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Exercise set

Air Quality and Emissions Control Systems Exercises

Worked environmental engineering exercises for air emissions covering stack mass rate, capture flow, removal efficiency, fan power, filter pressure drop, carbon-bed capacity, bypass emissions, monitoring uncertainty, and corrective-action evidence.

Branch
Environmental Engineering
Content
Exercise set
Updated
Revision
v1.1.0 · reviewed

These exercises practise first-pass calculations used in air quality and emissions control engineering. They connect source definition, capture flow, stack load, removal efficiency, pressure drop, fan energy, treatment-media capacity, bypass governance, monitoring uncertainty, and corrective-action evidence.

Assume simplified nominal values unless an exercise states otherwise. Real emissions decisions require approved test methods, gas-condition corrections, process operating data, permit limits, safety review, monitoring quality assurance, control-device inspection, and responsible engineering review.

How to Use These Exercises

For each problem:

  1. define the emission source, operating mode, pollutant, and control boundary;
  2. state whether the value is concentration, mass rate, total load, or control efficiency;
  3. keep flow, concentration, pressure, power, and time units consistent;
  4. separate nominal control performance from verified operating evidence;
  5. identify which alarm, inspection, or record would confirm the result in service.

The most common mistake is treating a control device as the whole system. Air emissions control also depends on capture, duct balance, fan capacity, bypass state, monitoring quality, maintenance, and operating envelope.

For each result, state whether it supports permit compliance, capture verification, control-device performance, maintenance action, bypass approval, monitoring validity, or corrective-action closeout. An emissions number is defensible only when source condition, measurement basis, control state, and acceptance criterion are documented together.

Exercise 1: Stack Emission Mass Rate

A stack exhausts Q=3.2\ \text{m}^3/\text{s} with measured pollutant concentration C=46\ \text{mg/m}^3 on the stated reporting basis.

Estimate the pollutant mass rate in \text{g/s} and \text{kg/h}.

Solution

Mass rate:

\dot M=QC
\dot M=3.2(46)=147.2\ \text{mg/s}

Convert:

147.2\ \text{mg/s}=0.147\ \text{g/s}

Hourly mass:

0.147(3600)=529.9\ \text{g/h}=0.530\ \text{kg/h}

Engineering Comment

The calculation is only as reliable as the flow and concentration basis. Temperature, moisture, oxygen correction, sampling location, averaging period, and instrument calibration must match the compliance method.

Exercise 2: Hood Capture Flow

A local exhaust hood has rectangular opening 1.2\ \text{m}\times0.8\ \text{m}. The design face velocity is 0.65\ \text{m/s}.

Estimate the required volumetric flow rate.

Solution

Hood area:

A=1.2(0.8)=0.96\ \text{m}^2

Volumetric flow:

Q=vA
Q=0.65(0.96)=0.624\ \text{m}^3/\text{s}

Convert to cubic metres per hour:

Q=0.624(3600)=2246\ \text{m}^3/\text{h}

Engineering Comment

Face velocity alone does not prove capture. Cross-drafts, source distance, thermal plume, make-up air, operator position, enclosure leakage, and duct balance can make actual capture weaker than the nominal flow suggests.

Exercise 3: Control-Device Removal Efficiency

A particulate control device receives inlet concentration C_{in}=180\ \text{mg/m}^3 and has outlet concentration C_{out}=12\ \text{mg/m}^3.

Find the removal efficiency.

Solution

Removal efficiency:

\displaystyle \eta_c=\frac{C_{in}-C_{out}}{C_{in}}
\displaystyle \eta_c=\frac{180-12}{180}=0.933=93.3\%

Engineering Comment

Overall efficiency can hide particle-size performance. A collector may remove coarse particles well while passing fine particles. Test method, flow condition, moisture, filter condition, and operating load should be recorded.

Exercise 4: Residual Emissions After Control

An uncontrolled source emits 18\ \text{kg/day} of a pollutant. The control system has verified average removal efficiency of 94\% during the current operating envelope.

