Question 1 of 5: Define and Differentiate

Question 1: Define and Differentiate (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.

Part (i) — Temporary and permanent hardness (5 marks)

Hardness is the concentration of multivalent metallic cations in water, overwhelmingly Ca²⁺ and Mg²⁺, conventionally expressed as an equivalent concentration of calcium carbonate. Total hardness is split not by which cation is present but by which anion balances it. Temporary (carbonate) hardness is that portion of the total hardness associated with bicarbonate and carbonate alkalinity; it is called temporary because simply boiling the water destroys it, driving the reaction Ca(HCO₃)₂ → CaCO₃↓ + CO₂↑ + H₂O and depositing the familiar kettle scale. Permanent (non-carbonate) hardness is the remainder, associated with sulphate, chloride and nitrate; boiling does nothing to it, and it must be removed by lime–soda softening with added soda ash, by ion exchange, or by a membrane.

Given. A representative groundwater: Ca²⁺ = 60 mg/L, Mg²⁺ = 20 mg/L, total alkalinity = 150 mg/L as CaCO₃. Find. The split of total hardness into its temporary and permanent parts, to show how the definition is applied numerically.

Converting each cation to the CaCO₃ scale by the ratio of equivalent weights,

which gives $60 \times 50.04/20.04 = 149.8$ mg/L from calcium and $20 \times 50.04/12.15 = 82.4$ mg/L from magnesium, so the total hardness is 232.2 mg/L as CaCO₃. Because the alkalinity (150) is smaller than the total hardness, all of the alkalinity is tied up as carbonate hardness and the balance is non-carbonate:

The practical consequence of the distinction is a chemical bill: the 150 mg/L of carbonate hardness is removed with lime alone, while the 82 mg/L of non-carbonate hardness additionally consumes soda ash, which is the more expensive reagent.

Part (ii) — Organic, ortho and poly phosphorus in wastewater (5 marks)

Total phosphorus in municipal wastewater is reported as three operationally defined fractions, distinguished by the chemical bonding of the phosphorus atom. Orthophosphate is the simple, fully hydrolysed inorganic ion — PO₄³⁻, HPO₄²⁻ and H₂PO₄⁻ depending on pH. It is the only form directly available to algae and the only form that reacts immediately with a metal-salt coagulant, and it is measured directly by the ascorbic-acid molybdenum-blue method with no digestion. Polyphosphates (condensed phosphates such as pyrophosphate and tripolyphosphate) are P–O–P chains contributed mostly by detergents and by corrosion-control chemicals; they are not reactive in the direct test and must first be hydrolysed by acid digestion, which they undergo slowly in the sewer and rapidly in a biological reactor. Organic phosphorus is phosphorus bound into biological molecules — phospholipids, nucleic acids, ATP — and is released only by a strong acid-persulphate digestion that mineralises the organic matter.

Given. A typical raw municipal wastewater with total phosphorus 7.0 mg P/L, made up of 4.5 mg/L ortho-P, 1.0 mg/L poly-P and 1.5 mg/L organic P. Find. Why the fractionation matters to the designer.

The ortho fraction is 64 per cent of the total and sets the immediate chemical demand. At an aluminium-to-phosphorus molar ratio of 2:1 — the practical ratio, well above the 1:1 stoichiometry, because hydroxide precipitation competes for the metal — the ortho-P alone requires

of alum, Al₂(SO₄)₃·14H₂O. The remaining 2.5 mg/L is not removed by that dose at the point of addition, but it hydrolyses and mineralises through the biological process and reappears as orthophosphate downstream, which is precisely why a permit is written on total phosphorus and why chemical addition at a single point rarely achieves a low total-P limit on its own.

Part (iii) — Self-cleansing and scouring velocity in sewers (5 marks)

Both terms describe the velocity needed to keep a gravity sewer free of deposits, but they refer to two different physical events and therefore to two different design checks. The self-cleansing velocity is the minimum flow velocity that must be achieved at least once each day — conventionally at the daily peak or at the minimum design flow — so that the organic and grit solids carried by the sewage remain in suspension and do not settle out; it is the ordinary lower design limit, 0.6 m/s in most Canadian municipal standards (0.75 m/s for larger trunk sewers). The scouring velocity is the higher velocity required to re-entrain material that has already deposited and consolidated on the invert, and it is also used to describe the upper limit at which the flow begins to abrade the pipe wall and its lining, typically 3 m/s. Self-cleansing prevents a deposit forming; scouring removes one that has formed.

Given. The 300 mm sewer of Question 5 (hydraulic radius 0.075 m running full, n = 0.013), carrying grit of specific gravity 2.65 and particle size 1 mm. Find. The two velocities, to show the size of the gap between them.

