Principles and Practice of Engineering Exam (PE) Environmental Engineering (PE Environmental) Syllabus

Name the two phases of anaerobic digestion and the principal end product gas.

Phase 1: acidogenesis/acetogenesis (acid-forming bacteria convert organics to volatile fatty acids). Phase 2: methanogenesis (methanogens convert acetate/$\ce{H2}$ to gas). Biogas is roughly $60\text{–}70\%$ $\ce{CH4}$ and $30\text{–}40\%$ $\ce{CO2}$.

Write the Hazen–Williams equation for head loss in a pressurized pipe (US units).

$$h_f = \frac{10.44\, L\, Q^{1.85}}{C^{1.85}\, D^{4.87}}$$ where $h_f$ is head loss (ft), $L$ pipe length (ft), $Q$ flow (gpm), $C$ the Hazen–Williams roughness coefficient, and $D$ diameter (in).

Write the Darcy–Weisbach equation for friction head loss in a pipe.

$$h_f = f\frac{L}{D}\frac{v^{2}}{2g}$$ where $f$ is the Darcy friction factor, $L$ length, $D$ diameter, $v$ mean velocity, and $g$ gravitational acceleration.

State Manning's equation for open-channel (gravity sewer) flow in US units.

$$v = \frac{1.49}{n}R^{2/3}S^{1/2}$$ where $v$ is velocity (ft/s), $n$ Manning's roughness, $R$ the hydraulic radius (area/wetted perimeter), and $S$ the channel slope. Flow $Q = vA$.

What minimum velocity is typically required in sanitary sewers and why?

A minimum self-cleansing velocity of about $2$ ft/s ($0.6$ m/s) is required at design flow to prevent deposition and keep solids in suspension. Maximum velocity is limited (~$10$ ft/s) to avoid scour/abrasion.

What is the Hardy Cross method used for in water distribution analysis?

It is an iterative technique to balance flows in a looped pipe network so that (1) flow into each node equals flow out, and (2) the algebraic sum of head losses around each loop equals zero. Flow corrections are computed as $$\Delta Q = -\frac{\sum h_f}{n \sum \frac{h_f}{Q}}$$

Using the Rational Method, what is the formula for peak stormwater runoff and what does each term mean?

$$Q = C\, i\, A$$ where $Q$ is peak runoff (cfs), $C$ the dimensionless runoff coefficient, $i$ rainfall intensity (in/hr) at the time of concentration, and $A$ the drainage area (acres). (Numerically $1\text{ in/hr}\cdot1\text{ acre} \approx 1$ cfs.)

List the six EPA criteria (NAAQS) air pollutants.

Particulate matter ($\ce{PM10}$/$\ce{PM2.5}$), ground-level ozone ($\ce{O3}$), carbon monoxide ($\ce{CO}$), sulfur dioxide ($\ce{SO2}$), nitrogen dioxide ($\ce{NO2}$), and lead ($\ce{Pb}$).

What is the difference between primary and secondary air pollutants, with examples?

Primary pollutants are emitted directly from sources (e.g., $\ce{CO}$, $\ce{SO2}$, $\ce{NO}$, $\ce{PM}$, $\ce{Pb}$). Secondary pollutants form in the atmosphere through reactions (e.g., ground-level ozone $\ce{O3}$, peroxyacetyl nitrate (PAN), and much sulfate/nitrate $\ce{PM2.5}$).

Write the simplified photochemical smog cycle producing ground-level ozone.

$$\ce{NO2 + h\nu -> NO + O}$$ $$\ce{O + O2 -> O3}$$ VOCs consume $\ce{NO}$, allowing $\ce{O3}$ to accumulate. Net result is ozone formation in the presence of sunlight, $\ce{NO_x}$, and VOCs.

What is the primary distinction between $\ce{PM10}$ and $\ce{PM2.5}$ and why does it matter for health?

$\ce{PM10}$ is particulate matter with aerodynamic diameter $\leq 10\,\mu m$ (coarse); $\ce{PM2.5}$ is $\leq 2.5\,\mu m$ (fine). $\ce{PM2.5}$ penetrates deeper into the alveoli and is more strongly linked to cardiovascular and respiratory disease.

Compare the main particulate control devices: ESP, baghouse (fabric filter), cyclone, and wet scrubber.

Cyclone: inertial separation, best for coarse PM ($>10\,\mu m$), low efficiency on fines. ESP: charges particles and collects on plates, high efficiency, low pressure drop, handles high gas volumes. Baghouse: fabric filtration, very high efficiency even on fines, higher pressure drop. Wet scrubber: captures PM and soluble gases simultaneously, generates wastewater.

