Question 1 of 6: Discrete Settling Theory & Indicator Organisms

Question A1: 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 (Type I) Settling — Surface Area, Not Depth

In an ideal rectangular sedimentation basin (Hazen’s idealized-settling model), water moves horizontally from inlet to outlet while a discrete particle simultaneously settles vertically at its own characteristic velocity. A particle is removed if it reaches the tank floor before the water carrying it exits — the worst-case (limiting) particle is one that enters right at the water surface at the inlet, since it has the maximum possible vertical distance to fall. Setting up the geometry and timing of that limiting trajectory shows algebraically that the tank depth cancels out of the removal criterion entirely.

Given.

Find. Show that the critical settling velocity below which particles are NOT fully removed depends only on $Q$ and the tank’s plan (surface) area — not on $D$.

Approach. Write the horizontal flow-through time and the vertical settling time for the worst-case (surface-entering) particle, require the settling time not exceed the flow-through time, and simplify.

1. Horizontal (flow-through) velocity and detention time. The water's average horizontal velocity through the tank's cross-section ($W\times D$) is $$v_H=\frac{Q}{W\,D},$$ so the nominal time for a parcel of water to traverse the full length $L$ is $$t_d=\frac{L}{v_H}=\frac{L\,W\,D}{Q}=\frac{V}{Q},$$ where $V=L\,W\,D$ is the tank volume — the familiar hydraulic detention time.
2. Vertical settling time for the worst-case particle. A particle entering at the water surface must fall the full depth $D$ to be captured on the tank floor. At settling velocity $v_s$ this takes $$t_s=\frac{D}{v_s}.$$
3. Removal criterion. The particle is captured only if it reaches the bottom no later than the water carrying it reaches the outlet, i.e. $t_s\le t_d$: $$\frac{D}{v_s}\le\frac{L\,W\,D}{Q}.$$ The depth $D$ appears on both sides and cancels exactly, leaving $$\frac{1}{v_s}\le\frac{L\,W}{Q}\quad\Longrightarrow\quad v_s\ge\frac{Q}{L\,W}.$$
4. Identify the surface-loading (overflow) rate. $L\times W=A_s$ is the tank's plan (surface) area, so the critical settling velocity — the boundary between particles that are 100% removed and those that are not — is $$\boxed{v_0=\frac{Q}{A_s}}\ \ \text{(surface overflow rate)}.$$ Every particle with $v_s\ge v_0$ is removed with 100% efficiency regardless of where in the depth it enters (even at the very surface); particles with $v_s

(ii) Indicator Organisms in Water Quality Examination

An indicator organism is a microorganism whose presence in a water sample is used as circumstantial evidence of fecal contamination and therefore of the possible presence of waterborne pathogens, without having to test directly for every pathogen (bacteria, viruses, protozoa) that might be present. The classic example is the coliform group, and more specifically Escherichia coli and the thermotolerant (fecal) coliforms, used worldwide including in the Guidelines for Canadian Drinking Water Quality.

To be useful as an indicator, an organism should satisfy several criteria:

• It should be consistently and exclusively (or predominantly) present in the feces of warm-blooded animals, so its presence specifically signals fecal contamination rather than some other source.
• It should be present in numbers well above those of the pathogens it is meant to indicate, so a small pathogen load is detectable through a comfortably larger indicator signal.
• It should survive in the water environment at least as long as (or longer than) the pathogens of concern, so its absence can be trusted to mean the pathogens are also absent (no faster die-off that would give a false negative).
• It should not multiply significantly in the water itself, so its numbers reflect the degree of contamination rather than in-situ regrowth.
• It should be non-pathogenic itself (safe to culture and handle in a lab) and should not be naturally present in unpolluted water.
• It should be detectable by a simple, rapid, inexpensive and reliable standardized test (e.g. membrane filtration or multiple-tube fermentation), reproducible between labs.
• Its response to disinfection (chlorination, UV) should parallel that of the pathogens, so a disinfected sample testing indicator-negative can be trusted to also be pathogen-safe.

No single organism meets every criterion perfectly (e.g. some coliforms can regrow in distribution biofilms, and some protozoan cysts like Giardia/Cryptosporidium are markedly more chlorine-resistant than E. coli), which is why modern practice sometimes supplements total/fecal coliform monitoring with additional indicators (e.g. Clostridium perfringens spores as a surrogate for protozoan resistance).