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Open CalculatorAll Environmental PE Equations (9)
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Average Daily Dose (ADD)
Chronic average daily dose for exposure/risk assessment (ingestion example).
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BOD Exertion (Ultimate vs. BODt)
Biochemical oxygen demand exerted at time t for first-order BOD kinetics.
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Clarifier Surface Overflow Rate
Surface overflow rate (SOR) or surface loading rate for settlers and clarifiers.
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CSTR Effluent Concentration (First-Order)
Completely mixed flow reactor (CSTR) with first-order decay.
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Groundwater Flow (Darcy’s Law)
Darcy’s law for volumetric flow and seepage velocity in porous media.
basicHigh Frequency -
Detention Time (Tank / Basin)
Hydraulic detention time in a tank, reactor, basin, or storage unit.
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First-Order Decay (Batch System)
First-order decay of a contaminant, disinfectant, or microorganism in a batch system.
basicHigh Frequency -
Plug Flow Reactor Effluent (First-Order)
Effluent concentration from a plug flow reactor with first-order decay.
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Two-Stream Mixing Concentration
Resulting concentration from mixing two completely mixed streams.
basicHigh Frequency
Frequently Asked Questions
How do I use Average Daily Dose (ADD) on the PE exam?
The PE exam often provides EPA default exposure parameters. For cancer risk, AT = 70 years × 365.25 days = 25,550 days regardless of actual exposure duration. For non-cancer effects, AT = ED × 365.25. Always check which type of assessment is required before selecting AT values.
How do I use BOD Exertion (Ultimate vs. BODt) on the PE exam?
Standard BOD₅ test assumes k ≈ 0.23 day⁻¹ at 20°C. Remember that BOD₅ is typically 65-70% of ultimate BOD for domestic wastewater. Temperature corrections use k₍T₎ = k₂₀ × θ^(T-20) where θ = 1.047.
How do I use Clarifier Surface Overflow Rate on the PE exam?
Surface overflow rate is a key design parameter - memorize typical ranges! Primary clarifiers: 600-800 gpd/ft², Secondary: 300-800 gpd/ft². Always check if the problem gives diameter (calculate area first) or surface area directly. Watch units carefully - flow is often given in MGD but answer needed in gpd.
How do I use CSTR Effluent Concentration (First-Order) on the PE exam?
This is the fundamental CSTR equation - memorize it! Often given as part of treatment train calculations. Watch units carefully: detention time θ = V/Q must match k units (usually hours). Common on activated sludge and disinfection problems.
How do I use Groundwater Flow (Darcy’s Law) on the PE exam?
Darcy's law appears frequently on PE Environmental exams for groundwater flow calculations and contaminant transport problems. Remember: Q is total volumetric flow, while v is actual seepage velocity through pores (always less than Darcy velocity). Know typical K values for different materials and be ready to calculate travel times for contaminant plumes.