18-Env-A4 Water and Wastewater Engineering · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams / EGBC — May 2015 — 04-ENV-A4 Water and Wastewater Engineering. Three-hour exam; Question 1 is compulsory (25 marks) and any three of the remaining four questions are required (25 marks each); all five are solved below for completeness. Closed book, one double-sided aid sheet permitted, approved calculator permitted.
Reference texts: Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.) — nitrogen and solids characterization, BOD test theory, nitrification/alkalinity, disinfection chemistry, activated-sludge and sludge-processing design; Davis & Cornwell, Introduction to Environmental Engineering (6th ed.) — the Streeter–Phelps oxygen sag, pH and coagulation–flocculation chemistry, jar testing; MWH's Water Treatment: Principles and Design (3rd ed.) — granular filtration (headloss, backwash) and chemical phosphorus removal.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
pH is the negative base-10 logarithm of the hydrogen-ion activity, $\text{pH}=-\log_{10}[H^+]$, a dimensionless measure on a 0–14 scale of how acidic (pH<7) or basic (pH>7) a water is at 25 °C. For disinfection, pH controls the speciation of aqueous chlorine between hypochlorous acid ($HOCl$, $pK_a\approx7.5$ at 20 °C) and hypochlorite ion ($OCl^-$); $HOCl$ is roughly 80–100 times more effective a biocide than $OCl^-$ because its neutral charge lets it penetrate microbial cell walls far more readily, so disinfection is markedly less efficient at high pH (where $OCl^-$ dominates) and a higher CT (concentration × time) is needed to compensate. For coagulation–flocculation, each coagulant has a narrow optimum pH range where its metal-hydroxide floc has minimum solubility and forms an effective, rapidly settling precipitate through charge neutralization and sweep-floc capture (roughly pH 5.5–7.5 for alum, pH 5–8.5 for ferric salts); outside that band the metal stays in soluble form or forms a fragile floc, and coagulant is wasted without achieving turbidity/colour removal. Operators therefore control (and often pre-adjust with lime, soda ash, or acid) pH ahead of both disinfection and coagulation to keep each process in its effective window.
Given. A raw sewage sample is diluted in a standard BOD bottle and incubated at 20 °C; 5% of the observed 3-day oxygen depletion is attributed to the seed organisms already present in the sample (not the sewage itself).
| Quantity | Value |
|---|---|
| Sample volume $V_s$ | 5 mL |
| Total bottle (diluted) volume $V_t$ | 300 mL |
| Initial DO, $DO_i$ | 7.5 mg/L |
| DO after 3 days, $DO_f$ | 4.3 mg/L |
| Incubation time, temperature | 3 days at 20 °C |
| Seed contribution to depletion | 5% |
Find. The 3-day BOD ($\text{BOD}_3$), 5-day BOD ($\text{BOD}_5$) and ultimate BOD ($\text{BOD}_u$) of the undiluted sewage sample.
Approach. Compute the dilution fraction, correct the observed DO depletion for the seed's own contribution, scale by the dilution to get $\text{BOD}_3$ of the undiluted sample, then use the assumed first-order BOD-exertion model $\text{BOD}_t=\text{BOD}_u(1-10^{-k_1t})$ to back out $\text{BOD}_u$ and forward-compute $\text{BOD}_5$.
| Quantity | Result |
|---|---|
| Dilution fraction $P$ | 0.01667 |
| 3-day BOD, $\text{BOD}_3$ | 182.4 mg/L |
| 5-day BOD, $\text{BOD}_5$ | 250.0 mg/L |
| Ultimate BOD, $\text{BOD}_u$ | 365.7 mg/L |
