FE Environmental — Class Review — 120 Cards

Original FE review from our class-to-exam study pack: mass balances, treatment, oxygen demand, stoichiometry, chemical fate, hydraulics, hydrology, erosion, and water distribution/disinfection. Includes recognition cues, units, assumptions, and short worked examples. Updated September 8, 2026.

[Mass Balance and Units] What does a mass balance track?

The mass of a chosen substance entering, leaving, being generated or consumed, and accumulating in a defined system. Write: accumulation = in - out + generation - consumption.

[Mass Balance and Units] What does steady state mean?

The amount stored does not change with time, so accumulation is zero. Reactions and flow can still occur.

[Mass Balance and Units] What makes a substance conservative in a balance?

It is not generated or consumed by reaction within the selected boundary. It can still enter, leave, or accumulate.

[Mass Balance and Units] How do you calculate stored mass from concentration and volume?

M = C V. Match volume units: 10 mg/L in 2 m3 gives 10 mg/L x 2000 L = 20,000 mg = 20 g.

[Mass Balance and Units] What is mass loading and its recognition cue?

Mass per time, such as kg/day or lb/day. Given concentration and flow, start with mass rate = C Q and cancel the units.

[Mass Balance and Units] How do you calculate kg/day from mg/L and m3/day?

Load = C Q / 1000. Example: 200 mg/L x 500 m3/day / 1000 = 100 kg/day.

[Mass Balance and Units] How do you calculate lb/day from mg/L and MGD?

Load = 8.34 C Q. The factor applies specifically to mg/L and million US gallons/day. Example: 100 mg/L at 2 MGD gives 1668 lb/day.

[Mass Balance and Units] What is hydraulic residence time (HRT)?

Nominal average water residence time: theta = V/Q. Example: 600 m3 / (1200 m3/day) = 0.5 day = 12 hours.

[Mass Balance and Units] When can you use Cout = (Q1 C1 + Q2 C2)/(Q1 + Q2)?

For complete mixing at steady state with a conservative constituent and no other sources or sinks. Weight concentrations by their flow rates.

[Mass Balance and Units] How do you calculate percent concentration removal?

100(Cin - Cout)/Cin. Example: 200 to 20 mg/L is 90%. This equals mass removal efficiency only when inlet and outlet flows are equal.

[Mass Balance and Units] How do you calculate mass removal efficiency when flows differ?

100(Qin Cin - Qout Cout)/(Qin Cin). Put both loads on the same time and mass basis.

[Mass Balance and Units] What unit checks should you do before substituting?

Convert diameter to the required length unit, match time units, and distinguish mg from g and kg. 1 m3 = 1000 L; 1 kg = 1,000,000 mg; 1 day = 24 h.

[Treatment and Constituents] How are total, suspended, and dissolved solids related?

TS = TSS + TDS on a consistent analytical basis. Suspended solids are operationally retained by the test filter; dissolved solids pass through it.

[Treatment and Constituents] Are all suspended solids settleable?

No. Settleable solids are the portion that settles under the test conditions; fine or colloidal suspended particles may remain.

[Treatment and Constituents] What is preliminary wastewater treatment for?

Protect downstream equipment and remove coarse material. Typical operations include screening and grit removal; flow measurement supports operation.

[Treatment and Constituents] What does primary clarification mainly remove?

Settleable solids by gravity and floatable material by skimming. It does not remove all dissolved contaminants.

[Treatment and Constituents] What does secondary biological treatment mainly accomplish?

Microorganisms transform biodegradable material; the resulting biomass must also be separated from the water.

[Treatment and Constituents] What is tertiary or advanced treatment?

Additional treatment selected for the objective, such as nutrient removal, finer solids removal, adsorption, or membrane separation. Exact process sequences vary.

[Treatment and Constituents] How do coagulation and flocculation differ?

Coagulation destabilizes particles, commonly using rapid chemical mixing. Flocculation uses gentler mixing to grow particles into larger flocs.

[Treatment and Constituents] What is adsorption and how is it different from absorption?

Adsorption is accumulation at a surface, such as on activated carbon. Absorption is uptake into the bulk of another material.

[Treatment and Constituents] What does disinfection accomplish?

Inactivation of pathogens. It is not the same as removing all organisms or removing all chemical contaminants.

[Treatment and Constituents] How do suspended-growth and attached-growth processes differ?