Estimate residual emissions.

Solution

Residual fraction:

1-\eta=1-0.94=0.06

Residual emissions:

M_{out}=18(0.06)=1.08\ \text{kg/day}

Engineering Comment

The phrase “verified average” matters. If production rate, raw material, moisture, flow, temperature, or control-device condition changes, the verified efficiency may no longer apply.

Exercise 5: Fan Power from Pressure Drop

A fan moves Q=2.8\ \text{m}^3/\text{s} through ductwork and a control device with total pressure rise requirement \Delta p=950\ \text{Pa}. Combined fan and motor efficiency is \eta=0.62.

Estimate required input power.

Solution

Fan input power:

\displaystyle P_{in}=\frac{Q\Delta p}{\eta}
\displaystyle P_{in}=\frac{2.8(950)}{0.62}=4290\ \text{W}
P_{in}=4.29\ \text{kW}

Engineering Comment

The fan should be checked against its curve, not only this single point. Filter loading, damper position, duct fouling, temperature, gas density, and future airflow changes can shift the operating point.

Exercise 6: Filter Pressure-Drop Trend

A filter bank has clean pressure drop of 320\ \text{Pa}. The maintenance trigger is 900\ \text{Pa}. Weekly readings are:

410,\ 560,\ 730,\ 920\ \text{Pa}

Identify the maintenance state after the fourth reading.

Solution

Fourth reading:

\Delta p_4=920\ \text{Pa}

Since:

920>900

the maintenance trigger has been exceeded.

Engineering Comment

The action should be defined before the reading occurs. It may include filter inspection, replacement, leak check, production-rate review, alarm verification, and confirmation that bypass dampers were not opened to compensate for pressure drop.

Exercise 7: Activated Carbon Media Capacity

An activated carbon bed has usable pollutant capacity of 48\ \text{kg} before changeout. The inlet pollutant mass rate after upstream control is 0.32\ \text{kg/h}. Assume no safety factor for this screening calculation.

Estimate ideal operating time to capacity.

Solution

Operating time:

\displaystyle t=\frac{Capacity}{\dot M}
\displaystyle t=\frac{48}{0.32}=150\ \text{h}

Engineering Comment

Actual breakthrough can occur earlier because of humidity, temperature, competing compounds, channeling, media aging, concentration peaks, and incomplete use of bed depth. Changeout should use monitoring or conservative service life, not only ideal capacity.

Exercise 8: Bypass Emissions During Maintenance

A control device is bypassed for 35\ \text{min} during maintenance. During bypass, the source emits 0.42\ \text{kg/h}.

Estimate uncontrolled mass emitted during the bypass period.

Solution

Convert time:

\displaystyle 35\ \text{min}=\frac{35}{60}=0.583\ \text{h}

Mass emitted:

M=0.42(0.583)=0.245\ \text{kg}

Engineering Comment

Bypass governance should state who approved the bypass, why it was necessary, whether production was reduced, which monitoring was active, and how return to normal control was verified.

Exercise 9: Analyzer Signal-to-Noise Ratio

An analyzer reports a pollutant signal of 7.5\ \text{ppm} above baseline. The estimated combined noise and drift over the reporting interval is 1.8\ \text{ppm}.

Estimate the signal-to-noise ratio.

Solution

Signal-to-noise ratio:

\displaystyle SNR=\frac{7.5}{1.8}=4.17

Engineering Comment

The signal is clearly above the stated noise scale, but measurement quality still depends on calibration gas, sampling line losses, response time, interference, condensation control, and data validation rules.

Exercise 10: Corrective-Action Evidence

An emissions-event closeout requires eight records: process log, fan status, damper status, pressure-drop trend, analyzer calibration, maintenance work order, follow-up reading, and supervisor approval. Six are accepted, one calibration record is missing, and one follow-up reading is pending.

