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

24 sample cards from the Environmental Engineering (PE Environmental) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. 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 $= v_s / R$.

2. 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).

3. 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.

4. 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).

5. 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.

6. 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).

7. 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 $\ce{CaCO3}$.

8. 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 $$pH + pOH = 14, \qquad pH = -\log_{10}[\ce{H+}]$$

9. 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).

10. 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.

11. 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 $\mu = \tfrac{1}{2}\mu_{max}$).

12. 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).

13. 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.

14. 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 $10^{-4}$.

15. 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).

16. 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.

17. 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.

18. 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.

19. 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.

20. 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 $$t_c = \frac{1}{k_r - k_d}\ln\!\left[\frac{k_r}{k_d}\left(1 - \frac{D_0(k_r - k_d)}{k_d L_0}\right)\right]$$

21. 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.

22. 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.

23. 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.

24. 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.

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