Activated sludge holds much of its biomass in suspension. Trickling filters and rotating biological contactors support attached biofilms.

[Treatment and Constituents] How do aerobic, anoxic, and anaerobic conditions differ?

Aerobic: dissolved oxygen is available. Anoxic denitrification: little or no dissolved oxygen, with nitrate/nitrite as electron acceptors. Anaerobic: neither dissolved oxygen nor nitrate/nitrite is available for those respiration pathways.

[Treatment and Constituents] What is the difference between HRT and solids retention time (SRT)?

HRT tracks water residence time. SRT tracks average solids/biomass retention: mass of solids in the system divided by solids leaving per time, using a consistent system boundary.

[Oxygen Demand and Kinetics] What is dissolved oxygen (DO)?

Oxygen actually dissolved in the water at the time of measurement, commonly in mg O2/L. Oxygen demand measures potential consumption rather than oxygen currently present.

[Oxygen Demand and Kinetics] What is BOD5?

Biochemical oxygen demand exerted over five days under specified test conditions, commonly at 20 degrees C. Results can include nitrogenous demand unless it is inhibited; CBOD measures carbonaceous demand.

[Oxygen Demand and Kinetics] What does COD measure?

Oxygen-equivalent demand of material oxidized by the specified chemical test. It can include biodegradable and less biodegradable material and some inorganic reducing substances.

[Oxygen Demand and Kinetics] What does a higher BOD5/COD ratio suggest?

Generally a larger readily biodegradable fraction for comparable valid samples. It is a screening indicator, not proof of treatment performance or a universal cutoff.

[Oxygen Demand and Kinetics] What is the simple unseeded BOD5 calculation?

BOD5 = (D1 - D2)/P, where D1 and D2 are initial and final bottle DO and P is the decimal fraction of sample in the bottle. Use only when seed correction is unnecessary and the test is valid.

[Oxygen Demand and Kinetics] Work a simple BOD bottle example: D1 = 8, D2 = 3 mg/L, P = 0.05.

DO depletion = 5 mg/L. Divide by sample fraction: BOD5 = 5/0.05 = 100 mg O2/L. The dilution factor is 1/P = 20.

[Oxygen Demand and Kinetics] How is seed oxygen demand accounted for in a seeded BOD calculation?

Subtract the appropriate seed-correction oxygen depletion before dividing by P. A common form is [(D1-D2) - f(B1-B2)]/P; use the problem's definition of f and seed-control data.

[Oxygen Demand and Kinetics] What is first-order decay and when do you use it?

Removal rate is proportional to current concentration. For a batch system or ideal plug-flow travel time with constant k: C = C0 exp(-kt). k has inverse-time units.

[Oxygen Demand and Kinetics] What is the first-order half-life?

t_half = ln(2)/k = 0.693/k. Example: k = 0.10 per day gives a half-life of 6.93 days.

[Oxygen Demand and Kinetics] How are exerted BOD and remaining oxygen demand related?

BOD exerted by time t = L0[1-exp(-kt)]; remaining demand = L0 exp(-kt). L0 is ultimate demand and k is a natural-base first-order rate constant.

[Oxygen Demand and Kinetics] How do you find ultimate demand from BOD5?

L0 = BOD5/[1-exp(-5k)] for k in per day using base e. Example: BOD5 = 100 and k = 0.20/day gives L0 about 158.2 mg/L.

[Oxygen Demand and Kinetics] What is the steady-state completely mixed reactor result for first-order removal?

Cout = Cin/(1+k theta), for equal constant flows and complete mixing. Do not use the plug-flow exponential equation for this reactor model.

[Stoichiometry and Redox] What is the reliable mass-to-mass stoichiometry path?

Balance the reaction; convert grams given to moles; multiply by wanted/given coefficient ratio; convert wanted moles to grams.

[Stoichiometry and Redox] What do balanced reaction coefficients compare?

Numbers of molecules or moles, not masses in grams. Molecular weights are needed to convert between mole and mass ratios.

[Stoichiometry and Redox] How do you calculate molar mass?

Sum each element's atomic mass multiplied by its atom count. Example: H2O is approximately 2(1) + 16 = 18 g/mol.

[Stoichiometry and Redox] How many moles are in 36 g of water using 18 g/mol?

n = m/MW = 36 g / (18 g/mol) = 2 mol. Grams cancel.

