g., scrubbers, baghouses), and to report to regulatory agencies. Accurate stack emission rates are required for dispersion modelling, health risk assessments, and greenhouse gas reporting. By quantifying emissions, facilities can identify major sources, implement reduction strategies, and demonstrate environmental stewardship.
- Compliance with air permits and emission standards
- Inventory of pollutants for reporting (e.g., EPA TRI, E‑Permitting)
- Design and performance testing of air pollution control devices
- Fugitive emission estimation and leak detection programmes
- Modelling of atmospheric dispersion and human health risk
Frequently Asked Questions
The stack emission rate (mass emission rate) is the mass of a pollutant emitted per unit time from an industrial stack. It is calculated as E = C × Q, where C is the concentration of the pollutant in the stack gas (e.g., mg/m³) and Q is the volumetric flow rate of the stack gas (m³/s or m³/h). The units of E are mass/time (e.g., kg/h).
Using the stack gas flow rate measured at actual (hot) conditions when the regulatory standard requires reporting at standard temperature and pressure (STP), or vice versa. Flow must be corrected to the reference conditions (e.g., dry basis, standard temperature and pressure).
Use the ideal gas law: Q_std = Q_actual × (P_actual / P_std) × (T_std / T_actual), where P and T are absolute pressure and temperature. Also, subtract moisture: Q_dry = Q_wet × (1 – moisture fraction).
Common units:
- kg/h, kg/day.
- g/s, g/min.
- tonnes/year.
Using a pitot tube or other velocity sensor to measure velocity and cross‑sectional area. The flow rate is Q = A × v, where A is the area and v is the average velocity. For velocity, EPA Method 2 is commonly used.
Concentration is the amount of pollutant per volume of gas (e.g., mg/m³). Emission rate is the mass of pollutant emitted per unit time (e.g., kg/h). Emission rate = concentration × flow rate.
If concentration varies with time, you need to integrate: E = ∫ C(t) × Q(t) dt over the measurement period. In practice, you take a representative sample and use average values.
Emission rates are regulated by permits and must be below specified limits. They are used to calculate annual emissions, which are reported to regulatory agencies and used for emissions inventories.
Multiply by the operating hours per year and divide by 1000. For example, 10 kg/h × 8760 h/year / 1000 = 87.6 tonnes/year.
- EPA Method 1‑4: velocity and flow rate.
- EPA Method 5: particulate matter.
- EPA Method 6, 7, 8, etc.: for specific gases (SO₂, NOₓ, HCl).
- Continuous emissions monitoring systems (CEMS).