Question 1 of 5: Definitions and their significance

Question 1: Definitions and their significance (25 marks)

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.

Given. The examination supplies no data with this question, so a single representative data set for one Canadian community is adopted and each definition is landed on one number drawn from it.

Find. For each of the five terms, a definition, its engineering significance, and one worked numerical illustration.

Approach. Take each term in turn: state what it is, state what design or regulatory decision it drives, then evaluate it once on the data above.

1. Part (i) — Population equivalent (5 marks). The population equivalent (PE) of a non-domestic discharge is the number of people whose ordinary sewage would exert the same pollutant load, almost always expressed on BOD$_5$. It converts a strong, small-volume industrial stream into the currency in which municipal plants are sized and surcharged: $$\mathrm{PE}=\frac{C\,Q}{L_{\text{cap}}}$$ where $C$ is the discharge strength, $Q$ its flow and $L_{\text{cap}}$ the per-capita load. For the dairy side-stream, $$C\,Q=\frac{1500\ \text{mg/L}\times 40\ \text{m}^3/\text{d}}{1000} =60\ \text{kg BOD}_5/\text{d},\qquad \mathrm{PE}=\frac{60}{0.080}=\boxed{750\ \text{persons}}$$ Its significance is threefold: a 40 m$^3$/d stream that is hydraulically trivial (1.8 per cent of the town's sewage) carries the organic load of 15 per cent of the population, it is the basis of the overstrength surcharge in a Canadian sewer-use by-law, and it is the figure that tells the designer whether aeration, not pipe size, governs the upgrade.
2. Part (ii) — Indicator organisms (5 marks). An indicator organism is a non-pathogenic micro-organism enumerated as a proxy for faecal contamination, because it is abundant in faeces, absent from clean water, at least as persistent as the pathogens of concern, harmless, and cheap and quick to count. Total coliforms, Escherichia coli and enterococci are the usual choices; E. coli is the specific faecal indicator in the GCDWQ. Directly counting Salmonella, Cryptosporidium or enteric viruses is slow, insensitive and hazardous, so the whole discipline of microbial water quality rests on the proxy. Normalising the plate count to the reporting basis of 100 mL, $$N=\frac{68\ \text{colonies}}{10\ \text{mL}}\times 100 =\boxed{680\ \text{CFU}/100\ \text{mL}}$$ Because the GCDWQ maximum acceptable concentration for E. coli in drinking water is none detectable per 100 mL, a result of this magnitude in distribution is an immediate boil-water advisory; in a raw surface water it is instead a design input, since it sets the log-removal credit the treatment train must earn.
3. Part (iii) — Harmon peaking factor (5 marks). The Harmon (or Harmon-Babbitt) factor is the empirical ratio of peak hourly sanitary flow to average daily flow, correlated against served population alone: $$\mathrm{PF}=1+\frac{14}{4+\sqrt{P}}\qquad(P\ \text{in thousands})$$ For $P=5$, $$\mathrm{PF}=1+\frac{14}{4+2.236}=1+2.245=\boxed{3.245}$$ Its significance is that sewers are gravity conduits sized for the peak, not the average, while treatment units are sized on load, so the same design has two flow bases. The factor falls as population rises — 3.25 at 5 000 against 2.31 at 100 000 — because independent household demands average out; that is exactly why small-community collection systems are so often oversized, run at low velocity, and then need flushing.
4. Part (iv) — Disinfection by-products (5 marks). Disinfection by-products (DBPs) are compounds formed when a chemical disinfectant reacts with natural organic matter and bromide in the water rather than with the target organisms. Free chlorine and humic material give trihalomethanes (chloroform, bromodichloromethane and their relatives) and haloacetic acids; ozone with bromide gives bromate; chloramination shifts the distribution towards nitrosamines such as NDMA. Compliance in Canada is judged on a locational running annual average (LRAA) of quarterly results: $$\text{LRAA}=\frac{52+71+88+49}{4}=\boxed{65\ \mu\text{g/L as TTHM}}$$ against the GCDWQ maximum acceptable concentration of 100 $\mu$g/L — compliant at 65 per cent of the MAC, although the 88 $\mu$g/L summer quarter shows how little margin a warm, long-residence-time distribution system leaves. The governing significance is the trade-off: DBPs are a chronic risk measured over a lifetime, microbial breakthrough is an acute one measured over hours, and disinfection must never be compromised to control DBPs. Precursor removal by enhanced coagulation is the correct lever.
5. Part (v) — Coagulation and flocculation (5 marks). The two words name two different physical processes that are routinely confused. Coagulation is the chemical destabilisation of colloids: a hydrolysing metal salt is dispersed in seconds at high velocity gradient ($G\approx 700$ s$^{-1}$, $t\approx 30$ s), compressing the double layer, neutralising the negative surface charge and precipitating an amorphous hydroxide that sweeps particles down with it. Flocculation is the subsequent gentle transport step ($G\approx 40$ s$^{-1}$, $t\approx 20$ min, so $Gt\approx 5\times 10^{4}$) in which the destabilised particles are brought into contact often enough to grow into settleable floc. With alum, $$\text{Al}_2(\text{SO}_4)_3\cdot 14\text{H}_2\text{O}+3\,\text{Ca(HCO}_3)_2 \rightarrow 2\,\text{Al(OH)}_3\downarrow+3\,\text{CaSO}_4 +6\,\text{CO}_2+14\,\text{H}_2\text{O}$$ so each milligram of alum destroys $3\times 100.09/594.4 = 0.505$ mg of alkalinity as CaCO$_3$, and the 30 mg/L jar-test dose consumes $$\Delta\text{Alk}=30\times 0.505=\boxed{15.2\ \text{mg/L as CaCO}_3}$$ The significance is that a soft, poorly buffered Canadian surface water can be driven out of the optimum coagulation pH band (about 6.0 to 6.8 for alum) by its own coagulant dose, which is why lime or soda ash is fed alongside.