[Stoichiometry and Redox] Use CH4 + 2O2 -> CO2 + 2H2O: how much O2 for 8 g CH4?

8 g CH4 x (1 mol/16 g) x (2 mol O2/1 mol CH4) x (32 g/mol O2) = 32 g O2, assuming complete reaction and approximate molar masses.

[Stoichiometry and Redox] How do you identify the limiting reactant?

Convert each available reactant to the amount of the same product it could form. The smaller product amount identifies the limiting reactant.

[Stoichiometry and Redox] What are the basic oxidation-number sum rules?

A free element is 0. A monatomic ion equals its charge. The sum is 0 in a neutral compound and equals the total charge in a polyatomic ion.

[Stoichiometry and Redox] What are common oxidation-number exceptions to remember?

Oxygen is usually -2 but is -1 in peroxides. Hydrogen is usually +1 but is -1 in metal hydrides. Fluorine is -1 in compounds; elemental F2 is 0.

[Stoichiometry and Redox] Find the oxidation number of nitrogen in nitrate, NO3-.

Let nitrogen be x. x + 3(-2) = -1, so x = +5.

[Stoichiometry and Redox] Find the oxidation number of nitrogen in ammonium, NH4+.

Let nitrogen be x. x + 4(+1) = +1, so x = -3. Conversion from ammonium to nitrate increases nitrogen's oxidation number.

[Stoichiometry and Redox] How do oxidation, reduction, and their agents relate?

Oxidation loses electrons and increases oxidation number. Reduction gains electrons and decreases it. The oxidizing agent is reduced; the reducing agent is oxidized.

[Stoichiometry and Redox] What is the theoretical oxygen requirement for ammonia-N to nitrate-N?

Ignoring synthesis, NH4+ + 2O2 -> NO3- + 2H+ + H2O gives 64/14 = 4.57 g O2 per g N. The basis is mass as nitrogen, not mass as NH4+.

[Chemical Fate and Partitioning] What is aqueous solubility?

The equilibrium concentration that can dissolve under specified conditions. Temperature, pH, and chemical form can matter; dissolved concentration is not total concentration including particles.

[Chemical Fate and Partitioning] What does vapor pressure describe?

Equilibrium vapor pressure above a substance at a specified temperature. Higher values indicate greater volatility under comparable conditions; it is not the same quantity as Henry's constant.

[Chemical Fate and Partitioning] What does Henry's law describe?

Dilute gas-water equilibrium at a given temperature. For the convention p = H Cwater, higher H means greater gas pressure at the same dissolved concentration.

[Chemical Fate and Partitioning] Why must you check Henry's-constant units and convention?

Some sources define H = p/Cwater, others use the inverse or a dimensionless concentration ratio. The meaning of a high numerical value reverses for inverse definitions.

[Chemical Fate and Partitioning] What is the octanol-water partition coefficient, Kow?

Kow = equilibrium concentration in octanol / concentration in water, with consistent concentration units. Larger values indicate greater preference for octanol for the chemical form tested.

[Chemical Fate and Partitioning] Does a high Kow prove biomagnification?

No. It signals affinity for an organic phase, but uptake, metabolism, elimination, ionization, and food-web processes also control accumulation.

[Chemical Fate and Partitioning] What is a soil-water distribution coefficient, Kd?

Kd = concentration sorbed on dry solids / dissolved concentration in water at equilibrium. Using mg/kg over mg/L gives L/kg.

[Chemical Fate and Partitioning] How do Koc and organic-carbon fraction relate to Kd?

For the linear organic-carbon partitioning approximation, Kd = Koc foc, with foc as a decimal mass fraction. Example: 500 L/kg x 0.02 = 10 L/kg.

[Chemical Fate and Partitioning] Work a Kd example: Kd = 10 L/kg and Cwater = 0.2 mg/L.

Csoil = Kd Cwater = 10 L/kg x 0.2 mg/L = 2 mg/kg dry solids. This assumes the stated equilibrium linear relationship.

[Chemical Fate and Partitioning] What is bioconcentration factor (BCF)?

An organism-to-water concentration ratio for uptake from water under defined conditions. With organism mg/kg and water mg/L, BCF has L/kg; dietary uptake is not bioconcentration.

[Chemical Fate and Partitioning] What is the relationship between pH, pKa, and a weak acid?

For HA ⇌ H+ + A−, pH = pKa + log10([A−]/[HA]) under the usual dilute-solution approximation. At pH = pKa, the two forms have equal concentrations.

