Question 2 of 5: Discrete Settling Theory & Indicator Organisms

Question 2: Discrete Settling Theory & Indicator Organisms (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.

(i) Discrete-Settling Removal Depends on Surface Area, Not Depth

Given. An ideal rectangular sedimentation tank with flow $Q$, plan dimensions $L\times W$ and depth $D$, treating particles of discrete settling velocity $v_s$:

Find. Show that the settling velocity $v_0$ separating fully-removed from partially-removed particles is independent of the tank depth $D$.

Approach. Compare the horizontal detention time available for a particle to cross the tank against the vertical time the worst-case (surface-entering) particle needs to reach the floor, and simplify the resulting inequality.

1. Horizontal detention time. Water crosses the tank's cross-section $(W\times D)$ at average velocity $v_H=Q/(WD)$, so a parcel takes $$t_d=\frac{L}{v_H}=\frac{L\,W\,D}{Q}=\frac{\forall}{Q}$$ to travel the length $L$, where $\forall=LWD$ is the tank volume.
2. Worst-case vertical settling time. The hardest particle to capture is one entering right at the water surface; at settling velocity $v_s$ it needs $$t_s=\frac{D}{v_s}$$ to reach the tank floor before the carrying water exits.
3. Impose the capture condition and cancel $D$. The particle is removed only if $t_s\le t_d$: $$\frac{D}{v_s}\le\frac{L\,W\,D}{Q}.$$ $D$ appears on both sides and cancels identically, leaving $$\frac{1}{v_s}\le\frac{L\,W}{Q}\ \Longrightarrow\ v_s\ge\frac{Q}{L\,W}.$$
4. Read off the overflow rate. With plan (surface) area $A_s=LW$, the boundary settling velocity is $$\boxed{v_0=\frac{Q}{A_s}}$$ — the surface overflow rate. Any particle with $v_s\ge v_0$ is 100% removed no matter how deep the tank is (it never had to rely on extra depth); particles with $v_s

(ii) Indicator Organisms

An indicator organism is a microorganism whose detection in a water sample is used as circumstantial evidence of fecal contamination, and therefore of the possible presence of the many waterborne pathogens (bacteria, viruses, protozoa) that would otherwise each require a separate, slow, expensive assay. The classic indicator group is total and thermotolerant (fecal) coliforms, with Escherichia coli the preferred specific indicator under the Guidelines for Canadian Drinking Water Quality.

To serve this purpose an organism should meet several criteria:

• Be present consistently and predominantly in the feces of warm-blooded animals, so its detection specifically flags fecal rather than some other contamination.
• Occur in numbers well above the pathogens it stands in for, so a small pathogen load is detectable through a comfortably larger indicator signal.
• Survive in the water environment at least as long as the target pathogens, so its absence can be trusted to mean the pathogens are also absent.
• Not multiply appreciably in the water itself, so counts reflect contamination rather than in-situ regrowth.
• Be non-pathogenic and easy/safe to culture, and absent from unpolluted water.
• Be detectable by a simple, rapid, inexpensive, reproducible standard test (membrane filtration or multiple-tube fermentation).
• Respond to disinfection in a manner that parallels the pathogens of concern, so a disinfected, indicator-negative sample can be trusted as pathogen-safe.

No single organism satisfies every criterion perfectly — some coliforms can regrow in distribution-system biofilms, and chlorine-resistant protozoan cysts (Giardia, Cryptosporidium) survive disinfection doses that eliminate coliforms — which is why modern monitoring sometimes supplements coliform counts with a second indicator such as Clostridium perfringens spores as a surrogate for protozoan resistance.