State the Deutsch–Anderson equation for electrostatic precipitator collection efficiency.

$$\eta = 1 - e^{-\frac{w A}{Q}}$$ where $w$ is the particle drift (migration) velocity, $A$ the collection plate area, and $Q$ the gas volumetric flow rate.

What control technologies are used to reduce $\ce{SO2}$ and $\ce{NO_x}$ from combustion sources?

$\ce{SO2}$: flue-gas desulfurization (wet limestone scrubbing) $\ce{SO2 + CaCO3 + 1/2 O2 -> CaSO4 + CO2}$, fuel switching. $\ce{NO_x}$: low-$\ce{NO_x}$ burners, selective catalytic reduction (SCR) and selective non-catalytic reduction (SNCR) using ammonia/urea: $\ce{4NO + 4NH3 + O2 -> 4N2 + 6H2O}$.

What is the air-to-cloth (filtering velocity) ratio for a baghouse and its formula?

$$v_f = \frac{Q}{A}$$ the gas flow rate divided by total fabric filter area (units ft/min = cfm/ft²). It sets bag area needed; too high a ratio causes excessive pressure drop and bag wear.

Describe atmospheric stability classes and how they affect plume dispersion.

Pasquill–Gifford classes A–F: A–C are unstable (strong daytime mixing, looping/coning plumes, good dispersion); D is neutral; E–F are stable (nighttime inversions, fanning plumes, poor dispersion and high ground concentrations).

Write the Gaussian plume equation for ground-level centerline concentration from an elevated point source.

$$C(x) = \frac{Q}{\pi u \sigma_y \sigma_z}\exp\!\left(-\frac{H^{2}}{2\sigma_z^{2}}\right)$$ where $Q$ is emission rate, $u$ wind speed, $\sigma_y,\sigma_z$ dispersion coefficients (functions of stability and $x$), and $H$ the effective stack height.

What is a temperature inversion and why does it worsen air pollution?

An inversion occurs when temperature increases with altitude (warm air over cool air), reversing the normal lapse rate. The stable layer caps vertical mixing, trapping pollutants near the ground and causing high concentrations (e.g., the London and Donora smog episodes).

Define the adiabatic lapse rate and how comparing ambient lapse rate to it determines stability.

The dry adiabatic lapse rate is $\Gamma_d \approx 9.8\,^{\circ}\text{C/km}$ ($5.4\,^{\circ}\text{F}/1000\text{ft}$). If the environmental lapse rate is steeper (superadiabatic) the atmosphere is unstable; if less steep (subadiabatic) or inverted, it is stable.

What U.S. law regulates air quality, and what are NSPS and NESHAP?

The Clean Air Act (CAA). NSPS (New Source Performance Standards) set technology-based emission limits for new/modified sources by category. NESHAP regulate hazardous air pollutants (HAPs) using MACT (Maximum Achievable Control Technology) standards.

List the EPA integrated solid waste management hierarchy in priority order.

1) Source reduction/prevention, 2) Reuse, 3) Recycling/composting, 4) Energy recovery (combustion/waste-to-energy), 5) Treatment and landfilling (disposal) as the least preferred option.

What is leachate in a landfill, and what liner/collection systems control it?

Leachate is liquid that percolates through waste, dissolving contaminants. Modern Subtitle D landfills use a composite bottom liner (compacted clay plus a geomembrane such as HDPE) and a leachate collection and removal system (drainage layer + perforated pipes) above the liner.

Which gases dominate landfill gas and in what approximate proportions?

Landfill gas from anaerobic decomposition is roughly $50\%$ methane ($\ce{CH4}$) and $50\%$ carbon dioxide ($\ce{CO2}$), with trace amounts of $\ce{H2S}$, $\ce{N2}$, and VOCs. $\ce{CH4}$ is collected for energy or flared.

How is the required landfill volume related to waste mass and compacted density?

$$V = \frac{M}{\rho_c}$$ where $M$ is the mass of waste (plus daily cover) and $\rho_c$ is the in-place compacted density. Higher compaction density extends landfill life by reducing required volume.

Under RCRA, what are the four characteristics that make a solid waste 'hazardous'?

Ignitability, Corrosivity, Reactivity, and Toxicity. Toxicity is determined by the TCLP (Toxicity Characteristic Leaching Procedure). Wastes may also be hazardous by being specifically listed (F, K, P, U lists).

Contrast RCRA and CERCLA (Superfund) in scope.