[Chemical Fate and Partitioning] How do sorption and persistence affect contaminant transport?

Sorption can reduce dissolved mobility but allow transport on eroded particles. Persistence slows degradation. Strong sorption alone does not prove rapid degradation or complete immobility.

[Hydraulics] What is the continuity equation for steady incompressible flow?

Q = A v. Q is volumetric flow, A is flow area, and v is cross-sectional mean velocity. The same Q passes serial pipe sections without leaks or branches.

[Hydraulics] How do you calculate the area of a full circular pipe?

A = pi D^2/4. Convert diameter to compatible units before squaring it. Do not confuse radius and diameter.

[Hydraulics] Work Q = Av: D = 0.20 m and v = 2 m/s.

A = pi(0.20)^2/4 = 0.03142 m2. Q = 0.03142 x 2 = 0.06283 m3/s, or 62.83 L/s.

[Hydraulics] What happens to velocity if pipe diameter halves at fixed flow?

Area becomes one-quarter; velocity becomes four times as large because v = Q/A.

[Hydraulics] How do you calculate hydrostatic gauge pressure at depth h?

p = rho g h for a constant-density fluid below an atmospheric free surface. Example: 1000 x 9.81 x 3 = 29,430 Pa = 29.43 kPa.

[Hydraulics] How do gauge and absolute pressure differ?

Absolute pressure = gauge pressure + local atmospheric pressure. Use absolute pressure in ideal-gas calculations.

[Hydraulics] What are the three basic Bernoulli head terms?

Elevation head z, pressure head p/(rho g), and velocity head v^2/(2g), all in length units. Basic Bernoulli assumes steady incompressible flow without losses or added work along the relevant path.

[Hydraulics] How do pumps and losses enter the energy equation?

Upstream total head + pump head - turbine head = downstream total head + head loss. Draw the system and define the direction before substituting.

[Hydraulics] How do you calculate pump input power?

Pinput = rho g Q H/eta for the stated overall efficiency eta as a decimal. For rho=1000, Q=0.01 m3/s, H=20 m, eta=0.70: about 2.80 kW.

[Hydraulics] What is hydraulic radius?

Rh = flow area / wetted perimeter. Wetted perimeter excludes a free water surface. A full circular pipe has Rh = D/4.

[Hydraulics] What is Manning's equation in SI units?

Q = (1/n) A Rh^(2/3) S^(1/2), with m3/s, m2, m, and dimensionless energy slope S. For uniform flow, energy slope equals bed slope. US customary units require the appropriate conversion factor.

[Hydraulics] How do you distinguish subcritical and supercritical open-channel flow?

Fr = v/sqrt(g A/T), with top width T. Fr < 1 is subcritical, Fr > 1 supercritical, and Fr = 1 critical. For a rectangular channel A/T equals flow depth.

[Hydrology and Surface Water] What is the basic water-budget idea?

Change in storage = total water inflow - total water outflow over the same period. Choose a boundary and avoid double-counting infiltration as both an internal transfer and an external loss.

[Hydrology and Surface Water] Work a simple catchment water budget: P=100, ET=40, runoff=30 mm.

If other boundary fluxes are zero, storage change = 100 - 40 - 30 = +30 mm for the period.

[Hydrology and Surface Water] How are infiltration and runoff different?

Infiltration enters the soil at the surface. Surface runoff travels overland. Soil capacity, antecedent moisture, rainfall intensity, and land cover influence the partition.

[Hydrology and Surface Water] What does the Rational Method estimate?

Peak runoff rate for suitable small catchments under its assumptions. It does not directly give total runoff volume.

[Hydrology and Surface Water] What is the Rational Method with intensity in mm/h and area in hectares?

Qpeak = 0.00278 C i A in m3/s. C is dimensionless. Example: C=0.6, i=50 mm/h, A=10 ha gives about 0.834 m3/s.

[Hydrology and Surface Water] Which rainfall duration is typically used for Rational Method design intensity?

Use an intensity for the selected frequency and a duration corresponding to the time of concentration, consistent with the method and problem assumptions.

[Hydrology and Surface Water] What is time of concentration?

Travel time from the hydraulically most distant contributing location to the outlet, considering the relevant flow paths.

[Hydrology and Surface Water] What does the curve-number rainfall-runoff method estimate?