Find the accepted-evidence percentage and unresolved item count.

Solution

Accepted-evidence percentage:

\displaystyle C_e=\frac{6}{8}\times100=75\%

Unresolved items:

N_u=1+1=2

Engineering Comment

The event should not be closed. Missing calibration evidence can undermine the measured exceedance or non-exceedance, and a pending follow-up reading means restored performance has not been verified.

Review Checklist

Before accepting an air-quality screening calculation, check:

  • whether flow and concentration use the same reporting basis;
  • whether capture is verified, not only control-device performance;
  • whether pressure drop, fan curve, and filter condition support the required flow;
  • whether removal efficiency applies to the pollutant form and particle-size range of concern;
  • whether bypass states are approved, logged, limited, and verified after restoration;
  • whether analyzers have calibration, detection limit, response time, and drift evidence;
  • whether environmental controls create unmanaged energy, waste, water, or safety impacts;
  • whether operating mode, production rate, moisture, temperature, oxygen correction, and averaging period match the permit or test-method basis;
  • whether open events separate root-cause evidence from restored-performance evidence;
  • whether corrective actions remain open until cause and restored performance are both documented.

Good air-emissions engineering keeps the source, capture path, treatment device, monitoring system, and operating envelope tied together.

REF

See also

  1. Air Quality and Emissions Control Systems Environmental Engineering
  2. Environmental Impact Assessment, Permitting, and Compliance Engineering Environmental Engineering
  3. Environmental Impact Assessment, Permitting, and Compliance Engineering Exercises Environmental Engineering
  4. Solid Waste and Resource Recovery Systems Environmental Engineering
  5. Solid Waste and Resource Recovery Systems Exercises Environmental Engineering
  6. Environmental Water and Wastewater Systems Environmental Engineering
  7. Stormwater and Urban Flood Resilience Environmental Engineering
  8. Chemical Process Safety and Hazard Control Chemical Engineering
  9. Separation Processes and Distillation Engineering Chemical Engineering
  10. Separation Processes and Distillation Engineering Exercises Chemical Engineering
  11. Mechanical Fluid Flow and Piping Systems Mechanical Engineering
  12. Mechanical Fluid Flow and Piping Systems Exercises Mechanical Engineering
  13. Building Energy Systems and HVAC Performance Energy Engineering
  14. Power Generation and Grid Integration Energy Engineering
  15. Thermal Energy Systems and Heat Exchangers Energy Engineering
  16. Quality Engineering and Process Improvement Industrial and Management Engineering
  17. Air Emissions Environmental Engineering quantity
  18. Environmental Compliance Environmental Engineering concept
  19. Environmental Monitoring Environmental Engineering method
  20. Pollutant Load Environmental Engineering quantity
  21. Mass Balance Chemical Engineering model
  22. Flow Rate Mechanical Engineering quantity
  23. Density Materials Engineering quantity
  24. Continuity Equation Mechanical Engineering model
  25. Reynolds Number Mechanical Engineering quantity
  26. Turbulence Mechanical Engineering phenomenon
  27. Viscosity Mechanical Engineering quantity
  28. Gauge Pressure Mechanical Engineering quantity
  29. Vapor Pressure Chemical Engineering quantity
  30. Oxidation Chemical Engineering process
  31. Efficiency Energy Engineering metric
  32. Power Electrical Engineering quantity
  33. Heat Exchanger Energy Engineering device
  34. Thermal Efficiency Energy Engineering metric
  35. Closed-Loop Control Automation and Control Engineering concept
  36. Signal-to-Noise Ratio Telecommunications Engineering metric
  37. Error Budget Electronic Engineering method
  38. Uncertainty Analysis Mathematical Engineering method
  39. Validation Industrial and Management Engineering method
  40. Reliability Industrial and Management Engineering metric
  41. Failure Mode Industrial and Management Engineering concept
  42. Interlock Industrial and Management Engineering device
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