RCRA governs 'cradle-to-grave' management of currently generated hazardous waste (generation, transport, treatment, storage, disposal). CERCLA addresses cleanup of past/abandoned contaminated sites and assigns liability to responsible parties via the Superfund.

What does Darcy's law describe for groundwater flow, and give its form.

It describes laminar flow through porous media: $$q = -K\frac{dh}{dl}, \qquad Q = -KA\frac{dh}{dl}$$ where $q$ is specific discharge (Darcy velocity), $K$ hydraulic conductivity, $A$ cross-sectional area, and $\frac{dh}{dl}$ the hydraulic gradient.

How does seepage (actual pore) velocity relate to Darcy velocity?

$$v_s = \frac{q}{n_e} = \frac{K}{n_e}\frac{dh}{dl}$$ where $n_e$ is the effective porosity. The seepage velocity is faster than the Darcy velocity because water flows only through the pore spaces.

What is the retardation factor in contaminant transport and its formula?

$$R = 1 + \frac{\rho_b K_d}{n}$$ where $\rho_b$ is bulk density, $K_d$ the soil-water partition (distribution) coefficient, and $n$ porosity. $R$ measures how much slower a sorbing contaminant moves relative to groundwater; contaminant velocity $= v_s / R$.

Distinguish an unconfined aquifer from a confined aquifer.

An unconfined (water-table) aquifer has its upper boundary at the water table, open to atmospheric pressure, recharged directly from above. A confined (artesian) aquifer is bounded above and below by low-permeability layers; water is under pressure and rises above the aquifer top in wells (potentiometric surface).

What is the equilibrium partitioning relationship governing sorption (linear isotherm)?

$$q = K_d C$$ where $q$ is the mass of contaminant sorbed per mass of solid, $C$ the aqueous concentration, and $K_d$ the distribution coefficient. For organics, $K_d = K_{oc}\, f_{oc}$, relating sorption to organic-carbon content.

Define Henry's law constant and its role in air–water partitioning.

Henry's law relates a volatile compound's gas-phase partial pressure (or air concentration) to its dissolved concentration: $$p = H\, C$$ A higher Henry's constant means the compound more readily volatilizes from water to air (favoring air stripping).

Name common groundwater/soil remediation technologies and what each targets.

Pump-and-treat (hydraulic containment + aboveground treatment), air sparging + soil vapor extraction (volatile organics), bioremediation (biodegradable contaminants), permeable reactive barriers (in-situ passive treatment), and excavation/dig-and-haul for hot spots.

Write the carbonate equilibrium reactions describing the carbonate buffering system in natural water.

$$\ce{CO2 + H2O <=> H2CO3 <=> H+ + HCO3- <=> 2H+ + CO3^{2-}}$$ with $pK_{a1}\approx 6.3$ and $pK_{a2}\approx 10.3$. This system buffers pH; bicarbonate $\ce{HCO3-}$ dominates at typical natural pH (6.3–10.3).

Define alkalinity and how it is expressed.

Alkalinity is water's acid-neutralizing capacity, primarily from $\ce{HCO3-}$, $\ce{CO3^{2-}}$, and $\ce{OH-}$: $$\text{Alk} = [\ce{HCO3-}] + 2[\ce{CO3^{2-}}] + [\ce{OH-}] - [\ce{H+}]$$ It is conventionally reported as mg/L as $\ce{CaCO3}$.

What is the relationship between pH, pOH, and the ion product of water at 25°C?

$$K_w = [\ce{H+}][\ce{OH-}] = 1.0 \times 10^{-14}$$ so $$pH + pOH = 14, \qquad pH = -\log_{10}[\ce{H+}]$$

What do total, fecal, and E. coli coliform tests indicate in water microbiology?

Coliforms are indicator organisms for fecal contamination. Total coliforms screen for general contamination; fecal coliforms and especially E. coli specifically indicate recent fecal pollution and possible pathogens. Drinking water standard: no coliforms detectable (MCLG = 0).

Distinguish aerobic, anaerobic, and facultative microorganisms by electron acceptor.

Aerobes use molecular oxygen $\ce{O2}$ as the terminal electron acceptor. Anaerobes function without $\ce{O2}$, using $\ce{NO3-}$, $\ce{SO4^{2-}}$, or $\ce{CO2}$. Facultative organisms can switch between aerobic and anaerobic metabolism depending on oxygen availability.

Write the Monod equation describing microbial specific growth rate.

$$\mu = \mu_{max}\frac{S}{K_s + S}$$ where $\mu$ is specific growth rate, $\mu_{max}$ the maximum rate, $S$ the limiting substrate concentration, and $K_s$ the half-saturation constant (substrate concentration at $\mu = \tfrac{1}{2}\mu_{max}$).