Direct runoff depth from a storm using rainfall, retention, and initial abstraction assumptions. A separate timing model is needed to obtain peak flow.

[Hydrology and Surface Water] What is the traditional curve-number retention equation?

S = 1000/CN - 10 in inches, or S = 25400/CN - 254 in millimeters. Use the same length units for S, rainfall P, initial abstraction Ia, and runoff.

[Hydrology and Surface Water] What is the curve-number runoff-depth equation?

For P > Ia, runoff depth = (P-Ia)^2/(P-Ia+S); otherwise zero. Traditional problems often specify Ia = 0.2S. Use the ratio actually specified; do not mix calibrated conventions.

[Hydrology and Surface Water] What is dissolved-oxygen deficit in an oxygen-sag problem?

D = saturation DO - actual DO. A larger deficit means less actual oxygen at the same saturation concentration.

[Hydrology and Surface Water] What processes compete in the basic Streeter-Phelps model?

Deoxygenation increases deficit while reaeration reduces it: dD/dt = kd L - kr D. In the simple model L is remaining ultimate oxygen demand; actual DO is saturation DO minus deficit.

[Erosion and Sediment] What does the Universal Soil Loss Equation estimate?

Long-term average sheet and rill soil loss per unit area under its intended conditions: A = R K L S C P. It is not a complete model of gully erosion or sediment delivery.

[Erosion and Sediment] What is R in USLE?

Rainfall-runoff erosivity: the erosive forcing. Use R and K from a compatible unit system and reference basis.

[Erosion and Sediment] What is K in USLE?

Soil erodibility: susceptibility of the soil under the reference conditions. It is distinct from rainfall erosivity R.

[Erosion and Sediment] What are L and S in USLE?

Slope-length and slope-steepness factors. If a combined LS factor is given, multiply it once, not again by separate L and S factors.

[Erosion and Sediment] What is C in USLE?

Cover and management factor relative to the reference condition. Lower C means lower predicted erosion when other factors stay fixed.

[Erosion and Sediment] What is P in USLE?

Support-practice factor, such as for contouring or strip cropping relative to the reference practice. Lower P reduces predicted erosion when other factors stay fixed.

[Erosion and Sediment] Work USLE: R=100, K=0.3, LS=2, C=0.2, P=0.5.

A = 100 x 0.3 x 2 x 0.2 x 0.5 = 6 mass/area/year in the unit system implied by compatible R and K. State that unit system before interpreting the result.

[Erosion and Sediment] What if C falls from 0.4 to 0.1 with other factors fixed?

New loss/old loss = 0.1/0.4 = 0.25. Predicted loss becomes one-quarter, a 75% reduction.

[Erosion and Sediment] How do you turn soil-loss rate into total mass per year?

Multiply mass/area/year by contributing area. Example: 6 Mg/ha/year x 10 ha = 60 Mg/year. One Mg is 1000 kg.

[Erosion and Sediment] What is the standard sediment delivery ratio?

SDR = sediment yield delivered to the defined location / gross erosion for the same area and period. Use a decimal fraction when multiplying gross erosion by SDR.

[Erosion and Sediment] Work sediment delivery: gross erosion=60 Mg/year and SDR=0.20.

Yield = 60 x 0.20 = 12 Mg/year delivered. In this simplified accounting, 48 Mg/year is not delivered to that outlet during the period.

[Erosion and Sediment] How do erosion, transport, and deposition differ?

Erosion detaches material; transport moves it; deposition stores it when transport capacity is insufficient. Sediment-bound contaminants can move with particles.

[Water Distribution and Disinfection] What three distribution functions recur throughout Lecture 01.A?

Transmission moves water, pumping adds hydraulic energy, and storage buffers differences between supply and demand. The overall objective includes both adequate quantity and acceptable quality.

[Water Distribution and Disinfection] Why does source-water quality affect treatment selection?

Different sources contain different contaminants and variability. Select processes for the actual source and treated-water objectives; source labels alone do not establish a complete treatment train.

[Water Distribution and Disinfection] How are raw-water and finished-water storage different?

Raw-water storage is before treatment. Finished-water storage holds treated water and must preserve its quality while meeting hydraulic and supply objectives.

[Water Distribution and Disinfection] What is the purpose of a clearwell?

It holds finished water, can provide disinfectant contact time, and buffers treatment production against distribution withdrawal. Available volume and hydraulic behavior affect its functions.