Camp's form of the Shields criterion gives both from one expression, the difference being only the dimensionless constant K:

With K = 0.04 for incipient motion of clean grit, $V = 0.41$ m/s; with K = 0.8, the value appropriate to dislodging a cohesive, consolidated deposit, $V = 1.82$ m/s — more than four times as large.

Modern practice states the same criterion as a boundary shear (tractive force) $\tau = \rho g R S$, because that form is independent of pipe size: about 1.5 Pa is required for self-cleansing and 3–4 Pa to scour. The Question 5 pipe develops 2.14 Pa at the stated depth — comfortably self-cleansing, but not enough to clear an established deposit, which is exactly why a sewer that has once silted usually needs jetting rather than a flush.

Part (iv) — Type 1 and Type 2 settling (5 marks)

The four classical settling regimes are distinguished by the concentration of the suspension and by whether the particles interact. Type 1 (discrete) settling occurs in dilute suspensions of particles that do not change size, shape or density as they fall: each particle accelerates until drag balances buoyant weight and then descends at a constant terminal velocity given by Stokes' law. Because the velocity is constant, removal in an ideal basin depends only on the surface overflow rate and not on depth — the classic result that a grit chamber is sized on area. Type 2 (flocculent) settling occurs in dilute suspensions of particles that do coalesce as they fall: collisions between fast and slow particles build larger aggregates, so the settling velocity of any given mass of solids increases with depth of fall and with detention time. No closed-form law applies; the design settling velocity must be obtained from a settling-column test in which samples are drawn at several depths and times, and depth genuinely matters.

Given. Grit of density 2650 kg/m³ in water at 20 °C ($\mu = 1.002\times10^{-3}$ Pa·s). Find. The Type 1 settling velocity for a 0.2 mm and a 0.1 mm particle.

gives $v_s = 0.0359$ m/s = 3105 m/d for the 0.2 mm grain and 0.00898 m/s = 776 m/d for the 0.1 mm grain — a fourfold change for a twofold change in diameter, since $v_s \propto d^2$. A grit chamber designed at a surface overflow rate of about 1000 m/d therefore captures everything down to roughly 0.12 mm and lets finer material pass.

The two regimes belong to different unit processes: grit chambers and the upper reaches of a primary clarifier are Type 1; the flocculated solids of a chemically dosed clarifier, and the upper zone of a secondary clarifier, are Type 2. Below them lie Type 3 (hindered or zone settling, where the sludge blanket subsides as a mass) and Type 4 (compression), which govern the lower part of a secondary clarifier.

Part (v) — Chloramines and disinfection by-products (5 marks)

The two terms sit on opposite sides of the disinfection ledger: one is a disinfectant that is deliberately made, the other is a contaminant that is inadvertently made. Chloramines are the combined-chlorine species NH₂Cl (monochloramine), NHCl₂ and NCl₃, formed when free chlorine meets ammonia. They form unavoidably where ammonia is present in the raw water, and are formed on purpose in chloramination by dosing ammonia at a chlorine-to-nitrogen mass ratio of about 4:1 to 5:1 — safely below the breakpoint ratio of 7.6:1 at which the reaction 2NH₃ + 3Cl₂ → N₂ + 6HCl destroys both. Monochloramine is a weak, slow primary disinfectant (roughly two orders of magnitude less potent than HOCl) but an excellent secondary disinfectant: it is stable, persists to the end of the distribution system, and penetrates biofilm.

Disinfection by-products (DBPs) are the halogenated organics produced when a chemical oxidant reacts with natural organic matter and bromide in the water — trihalomethanes (chloroform and its brominated analogues), haloacetic acids, haloacetonitriles, chlorite and bromate from chlorine dioxide and ozone, and N-nitrosodimethylamine (NDMA) from chloramination. They are regulated because of chronic health risk: the Guidelines for Canadian Drinking Water Quality set a maximum acceptable concentration of 0.100 mg/L for total THMs and 0.080 mg/L for the five haloacetic acids, both as a running annual average of quarterly samples.

The relationship between the two is the heart of the utility's dilemma. Switching a secondary disinfectant from free chlorine to chloramine typically cuts THM and HAA formation by 60–90 per cent, which is why most large Canadian utilities chloraminate; but chloramine trades those regulated DBPs for NDMA, for a much weaker residual disinfecting power, and for the risk of nitrification in a warm, long-detention distribution system. The engineering answer to the trade-off is upstream, not downstream: removing the precursor organic matter by enhanced coagulation or GAC reduces DBPs without weakening disinfection at all.