In risk assessment, what are the four steps of the EPA human health risk assessment paradigm?

1) Hazard identification, 2) Dose–response assessment, 3) Exposure assessment, 4) Risk characterization (combining the prior steps to estimate risk).

How is chronic daily intake / average daily dose computed in exposure assessment?

$$ADD = \frac{C \cdot IR \cdot EF \cdot ED}{BW \cdot AT}$$ where $C$ is contaminant concentration, $IR$ intake rate, $EF$ exposure frequency, $ED$ exposure duration, $BW$ body weight, and $AT$ averaging time.

How is excess lifetime cancer risk calculated for a carcinogen, and what risk range is generally acceptable?

$$\text{Risk} = CDI \times SF$$ where $CDI$ is chronic daily intake (mg/kg·day) and $SF$ the cancer slope factor (per mg/kg·day). EPA generally considers acceptable risk in the range $10^{-6}$ to $10^{-4}$.

For non-carcinogenic effects, what is the hazard quotient and what does $HQ > 1$ mean?

$$HQ = \frac{ADD}{RfD}$$ where $RfD$ is the reference dose (threshold considered safe). $HQ \leq 1$ implies adverse effects are unlikely; $HQ > 1$ indicates potential for non-cancer health effects. The sum of HQs is the Hazard Index (HI).

Differentiate an MCL from an MCLG under the Safe Drinking Water Act.

The MCLG (Maximum Contaminant Level Goal) is a non-enforceable, health-based target with no known adverse effect (often zero for carcinogens). The MCL is the enforceable standard, set as close to the MCLG as feasible considering treatment technology and cost.

What does the Clean Water Act regulate, and what is an NPDES permit?

The CWA regulates discharges of pollutants into navigable waters of the U.S. and sets water-quality standards. The NPDES (National Pollutant Discharge Elimination System) permit authorizes and limits point-source discharges, specifying effluent limits and monitoring.

What is a TMDL under the Clean Water Act?

A Total Maximum Daily Load is the maximum amount of a pollutant a water body can receive and still meet water-quality standards. It allocates that load among point sources (waste load allocation), nonpoint sources (load allocation), and a margin of safety.

Write the Streeter–Phelps dissolved oxygen sag equation for a river below a waste discharge.

$$D = \frac{k_d L_0}{k_r - k_d}\left(e^{-k_d t} - e^{-k_r t}\right) + D_0 e^{-k_r t}$$ where $D$ is the DO deficit, $L_0$ ultimate BOD, $k_d$ deoxygenation rate, $k_r$ reaeration rate, $D_0$ initial deficit, and $t$ travel time.

At the critical point of the DO sag curve, what condition holds and how is the critical time found?

At the critical (minimum DO) point the rate of deoxygenation equals reaeration, so $\frac{dD}{dt}=0$. The critical time is $$t_c = \frac{1}{k_r - k_d}\ln\!\left[\frac{k_r}{k_d}\left(1 - \frac{D_0(k_r - k_d)}{k_d L_0}\right)\right]$$

What does a completely mixed flow reactor (CMFR/CSTR) mass balance at steady state look like for a first-order reaction?

For a CSTR with first-order decay ($r=-kC$) at steady state: $$Q C_0 = Q C + k C V \;\Rightarrow\; \frac{C}{C_0} = \frac{1}{1 + k\theta}$$ where $\theta = V/Q$ is the detention time.

Compare effluent quality of a PFR versus a CSTR for the same first-order reaction and detention time.

PFR: $\frac{C}{C_0} = e^{-k\theta}$. CSTR: $\frac{C}{C_0} = \frac{1}{1+k\theta}$. For the same $k$ and $\theta$, the plug-flow reactor achieves greater conversion (lower effluent concentration) than the completely mixed reactor.

What is the Reynolds number and what threshold separates laminar and turbulent pipe flow?

$$Re = \frac{\rho v D}{\mu} = \frac{vD}{\nu}$$ For pipe flow, $Re < 2100$ is laminar, $Re > 4000$ is turbulent, with a transitional zone between. It is the ratio of inertial to viscous forces.

In a rapid sand filter, define the filtration (loading) rate and a typical design value.

$$\text{Loading rate} = \frac{Q}{A}$$ (flow per unit filter plan area, gpm/ft² or m/h). Conventional rapid sand filters operate around $2\text{–}5$ gpm/ft² ($5\text{–}12$ m/h). Backwashing periodically removes captured solids.